LMFDB - Embedded newform 2001.4.a.c.1.2

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:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-5.35351 q^{2} -3.00000 q^{3} +20.6601 q^{4} +11.7950 q^{5} +16.0605 q^{6} +34.3287 q^{7} -67.7759 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.35351 q^{2} -3.00000 q^{3} +20.6601 q^{4} +11.7950 q^{5} +16.0605 q^{6} +34.3287 q^{7} -67.7759 q^{8} +9.00000 q^{9} -63.1444 q^{10} -22.6942 q^{11} -61.9802 q^{12} -45.8267 q^{13} -183.779 q^{14} -35.3849 q^{15} +197.558 q^{16} -59.5211 q^{17} -48.1816 q^{18} +19.1412 q^{19} +243.685 q^{20} -102.986 q^{21} +121.494 q^{22} +23.0000 q^{23} +203.328 q^{24} +14.1209 q^{25} +245.334 q^{26} -27.0000 q^{27} +709.234 q^{28} -29.0000 q^{29} +189.433 q^{30} +65.5652 q^{31} -515.423 q^{32} +68.0826 q^{33} +318.647 q^{34} +404.906 q^{35} +185.941 q^{36} +24.7457 q^{37} -102.472 q^{38} +137.480 q^{39} -799.413 q^{40} -129.649 q^{41} +551.338 q^{42} +268.389 q^{43} -468.864 q^{44} +106.155 q^{45} -123.131 q^{46} -222.674 q^{47} -592.675 q^{48} +835.461 q^{49} -75.5965 q^{50} +178.563 q^{51} -946.783 q^{52} +124.414 q^{53} +144.545 q^{54} -267.677 q^{55} -2326.66 q^{56} -57.4235 q^{57} +155.252 q^{58} -581.664 q^{59} -731.054 q^{60} -569.215 q^{61} -351.004 q^{62} +308.958 q^{63} +1178.86 q^{64} -540.523 q^{65} -364.481 q^{66} -425.278 q^{67} -1229.71 q^{68} -69.0000 q^{69} -2167.67 q^{70} +502.965 q^{71} -609.983 q^{72} +282.494 q^{73} -132.476 q^{74} -42.3627 q^{75} +395.458 q^{76} -779.063 q^{77} -736.001 q^{78} -88.1207 q^{79} +2330.19 q^{80} +81.0000 q^{81} +694.076 q^{82} +1012.05 q^{83} -2127.70 q^{84} -702.049 q^{85} -1436.83 q^{86} +87.0000 q^{87} +1538.12 q^{88} -1616.80 q^{89} -568.300 q^{90} -1573.17 q^{91} +475.182 q^{92} -196.696 q^{93} +1192.09 q^{94} +225.769 q^{95} +1546.27 q^{96} -772.980 q^{97} -4472.65 q^{98} -204.248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 8 q^{2} - 111 q^{3} + 138 q^{4} - 15 q^{5} + 24 q^{6} - 6 q^{7} - 141 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 8 * q^2 - 111 * q^3 + 138 * q^4 - 15 * q^5 + 24 * q^6 - 6 * q^7 - 141 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} - 111 q^{3} + 138 q^{4} - 15 q^{5} + 24 q^{6} - 6 q^{7} - 141 q^{8} + 333 q^{9} + 26 q^{10} - 109 q^{11} - 414 q^{12} + 115 q^{13} - 243 q^{14} + 45 q^{15} + 406 q^{16} - 228 q^{17} - 72 q^{18} - 135 q^{19} - 73 q^{20} + 18 q^{21} - 40 q^{22} + 851 q^{23} + 423 q^{24} + 942 q^{25} - 543 q^{26} - 999 q^{27} + 853 q^{28} - 1073 q^{29} - 78 q^{30} - 518 q^{31} - 1596 q^{32} + 327 q^{33} + 312 q^{34} - 37 q^{35} + 1242 q^{36} + 245 q^{37} - 59 q^{38} - 345 q^{39} + 293 q^{40} - 915 q^{41} + 729 q^{42} - 389 q^{43} - 832 q^{44} - 135 q^{45} - 184 q^{46} - 926 q^{47} - 1218 q^{48} + 1655 q^{49} - 439 q^{50} + 684 q^{51} + 1290 q^{52} - 1134 q^{53} + 216 q^{54} - 404 q^{55} - 1141 q^{56} + 405 q^{57} + 232 q^{58} - 179 q^{59} + 219 q^{60} + 10 q^{61} + 1378 q^{62} - 54 q^{63} + 1359 q^{64} + 110 q^{65} + 120 q^{66} + 1385 q^{67} - 3375 q^{68} - 2553 q^{69} - 637 q^{70} - 2432 q^{71} - 1269 q^{72} - 1638 q^{73} - 2193 q^{74} - 2826 q^{75} - 1319 q^{76} - 3703 q^{77} + 1629 q^{78} - 4728 q^{79} - 1567 q^{80} + 2997 q^{81} + 537 q^{82} - 1416 q^{83} - 2559 q^{84} - 2093 q^{85} - 1187 q^{86} + 3219 q^{87} + 1497 q^{88} - 4019 q^{89} + 234 q^{90} - 545 q^{91} + 3174 q^{92} + 1554 q^{93} + 108 q^{94} - 807 q^{95} + 4788 q^{96} - 754 q^{97} - 5561 q^{98} - 981 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 - 111 * q^3 + 138 * q^4 - 15 * q^5 + 24 * q^6 - 6 * q^7 - 141 * q^8 + 333 * q^9 + 26 * q^10 - 109 * q^11 - 414 * q^12 + 115 * q^13 - 243 * q^14 + 45 * q^15 + 406 * q^16 - 228 * q^17 - 72 * q^18 - 135 * q^19 - 73 * q^20 + 18 * q^21 - 40 * q^22 + 851 * q^23 + 423 * q^24 + 942 * q^25 - 543 * q^26 - 999 * q^27 + 853 * q^28 - 1073 * q^29 - 78 * q^30 - 518 * q^31 - 1596 * q^32 + 327 * q^33 + 312 * q^34 - 37 * q^35 + 1242 * q^36 + 245 * q^37 - 59 * q^38 - 345 * q^39 + 293 * q^40 - 915 * q^41 + 729 * q^42 - 389 * q^43 - 832 * q^44 - 135 * q^45 - 184 * q^46 - 926 * q^47 - 1218 * q^48 + 1655 * q^49 - 439 * q^50 + 684 * q^51 + 1290 * q^52 - 1134 * q^53 + 216 * q^54 - 404 * q^55 - 1141 * q^56 + 405 * q^57 + 232 * q^58 - 179 * q^59 + 219 * q^60 + 10 * q^61 + 1378 * q^62 - 54 * q^63 + 1359 * q^64 + 110 * q^65 + 120 * q^66 + 1385 * q^67 - 3375 * q^68 - 2553 * q^69 - 637 * q^70 - 2432 * q^71 - 1269 * q^72 - 1638 * q^73 - 2193 * q^74 - 2826 * q^75 - 1319 * q^76 - 3703 * q^77 + 1629 * q^78 - 4728 * q^79 - 1567 * q^80 + 2997 * q^81 + 537 * q^82 - 1416 * q^83 - 2559 * q^84 - 2093 * q^85 - 1187 * q^86 + 3219 * q^87 + 1497 * q^88 - 4019 * q^89 + 234 * q^90 - 545 * q^91 + 3174 * q^92 + 1554 * q^93 + 108 * q^94 - 807 * q^95 + 4788 * q^96 - 754 * q^97 - 5561 * 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 $

$2$	−5.35351	−1.89275	−0.946376	−	0.323067i	$-0.895286\pi$
$2$	−5.35351	−1.89275	−0.946376	+	0.323067i	$0.895286\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	20.6601	2.58251
$5$	11.7950	1.05497	0.527486	−	0.849564i	$-0.323135\pi$
$5$	11.7950	1.05497	0.527486	+	0.849564i	$0.323135\pi$
$6$	16.0605	1.09278
$7$	34.3287	1.85358	0.926788	−	0.375584i	$-0.122558\pi$
$7$	34.3287	1.85358	0.926788	+	0.375584i	$0.122558\pi$
$8$	−67.7759	−2.99530
$9$	9.00000	0.333333
$10$	−63.1444	−1.99680
$11$	−22.6942	−0.622051	−0.311026	−	0.950402i	$-0.600672\pi$
$11$	−22.6942	−0.622051	−0.311026	+	0.950402i	$0.600672\pi$
$12$	−61.9802	−1.49101
$13$	−45.8267	−0.977695	−0.488847	−	0.872369i	$-0.662582\pi$
$13$	−45.8267	−0.977695	−0.488847	+	0.872369i	$0.662582\pi$
$14$	−183.779	−3.50836
$15$	−35.3849	−0.609089
$16$	197.558	3.08685
$17$	−59.5211	−0.849176	−0.424588	−	0.905387i	$-0.639581\pi$
$17$	−59.5211	−0.849176	−0.424588	+	0.905387i	$0.639581\pi$
$18$	−48.1816	−0.630917
$19$	19.1412	0.231120	0.115560	−	0.993300i	$-0.463134\pi$
$19$	19.1412	0.231120	0.115560	+	0.993300i	$0.463134\pi$
$20$	243.685	2.72448
$21$	−102.986	−1.07016
$22$	121.494	1.17739
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	203.328	1.72934
$25$	14.1209	0.112967
$26$	245.334	1.85053
$27$	−27.0000	−0.192450
$28$	709.234	4.78688
