LMFDB - Embedded newform 2001.4.a.h.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2001.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$118.062821921$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-4.54386 q^{2} +3.00000 q^{3} +12.6466 q^{4} +13.4410 q^{5} -13.6316 q^{6} +1.08944 q^{7} -21.1137 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.54386 q^{2} +3.00000 q^{3} +12.6466 q^{4} +13.4410 q^{5} -13.6316 q^{6} +1.08944 q^{7} -21.1137 q^{8} +9.00000 q^{9} -61.0740 q^{10} -31.6614 q^{11} +37.9399 q^{12} +14.7970 q^{13} -4.95027 q^{14} +40.3230 q^{15} -5.23550 q^{16} +82.0410 q^{17} -40.8947 q^{18} +13.2878 q^{19} +169.984 q^{20} +3.26832 q^{21} +143.865 q^{22} +23.0000 q^{23} -63.3411 q^{24} +55.6607 q^{25} -67.2357 q^{26} +27.0000 q^{27} +13.7778 q^{28} -29.0000 q^{29} -183.222 q^{30} +48.1932 q^{31} +192.699 q^{32} -94.9842 q^{33} -372.783 q^{34} +14.6432 q^{35} +113.820 q^{36} -275.453 q^{37} -60.3781 q^{38} +44.3911 q^{39} -283.789 q^{40} -218.536 q^{41} -14.8508 q^{42} +407.412 q^{43} -400.411 q^{44} +120.969 q^{45} -104.509 q^{46} +176.761 q^{47} -15.7065 q^{48} -341.813 q^{49} -252.914 q^{50} +246.123 q^{51} +187.133 q^{52} +61.0761 q^{53} -122.684 q^{54} -425.561 q^{55} -23.0021 q^{56} +39.8635 q^{57} +131.772 q^{58} -283.298 q^{59} +509.951 q^{60} +204.035 q^{61} -218.983 q^{62} +9.80497 q^{63} -833.713 q^{64} +198.887 q^{65} +431.595 q^{66} +1046.48 q^{67} +1037.54 q^{68} +69.0000 q^{69} -66.5366 q^{70} -577.607 q^{71} -190.023 q^{72} +949.814 q^{73} +1251.62 q^{74} +166.982 q^{75} +168.047 q^{76} -34.4933 q^{77} -201.707 q^{78} -443.126 q^{79} -70.3704 q^{80} +81.0000 q^{81} +992.996 q^{82} +1392.41 q^{83} +41.3334 q^{84} +1102.71 q^{85} -1851.22 q^{86} -87.0000 q^{87} +668.490 q^{88} -422.152 q^{89} -549.666 q^{90} +16.1205 q^{91} +290.873 q^{92} +144.579 q^{93} -803.175 q^{94} +178.602 q^{95} +578.097 q^{96} +846.974 q^{97} +1553.15 q^{98} -284.953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) $ 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * 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 $

$2$	−4.54386	−1.60650	−0.803248	−	0.595644i	$-0.796897\pi$
$2$	−4.54386	−1.60650	−0.803248	+	0.595644i	$0.796897\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	12.6466	1.58083
$5$	13.4410	1.20220	0.601100	−	0.799174i	$-0.294729\pi$
$5$	13.4410	1.20220	0.601100	+	0.799174i	$0.294729\pi$
$6$	−13.6316	−0.927511
$7$	1.08944	0.0588243	0.0294122	−	0.999567i	$-0.490636\pi$
$7$	1.08944	0.0588243	0.0294122	+	0.999567i	$0.490636\pi$
$8$	−21.1137	−0.933103
$9$	9.00000	0.333333
$10$	−61.0740	−1.93133
$11$	−31.6614	−0.867843	−0.433922	−	0.900951i	$-0.642871\pi$
$11$	−31.6614	−0.867843	−0.433922	+	0.900951i	$0.642871\pi$
$12$	37.9399	0.912693
$13$	14.7970	0.315689	0.157845	−	0.987464i	$-0.449545\pi$
$13$	14.7970	0.315689	0.157845	+	0.987464i	$0.449545\pi$
$14$	−4.95027	−0.0945011
$15$	40.3230	0.694091
$16$	−5.23550	−0.0818047
$17$	82.0410	1.17046	0.585231	−	0.810866i	$-0.301004\pi$
$17$	82.0410	1.17046	0.585231	+	0.810866i	$0.301004\pi$
$18$	−40.8947	−0.535499
$19$	13.2878	0.160444	0.0802221	−	0.996777i	$-0.474437\pi$
$19$	13.2878	0.160444	0.0802221	+	0.996777i	$0.474437\pi$
$20$	169.984	1.90048
$21$	3.26832	0.0339622
$22$	143.865	1.39419
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−63.3411	−0.538727
$25$	55.6607	0.445285
$26$	−67.2357	−0.507154
$27$	27.0000	0.192450
$28$	13.7778	0.0929913
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−183.222	−1.11505
$31$	48.1932	0.279218	0.139609	−	0.990207i	$-0.455415\pi$
$31$	48.1932	0.279218	0.139609	+	0.990207i	$0.455415\pi$
$32$	192.699	1.06452
$33$	−94.9842	−0.501050
$34$	−372.783	−1.88034
$35$	14.6432	0.0707186
$36$	113.820	0.526944
$37$	−275.453	−1.22390	−0.611949	−	0.790898i	$-0.709614\pi$
$37$	−275.453	−1.22390	−0.611949	+	0.790898i	$0.709614\pi$
$38$	−60.3781	−0.257753
$39$	44.3911	0.182263
$40$	−283.789	−1.12178
$41$	−218.536	−0.832429	−0.416214	−	0.909267i	$-0.636643\pi$
$41$	−218.536	−0.832429	−0.416214	+	0.909267i	$0.636643\pi$
$42$	−14.8508	−0.0545602
$43$	407.412	1.44488	0.722438	−	0.691435i	$-0.243021\pi$
$43$	407.412	1.44488	0.722438	+	0.691435i	$0.243021\pi$
$44$	−400.411	−1.37191
$45$	120.969	0.400733
$46$	−104.509	−0.334978
$47$	176.761	0.548579	0.274289	−	0.961647i	$-0.411557\pi$
$47$	176.761	0.548579	0.274289	+	0.961647i	$0.411557\pi$
$48$	−15.7065	−0.0472299
$49$	−341.813	−0.996540
$50$	−252.914	−0.715349
$51$	246.123	0.675767
$52$	187.133	0.499051
$53$	61.0761	0.158291	0.0791457	−	0.996863i	$-0.474781\pi$
$53$	61.0761	0.158291	0.0791457	+	0.996863i	$0.474781\pi$
$54$	−122.684	−0.309170
$55$	−425.561	−1.04332
$56$	−23.0021	−0.0548891
$57$	39.8635	0.0926325
$58$	131.772	0.298319
$59$	−283.298	−0.625123	−0.312562	−	0.949898i	$-0.601187\pi$