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	189.433	1.15285
$31$	65.5652	0.379866	0.189933	−	0.981797i	$-0.439173\pi$
$31$	65.5652	0.379866	0.189933	+	0.981797i	$0.439173\pi$
$32$	−515.423	−2.84734
$33$	68.0826	0.359141
$34$	318.647	1.60728
$35$	404.906	1.95547
$36$	185.941	0.860837
$37$	24.7457	0.109950	0.0549751	−	0.998488i	$-0.482492\pi$
$37$	24.7457	0.109950	0.0549751	+	0.998488i	$0.482492\pi$
$38$	−102.472	−0.437453
$39$	137.480	0.564472
$40$	−799.413	−3.15996
$41$	−129.649	−0.493847	−0.246924	−	0.969035i	$-0.579420\pi$
$41$	−129.649	−0.493847	−0.246924	+	0.969035i	$0.579420\pi$
$42$	551.338	2.02555
$43$	268.389	0.951837	0.475919	−	0.879489i	$-0.342116\pi$
$43$	268.389	0.951837	0.475919	+	0.879489i	$0.342116\pi$
$44$	−468.864	−1.60645
$45$	106.155	0.351658
$46$	−123.131	−0.394666
$47$	−222.674	−0.691071	−0.345536	−	0.938406i	$-0.612303\pi$
$47$	−222.674	−0.691071	−0.345536	+	0.938406i	$0.612303\pi$
$48$	−592.675	−1.78219
$49$	835.461	2.43575
$50$	−75.5965	−0.213819
$51$	178.563	0.490272
$52$	−946.783	−2.52491
$53$	124.414	0.322445	0.161222	−	0.986918i	$-0.448456\pi$
$53$	124.414	0.322445	0.161222	+	0.986918i	$0.448456\pi$
$54$	144.545	0.364260
$55$	−267.677	−0.656247
$56$	−2326.66	−5.55202
$57$	−57.4235	−0.133437
$58$	155.252	0.351475
$59$	−581.664	−1.28350	−0.641748	−	0.766916i	$-0.721790\pi$
$59$	−581.664	−1.28350	−0.641748	+	0.766916i	$0.721790\pi$
$60$	−731.054	−1.57298
$61$	−569.215	−1.19476	−0.597381	−	0.801957i	$-0.703792\pi$
$61$	−569.215	−1.19476	−0.597381	+	0.801957i	$0.703792\pi$
$62$	−351.004	−0.718993
$63$	308.958	0.617859
$64$	1178.86	2.30246
$65$	−540.523	−1.03144
$66$	−364.481	−0.679766
$67$	−425.278	−0.775462	−0.387731	−	0.921773i	$-0.626741\pi$
$67$	−425.278	−0.775462	−0.387731	+	0.921773i	$0.626741\pi$
$68$	−1229.71	−2.19301
$69$	−69.0000	−0.120386
$70$	−2167.67	−3.70122
$71$	502.965	0.840719	0.420359	−	0.907358i	$-0.361904\pi$
$71$	502.965	0.840719	0.420359	+	0.907358i	$0.361904\pi$
$72$	−609.983	−0.998433
$73$	282.494	0.452923	0.226462	−	0.974020i	$-0.427284\pi$
$73$	282.494	0.452923	0.226462	+	0.974020i	$0.427284\pi$
$74$	−132.476	−0.208109
$75$	−42.3627	−0.0652217
$76$	395.458	0.596870
$77$	−779.063	−1.15302
$78$	−736.001	−1.06841
$79$	−88.1207	−0.125498	−0.0627491	−	0.998029i	$-0.519987\pi$
$79$	−88.1207	−0.125498	−0.0627491	+	0.998029i	$0.519987\pi$
$80$	2330.19	3.25654
$81$	81.0000	0.111111
$82$	694.076	0.934730
$83$	1012.05	1.33840	0.669198	−	0.743084i	$-0.266638\pi$
$83$	1012.05	1.33840	0.669198	+	0.743084i	$0.266638\pi$
$84$	−2127.70	−2.76371
$85$	−702.049	−0.895858
$86$	−1436.83	−1.80159
$87$	87.0000	0.107211
$88$	1538.12	1.86323
$89$	−1616.80	−1.92563	−0.962813	−	0.270170i	$-0.912920\pi$
$89$	−1616.80	−1.92563	−0.962813	+	0.270170i	$0.912920\pi$
$90$	−568.300	−0.665601
$91$	−1573.17	−1.81223
$92$	475.182	0.538491
$93$	−196.696	−0.219316
$94$	1192.09	1.30803
$95$	225.769	0.243825
$96$	1546.27	1.64391
$97$	−772.980	−0.809116	−0.404558	−	0.914512i	$-0.632575\pi$
$97$	−772.980	−0.809116	−0.404558	+	0.914512i	$0.632575\pi$
$98$	−4472.65	−4.61026
$99$	−204.248	−0.207350
$100$	291.739	0.291739
$101$	−767.805	−0.756430	−0.378215	−	0.925718i	$-0.623462\pi$
$101$	−767.805	−0.756430	−0.378215	+	0.925718i	$0.623462\pi$
$102$	−955.941	−0.927964
$103$	1050.37	1.00482	0.502410	−	0.864629i	$-0.332447\pi$
$103$	1050.37	1.00482	0.502410	+	0.864629i	$0.332447\pi$
$104$	3105.94	2.92849
$105$	−1214.72	−1.12899
$106$	−666.051	−0.610308
$107$	−1688.85	−1.52587	−0.762933	−	0.646477i	$-0.776242\pi$
$107$	−1688.85	−1.52587	−0.762933	+	0.646477i	$0.776242\pi$
$108$	−557.822	−0.497004
$109$	1200.80	1.05519	0.527595	−	0.849496i	$-0.323094\pi$
$109$	1200.80	1.05519	0.527595	+	0.849496i	$0.323094\pi$
$110$	1433.01	1.24211
$111$	−74.2370	−0.0634798
$112$	6781.92	5.72171
$113$	1349.79	1.12370	0.561850	−	0.827239i	$-0.310090\pi$
$113$	1349.79	1.12370	0.561850	+	0.827239i	$0.310090\pi$
$114$	307.417	0.252564
$115$	271.284	0.219977
$116$	−599.142	−0.479560
$117$	−412.440	−0.325898
$118$	3113.95	2.42934
$119$	−2043.28	−1.57401
$120$	2398.24	1.82440
$121$	−815.973	−0.613052
$122$	3047.30	2.26139
$123$	388.946	0.285123
$124$	1354.58	0.981008
$125$	−1307.81	−0.935795
$126$	−1654.01	−1.16945
$127$	−1919.71	−1.34131	−0.670657	−	0.741768i	$-0.733988\pi$
$127$	−1919.71	−1.34131	−0.670657	+	0.741768i	$0.733988\pi$
$128$	−2187.65	−1.51064
$129$	−805.168	−0.549544
$130$	2893.70	1.95226
$131$	325.904	0.217362	0.108681	−	0.994077i	$-0.465337\pi$
$131$	325.904	0.217362	0.108681	+	0.994077i	$0.465337\pi$
$132$	1406.59	0.927486
$133$	657.091	0.428399
$134$	2276.73	1.46776
$135$	−318.464	−0.203030
$136$	4034.10	2.54354
$137$	−177.492	−0.110687	−0.0553437	−	0.998467i	$-0.517625\pi$
$137$	−177.492	−0.110687	−0.0553437	+	0.998467i	$0.517625\pi$
$138$	369.392	0.227861
$139$	2393.96	1.46081	0.730406	−	0.683013i	$-0.239331\pi$
$139$	2393.96	1.46081	0.730406	+	0.683013i	$0.239331\pi$
$140$	8365.38	5.05003
$141$	668.022	0.398990
$142$	−2692.63	−1.59127
$143$	1040.00	0.608176
$144$	1778.02	1.02895
$145$	−342.054	−0.195904
$146$	−1512.33	−0.857271
$147$	−2506.38	−1.40628
$148$	511.247	0.283948
$149$	677.596	0.372556	0.186278	−	0.982497i	$-0.440357\pi$
$149$	677.596	0.372556	0.186278	+	0.982497i	$0.440357\pi$
$150$	226.789	0.123449
$151$	−1053.04	−0.567516	−0.283758	−	0.958896i	$-0.591581\pi$
$151$	−1053.04	−0.567516	−0.283758	+	0.958896i	$0.591581\pi$
$152$	−1297.31	−0.692274
$153$	−535.690	−0.283059
$154$	4170.72	2.18238
$155$	773.338	0.400748
$156$	2840.35	1.45776
$157$	−1679.07	−0.853531	−0.426766	−	0.904362i	$-0.640347\pi$
$157$	−1679.07	−0.853531	−0.426766	+	0.904362i	$0.640347\pi$
$158$	471.755	0.237537
$159$	−373.242	−0.186163
$160$	−6079.39	−3.00386
$161$	789.561	0.386497
$162$	−433.634	−0.210306
$163$	2654.97	1.27579	0.637893	−	0.770125i	$-0.279806\pi$
$163$	2654.97	1.27579	0.637893	+	0.770125i	$0.279806\pi$
$164$	−2678.55	−1.27537
$165$	803.032	0.378884
$166$	−5418.02	−2.53325
$167$	−900.898	−0.417446	−0.208723	−	0.977975i	$-0.566931\pi$
$167$	−900.898	−0.417446	−0.208723	+	0.977975i	$0.566931\pi$
$168$	6979.98	3.20546
$169$	−96.9166	−0.0441132
$170$	3758.43	1.69564
$171$	172.270	0.0770400
$172$	5544.95	2.45813
$173$	−2196.61	−0.965346	−0.482673	−	0.875801i	$-0.660334\pi$
$173$	−2196.61	−0.965346	−0.482673	+	0.875801i	$0.660334\pi$
$174$	−465.755	−0.202924
$175$	484.753	0.209394
$176$	−4483.43	−1.92018
$177$	1744.99	0.741027
$178$	8655.57	3.64473
$179$	−908.041	−0.379163	−0.189582	−	0.981865i	$-0.560713\pi$
$179$	−908.041	−0.379163	−0.189582	+	0.981865i	$0.560713\pi$
$180$	2193.16	0.908159
$181$	−1067.15	−0.438237	−0.219119	−	0.975698i	$-0.570318\pi$
$181$	−1067.15	−0.438237	−0.219119	+	0.975698i	$0.570318\pi$
$182$	8421.99	3.43011
$183$	1707.65	0.689797
$184$	−1558.85	−0.624563
$185$	291.874	0.115995
$186$	1053.01	0.415111
$187$	1350.79	0.528231
$188$	−4600.46	−1.78470
$189$	−926.875	−0.356721
$190$	−1208.66	−0.461501
$191$	−2688.27	−1.01841	−0.509206	−	0.860645i	$-0.670061\pi$
$191$	−2688.27	−1.01841	−0.509206	+	0.860645i	$0.670061\pi$
$192$	−3536.58	−1.32932
$193$	−406.265	−0.151521	−0.0757606	−	0.997126i	$-0.524138\pi$
$193$	−406.265	−0.151521	−0.0757606	+	0.997126i	$0.524138\pi$
$194$	4138.16	1.53146
$195$	1621.57	0.595503
$196$	17260.7	6.29034
$197$	−4158.28	−1.50389	−0.751943	−	0.659228i	$-0.770883\pi$
$197$	−4158.28	−1.50389	−0.751943	+	0.659228i	$0.770883\pi$
$198$	1093.44	0.392463
$199$	−4462.93	−1.58979	−0.794896	−	0.606745i	$-0.792475\pi$
$199$	−4462.93	−1.58979	−0.794896	+	0.606745i	$0.792475\pi$
$200$	−957.058	−0.338371
$201$	1275.83	0.447713
$202$	4110.45	1.43174
$203$	−995.533	−0.344201
$204$	3689.13	1.26613
$205$	−1529.20	−0.520995
$206$	−5623.19	−1.90188
$207$	207.000	0.0695048
$208$	−9053.44	−3.01799
$209$	−434.393	−0.143769
$210$	6503.00	2.13690
$211$	1000.05	0.326284	0.163142	−	0.986603i	$-0.447837\pi$
$211$	1000.05	0.326284	0.163142	+	0.986603i	$0.447837\pi$
$212$	2570.40	0.832716
$213$	−1508.90	−0.485389
$214$	9041.30	2.88809
$215$	3165.64	1.00416
$216$	1829.95	0.576446
$217$	2250.77	0.704111
$218$	−6428.49	−1.99721
$219$	−847.481	−0.261495
$220$	−5530.23	−1.69476
$221$	2727.66	0.830235
$222$	397.428	0.120152
$223$	−2305.39	−0.692289	−0.346144	−	0.938181i	$-0.612509\pi$
$223$	−2305.39	−0.692289	−0.346144	+	0.938181i	$0.612509\pi$
$224$	−17693.8	−5.27776
$225$	127.088	0.0376558
$226$	−7226.14	−2.12688
$227$	5895.99	1.72392	0.861962	−	0.506973i	$-0.169236\pi$
$227$	5895.99	1.72392	0.861962	+	0.506973i	$0.169236\pi$
$228$	−1186.37	−0.344603
$229$	4685.62	1.35211	0.676057	−	0.736849i	$-0.263687\pi$
$229$	4685.62	1.35211	0.676057	+	0.736849i	$0.263687\pi$
$230$	−1452.32	−0.416362
$231$	2337.19	0.665696
$232$	1965.50	0.556213
$233$	−712.606	−0.200362	−0.100181	−	0.994969i	$-0.531942\pi$
$233$	−712.606	−0.200362	−0.100181	+	0.994969i	$0.531942\pi$
$234$	2208.00	0.616844
$235$	−2626.43	−0.729061
$236$	−12017.2	−3.31464
$237$	264.362	0.0724564
$238$	10938.7	2.97922
$239$	1519.00	0.411114	0.205557	−	0.978645i	$-0.434099\pi$
$239$	1519.00	0.411114	0.205557	+	0.978645i	$0.434099\pi$
$240$	−6990.57	−1.88016
$241$	−2672.37	−0.714284	−0.357142	−	0.934050i	$-0.616249\pi$
$241$	−2672.37	−0.714284	−0.357142	+	0.934050i	$0.616249\pi$
$242$	4368.32	1.16036
$243$	−243.000	−0.0641500
$244$	−11760.0	−3.08549
$245$	9854.22	2.56965
$246$	−2082.23	−0.539667
$247$	−877.175	−0.225965
$248$	−4443.74	−1.13781
$249$	−3036.15	−0.772723
$250$	7001.39	1.77123
$251$	3088.35	0.776633	0.388317	−	0.921526i	$-0.373057\pi$
$251$	3088.35	0.776633	0.388317	+	0.921526i	$0.373057\pi$
$252$	6383.11	1.59563
$253$	−521.967	−0.129707
$254$	10277.2	2.53877
$255$	2106.15	0.517224
$256$	2280.71	0.556815
$257$	−1451.14	−0.352217	−0.176109	−	0.984371i	$-0.556351\pi$
$257$	−1451.14	−0.352217	−0.176109	+	0.984371i	$0.556351\pi$
$258$	4310.48	1.04015
$259$	849.487	0.203801
$260$	−11167.3	−2.66371
$261$	−261.000	−0.0618984
$262$	−1744.73	−0.411412
$263$	8127.87	1.90565	0.952825	−	0.303519i	$-0.0981616\pi$
$263$	8127.87	1.90565	0.952825	+	0.303519i	$0.0981616\pi$
$264$	−4614.36	−1.07574
$265$	1467.46	0.340170
$266$	−3517.75	−0.810853
$267$	4850.41	1.11176
$268$	−8786.27	−2.00264
$269$	−6425.07	−1.45630	−0.728148	−	0.685420i	$-0.759619\pi$
$269$	−6425.07	−1.45630	−0.728148	+	0.685420i	$0.759619\pi$
$270$	1704.90	0.384285
$271$	1953.82	0.437956	0.218978	−	0.975730i	$-0.429728\pi$
$271$	1953.82	0.437956	0.218978	+	0.975730i	$0.429728\pi$
$272$	−11758.9	−2.62128
$273$	4719.51	1.04629
$274$	950.206	0.209504
$275$	−320.463	−0.0702715
$276$	−1425.55	−0.310898
$277$	938.980	0.203674	0.101837	−	0.994801i	$-0.467528\pi$
$277$	938.980	0.203674	0.101837	+	0.994801i	$0.467528\pi$
$278$	−12816.1	−2.76496
$279$	590.087	0.126622
$280$	−27442.8	−5.85723
$281$	−6286.39	−1.33457	−0.667286	−	0.744802i	$-0.732544\pi$
$281$	−6286.39	−1.33457	−0.667286	+	0.744802i	$0.732544\pi$
$282$	−3576.26	−0.755189
$283$	−6639.84	−1.39469	−0.697346	−	0.716735i	$-0.745636\pi$
$283$	−6639.84	−1.39469	−0.697346	+	0.716735i	$0.745636\pi$
$284$	10391.3	2.17116
$285$	−677.307	−0.140773
$286$	−5567.65	−1.15113
$287$	−4450.68	−0.915383
$288$	−4638.81	−0.949113
$289$	−1370.23	−0.278900
$290$	1831.19	0.370797
$291$	2318.94	0.467143
$292$	5836.34	1.16968
$293$	−5895.68	−1.17553	−0.587763	−	0.809033i	$-0.699991\pi$
$293$	−5895.68	−1.17553	−0.587763	+	0.809033i	$0.699991\pi$
$294$	13417.9	2.66174
$295$	−6860.71	−1.35405
$296$	−1677.16	−0.329334
$297$	612.744	0.119714
$298$	−3627.52	−0.705156
$299$	−1054.01	−0.203863
$300$	−875.218	−0.168436
$301$	9213.47	1.76430
$302$	5637.44	1.07417
$303$	2303.42	0.436725
$304$	3781.49	0.713433
$305$	−6713.86	−1.26044
$306$	2867.82	0.535760
$307$	3062.90	0.569410	0.284705	−	0.958615i	$-0.408104\pi$
$307$	3062.90	0.569410	0.284705	+	0.958615i	$0.408104\pi$
$308$	−16095.5	−2.97768
$309$	−3151.12	−0.580133
$310$	−4140.07	−0.758517
$311$	6191.78	1.12895	0.564475	−	0.825450i	$-0.309079\pi$
$311$	6191.78	1.12895	0.564475	+	0.825450i	$0.309079\pi$
$312$	−9317.83	−1.69076
$313$	7585.54	1.36984	0.684920	−	0.728618i	$-0.259837\pi$
$313$	7585.54	1.36984	0.684920	+	0.728618i	$0.259837\pi$
$314$	8988.92	1.61552
$315$	3644.15	0.651824
$316$	−1820.58	−0.324100
$317$	3717.89	0.658730	0.329365	−	0.944203i	$-0.393165\pi$
$317$	3717.89	0.658730	0.329365	+	0.944203i	$0.393165\pi$
$318$	1998.15	0.352361
$319$	658.132	0.115512
$320$	13904.6	2.42903
$321$	5066.56	0.880960
$322$	−4226.92	−0.731544
$323$	−1139.30	−0.196262