$59$	−283.298	−0.625123	−0.312562	+	0.949898i	$0.601187\pi$
$60$	509.951	1.09724
$61$	204.035	0.428263	0.214132	−	0.976805i	$-0.431308\pi$
$61$	204.035	0.428263	0.214132	+	0.976805i	$0.431308\pi$
$62$	−218.983	−0.448562
$63$	9.80497	0.0196081
$64$	−833.713	−1.62835
$65$	198.887	0.379522
$66$	431.595	0.804934
$67$	1046.48	1.90817	0.954085	−	0.299537i	$-0.0968323\pi$
$67$	1046.48	1.90817	0.954085	+	0.299537i	$0.0968323\pi$
$68$	1037.54	1.85030
$69$	69.0000	0.120386
$70$	−66.5366	−0.113609
$71$	−577.607	−0.965483	−0.482741	−	0.875763i	$-0.660359\pi$
$71$	−577.607	−0.965483	−0.482741	+	0.875763i	$0.660359\pi$
$72$	−190.023	−0.311034
$73$	949.814	1.52284	0.761420	−	0.648259i	$-0.224503\pi$
$73$	949.814	1.52284	0.761420	+	0.648259i	$0.224503\pi$
$74$	1251.62	1.96619
$75$	166.982	0.257086
$76$	168.047	0.253635
$77$	−34.4933	−0.0510503
$78$	−201.707	−0.292805
$79$	−443.126	−0.631083	−0.315541	−	0.948912i	$-0.602186\pi$
$79$	−443.126	−0.631083	−0.315541	+	0.948912i	$0.602186\pi$
$80$	−70.3704	−0.0983456
$81$	81.0000	0.111111
$82$	992.996	1.33729
$83$	1392.41	1.84140	0.920701	−	0.390268i	$-0.127618\pi$
$83$	1392.41	1.84140	0.920701	+	0.390268i	$0.127618\pi$
$84$	41.3334	0.0536886
$85$	1102.71	1.40713
$86$	−1851.22	−2.32119
$87$	−87.0000	−0.107211
$88$	668.490	0.809787
$89$	−422.152	−0.502787	−0.251394	−	0.967885i	$-0.580889\pi$
$89$	−422.152	−0.502787	−0.251394	+	0.967885i	$0.580889\pi$
$90$	−549.666	−0.643777
$91$	16.1205	0.0185702
$92$	290.873	0.329626
$93$	144.579	0.161206
$94$	−803.175	−0.881290
$95$	178.602	0.192886
$96$	578.097	0.614602
$97$	846.974	0.886569	0.443284	−	0.896381i	$-0.353813\pi$
$97$	846.974	0.886569	0.443284	+	0.896381i	$0.353813\pi$
$98$	1553.15	1.60094
$99$	−284.953	−0.289281
$100$	703.921	0.703921
$101$	1069.57	1.05372	0.526862	−	0.849951i	$-0.323369\pi$
$101$	1069.57	1.05372	0.526862	+	0.849951i	$0.323369\pi$
$102$	−1118.35	−1.08562
$103$	198.073	0.189483	0.0947415	−	0.995502i	$-0.469798\pi$
$103$	198.073	0.189483	0.0947415	+	0.995502i	$0.469798\pi$
$104$	−312.420	−0.294571
$105$	43.9296	0.0408294
$106$	−277.521	−0.254295
$107$	681.024	0.615300	0.307650	−	0.951500i	$-0.400457\pi$
$107$	681.024	0.615300	0.307650	+	0.951500i	$0.400457\pi$
$108$	341.459	0.304231
$109$	2034.87	1.78812	0.894062	−	0.447942i	$-0.147843\pi$
$109$	2034.87	1.78812	0.894062	+	0.447942i	$0.147843\pi$
$110$	1933.69	1.67609
$111$	−826.359	−0.706617
$112$	−5.70377	−0.00481210
$113$	284.625	0.236949	0.118474	−	0.992957i	$-0.462200\pi$
$113$	284.625	0.236949	0.118474	+	0.992957i	$0.462200\pi$
$114$	−181.134	−0.148814
$115$	309.143	0.250676
$116$	−366.753	−0.293553
$117$	133.173	0.105230
$118$	1287.27	1.00426
$119$	89.3789	0.0688517
$120$	−851.368	−0.647658
$121$	−328.555	−0.246848
$122$	−927.108	−0.688003
$123$	−655.608	−0.480603
$124$	609.482	0.441396
$125$	−931.990	−0.666878
$126$	−44.5524	−0.0315004
$127$	−1213.65	−0.847981	−0.423991	−	0.905667i	$-0.639371\pi$
$127$	−1213.65	−0.847981	−0.423991	+	0.905667i	$0.639371\pi$
$128$	2246.68	1.55141
$129$	1222.24	0.834200
$130$	−903.715	−0.609700
$131$	−1966.48	−1.31154	−0.655771	−	0.754960i	$-0.727656\pi$
$131$	−1966.48	−1.31154	−0.655771	+	0.754960i	$0.727656\pi$
$132$	−1201.23	−0.792075
$133$	14.4763	0.00943802
$134$	−4755.04	−3.06547
$135$	362.907	0.231364
$136$	−1732.19	−1.09216
$137$	524.224	0.326916	0.163458	−	0.986550i	$-0.447735\pi$
$137$	524.224	0.326916	0.163458	+	0.986550i	$0.447735\pi$
$138$	−313.526	−0.193399
$139$	−876.088	−0.534596	−0.267298	−	0.963614i	$-0.586131\pi$
$139$	−876.088	−0.534596	−0.267298	+	0.963614i	$0.586131\pi$
$140$	185.187	0.111794
$141$	530.282	0.316722
$142$	2624.56	1.55105
$143$	−468.495	−0.273969
$144$	−47.1195	−0.0272682
$145$	−389.789	−0.223243
$146$	−4315.82	−2.44644
$147$	−1025.44	−0.575352
$148$	−3483.56	−1.93477
$149$	3416.78	1.87861	0.939306	−	0.343079i	$-0.111470\pi$
$149$	3416.78	1.87861	0.939306	+	0.343079i	$0.111470\pi$
$150$	−758.743	−0.413007
$151$	2046.56	1.10296	0.551479	−	0.834189i	$-0.314064\pi$
$151$	2046.56	1.10296	0.551479	+	0.834189i	$0.314064\pi$
$152$	−280.555	−0.149711
$153$	738.369	0.390154
$154$	156.732	0.0820121
$155$	647.765	0.335676
$156$	561.399	0.288128
$157$	3009.02	1.52959	0.764796	−	0.644273i	$-0.222840\pi$
$157$	3009.02	1.52959	0.764796	+	0.644273i	$0.222840\pi$
$158$	2013.50	1.01383
$159$	183.228	0.0913896
$160$	2590.07	1.27977
$161$	25.0572	0.0122657
$162$	−368.053	−0.178500
$163$	−1956.94	−0.940365	−0.470182	−	0.882569i	$-0.655812\pi$
$163$	−1956.94	−0.940365	−0.470182	+	0.882569i	$0.655812\pi$
$164$	−2763.75	−1.31593
$165$	−1276.68	−0.602362
$166$	−6326.90	−2.95821
$167$	−1538.74	−0.713001	−0.356500	−	0.934295i	$-0.616030\pi$
$167$	−1538.74	−0.713001	−0.356500	+	0.934295i	$0.616030\pi$
$168$	−69.0064	−0.0316903