$324$	1673.47	0.286946
$325$	−647.114	−0.110448
$326$	−14213.4	−2.41475
$327$	−3602.40	−0.609214
$328$	8787.06	1.47922
$329$	−7644.11	−1.28095
$330$	−4299.04	−0.717134
$331$	−6550.84	−1.08781	−0.543907	−	0.839145i	$-0.683056\pi$
$331$	−6550.84	−1.08781	−0.543907	+	0.839145i	$0.683056\pi$
$332$	20909.0	3.45642
$333$	222.711	0.0366501
$334$	4822.97	0.790123
$335$	−5016.13	−0.818091
$336$	−20345.8	−3.30343
$337$	−9413.52	−1.52162	−0.760811	−	0.648973i	$-0.775199\pi$
$337$	−9413.52	−1.52162	−0.760811	+	0.648973i	$0.775199\pi$
$338$	518.844	0.0834953
$339$	−4049.38	−0.648768
$340$	−14504.4	−2.31356
$341$	−1487.95	−0.236296
$342$	−922.251	−0.145818
$343$	16905.6	2.66127
$344$	−18190.3	−2.85104
$345$	−813.852	−0.127004
$346$	11759.6	1.82716
$347$	7252.42	1.12199	0.560995	−	0.827819i	$-0.310419\pi$
$347$	7252.42	1.12199	0.560995	+	0.827819i	$0.310419\pi$
$348$	1797.43	0.276874
$349$	99.4368	0.0152514	0.00762569	−	0.999971i	$-0.497573\pi$
$349$	99.4368	0.0152514	0.00762569	+	0.999971i	$0.497573\pi$
$350$	−2595.13	−0.396330
$351$	1237.32	0.188157
$352$	11697.1	1.77119
$353$	−3553.84	−0.535842	−0.267921	−	0.963441i	$-0.586337\pi$
$353$	−3553.84	−0.535842	−0.267921	+	0.963441i	$0.586337\pi$
$354$	−9341.84	−1.40258
$355$	5932.45	0.886935
$356$	−33403.3	−4.97295
$357$	6129.85	0.908757
$358$	4861.21	0.717662
$359$	−9228.04	−1.35665	−0.678325	−	0.734762i	$-0.737294\pi$
$359$	−9228.04	−1.35665	−0.678325	+	0.734762i	$0.737294\pi$
$360$	−7194.72	−1.05332
$361$	−6492.62	−0.946584
$362$	5713.02	0.829475
$363$	2447.92	0.353946
$364$	−32501.8	−4.68011
$365$	3332.00	0.477822
$366$	−9141.90	−1.30561
$367$	2479.72	0.352698	0.176349	−	0.984328i	$-0.443571\pi$
$367$	2479.72	0.352698	0.176349	+	0.984328i	$0.443571\pi$
$368$	4543.84	0.643652
$369$	−1166.84	−0.164616
$370$	−1562.55	−0.219549
$371$	4270.97	0.597676
$372$	−4063.75	−0.566385
$373$	−2701.19	−0.374966	−0.187483	−	0.982268i	$-0.560033\pi$
$373$	−2701.19	−0.374966	−0.187483	+	0.982268i	$0.560033\pi$
$374$	−7231.45	−0.999811
$375$	3923.44	0.540282
$376$	15091.9	2.06996
$377$	1328.97	0.181553
$378$	4962.04	0.675184
$379$	745.505	0.101040	0.0505198	−	0.998723i	$-0.483912\pi$
$379$	745.505	0.101040	0.0505198	+	0.998723i	$0.483912\pi$
$380$	4664.41	0.629682
$381$	5759.13	0.774408
$382$	14391.7	1.92760
$383$	−11803.8	−1.57479	−0.787396	−	0.616447i	$-0.788571\pi$
$383$	−11803.8	−1.57479	−0.787396	+	0.616447i	$0.788571\pi$
$384$	6562.94	0.872170
$385$	−9189.02	−1.21640
$386$	2174.94	0.286792
$387$	2415.50	0.317279
$388$	−15969.8	−2.08955
$389$	−5065.13	−0.660186	−0.330093	−	0.943948i	$-0.607080\pi$
$389$	−5065.13	−0.660186	−0.330093	+	0.943948i	$0.607080\pi$
$390$	−8681.09	−1.12714
$391$	−1368.99	−0.177066
$392$	−56624.1	−7.29579
$393$	−977.712	−0.125494
$394$	22261.4	2.84648
$395$	−1039.38	−0.132397
$396$	−4219.78	−0.535484
$397$	6436.29	0.813674	0.406837	−	0.913501i	$-0.366632\pi$
$397$	6436.29	0.813674	0.406837	+	0.913501i	$0.366632\pi$
$398$	23892.3	3.00908
$399$	−1971.27	−0.247336
$400$	2789.70	0.348713
$401$	2969.95	0.369855	0.184928	−	0.982752i	$-0.440795\pi$
$401$	2969.95	0.369855	0.184928	+	0.982752i	$0.440795\pi$
$402$	−6830.19	−0.847410
$403$	−3004.63	−0.371393
$404$	−15862.9	−1.95349
$405$	955.391	0.117219
$406$	5329.60	0.651486
$407$	−561.583	−0.0683947
$408$	−12102.3	−1.46851
$409$	10488.0	1.26796	0.633981	−	0.773348i	$-0.281420\pi$
$409$	10488.0	1.26796	0.633981	+	0.773348i	$0.281420\pi$
$410$	8186.59	0.986115
$411$	532.476	0.0639054
$412$	21700.8	2.59496
$413$	−19967.8	−2.37906
$414$	−1108.18	−0.131555
$415$	11937.1	1.41197
$416$	23620.1	2.78383
$417$	−7181.88	−0.843400
$418$	2325.53	0.272118
$419$	−1549.01	−0.180606	−0.0903030	−	0.995914i	$-0.528784\pi$
$419$	−1549.01	−0.180606	−0.0903030	+	0.995914i	$0.528784\pi$
$420$	−25096.1	−2.91564
$421$	−1554.27	−0.179930	−0.0899651	−	0.995945i	$-0.528676\pi$
$421$	−1554.27	−0.179930	−0.0899651	+	0.995945i	$0.528676\pi$
$422$	−5353.76	−0.617575
$423$	−2004.07	−0.230357
$424$	−8432.26	−0.965818
$425$	−840.493	−0.0959292
$426$	8077.89	0.918721
$427$	−19540.4	−2.21458
$428$	−34891.9	−3.94057
$429$	−3120.00	−0.351131
$430$	−16947.3	−1.90063
$431$	−934.354	−0.104423	−0.0522114	−	0.998636i	$-0.516627\pi$
$431$	−934.354	−0.104423	−0.0522114	+	0.998636i	$0.516627\pi$
$432$	−5334.07	−0.594064
$433$	3853.34	0.427667	0.213833	−	0.976870i	$-0.431405\pi$
$433$	3853.34	0.427667	0.213833	+	0.976870i	$0.431405\pi$
$434$	−12049.5	−1.33271
$435$	1026.16	0.113105
$436$	24808.6	2.72504
$437$	440.247	0.0481919
$438$	4537.00	0.494946
$439$	−8666.40	−0.942197	−0.471099	−	0.882081i	$-0.656142\pi$
$439$	−8666.40	−0.942197	−0.471099	+	0.882081i	$0.656142\pi$
$440$	18142.1	1.96566
$441$	7519.15	0.811916
$442$	−14602.5	−1.57143
$443$	−14465.8	−1.55145	−0.775726	−	0.631070i	$-0.782616\pi$
$443$	−14465.8	−1.55145	−0.775726	+	0.631070i	$0.782616\pi$
$444$	−1533.74	−0.163937
$445$	−19070.1	−2.03148
$446$	12341.9	1.31033
$447$	−2032.79	−0.215095
$448$	40468.7	4.26778
$449$	−3815.83	−0.401069	−0.200535	−	0.979687i	$-0.564268\pi$
$449$	−3815.83	−0.401069	−0.200535	+	0.979687i	$0.564268\pi$
$450$	−680.368	−0.0712730
$451$	2942.28	0.307198
$452$	27886.9	2.90196
$453$	3159.11	0.327655
$454$	−31564.3	−3.26296
$455$	−18555.5	−1.91186
$456$	3891.93	0.399684
$457$	17670.8	1.80876	0.904381	−	0.426725i	$-0.140333\pi$
$457$	17670.8	1.80876	0.904381	+	0.426725i	$0.140333\pi$
$458$	−25084.5	−2.55922
$459$	1607.07	0.163424
$460$	5604.75	0.568093
$461$	6580.67	0.664843	0.332421	−	0.943131i	$-0.392134\pi$
$461$	6580.67	0.664843	0.332421	+	0.943131i	$0.392134\pi$
$462$	−12512.2	−1.26000
$463$	−16111.3	−1.61719	−0.808593	−	0.588368i	$-0.799771\pi$
$463$	−16111.3	−1.61719	−0.808593	+	0.588368i	$0.799771\pi$
$464$	−5729.19	−0.573213
$465$	−2320.01	−0.231372
$466$	3814.95	0.379236
$467$	6033.42	0.597844	0.298922	−	0.954278i	$-0.403373\pi$
$467$	6033.42	0.597844	0.298922	+	0.954278i	$0.403373\pi$
$468$	−8521.04	−0.841635
$469$	−14599.2	−1.43738
$470$	14060.6	1.37993
$471$	5037.21	0.492786
$472$	39422.8	3.84445
$473$	−6090.89	−0.592092
$474$	−1415.27	−0.137142
$475$	270.291	0.0261090
$476$	−42214.4	−4.06491
$477$	1119.73	0.107482
$478$	−8132.00	−0.778136
$479$	−5066.41	−0.483278	−0.241639	−	0.970366i	$-0.577685\pi$
$479$	−5066.41	−0.483278	−0.241639	+	0.970366i	$0.577685\pi$
$480$	18238.2	1.73428
$481$	−1134.01	−0.107498
$482$	14306.6	1.35196
$483$	−2368.68	−0.223144
$484$	−16858.1	−1.58321
$485$	−9117.26	−0.853595
$486$	1300.90	0.121420
$487$	4211.51	0.391872	0.195936	−	0.980617i	$-0.437225\pi$
$487$	4211.51	0.391872	0.195936	+	0.980617i	$0.437225\pi$
$488$	38579.1	3.57867
$489$	−7964.90	−0.736575
$490$	−52754.7	−4.86370
$491$	−5876.52	−0.540130	−0.270065	−	0.962842i	$-0.587045\pi$
$491$	−5876.52	−0.540130	−0.270065	+	0.962842i	$0.587045\pi$
$492$	8035.66	0.736332
$493$	1726.11	0.157688
$494$	4695.97	0.427695
$495$	−2409.09	−0.218749
$496$	12952.9	1.17259
$497$	17266.2	1.55834
$498$	16254.1	1.46257
$499$	−13673.5	−1.22667	−0.613335	−	0.789823i	$-0.710172\pi$
$499$	−13673.5	−1.22667	−0.613335	+	0.789823i	$0.710172\pi$
$500$	−27019.5	−2.41670
$501$	2702.69	0.241013
$502$	−16533.5	−1.46997
$503$	−8828.65	−0.782604	−0.391302	−	0.920262i	$-0.627975\pi$
$503$	−8828.65	−0.782604	−0.391302	+	0.920262i	$0.627975\pi$
$504$	−20939.9	−1.85067
$505$	−9056.23	−0.798014
$506$	2794.36	0.245502
$507$	290.750	0.0254687
$508$	−39661.4	−3.46396
$509$	9796.26	0.853068	0.426534	−	0.904471i	$-0.359734\pi$
$509$	9796.26	0.853068	0.426534	+	0.904471i	$0.359734\pi$
$510$	−11275.3	−0.978976
$511$	9697.65	0.839528
$512$	5291.33	0.456730
$513$	−516.811	−0.0444791
$514$	7768.71	0.666660
$515$	12389.1	1.06006
$516$	−16634.8	−1.41920
$517$	5053.41	0.429882
$518$	−4547.74	−0.385745
$519$	6589.82	0.557343
$520$	36634.4	3.08947
$521$	13297.5	1.11819	0.559093	−	0.829105i	$-0.311150\pi$
$521$	13297.5	1.11819	0.559093	+	0.829105i	$0.311150\pi$
$522$	1397.27	0.117158
$523$	19142.3	1.60045	0.800223	−	0.599703i	$-0.204715\pi$
$523$	19142.3	1.60045	0.800223	+	0.599703i	$0.204715\pi$
$524$	6733.20	0.561338
$525$	−1454.26	−0.120893
$526$	−43512.7	−3.60692
$527$	−3902.51	−0.322573
$528$	13450.3	1.10862
$529$	529.000	0.0434783
$530$	−7856.04	−0.643858
$531$	−5234.98	−0.427832
$532$	13575.6	1.10634
$533$	5941.37	0.482832
$534$	−25966.7	−2.10429
$535$	−19920.0	−1.60975
$536$	28823.6	2.32274
$537$	2724.12	0.218910
$538$	34396.7	2.75641
$539$	−18960.1	−1.51516
$540$	−6579.49	−0.524326
$541$	−7538.82	−0.599111	−0.299556	−	0.954079i	$-0.596838\pi$
$541$	−7538.82	−0.599111	−0.299556	+	0.954079i	$0.596838\pi$
$542$	−10459.8	−0.828943
$543$	3201.46	0.253017
$544$	30678.6	2.41789
$545$	14163.4	1.11320
$546$	−25266.0	−1.98037
$547$	3213.74	0.251206	0.125603	−	0.992081i	$-0.459913\pi$
$547$	3213.74	0.251206	0.125603	+	0.992081i	$0.459913\pi$
$548$	−3667.00	−0.285851
$549$	−5122.94	−0.398254
$550$	1715.60	0.133006
$551$	−555.093	−0.0429179
$552$	4676.54	0.360592
$553$	−3025.07	−0.232621
$554$	−5026.84	−0.385505
$555$	−875.621	−0.0669695
$556$	49459.4	3.77256
$557$	−15214.1	−1.15734	−0.578672	−	0.815561i	$-0.696429\pi$
$557$	−15214.1	−1.15734	−0.578672	+	0.815561i	$0.696429\pi$
$558$	−3159.03	−0.239664
$559$	−12299.4	−0.930606
$560$	79992.5	6.03625
$561$	−4052.36	−0.304974
$562$	33654.3	2.52601
$563$	12650.7	0.947004	0.473502	−	0.880793i	$-0.342990\pi$
$563$	12650.7	0.947004	0.473502	+	0.880793i	$0.342990\pi$
$564$	13801.4	1.03040
$565$	15920.8	1.18547
$566$	35546.5	2.63981
$567$	2780.63	0.205953
$568$	−34088.9	−2.51820
$569$	25650.1	1.88982	0.944912	−	0.327326i	$-0.106147\pi$
$569$	25650.1	1.88982	0.944912	+	0.327326i	$0.106147\pi$
$570$	3625.97	0.266448
$571$	5534.51	0.405625	0.202813	−	0.979218i	$-0.434992\pi$
$571$	5534.51	0.405625	0.202813	+	0.979218i	$0.434992\pi$
$572$	21486.5	1.57062
$573$	8064.82	0.587980
$574$	23826.7	1.73259
$575$	324.781	0.0235553
$576$	10609.7	0.767486
$577$	−21083.8	−1.52120	−0.760599	−	0.649222i	$-0.775095\pi$
$577$	−21083.8	−1.52120	−0.760599	+	0.649222i	$0.775095\pi$
$578$	7335.56	0.527888
$579$	1218.79	0.0874808
$580$	−7066.86	−0.505923
$581$	34742.4	2.48082
$582$	−12414.5	−0.884186
$583$	−2823.48	−0.200577
$584$	−19146.3	−1.35664
$585$	−4864.71	−0.343814
$586$	31562.6	2.22498
$587$	319.072	0.0224353	0.0112176	−	0.999937i	$-0.496429\pi$
$587$	319.072	0.0224353	0.0112176	+	0.999937i	$0.496429\pi$
$588$	−51782.1	−3.63173
$589$	1254.99	0.0877947
$590$	36728.9	2.56289
$591$	12474.9	0.868269
$592$	4888.71	0.339400
$593$	20318.0	1.40701	0.703507	−	0.710688i	$-0.251616\pi$
$593$	20318.0	1.40701	0.703507	+	0.710688i	$0.251616\pi$
$594$	−3280.33	−0.226589
$595$	−24100.4	−1.66054
$596$	13999.2	0.962130
$597$	13388.8	0.917867
$598$	5642.67	0.385863
$599$	−19115.9	−1.30393	−0.651964	−	0.758250i	$-0.726055\pi$
$599$	−19115.9	−1.30393	−0.651964	+	0.758250i	$0.726055\pi$
$600$	2871.17	0.195359
$601$	−10380.2	−0.704518	−0.352259	−	0.935902i	$-0.614586\pi$
$601$	−10380.2	−0.704518	−0.352259	+	0.935902i	$0.614586\pi$
$602$	−49324.4	−3.33939
$603$	−3827.50	−0.258487
$604$	−21755.8	−1.46561
$605$	−9624.36	−0.646753
$606$	−12331.4	−0.826613
$607$	−692.420	−0.0463006	−0.0231503	−	0.999732i	$-0.507370\pi$
$607$	−692.420	−0.0463006	−0.0231503	+	0.999732i	$0.507370\pi$
$608$	−9865.80	−0.658077
$609$	2986.60	0.198724
$610$	35942.8	2.38570
$611$	10204.4	0.675657
$612$	−11067.4	−0.731002
$613$	15787.6	1.04022	0.520109	−	0.854100i	$-0.325891\pi$
$613$	15787.6	1.04022	0.520109	+	0.854100i	$0.325891\pi$
$614$	−16397.3	−1.07775
$615$	4587.60	0.300797
$616$	52801.7	3.45364
$617$	−6477.78	−0.422667	−0.211333	−	0.977414i	$-0.567781\pi$
$617$	−6477.78	−0.422667	−0.211333	+	0.977414i	$0.567781\pi$
$618$	16869.6	1.09805
$619$	21209.1	1.37717	0.688583	−	0.725158i	$-0.258233\pi$
$619$	21209.1	1.37717	0.688583	+	0.725158i	$0.258233\pi$
$620$	15977.2	1.03494
$621$	−621.000	−0.0401286
$622$	−33147.8	−2.13682
$623$	−55502.7	−3.56929
$624$	27160.3	1.74244
$625$	−17190.7	−1.10021
$626$	−40609.3	−2.59277
$627$	1303.18	0.0830048
$628$	−34689.7	−2.20425
$629$	−1472.89	−0.0933672
$630$	−19509.0	−1.23374
$631$	−31552.9	−1.99065	−0.995325	−	0.0965873i	$-0.969207\pi$
$631$	−31552.9	−1.99065	−0.995325	+	0.0965873i	$0.969207\pi$
$632$	5972.46	0.375905
$633$	−3000.14	−0.188380
$634$	−19903.7	−1.24681
$635$	−22642.9	−1.41505
$636$	−7711.20	−0.480769
$637$	−38286.4	−2.38142
$638$	−3523.32	−0.218636
$639$	4526.69	0.280240
$640$	−25803.2	−1.59369
$641$	11093.2	0.683550	0.341775	−	0.939782i	$-0.388972\pi$