$169$	−1978.05	−0.900340
$170$	−5010.57	−2.26055
$171$	119.591	0.0534814
$172$	5152.39	2.28411
$173$	2007.03	0.882031	0.441015	−	0.897500i	$-0.354618\pi$
$173$	2007.03	0.882031	0.441015	+	0.897500i	$0.354618\pi$
$174$	395.316	0.172234
$175$	60.6391	0.0261936
$176$	165.763	0.0709936
$177$	−849.894	−0.360915
$178$	1918.20	0.807726
$179$	1796.56	0.750175	0.375088	−	0.926989i	$-0.377613\pi$
$179$	1796.56	0.750175	0.375088	+	0.926989i	$0.377613\pi$
$180$	1529.85	0.633492
$181$	842.709	0.346067	0.173033	−	0.984916i	$-0.444643\pi$
$181$	842.709	0.346067	0.173033	+	0.984916i	$0.444643\pi$
$182$	−73.2493	−0.0298330
$183$	612.106	0.247258
$184$	−485.615	−0.194565
$185$	−3702.37	−1.47137
$186$	−656.949	−0.258978
$187$	−2597.53	−1.01578
$188$	2235.43	0.867210
$189$	29.4149	0.0113207
$190$	−811.542	−0.309871
$191$	−3713.71	−1.40688	−0.703442	−	0.710753i	$-0.748354\pi$
$191$	−3713.71	−1.40688	−0.703442	+	0.710753i	$0.748354\pi$
$192$	−2501.14	−0.940126
$193$	−482.084	−0.179799	−0.0898994	−	0.995951i	$-0.528655\pi$
$193$	−482.084	−0.179799	−0.0898994	+	0.995951i	$0.528655\pi$
$194$	−3848.53	−1.42427
$195$	596.662	0.219117
$196$	−4322.79	−1.57536
$197$	−5124.32	−1.85326	−0.926631	−	0.375973i	$-0.877309\pi$
$197$	−5124.32	−1.85326	−0.926631	+	0.375973i	$0.877309\pi$
$198$	1294.78	0.464729
$199$	4357.88	1.55237	0.776186	−	0.630504i	$-0.217152\pi$
$199$	4357.88	1.55237	0.776186	+	0.630504i	$0.217152\pi$
$200$	−1175.20	−0.415497
$201$	3139.43	1.10168
$202$	−4859.97	−1.69280
$203$	−31.5938	−0.0109234
$204$	3112.63	1.06827
$205$	−2937.34	−1.00075
$206$	−900.018	−0.304404
$207$	207.000	0.0695048
$208$	−77.4699	−0.0258249
$209$	−420.712	−0.139240
$210$	−199.610	−0.0655923
$211$	5782.60	1.88669	0.943343	−	0.331818i	$-0.107662\pi$
$211$	5782.60	1.88669	0.943343	+	0.331818i	$0.107662\pi$
$212$	772.408	0.250232
$213$	−1732.82	−0.557422
$214$	−3094.48	−0.988477
$215$	5476.02	1.73703
$216$	−570.070	−0.179576
$217$	52.5036	0.0164248
$218$	−9246.18	−2.87262
$219$	2849.44	0.879212
$220$	−5381.92	−1.64931
$221$	1213.96	0.369503
$222$	3754.86	1.13518
$223$	2704.98	0.812283	0.406142	−	0.913810i	$-0.366874\pi$
$223$	2704.98	0.812283	0.406142	+	0.913810i	$0.366874\pi$
$224$	209.934	0.0626198
$225$	500.946	0.148428
$226$	−1293.29	−0.380658
$227$	−1845.96	−0.539739	−0.269870	−	0.962897i	$-0.586981\pi$
$227$	−1845.96	−0.539739	−0.269870	+	0.962897i	$0.586981\pi$
$228$	504.140	0.146436
$229$	3758.63	1.08462	0.542309	−	0.840179i	$-0.317550\pi$
$229$	3758.63	1.08462	0.542309	+	0.840179i	$0.317550\pi$
$230$	−1404.70	−0.402710
$231$	−103.480	−0.0294739
$232$	612.297	0.173273
$233$	−3436.85	−0.966332	−0.483166	−	0.875529i	$-0.660513\pi$
$233$	−3436.85	−0.966332	−0.483166	+	0.875529i	$0.660513\pi$
$234$	−605.121	−0.169051
$235$	2375.84	0.659501
$236$	−3582.77	−0.988214
$237$	−1329.38	−0.364356
$238$	−406.125	−0.110610
$239$	−1577.61	−0.426976	−0.213488	−	0.976946i	$-0.568482\pi$
$239$	−1577.61	−0.426976	−0.213488	+	0.976946i	$0.568482\pi$
$240$	−211.111	−0.0567799
$241$	−6678.30	−1.78501	−0.892504	−	0.451039i	$-0.851054\pi$
$241$	−6678.30	−1.78501	−0.892504	+	0.451039i	$0.851054\pi$
$242$	1492.91	0.396561
$243$	243.000	0.0641500
$244$	2580.36	0.677012
$245$	−4594.31	−1.19804
$246$	2978.99	0.772087
$247$	196.621	0.0506505
$248$	−1017.54	−0.260539
$249$	4177.22	1.06313
$250$	4234.83	1.07134
$251$	3030.29	0.762034	0.381017	−	0.924568i	$-0.375574\pi$
$251$	3030.29	0.762034	0.381017	+	0.924568i	$0.375574\pi$
$252$	124.000	0.0309971
$253$	−728.213	−0.180958
$254$	5514.63	1.36228
$255$	3308.14	0.812407
$256$	−3538.90	−0.863989
$257$	−5809.17	−1.40998	−0.704992	−	0.709215i	$-0.749049\pi$
$257$	−5809.17	−1.40998	−0.704992	+	0.709215i	$0.749049\pi$
$258$	−5553.66	−1.34014
$259$	−300.090	−0.0719949
$260$	2515.26	0.599960
$261$	−261.000	−0.0618984
$262$	8935.40	2.10699
$263$	−7189.56	−1.68565	−0.842827	−	0.538185i	$-0.819110\pi$
$263$	−7189.56	−1.68565	−0.842827	+	0.538185i	$0.819110\pi$
$264$	2005.47	0.467531
$265$	820.924	0.190298
$266$	−65.7784	−0.0151621
$267$	−1266.46	−0.290284
$268$	13234.4	3.01649
$269$	−1192.84	−0.270367	−0.135184	−	0.990821i	$-0.543162\pi$
$269$	−1192.84	−0.270367	−0.135184	+	0.990821i	$0.543162\pi$
$270$	−1649.00	−0.371685
$271$	−7768.18	−1.74127	−0.870633	−	0.491933i	$-0.836291\pi$
$271$	−7768.18	−1.74127	−0.870633	+	0.491933i	$0.836291\pi$
$272$	−429.526	−0.0957493
$273$	48.3615	0.0107215
$274$	−2382.00	−0.525189
$275$	−1762.30	−0.386438
$276$	872.619	0.190310
$277$	4088.68	0.886878	0.443439	−	0.896305i	$-0.353758\pi$
$277$	4088.68	0.886878	0.443439	+	0.896305i	$0.353758\pi$
$278$	3980.82	0.858826
$279$	433.738	0.0930726
$280$	−309.172	−0.0659877
$281$	−3425.63	−0.727245	−0.363622	−	0.931546i	$-0.618460\pi$
$281$	−3425.63	−0.727245	−0.363622	+	0.931546i	$0.618460\pi$