$641$	11093.2	0.683550	0.341775	+	0.939782i	$0.388972\pi$
$642$	−27123.9	−1.66744
$643$	22068.5	1.35350	0.676748	−	0.736215i	$-0.263389\pi$
$643$	22068.5	1.35350	0.676748	+	0.736215i	$0.263389\pi$
$644$	16312.4	0.998134
$645$	−9496.92	−0.579753
$646$	6099.27	0.371475
$647$	−3093.69	−0.187984	−0.0939919	−	0.995573i	$-0.529963\pi$
$647$	−3093.69	−0.187984	−0.0939919	+	0.995573i	$0.529963\pi$
$648$	−5489.85	−0.332811
$649$	13200.4	0.798400
$650$	3464.33	0.209050
$651$	−6752.31	−0.406519
$652$	54851.8	3.29473
$653$	−4672.94	−0.280040	−0.140020	−	0.990149i	$-0.544717\pi$
$653$	−4672.94	−0.280040	−0.140020	+	0.990149i	$0.544717\pi$
$654$	19285.5	1.15309
$655$	3844.02	0.229311
$656$	−25613.2	−1.52443
$657$	2542.44	0.150974
$658$	40922.8	2.42453
$659$	4171.17	0.246564	0.123282	−	0.992372i	$-0.460658\pi$
$659$	4171.17	0.246564	0.123282	+	0.992372i	$0.460658\pi$
$660$	16590.7	0.978473
$661$	−26475.3	−1.55790	−0.778948	−	0.627088i	$-0.784246\pi$
$661$	−26475.3	−1.55790	−0.778948	+	0.627088i	$0.784246\pi$
$662$	35070.0	2.05896
$663$	−8182.97	−0.479337
$664$	−68592.5	−4.00890
$665$	7750.36	0.451949
$666$	−1192.29	−0.0693695
$667$	−667.000	−0.0387202
$668$	−18612.6	−1.07806
$669$	6916.17	0.399693
$670$	26853.9	1.54844
$671$	12917.9	0.743204
$672$	53081.5	3.04712
$673$	−3119.02	−0.178647	−0.0893235	−	0.996003i	$-0.528470\pi$
$673$	−3119.02	−0.178647	−0.0893235	+	0.996003i	$0.528470\pi$
$674$	50395.4	2.88005
$675$	−381.265	−0.0217406
$676$	−2002.30	−0.113923
$677$	11403.1	0.647353	0.323677	−	0.946168i	$-0.395081\pi$
$677$	11403.1	0.647353	0.323677	+	0.946168i	$0.395081\pi$
$678$	21678.4	1.22796
$679$	−26535.4	−1.49976
$680$	47582.0	2.68336
$681$	−17688.0	−0.995308
$682$	7965.76	0.447250
$683$	30231.4	1.69367	0.846833	−	0.531859i	$-0.178506\pi$
$683$	30231.4	1.69367	0.846833	+	0.531859i	$0.178506\pi$
$684$	3559.12	0.198957
$685$	−2093.51	−0.116772
$686$	−90504.1	−5.03712
$687$	−14056.8	−0.780644
$688$	53022.6	2.93818
$689$	−5701.47	−0.315252
$690$	4356.96	0.240387
$691$	−6693.54	−0.368501	−0.184250	−	0.982879i	$-0.558986\pi$
$691$	−6693.54	−0.368501	−0.184250	+	0.982879i	$0.558986\pi$
$692$	−45382.0	−2.49301
$693$	−7011.57	−0.384340
$694$	−38825.9	−2.12365
$695$	28236.6	1.54112
$696$	−5896.50	−0.321130
$697$	7716.84	0.419363
$698$	−532.336	−0.0288671
$699$	2137.82	0.115679
$700$	10015.0	0.540761
$701$	−23090.2	−1.24409	−0.622043	−	0.782983i	$-0.713697\pi$
$701$	−23090.2	−1.24409	−0.622043	+	0.782983i	$0.713697\pi$
$702$	−6624.01	−0.356135
$703$	473.660	0.0254117
$704$	−26753.3	−1.43225
$705$	7879.29	0.420924
$706$	19025.5	1.01422
$707$	−26357.8	−1.40210
$708$	36051.7	1.91371
$709$	2034.90	0.107789	0.0538945	−	0.998547i	$-0.482837\pi$
$709$	2034.90	0.107789	0.0538945	+	0.998547i	$0.482837\pi$
$710$	−31759.5	−1.67875
$711$	−793.087	−0.0418327
$712$	109580.	5.76782
$713$	1508.00	0.0792076
$714$	−32816.2	−1.72005
$715$	12266.8	0.641609
$716$	−18760.2	−0.979193
$717$	−4557.01	−0.237357
$718$	49402.4	2.56780
$719$	−37361.8	−1.93791	−0.968957	−	0.247231i	$-0.920479\pi$
$719$	−37361.8	−1.93791	−0.968957	+	0.247231i	$0.920479\pi$
$720$	20971.7	1.08551
$721$	36058.0	1.86251
$722$	34758.3	1.79165
$723$	8017.11	0.412392
$724$	−22047.5	−1.13175
$725$	−409.507	−0.0209775
$726$	−13105.0	−0.669932
$727$	9496.45	0.484462	0.242231	−	0.970219i	$-0.422121\pi$
$727$	9496.45	0.484462	0.242231	+	0.970219i	$0.422121\pi$
$728$	106623.	5.42818
$729$	729.000	0.0370370
$730$	−17837.9	−0.904398
$731$	−15974.8	−0.808278
$732$	35280.1	1.78141
$733$	−37402.8	−1.88473	−0.942363	−	0.334593i	$-0.891401\pi$
$733$	−37402.8	−1.88473	−0.942363	+	0.334593i	$0.891401\pi$
$734$	−13275.2	−0.667570
$735$	−29562.7	−1.48359
$736$	−11854.7	−0.593711
$737$	9651.35	0.482377
$738$	6246.68	0.311577
$739$	−16518.8	−0.822265	−0.411133	−	0.911576i	$-0.634867\pi$
$739$	−16518.8	−0.822265	−0.411133	+	0.911576i	$0.634867\pi$
$740$	6030.14	0.299557
$741$	2631.53	0.130461
$742$	−22864.7	−1.13125
$743$	22520.9	1.11199	0.555997	−	0.831185i	$-0.312337\pi$
$743$	22520.9	1.11199	0.555997	+	0.831185i	$0.312337\pi$
$744$	13331.2	0.656917
$745$	7992.22	0.393036
$746$	14460.9	0.709718
$747$	9108.45	0.446132
$748$	27907.3	1.36416
$749$	−57976.2	−2.82831
$750$	−21004.2	−1.02262
$751$	1573.80	0.0764696	0.0382348	−	0.999269i	$-0.487827\pi$
$751$	1573.80	0.0764696	0.0382348	+	0.999269i	$0.487827\pi$
$752$	−43991.1	−2.13323
$753$	−9265.05	−0.448389
$754$	−7114.67	−0.343635
$755$	−12420.5	−0.598714
$756$	−19149.3	−0.921236
$757$	22367.3	1.07392	0.536958	−	0.843609i	$-0.319574\pi$
$757$	22367.3	1.07392	0.536958	+	0.843609i	$0.319574\pi$
$758$	−3991.07	−0.191243
$759$	1565.90	0.0748862
$760$	−15301.7	−0.730330
$761$	−26795.1	−1.27637	−0.638187	−	0.769882i	$-0.720315\pi$
$761$	−26795.1	−1.27637	−0.638187	+	0.769882i	$0.720315\pi$
$762$	−30831.6	−1.46576
$763$	41221.9	1.95587
$764$	−55539.9	−2.63006
$765$	−6318.44	−0.298619
$766$	63191.7	2.98069
$767$	26655.7	1.25487
$768$	−6842.14	−0.321477
$769$	16741.7	0.785071	0.392536	−	0.919737i	$-0.371598\pi$
$769$	16741.7	0.785071	0.392536	+	0.919737i	$0.371598\pi$
$770$	49193.5	2.30235
$771$	4353.43	0.203353
$772$	−8393.46	−0.391305
$773$	−9991.37	−0.464896	−0.232448	−	0.972609i	$-0.574674\pi$
$773$	−9991.37	−0.464896	−0.232448	+	0.972609i	$0.574674\pi$
$774$	−12931.4	−0.600531
$775$	925.840	0.0429125
$776$	52389.4	2.42354
$777$	−2548.46	−0.117665
$778$	27116.2	1.24957
$779$	−2481.63	−0.114138
$780$	33501.8	1.53789
$781$	−11414.4	−0.522970
$782$	7328.88	0.335141
$783$	783.000	0.0357371
$784$	165052.	7.51878
$785$	−19804.6	−0.900452
$786$	5234.19	0.237529
$787$	32588.1	1.47604	0.738018	−	0.674781i	$-0.235762\pi$
$787$	32588.1	1.47604	0.738018	+	0.674781i	$0.235762\pi$
$788$	−85910.5	−3.88380
$789$	−24383.6	−1.10023
$790$	5564.33	0.250595
$791$	46336.7	2.08286
$792$	13843.1	0.621076
$793$	26085.2	1.16811
$794$	−34456.8	−1.54008
$795$	−4402.37	−0.196397
$796$	−92204.5	−4.10566
$797$	2692.84	0.119681	0.0598403	−	0.998208i	$-0.480941\pi$
$797$	2692.84	0.119681	0.0598403	+	0.998208i	$0.480941\pi$
$798$	10553.2	0.468146
$799$	13253.8	0.586841
$800$	−7278.25	−0.321656
$801$	−14551.2	−0.641875
$802$	−15899.6	−0.700045
$803$	−6410.97	−0.281741