$282$	−2409.53	−0.508813
$283$	3626.92	0.761830	0.380915	−	0.924610i	$-0.375609\pi$
$283$	3626.92	0.761830	0.380915	+	0.924610i	$0.375609\pi$
$284$	−7304.79	−1.52627
$285$	535.806	0.111363
$286$	2128.78	0.440130
$287$	−238.082	−0.0489670
$288$	1734.29	0.354841
$289$	1817.73	0.369983
$290$	1771.15	0.358639
$291$	2540.92	0.511861
$292$	12012.0	2.40735
$293$	3914.65	0.780534	0.390267	−	0.920702i	$-0.372383\pi$
$293$	3914.65	0.780534	0.390267	+	0.920702i	$0.372383\pi$
$294$	4659.45	0.924302
$295$	−3807.81	−0.751523
$296$	5815.83	1.14202
$297$	−854.858	−0.167017
$298$	−15525.4	−3.01799
$299$	340.332	0.0658258
$300$	2111.76	0.406409
$301$	443.851	0.0849939
$302$	−9299.28	−1.77190
$303$	3208.71	0.608368
$304$	−69.5685	−0.0131251
$305$	2742.44	0.514858
$306$	−3355.04	−0.626781
$307$	9587.35	1.78234	0.891171	−	0.453667i	$-0.149884\pi$
$307$	9587.35	1.78234	0.891171	+	0.453667i	$0.149884\pi$
$308$	−436.224	−0.0807019
$309$	594.220	0.109398
$310$	−2943.35	−0.539262
$311$	−2394.27	−0.436548	−0.218274	−	0.975888i	$-0.570043\pi$
$311$	−2394.27	−0.436548	−0.218274	+	0.975888i	$0.570043\pi$
$312$	−937.261	−0.170070
$313$	1475.28	0.266414	0.133207	−	0.991088i	$-0.457473\pi$
$313$	1475.28	0.266414	0.133207	+	0.991088i	$0.457473\pi$
$314$	−13672.6	−2.45728
$315$	131.789	0.0235729
$316$	−5604.05	−0.997635
$317$	9147.92	1.62081	0.810407	−	0.585867i	$-0.199246\pi$
$317$	9147.92	1.62081	0.810407	+	0.585867i	$0.199246\pi$
$318$	−832.563	−0.146817
$319$	918.181	0.161154
$320$	−11205.9	−1.95760
$321$	2043.07	0.355243
$322$	−113.856	−0.0197048
$323$	1090.15	0.187794
$324$	1024.38	0.175648
$325$	823.614	0.140572
$326$	8892.06	1.51069
$327$	6104.62	1.03237
$328$	4614.10	0.776741
$329$	192.570	0.0322698
$330$	5801.07	0.967692
$331$	7063.42	1.17293	0.586467	−	0.809973i	$-0.300519\pi$
$331$	7063.42	1.17293	0.586467	+	0.809973i	$0.300519\pi$
$332$	17609.3	2.91095
$333$	−2479.08	−0.407966
$334$	6991.81	1.14543
$335$	14065.7	2.29400
$336$	−17.1113	−0.00277827
$337$	1522.05	0.246027	0.123014	−	0.992405i	$-0.460744\pi$
$337$	1522.05	0.246027	0.123014	+	0.992405i	$0.460744\pi$
$338$	8987.97	1.44639
$339$	853.874	0.136803
$340$	13945.6	2.22444
$341$	−1525.86	−0.242317
$342$	−543.402	−0.0859177
$343$	−746.064	−0.117445
$344$	−8601.97	−1.34822
$345$	927.430	0.144728
$346$	−9119.64	−1.41698
$347$	−221.513	−0.0342694	−0.0171347	−	0.999853i	$-0.505454\pi$
$347$	−221.513	−0.0342694	−0.0171347	+	0.999853i	$0.505454\pi$
$348$	−1100.26	−0.169483
$349$	1342.73	0.205945	0.102972	−	0.994684i	$-0.467165\pi$
$349$	1342.73	0.205945	0.102972	+	0.994684i	$0.467165\pi$
$350$	−275.535	−0.0420799
$351$	399.520	0.0607544
$352$	−6101.12	−0.923838
$353$	−12.3131	−0.00185654	−0.000928272	−	1.00000i	$-0.500295\pi$
$353$	−12.3131	−0.00185654	−0.000928272		1.00000i	$0.500295\pi$
$354$	3861.80	0.579809
$355$	−7763.61	−1.16070
$356$	−5338.81	−0.794821
$357$	268.137	0.0397515
$358$	−8163.32	−1.20515
$359$	−1523.21	−0.223933	−0.111966	−	0.993712i	$-0.535715\pi$
$359$	−1523.21	−0.223933	−0.111966	+	0.993712i	$0.535715\pi$
$360$	−2554.11	−0.373925
$361$	−6682.43	−0.974258
$362$	−3829.15	−0.555955
$363$	−985.664	−0.142518
$364$	203.870	0.0293564
$365$	12766.5	1.83076
$366$	−2781.32	−0.397219
$367$	10596.6	1.50719	0.753593	−	0.657341i	$-0.228319\pi$
$367$	10596.6	1.50719	0.753593	+	0.657341i	$0.228319\pi$
$368$	−120.416	−0.0170575
$369$	−1966.82	−0.277476
$370$	16823.0	2.36375
$371$	66.5388	0.00931138
$372$	1828.45	0.254840
$373$	−2089.66	−0.290077	−0.145038	−	0.989426i	$-0.546331\pi$
$373$	−2089.66	−0.290077	−0.145038	+	0.989426i	$0.546331\pi$
$374$	11802.8	1.63184
$375$	−2795.97	−0.385022
$376$	−3732.07	−0.511880
$377$	−429.114	−0.0586220
$378$	−133.657	−0.0181867
$379$	14022.5	1.90050	0.950248	−	0.311494i	$-0.100829\pi$
$379$	14022.5	1.90050	0.950248	+	0.311494i	$0.100829\pi$
$380$	2258.72	0.304920
$381$	−3640.94	−0.489582
$382$	16874.6	2.26015
$383$	8703.93	1.16123	0.580614	−	0.814179i	$-0.302813\pi$
$383$	8703.93	1.16123	0.580614	+	0.814179i	$0.302813\pi$
$384$	6740.04	0.895707
$385$	−463.624	−0.0613727
$386$	2190.52	0.288846
$387$	3666.71	0.481626
$388$	10711.4	1.40152
$389$	7710.25	1.00495	0.502475	−	0.864592i	$-0.332423\pi$
$389$	7710.25	1.00495	0.502475	+	0.864592i	$0.332423\pi$
$390$	−2711.15	−0.352011
$391$	1886.94	0.244058
$392$	7216.94	0.929874
$393$	−5899.44	−0.757219
$394$	23284.2	2.97726
$395$	−5956.05	−0.758688
$396$	−3603.70	−0.457304
$397$	−2114.20	−0.267276	−0.133638	−	0.991030i	$-0.542666\pi$
$397$	−2114.20	−0.267276	−0.133638	+	0.991030i	$0.542666\pi$
$398$	−19801.6	−2.49388
$399$	43.4290	0.00544904
$400$	−291.411	−0.0364264
$401$	−6033.97	−0.751427	−0.375713	−	0.926736i	$-0.622602\pi$
$401$	−6033.97	−0.751427	−0.375713	+	0.926736i	$0.622602\pi$
$402$	−14265.1	−1.76985