$804$	26358.8	1.15622
$805$	9312.83	0.407744
$806$	16085.3	0.702955
$807$	19275.2	0.840793
$808$	52038.7	2.26574
$809$	25763.9	1.11967	0.559834	−	0.828605i	$-0.310865\pi$
$809$	25763.9	1.11967	0.559834	+	0.828605i	$0.310865\pi$
$810$	−5114.70	−0.221867
$811$	−25119.2	−1.08761	−0.543806	−	0.839211i	$-0.683017\pi$
$811$	−25119.2	−1.08761	−0.543806	+	0.839211i	$0.683017\pi$
$812$	−20567.8	−0.888901
$813$	−5861.46	−0.252854
$814$	3006.44	0.129454
$815$	31315.2	1.34592
$816$	35276.7	1.51340
$817$	5137.28	0.219989
$818$	−56147.5	−2.39994
$819$	−14158.5	−0.604077
$820$	−31593.4	−1.34548
$821$	15361.7	0.653016	0.326508	−	0.945194i	$-0.394128\pi$
$821$	15361.7	0.653016	0.326508	+	0.945194i	$0.394128\pi$
$822$	−2850.62	−0.120957
$823$	23725.9	1.00490	0.502450	−	0.864606i	$-0.332432\pi$
$823$	23725.9	1.00490	0.502450	+	0.864606i	$0.332432\pi$
$824$	−71190.1	−3.00974
$825$	961.389	0.0405712
$826$	106898.	4.50297
$827$	−37010.3	−1.55620	−0.778099	−	0.628142i	$-0.783816\pi$
$827$	−37010.3	−1.55620	−0.778099	+	0.628142i	$0.783816\pi$
$828$	4276.64	0.179497
$829$	25222.8	1.05673	0.528363	−	0.849019i	$-0.322806\pi$
$829$	25222.8	1.05673	0.528363	+	0.849019i	$0.322806\pi$
$830$	−63905.3	−2.67251
$831$	−2816.94	−0.117592
$832$	−54023.2	−2.25110
$833$	−49727.6	−2.06838
$834$	38448.2	1.59635
$835$	−10626.0	−0.440395
$836$	−8974.60	−0.371284
$837$	−1770.26	−0.0731053
$838$	8292.62	0.341842
$839$	−20965.3	−0.862696	−0.431348	−	0.902186i	$-0.641962\pi$
$839$	−20965.3	−0.862696	−0.431348	+	0.902186i	$0.641962\pi$
$840$	82328.5	3.38167
$841$	841.000	0.0344828
$842$	8320.82	0.340563
$843$	18859.2	0.770515
$844$	20661.0	0.842633
$845$	−1143.13	−0.0465382
$846$	10728.8	0.436009
$847$	−28011.3	−1.13634
$848$	24579.0	0.995337
$849$	19919.5	0.805226
$850$	4499.59	0.181570
$851$	569.150	0.0229262
$852$	−31173.9	−1.25352
$853$	−2809.40	−0.112769	−0.0563845	−	0.998409i	$-0.517957\pi$
$853$	−2809.40	−0.112769	−0.0563845	+	0.998409i	$0.517957\pi$
$854$	104610.	4.19166
$855$	2031.92	0.0812751
$856$	114464.	4.57043
$857$	37562.7	1.49722	0.748609	−	0.663011i	$-0.230722\pi$
$857$	37562.7	1.49722	0.748609	+	0.663011i	$0.230722\pi$
$858$	16703.0	0.664603
$859$	8757.71	0.347857	0.173929	−	0.984758i	$-0.444354\pi$
$859$	8757.71	0.347857	0.173929	+	0.984758i	$0.444354\pi$
$860$	65402.4	2.59326
$861$	13352.0	0.528497
$862$	5002.08	0.197647
$863$	11740.2	0.463082	0.231541	−	0.972825i	$-0.425623\pi$
$863$	11740.2	0.463082	0.231541	+	0.972825i	$0.425623\pi$
$864$	13916.4	0.547971
$865$	−25908.9	−1.01841
$866$	−20628.9	−0.809467
$867$	4110.70	0.161023
$868$	46501.1	1.81837
$869$	1999.83	0.0780663
$870$	−5493.56	−0.214080
$871$	19489.1	0.758165
$872$	−81385.2	−3.16061
$873$	−6956.82	−0.269705
$874$	−2356.86	−0.0912153
$875$	−44895.6	−1.73457
$876$	−17509.0	−0.675314
$877$	−5229.73	−0.201363	−0.100682	−	0.994919i	$-0.532102\pi$
$877$	−5229.73	−0.201363	−0.100682	+	0.994919i	$0.532102\pi$
$878$	46395.6	1.78335
$879$	17687.0	0.678690
$880$	−52881.8	−2.02573
$881$	5376.90	0.205621	0.102811	−	0.994701i	$-0.467216\pi$
$881$	5376.90	0.205621	0.102811	+	0.994701i	$0.467216\pi$
$882$	−40253.8	−1.53675
$883$	−35156.5	−1.33988	−0.669938	−	0.742417i	$-0.733680\pi$
$883$	−35156.5	−1.33988	−0.669938	+	0.742417i	$0.733680\pi$
$884$	56353.6	2.14409
$885$	20582.1	0.781763
$886$	77443.0	2.93651
$887$	−801.067	−0.0303238	−0.0151619	−	0.999885i	$-0.504826\pi$
$887$	−801.067	−0.0303238	−0.0151619	+	0.999885i	$0.504826\pi$
$888$	5031.48	0.190141
$889$	−65901.2	−2.48623
$890$	102092.	3.84509
$891$	−1838.23	−0.0691168
$892$	−47629.5	−1.78784
$893$	−4262.24	−0.159720
$894$	10882.6	0.407122
$895$	−10710.3	−0.400007
$896$	−75099.1	−2.80009
$897$	3162.04	0.117701
$898$	20428.1	0.759125
$899$	−1901.39	−0.0705394
$900$	2625.65	0.0972464
$901$	−7405.26	−0.273812
$902$	−15751.5	−0.581450
$903$	−27640.4	−1.01862
$904$	−91483.5	−3.36582
$905$	−12587.0	−0.462329
$906$	−16912.3	−0.620170
$907$	−43882.3	−1.60649	−0.803247	−	0.595647i	$-0.796896\pi$
$907$	−43882.3	−1.60649	−0.803247	+	0.595647i	$0.796896\pi$
$908$	121812.	4.45205
$909$	−6910.25	−0.252143
$910$	99336.9	3.61867
$911$	−32201.7	−1.17112	−0.585559	−	0.810630i	$-0.699125\pi$
$911$	−32201.7	−1.17112	−0.585559	+	0.810630i	$0.699125\pi$
$912$	−11344.5	−0.411901
$913$	−22967.7	−0.832551
$914$	−94600.8	−3.42354
$915$	20141.6	0.727716
$916$	96805.2	3.49185
$917$	11187.9	0.402896
$918$	−8603.47	−0.309321
$919$	−13401.5	−0.481041	−0.240520	−	0.970644i	$-0.577318\pi$
$919$	−13401.5	−0.481041	−0.240520	+	0.970644i	$0.577318\pi$
$920$	−18386.5	−0.658897
$921$	−9188.70	−0.328749
$922$	−35229.7	−1.25838
$923$	−23049.2	−0.821966
$924$	48286.5	1.71917
$925$	349.431	0.0124208
$926$	86252.2	3.06093
$927$	9453.37	0.334940
$928$	14947.3	0.528738
$929$	573.101	0.0202399	0.0101199	−	0.999949i	$-0.496779\pi$
$929$	573.101	0.0202399	0.0101199	+	0.999949i	$0.496779\pi$
$930$	12420.2	0.437930
$931$	15991.7	0.562950
$932$	−14722.5	−0.517437
$933$	−18575.3	−0.651800
$934$	−32300.0	−1.13157
$935$	15932.5	0.557269
$936$	27953.5	0.976163
$937$	−15097.3	−0.526369	−0.263184	−	0.964746i	$-0.584773\pi$
$937$	−15097.3	−0.526369	−0.263184	+	0.964746i	$0.584773\pi$
$938$	78157.2	2.72060
$939$	−22756.6	−0.790878
$940$	−54262.2	−1.88281
$941$	−10576.3	−0.366395	−0.183198	−	0.983076i	$-0.558645\pi$
$941$	−10576.3	−0.366395	−0.183198	+	0.983076i	$0.558645\pi$
$942$	−26966.8	−0.932723
$943$	−2981.92	−0.102974
$944$	−114913.	−3.96196
$945$	−10932.5	−0.376331
$946$	32607.6	1.12068
$947$	−4820.48	−0.165412	−0.0827058	−	0.996574i	$-0.526356\pi$
$947$	−4820.48	−0.165412	−0.0827058	+	0.996574i	$0.526356\pi$
$948$	5461.74	0.187119
$949$	−12945.7	−0.442821
$950$	−1447.00	−0.0494179
$951$	−11153.7	−0.380318
$952$	138485.	4.71464
$953$	35679.2	1.21276	0.606381	−	0.795174i	$-0.292621\pi$
$953$	35679.2	1.21276	0.606381	+	0.795174i	$0.292621\pi$
$954$	−5994.46	−0.203436
$955$	−31708.1	−1.07440
$956$	31382.7	1.06171
$957$	−1974.40	−0.0666909
$958$	27123.1	0.914726
$959$	−6093.08	−0.205168
$960$	−41713.7	−1.40240
$961$	−25492.2	−0.855702
$962$	6070.94	0.203467
$963$	−15199.7	−0.508622
$964$	−55211.4	−1.84465
$965$	−4791.87	−0.159851
$966$	12680.8	0.422357
$967$	21278.7	0.707629	0.353815	−	0.935316i	$-0.384884\pi$