$403$	713.116	0.0881461
$404$	13526.5	1.66576
$405$	1088.72	0.133578
$406$	143.558	0.0175484
$407$	8721.23	1.06215
$408$	−5196.57	−0.630560
$409$	−16230.0	−1.96216	−0.981081	−	0.193599i	$-0.937984\pi$
$409$	−16230.0	−1.96216	−0.981081	+	0.193599i	$0.937984\pi$
$410$	13346.9	1.60769
$411$	1572.67	0.188745
$412$	2504.96	0.299541
$413$	−308.637	−0.0367724
$414$	−940.579	−0.111659
$415$	18715.3	2.21374
$416$	2851.38	0.336058
$417$	−2628.26	−0.308649
$418$	1911.65	0.223689
$419$	−10962.6	−1.27818	−0.639089	−	0.769133i	$-0.720688\pi$
$419$	−10962.6	−1.27818	−0.639089	+	0.769133i	$0.720688\pi$
$420$	555.562	0.0645444
$421$	15779.8	1.82675	0.913375	−	0.407120i	$-0.133467\pi$
$421$	15779.8	1.82675	0.913375	+	0.407120i	$0.133467\pi$
$422$	−26275.3	−3.03096
$423$	1590.85	0.182860
$424$	−1289.54	−0.147702
$425$	4566.46	0.521190
$426$	7873.69	0.895496
$427$	222.285	0.0251923
$428$	8612.67	0.972685
$429$	−1405.49	−0.158176
$430$	−24882.3	−2.79053
$431$	−2985.58	−0.333667	−0.166833	−	0.985985i	$-0.553354\pi$
$431$	−2985.58	−0.333667	−0.166833	+	0.985985i	$0.553354\pi$
$432$	−141.358	−0.0157433
$433$	10609.5	1.17750	0.588750	−	0.808315i	$-0.299620\pi$
$433$	10609.5	1.17750	0.588750	+	0.808315i	$0.299620\pi$
$434$	−238.569	−0.0263864
$435$	−1169.37	−0.128889
$436$	25734.3	2.82672
$437$	305.620	0.0334549
$438$	−12947.5	−1.41245
$439$	9161.61	0.996036	0.498018	−	0.867167i	$-0.334061\pi$
$439$	9161.61	0.996036	0.498018	+	0.867167i	$0.334061\pi$
$440$	8985.18	0.973526
$441$	−3076.32	−0.332180
$442$	−5516.08	−0.593605
$443$	9832.17	1.05449	0.527246	−	0.849712i	$-0.323224\pi$
$443$	9832.17	1.05449	0.527246	+	0.849712i	$0.323224\pi$
$444$	−10450.7	−1.11704
$445$	−5674.15	−0.604451
$446$	−12291.1	−1.30493
$447$	10250.3	1.08462
$448$	−908.282	−0.0957863
$449$	−13866.9	−1.45750	−0.728751	−	0.684779i	$-0.759899\pi$
$449$	−13866.9	−1.45750	−0.728751	+	0.684779i	$0.759899\pi$
$450$	−2276.23	−0.238450
$451$	6919.15	0.722417
$452$	3599.55	0.374576
$453$	6139.68	0.636793
$454$	8387.79	0.867089
$455$	216.676	0.0223251
$456$	−841.666	−0.0864356
$457$	2413.77	0.247071	0.123536	−	0.992340i	$-0.460577\pi$
$457$	2413.77	0.247071	0.123536	+	0.992340i	$0.460577\pi$
$458$	−17078.7	−1.74243
$459$	2215.11	0.225256
$460$	3909.62	0.396276
$461$	−2117.32	−0.213912	−0.106956	−	0.994264i	$-0.534110\pi$
$461$	−2117.32	−0.213912	−0.106956	+	0.994264i	$0.534110\pi$
$462$	470.197	0.0473497
$463$	64.3000	0.00645415	0.00322708	−	0.999995i	$-0.498973\pi$
$463$	64.3000	0.00645415	0.00322708	+	0.999995i	$0.498973\pi$
$464$	151.829	0.0151907
$465$	1943.29	0.193802
$466$	15616.5	1.55241
$467$	16469.6	1.63196	0.815979	−	0.578082i	$-0.196199\pi$
$467$	16469.6	1.63196	0.815979	+	0.578082i	$0.196199\pi$
$468$	1684.20	0.166350
$469$	1140.07	0.112247
$470$	−10795.5	−1.05949
$471$	9027.06	0.883110
$472$	5981.47	0.583304
$473$	−12899.2	−1.25393
$474$	6040.50	0.585336
$475$	739.610	0.0714435
$476$	1130.34	0.108843
$477$	549.685	0.0527638
$478$	7168.45	0.685935
$479$	−18506.6	−1.76532	−0.882659	−	0.470014i	$-0.844249\pi$
$479$	−18506.6	−1.76532	−0.882659	+	0.470014i	$0.844249\pi$
$480$	7770.21	0.738874
$481$	−4075.89	−0.386371
$482$	30345.2	2.86761
$483$	75.1715	0.00708162
$484$	−4155.12	−0.390225
$485$	11384.2	1.06583
$486$	−1104.16	−0.103057
$487$	17054.4	1.58688	0.793439	−	0.608650i	$-0.208289\pi$
$487$	17054.4	1.58688	0.793439	+	0.608650i	$0.208289\pi$
$488$	−4307.94	−0.399614
$489$	−5870.82	−0.542920
$490$	20875.9	1.92465
$491$	8271.83	0.760290	0.380145	−	0.924927i	$-0.375874\pi$
$491$	8271.83	0.760290	0.380145	+	0.924927i	$0.375874\pi$
$492$	−8291.24	−0.759752
$493$	−2379.19	−0.217349
$494$	−893.417	−0.0813699
$495$	−3830.05	−0.347774
$496$	−252.315	−0.0228413
$497$	−629.269	−0.0567939
$498$	−18980.7	−1.70792
$499$	−7583.43	−0.680322	−0.340161	−	0.940367i	$-0.610482\pi$
$499$	−7583.43	−0.680322	−0.340161	+	0.940367i	$0.610482\pi$
$500$	−11786.6	−1.05422
$501$	−4616.21	−0.411651
$502$	−13769.2	−1.22420
$503$	−4358.95	−0.386394	−0.193197	−	0.981160i	$-0.561886\pi$
$503$	−4358.95	−0.386394	−0.193197	+	0.981160i	$0.561886\pi$
$504$	−207.019	−0.0182964
$505$	14376.1	1.26679
$506$	3308.89	0.290708
$507$	−5934.14	−0.519812
$508$	−15348.5	−1.34051
$509$	−6710.28	−0.584338	−0.292169	−	0.956367i	$-0.594377\pi$
$509$	−6710.28	−0.584338	−0.292169	+	0.956367i	$0.594377\pi$
$510$	−15031.7	−1.30513
$511$	1034.77	0.0895800
$512$	−1893.20	−0.163415
$513$	358.772	0.0308775
$514$	26396.0	2.26513
$515$	2662.31	0.227797
$516$	15457.2	1.31873
$517$	−5596.49	−0.476080
$518$	1363.57	0.115660
$519$	6021.08	0.509241
$520$	−4199.25	−0.354133
$521$	6944.88	0.583994	0.291997	−	0.956419i	$-0.405680\pi$
$521$	6944.88	0.583994	0.291997	+	0.956419i	$0.405680\pi$
$522$	1185.95	0.0994396
$523$	7287.00	0.609251	0.304626	−	0.952472i	$-0.401469\pi$
$523$	7287.00	0.609251	0.304626	+	0.952472i	$0.401469\pi$
$524$	−24869.4	−2.07333
$525$	181.917	0.0151229
$526$	32668.3	2.70800
$527$	3953.82	0.326814
$528$	497.290	0.0409882
$529$	529.000	0.0434783
$530$	−3730.16	−0.305713
$531$	−2549.68	−0.208374
$532$	183.077	0.0149199
$533$	−3233.69	−0.262789
$534$	5754.60	0.466341
$535$	9153.65	0.739714
$536$	−22095.0	−1.78052
$537$	5389.69	0.433114
$538$	5420.10	0.434344
$539$	10822.3	0.864840
$540$	4589.56	0.365747
$541$	−3478.74	−0.276456	−0.138228	−	0.990400i	$-0.544141\pi$
$541$	−3478.74	−0.276456	−0.138228	+	0.990400i	$0.544141\pi$
$542$	35297.5	2.79734
$543$	2528.13	0.199802
$544$	15809.2	1.24598
$545$	27350.8	2.14968
$546$	−219.748	−0.0172241
$547$	−5212.98	−0.407479	−0.203740	−	0.979025i	$-0.565310\pi$
$547$	−5212.98	−0.407479	−0.203740	+	0.979025i	$0.565310\pi$
$548$	6629.67	0.516799
$549$	1836.32	0.142754
$550$	8007.62	0.620811
$551$	−385.347	−0.0297937
$552$	−1456.85	−0.112332
$553$	−482.759	−0.0371230
$554$	−18578.4	−1.42477
$555$	−11107.1	−0.849496
$556$	−11079.6	−0.845105
$557$	13725.8	1.04413	0.522067	−	0.852905i	$-0.325161\pi$
$557$	13725.8	1.04413	0.522067	+	0.852905i	$0.325161\pi$
$558$	−1970.85	−0.149521
$559$	6028.49	0.456132
$560$	−76.6644	−0.00578511
$561$	−7792.60	−0.586460
$562$	15565.6	1.16832
$563$	−22634.6	−1.69438	−0.847189	−	0.531292i	$-0.821707\pi$
$563$	−22634.6	−1.69438	−0.847189	+	0.531292i	$0.821707\pi$
$564$	6706.29	0.500684
$565$	3825.64	0.284860
$566$	−16480.2	−1.22388
$567$	88.2448	0.00653604
$568$	12195.4	0.900895
$569$	9653.99	0.711277	0.355638	−	0.934624i	$-0.384264\pi$
$569$	9653.99	0.711277	0.355638	+	0.934624i	$0.384264\pi$
$570$	−2434.63	−0.178904
$571$	11320.5	0.829683	0.414841	−	0.909894i	$-0.363837\pi$
$571$	11320.5	0.829683	0.414841	+	0.909894i	$0.363837\pi$
$572$	−5924.90	−0.433098
$573$	−11141.1	−0.812265
$574$	1081.81	0.0786654
$575$	1280.20	0.0928484
$576$	−7503.42	−0.542782
$577$	20441.0	1.47482	0.737409	−	0.675447i	$-0.236049\pi$
$577$	20441.0	1.47482	0.737409	+	0.675447i	$0.236049\pi$
$578$	−8259.49	−0.594376
$579$	−1446.25	−0.103807
$580$	−4929.53	−0.352909
$581$	1516.95	0.108319
$582$	−11545.6	−0.822302
$583$	−1933.75	−0.137372
$584$	−20054.1	−1.42097
$585$	1789.98	0.126507
$586$	−17787.6	−1.25392
$587$	−23896.1	−1.68024	−0.840118	−	0.542404i	$-0.817514\pi$
$587$	−23896.1	−1.68024	−0.840118	+	0.542404i	$0.817514\pi$
$588$	−12968.4	−0.909535
$589$	640.383	0.0447988
$590$	17302.2	1.20732
$591$	−15373.0	−1.06998
$592$	1442.13	0.100120
$593$	18688.7	1.29419	0.647093	−	0.762411i	$-0.275985\pi$
$593$	18688.7	1.29419	0.647093	+	0.762411i	$0.275985\pi$
$594$	3884.35	0.268311
$595$	1201.34	0.0827735
$596$	43210.8	2.96977
$597$	13073.6	0.896263
$598$	−1546.42	−0.105749
$599$	28292.8	1.92990	0.964952	−	0.262426i	$-0.0845225\pi$
$599$	28292.8	1.92990	0.964952	+	0.262426i	$0.0845225\pi$
$600$	−3525.61	−0.239887
$601$	−16981.9	−1.15259	−0.576293	−	0.817243i	$-0.695501\pi$
$601$	−16981.9	−1.15259	−0.576293	+	0.817243i	$0.695501\pi$
$602$	−2016.80	−0.136542
$603$	9418.28	0.636056
$604$	25882.1	1.74359
$605$	−4416.11	−0.296761
$606$	−14579.9	−0.977340
$607$	612.871	0.0409813	0.0204907	−	0.999790i	$-0.493477\pi$
$607$	612.871	0.0409813	0.0204907	+	0.999790i	$0.493477\pi$
$608$	2560.55	0.170796
$609$	−94.7814	−0.00630663
$610$	−12461.3	−0.827118
$611$	2615.54	0.173180
$612$	9337.89	0.616768
$613$	−16958.5	−1.11737	−0.558685	−	0.829380i	$-0.688694\pi$
$613$	−16958.5	−1.11737	−0.558685	+	0.829380i	$0.688694\pi$
$614$	−43563.6	−2.86333
$615$	−8812.03	−0.577781
$616$	728.281	0.0476352
$617$	27616.8	1.80196	0.900982	−	0.433857i	$-0.142848\pi$
$617$	27616.8	1.80196	0.900982	+	0.433857i	$0.142848\pi$
$618$	−2700.05	−0.175748
$619$	22415.0	1.45547	0.727734	−	0.685859i	$-0.240573\pi$
$619$	22415.0	1.45547	0.727734	+	0.685859i	$0.240573\pi$
$620$	8192.05	0.530646
$621$	621.000	0.0401286
$622$	10879.2	0.701313
$623$	−459.910	−0.0295761
$624$	−232.410	−0.0149100
$625$	−19484.5	−1.24701
$626$	−6703.44	−0.427993
$627$	−1262.14	−0.0803905
$628$	38054.0	2.41803
$629$	−22598.4	−1.43253
$630$	−598.829	−0.0378697
$631$	−4596.39	−0.289983	−0.144992	−	0.989433i	$-0.546316\pi$
$631$	−4596.39	−0.289983	−0.144992	+	0.989433i	$0.546316\pi$
$632$	9356.02	0.588865
$633$	17347.8	1.08928
$634$	−41566.8	−2.60383
$635$	−16312.6	−1.01944
$636$	2317.22	0.144471
$637$	−5057.82	−0.314597
$638$	−4172.08	−0.258894
$639$	−5198.46	−0.321828
$640$	30197.7	1.86511
$641$	−4814.44	−0.296660	−0.148330	−	0.988938i	$-0.547390\pi$
$641$	−4814.44	−0.296660	−0.148330	+	0.988938i	$0.547390\pi$
$642$	−9283.43	−0.570697
$643$	17323.6	1.06248	0.531240	−	0.847221i	$-0.321726\pi$
$643$	17323.6	1.06248	0.531240	+	0.847221i	$0.321726\pi$
$644$	316.889	0.0193900
$645$	16428.1	1.00288