$967$	21278.7	0.707629	0.353815	+	0.935316i	$0.384884\pi$
$968$	55303.3	1.83628
$969$	3417.91	0.113312
$970$	48809.4	1.61564
$971$	19940.1	0.659019	0.329509	−	0.944152i	$-0.393117\pi$
$971$	19940.1	0.659019	0.329509	+	0.944152i	$0.393117\pi$
$972$	−5020.40	−0.165668
$973$	82181.5	2.70773
$974$	−22546.4	−0.741717
$975$	1941.34	0.0637669
$976$	−112453.	−3.68805
$977$	28293.5	0.926498	0.463249	−	0.886228i	$-0.346684\pi$
$977$	28293.5	0.926498	0.463249	+	0.886228i	$0.346684\pi$
$978$	42640.2	1.39415
$979$	36692.0	1.19784
$980$	203589.	6.63614
$981$	10807.2	0.351730
$982$	31460.0	1.02233
$983$	59702.0	1.93713	0.968564	−	0.248764i	$-0.0800244\pi$
$983$	59702.0	1.93713	0.968564	+	0.248764i	$0.0800244\pi$
$984$	−26361.2	−0.854028
$985$	−49046.8	−1.58656
$986$	−9240.77	−0.298464
$987$	22932.3	0.739559
$988$	−18122.5	−0.583557
$989$	6172.96	0.198472
$990$	12897.1	0.414038
$991$	−28972.2	−0.928692	−0.464346	−	0.885654i	$-0.653711\pi$
$991$	−28972.2	−0.928692	−0.464346	+	0.885654i	$0.653711\pi$
$992$	−33793.8	−1.08161
$993$	19652.5	0.628050
$994$	−92434.6	−2.94954
$995$	−52640.0	−1.67719
$996$	−62727.1	−1.99557
$997$	22480.8	0.714118	0.357059	−	0.934082i	$-0.383780\pi$
$997$	22480.8	0.714118	0.357059	+	0.934082i	$0.383780\pi$
$998$	73201.0	2.32178
$999$	−668.133	−0.0211599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.c.1.2	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.c.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-5.35351 q^{2} -3.00000 q^{3} +20.6601 q^{4} +11.7950 q^{5} +16.0605 q^{6} +34.3287 q^{7} -67.7759 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.35351 q^{2} -3.00000 q^{3} +20.6601 q^{4} +11.7950 q^{5} +16.0605 q^{6} +34.3287 q^{7} -67.7759 q^{8} +9.00000 q^{9} -63.1444 q^{10} -22.6942 q^{11} -61.9802 q^{12} -45.8267 q^{13} -183.779 q^{14} -35.3849 q^{15} +197.558 q^{16} -59.5211 q^{17} -48.1816 q^{18} +19.1412 q^{19} +243.685 q^{20} -102.986 q^{21} +121.494 q^{22} +23.0000 q^{23} +203.328 q^{24} +14.1209 q^{25} +245.334 q^{26} -27.0000 q^{27} +709.234 q^{28} -29.0000 q^{29} +189.433 q^{30} +65.5652 q^{31} -515.423 q^{32} +68.0826 q^{33} +318.647 q^{34} +404.906 q^{35} +185.941 q^{36} +24.7457 q^{37} -102.472 q^{38} +137.480 q^{39} -799.413 q^{40} -129.649 q^{41} +551.338 q^{42} +268.389 q^{43} -468.864 q^{44} +106.155 q^{45} -123.131 q^{46} -222.674 q^{47} -592.675 q^{48} +835.461 q^{49} -75.5965 q^{50} +178.563 q^{51} -946.783 q^{52} +124.414 q^{53} +144.545 q^{54} -267.677 q^{55} -2326.66 q^{56} -57.4235 q^{57} +155.252 q^{58} -581.664 q^{59} -731.054 q^{60} -569.215 q^{61} -351.004 q^{62} +308.958 q^{63} +1178.86 q^{64} -540.523 q^{65} -364.481 q^{66} -425.278 q^{67} -1229.71 q^{68} -69.0000 q^{69} -2167.67 q^{70} +502.965 q^{71} -609.983 q^{72} +282.494 q^{73} -132.476 q^{74} -42.3627 q^{75} +395.458 q^{76} -779.063 q^{77} -736.001 q^{78} -88.1207 q^{79} +2330.19 q^{80} +81.0000 q^{81} +694.076 q^{82} +1012.05 q^{83} -2127.70 q^{84} -702.049 q^{85} -1436.83 q^{86} +87.0000 q^{87} +1538.12 q^{88} -1616.80 q^{89} -568.300 q^{90} -1573.17 q^{91} +475.182 q^{92} -196.696 q^{93} +1192.09 q^{94} +225.769 q^{95} +1546.27 q^{96} -772.980 q^{97} -4472.65 q^{98} -204.248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 8 q^{2} - 111 q^{3} + 138 q^{4} - 15 q^{5} + 24 q^{6} - 6 q^{7} - 141 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 8 * q^2 - 111 * q^3 + 138 * q^4 - 15 * q^5 + 24 * q^6 - 6 * q^7 - 141 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} - 111 q^{3} + 138 q^{4} - 15 q^{5} + 24 q^{6} - 6 q^{7} - 141 q^{8} + 333 q^{9} + 26 q^{10} - 109 q^{11} - 414 q^{12} + 115 q^{13} - 243 q^{14} + 45 q^{15} + 406 q^{16} - 228 q^{17} - 72 q^{18} - 135 q^{19} - 73 q^{20} + 18 q^{21} - 40 q^{22} + 851 q^{23} + 423 q^{24} + 942 q^{25} - 543 q^{26} - 999 q^{27} + 853 q^{28} - 1073 q^{29} - 78 q^{30} - 518 q^{31} - 1596 q^{32} + 327 q^{33} + 312 q^{34} - 37 q^{35} + 1242 q^{36} + 245 q^{37} - 59 q^{38} - 345 q^{39} + 293 q^{40} - 915 q^{41} + 729 q^{42} - 389 q^{43} - 832 q^{44} - 135 q^{45} - 184 q^{46} - 926 q^{47} - 1218 q^{48} + 1655 q^{49} - 439 q^{50} + 684 q^{51} + 1290 q^{52} - 1134 q^{53} + 216 q^{54} - 404 q^{55} - 1141 q^{56} + 405 q^{57} + 232 q^{58} - 179 q^{59} + 219 q^{60} + 10 q^{61} + 1378 q^{62} - 54 q^{63} + 1359 q^{64} + 110 q^{65} + 120 q^{66} + 1385 q^{67} - 3375 q^{68} - 2553 q^{69} - 637 q^{70} - 2432 q^{71} - 1269 q^{72} - 1638 q^{73} - 2193 q^{74} - 2826 q^{75} - 1319 q^{76} - 3703 q^{77} + 1629 q^{78} - 4728 q^{79} - 1567 q^{80} + 2997 q^{81} + 537 q^{82} - 1416 q^{83} - 2559 q^{84} - 2093 q^{85} - 1187 q^{86} + 3219 q^{87} + 1497 q^{88} - 4019 q^{89} + 234 q^{90} - 545 q^{91} + 3174 q^{92} + 1554 q^{93} + 108 q^{94} - 807 q^{95} + 4788 q^{96} - 754 q^{97} - 5561 q^{98} - 981 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 - 111 * q^3 + 138 * q^4 - 15 * q^5 + 24 * q^6 - 6 * q^7 - 141 * q^8 + 333 * q^9 + 26 * q^10 - 109 * q^11 - 414 * q^12 + 115 * q^13 - 243 * q^14 + 45 * q^15 + 406 * q^16 - 228 * q^17 - 72 * q^18 - 135 * q^19 - 73 * q^20 + 18 * q^21 - 40 * q^22 + 851 * q^23 + 423 * q^24 + 942 * q^25 - 543 * q^26 - 999 * q^27 + 853 * q^28 - 1073 * q^29 - 78 * q^30 - 518 * q^31 - 1596 * q^32 + 327 * q^33 + 312 * q^34 - 37 * q^35 + 1242 * q^36 + 245 * q^37 - 59 * q^38 - 345 * q^39 + 293 * q^40 - 915 * q^41 + 729 * q^42 - 389 * q^43 - 832 * q^44 - 135 * q^45 - 184 * q^46 - 926 * q^47 - 1218 * q^48 + 1655 * q^49 - 439 * q^50 + 684 * q^51 + 1290 * q^52 - 1134 * q^53 + 216 * q^54 - 404 * q^55 - 1141 * q^56 + 405 * q^57 + 232 * q^58 - 179 * q^59 + 219 * q^60 + 10 * q^61 + 1378 * q^62 - 54 * q^63 + 1359 * q^64 + 110 * q^65 + 120 * q^66 + 1385 * q^67 - 3375 * q^68 - 2553 * q^69 - 637 * q^70 - 2432 * q^71 - 1269 * q^72 - 1638 * q^73 - 2193 * q^74 - 2826 * q^75 - 1319 * q^76 - 3703 * q^77 + 1629 * q^78 - 4728 * q^79 - 1567 * q^80 + 2997 * q^81 + 537 * q^82 - 1416 * q^83 - 2559 * q^84 - 2093 * q^85 - 1187 * q^86 + 3219 * q^87 + 1497 * q^88 - 4019 * q^89 + 234 * q^90 - 545 * q^91 + 3174 * q^92 + 1554 * q^93 + 108 * q^94 - 807 * q^95 + 4788 * q^96 - 754 * q^97 - 5561 * q^98 - 981 * q^99

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