$646$	−4953.48	−0.301690
$647$	−18227.5	−1.10757	−0.553783	−	0.832661i	$-0.686816\pi$
$647$	−18227.5	−1.10757	−0.553783	+	0.832661i	$0.686816\pi$
$648$	−1710.21	−0.103678
$649$	8969.62	0.542509
$650$	−3742.38	−0.225828
$651$	157.511	0.00948286
$652$	−24748.7	−1.48656
$653$	6700.49	0.401547	0.200774	−	0.979638i	$-0.435654\pi$
$653$	6700.49	0.401547	0.200774	+	0.979638i	$0.435654\pi$
$654$	−27738.5	−1.65851
$655$	−26431.5	−1.57674
$656$	1144.14	0.0680965
$657$	8548.32	0.507613
$658$	−875.013	−0.0518413
$659$	26568.4	1.57050	0.785249	−	0.619181i	$-0.212535\pi$
$659$	26568.4	1.57050	0.785249	+	0.619181i	$0.212535\pi$
$660$	−16145.8	−0.952232
$661$	−24091.2	−1.41761	−0.708804	−	0.705405i	$-0.750765\pi$
$661$	−24091.2	−1.41761	−0.708804	+	0.705405i	$0.750765\pi$
$662$	−32095.2	−1.88431
$663$	3641.89	0.213332
$664$	−29398.9	−1.71822
$665$	194.576	0.0113464
$666$	11264.6	0.655395
$667$	−667.000	−0.0387202
$668$	−19459.9	−1.12713
$669$	8114.95	0.468972
$670$	−63912.5	−3.68531
$671$	−6460.05	−0.371665
$672$	629.803	0.0361535
$673$	18129.6	1.03840	0.519200	−	0.854653i	$-0.326230\pi$
$673$	18129.6	1.03840	0.519200	+	0.854653i	$0.326230\pi$
$674$	−6915.97	−0.395242
$675$	1502.84	0.0856952
$676$	−25015.7	−1.42329
$677$	−8255.36	−0.468655	−0.234327	−	0.972158i	$-0.575289\pi$
$677$	−8255.36	−0.468655	−0.234327	+	0.972158i	$0.575289\pi$
$678$	−3879.88	−0.219773
$679$	922.729	0.0521518
$680$	−23282.4	−1.31300
$681$	−5537.89	−0.311619
$682$	6933.31	0.389282
$683$	−11541.3	−0.646583	−0.323292	−	0.946299i	$-0.604789\pi$
$683$	−11541.3	−0.646583	−0.323292	+	0.946299i	$0.604789\pi$
$684$	1512.42	0.0845450
$685$	7046.10	0.393018
$686$	3390.01	0.188675
$687$	11275.9	0.626204
$688$	−2133.00	−0.118198
$689$	903.745	0.0499709
$690$	−4214.11	−0.232505
$691$	−11519.1	−0.634166	−0.317083	−	0.948398i	$-0.602703\pi$
$691$	−11519.1	−0.634166	−0.317083	+	0.948398i	$0.602703\pi$
$692$	25382.1	1.39434
$693$	−310.439	−0.0170168
$694$	1006.53	0.0550536
$695$	−11775.5	−0.642691
$696$	1836.89	0.100039
$697$	−17928.9	−0.974326
$698$	−6101.18	−0.330850
$699$	−10310.5	−0.557912
$700$	766.881	0.0414077
$701$	−26238.5	−1.41371	−0.706856	−	0.707357i	$-0.749887\pi$
$701$	−26238.5	−1.41371	−0.706856	+	0.707357i	$0.749887\pi$
$702$	−1815.36	−0.0976018
$703$	−3660.17	−0.196367
$704$	26396.5	1.41315
$705$	7127.52	0.380763
$706$	55.9490	0.00298253
$707$	1165.23	0.0619846
$708$	−10748.3	−0.570545
$709$	−8661.16	−0.458783	−0.229391	−	0.973334i	$-0.573674\pi$
$709$	−8661.16	−0.458783	−0.229391	+	0.973334i	$0.573674\pi$
$710$	35276.8	1.86467
$711$	−3988.13	−0.210361
$712$	8913.20	0.469152
$713$	1108.44	0.0582209
$714$	−1218.37	−0.0638607
$715$	−6297.05	−0.329365
$716$	22720.5	1.18590
$717$	−4732.84	−0.246515
$718$	6921.25	0.359747
$719$	31638.8	1.64107	0.820535	−	0.571597i	$-0.193676\pi$
$719$	31638.8	1.64107	0.820535	+	0.571597i	$0.193676\pi$
$720$	−633.333	−0.0327819
$721$	215.789	0.0111462
$722$	30364.0	1.56514
$723$	−20034.9	−1.03058
$724$	10657.4	0.547073
$725$	−1614.16	−0.0826874
$726$	4478.72	0.228954
$727$	3417.03	0.174320	0.0871601	−	0.996194i	$-0.472221\pi$
$727$	3417.03	0.174320	0.0871601	+	0.996194i	$0.472221\pi$
$728$	−340.364	−0.0173279
$729$	729.000	0.0370370
$730$	−58008.9	−2.94111
$731$	33424.5	1.69117
$732$	7741.09	0.390873
$733$	−32192.4	−1.62217	−0.811087	−	0.584926i	$-0.801124\pi$
$733$	−32192.4	−1.62217	−0.811087	+	0.584926i	$0.801124\pi$
$734$	−48149.4	−2.42129
$735$	−13782.9	−0.691689
$736$	4432.08	0.221968
$737$	−33132.9	−1.65599
$738$	8936.96	0.445764
$739$	−21542.9	−1.07235	−0.536177	−	0.844105i	$-0.680132\pi$
$739$	−21542.9	−1.07235	−0.536177	+	0.844105i	$0.680132\pi$
$740$	−46822.5	−2.32599
$741$	589.862	0.0292431
$742$	−302.343	−0.0149587
$743$	−5074.41	−0.250555	−0.125277	−	0.992122i	$-0.539982\pi$
$743$	−5074.41	−0.250555	−0.125277	+	0.992122i	$0.539982\pi$
$744$	−3052.61	−0.150422
$745$	45924.9	2.25847
$746$	9495.13	0.466007
$747$	12531.7	0.613801
$748$	−32850.1	−1.60577
$749$	741.936	0.0361946
$750$	12704.5	0.618537
$751$	−11444.3	−0.556071	−0.278036	−	0.960571i	$-0.589683\pi$
$751$	−11444.3	−0.556071	−0.278036	+	0.960571i	$0.589683\pi$
$752$	−925.430	−0.0448763
$753$	9090.88	0.439960
$754$	1949.83	0.0941761
$755$	27507.8	1.32598
$756$	372.000	0.0178962
$757$	774.290	0.0371758	0.0185879	−	0.999827i	$-0.494083\pi$
$757$	774.290	0.0371758	0.0185879	+	0.999827i	$0.494083\pi$
$758$	−63716.3	−3.05314
$759$	−2184.64	−0.104476
$760$	−3770.95	−0.179982
$761$	−13315.8	−0.634295	−0.317148	−	0.948376i	$-0.602725\pi$
$761$	−13315.8	−0.634295	−0.317148	+	0.948376i	$0.602725\pi$
$762$	16543.9	0.786512
$763$	2216.88	0.105185
$764$	−46966.0	−2.22404
$765$	9924.42	0.469043
$766$	−39549.4	−1.86551
$767$	−4191.97	−0.197345
$768$	−10616.7	−0.498824
$769$	3410.17	0.159914	0.0799570	−	0.996798i	$-0.474522\pi$
$769$	3410.17	0.159914	0.0799570	+	0.996798i	$0.474522\pi$
$770$	2106.64	0.0985950
$771$	−17427.5	−0.814054
$772$	−6096.75	−0.284231
$773$	−19806.6	−0.921598	−0.460799	−	0.887504i	$-0.652437\pi$
$773$	−19806.6	−0.921598	−0.460799	+	0.887504i	$0.652437\pi$
$774$	−16661.0	−0.773730
$775$	2682.46	0.124332
$776$	−17882.8	−0.827260
$777$	−900.270	−0.0415663
$778$	−35034.3	−1.61445
$779$	−2903.87	−0.133558
$780$	7545.77	0.346387
$781$	18287.8	0.837888
$782$	−8574.00	−0.392079
$783$	−783.000	−0.0357371
$784$	1789.56	0.0815216
$785$	40444.3	1.83888
$786$	26806.2	1.21647
$787$	−27060.0	−1.22565	−0.612823	−	0.790220i	$-0.709966\pi$
$787$	−27060.0	−1.22565	−0.612823	+	0.790220i	$0.709966\pi$
$788$	−64805.4	−2.92969
$789$	−21568.7	−0.973213
$790$	27063.5	1.21883
$791$	310.082	0.0139384
$792$	6016.41	0.269929
$793$	3019.12	0.135198
$794$	9606.61	0.429378
$795$	2462.77	0.109869
$796$	55112.6	2.45404
$797$	−1418.91	−0.0630620	−0.0315310	−	0.999503i	$-0.510038\pi$
$797$	−1418.91	−0.0630620	−0.0315310	+	0.999503i	$0.510038\pi$
$798$	−197.335	−0.00875387
$799$	14501.6	0.642091
$800$	10725.8	0.474016
$801$	−3799.37	−0.167596
$802$	27417.5	1.20716
$803$	−30072.4	−1.32159
$804$	39703.2	1.74157
$805$	336.793	0.0147458
$806$	−3240.30	−0.141606
$807$	−3578.52	−0.156097
$808$	−22582.6	−0.983232
$809$	84.3982	0.00366784	0.00183392	−	0.999998i	$-0.499416\pi$
$809$	84.3982	0.00366784	0.00183392	+	0.999998i	$0.499416\pi$
$810$	−4947.00	−0.214592
$811$	9902.34	0.428752	0.214376	−	0.976751i	$-0.431228\pi$
$811$	9902.34	0.428752	0.214376	+	0.976751i	$0.431228\pi$
$812$	−399.556	−0.0172681
$813$	−23304.5	−1.00532
$814$	−39628.0	−1.70634
$815$	−26303.3	−1.13051
$816$	−1288.58	−0.0552809
$817$	5413.62	0.231822
$818$	73747.0	3.15221
$819$	145.085	0.00619007
$820$	−37147.5	−1.58201
$821$	2476.25	0.105264	0.0526319	−	0.998614i	$-0.483239\pi$
$821$	2476.25	0.105264	0.0526319	+	0.998614i	$0.483239\pi$
$822$	−7146.00	−0.303218
$823$	−11646.8	−0.493297	−0.246648	−	0.969105i	$-0.579329\pi$
$823$	−11646.8	−0.493297	−0.246648	+	0.969105i	$0.579329\pi$
$824$	−4182.06	−0.176807
$825$	−5286.89	−0.223110
$826$	1402.40	0.0590748
$827$	36045.6	1.51563	0.757816	−	0.652468i	$-0.226266\pi$
$827$	36045.6	1.51563	0.757816	+	0.652468i	$0.226266\pi$
$828$	2617.86	0.109875
$829$	19283.5	0.807895	0.403948	−	0.914782i	$-0.367638\pi$
$829$	19283.5	0.807895	0.403948	+	0.914782i	$0.367638\pi$
$830$	−85039.9	−3.55636
$831$	12266.1	0.512039
$832$	−12336.5	−0.514051
$833$	−28042.7	−1.16641
$834$	11942.5	0.495843
$835$	−20682.2	−0.857170
$836$	−5320.59	−0.220115
$837$	1301.22	0.0537355
$838$	49812.4	2.05339
$839$	−28350.5	−1.16659	−0.583295	−	0.812260i	$-0.698237\pi$
$839$	−28350.5	−1.16659	−0.583295	+	0.812260i	$0.698237\pi$
$840$	−927.516	−0.0380980
$841$	841.000	0.0344828
$842$	−71701.3	−2.93467
$843$	−10276.9	−0.419875
$844$	73130.6	2.98253
$845$	−26587.0	−1.08239
$846$	−7228.58	−0.293763
$847$	−357.941	−0.0145207
$848$	−319.764	−0.0129490
$849$	10880.8	0.439843
$850$	−20749.3	−0.837290
$851$	−6335.42	−0.255200
$852$	−21914.4	−0.881190
$853$	−9402.80	−0.377428	−0.188714	−	0.982032i	$-0.560432\pi$
$853$	−9402.80	−0.377428	−0.188714	+	0.982032i	$0.560432\pi$
$854$	−1010.03	−0.0404713
$855$	1607.42	0.0642953
$856$	−14378.9	−0.574138
$857$	7102.63	0.283105	0.141553	−	0.989931i	$-0.454791\pi$
$857$	7102.63	0.283105	0.141553	+	0.989931i	$0.454791\pi$
$858$	6386.33	0.254109
$859$	7556.94	0.300162	0.150081	−	0.988674i	$-0.452046\pi$
$859$	7556.94	0.300162	0.150081	+	0.988674i	$0.452046\pi$
$860$	69253.3	2.74595
$861$	−714.246	−0.0282711
$862$	13566.1	0.536035
$863$	16528.3	0.651947	0.325974	−	0.945379i	$-0.394308\pi$
$863$	16528.3	0.651947	0.325974	+	0.945379i	$0.394308\pi$
$864$	5202.87	0.204867
$865$	26976.4	1.06038
$866$	−48207.8	−1.89165
$867$	5453.18	0.213610
$868$	663.995	0.0259648
$869$	14030.0	0.547681
$870$	5313.44	0.207060
$871$	15484.7	0.602389
$872$	−42963.7	−1.66850
$873$	7622.77	0.295523
$874$	−1388.70	−0.0537452
$875$	−1015.35	−0.0392286
$876$	36035.9	1.38989
$877$	−12253.0	−0.471782	−0.235891	−	0.971779i	$-0.575801\pi$
$877$	−12253.0	−0.471782	−0.235891	+	0.971779i	$0.575801\pi$
$878$	−41629.1	−1.60013
$879$	11744.0	0.450641
$880$	2228.03	0.0853486
$881$	29227.7	1.11771	0.558857	−	0.829264i	$-0.311240\pi$
$881$	29227.7	1.11771	0.558857	+	0.829264i	$0.311240\pi$
$882$	13978.4	0.533646
$883$	−37171.5	−1.41667	−0.708335	−	0.705877i	$-0.750553\pi$
$883$	−37171.5	−1.41667	−0.708335	+	0.705877i	$0.750553\pi$
$884$	15352.6	0.584121
$885$	−11423.4	−0.433892
$886$	−44676.0	−1.69404
$887$	17250.9	0.653021	0.326510	−	0.945194i	$-0.394127\pi$
$887$	17250.9	0.653021	0.326510	+	0.945194i	$0.394127\pi$
$888$	17447.5	0.659347
$889$	−1322.20	−0.0498819
$890$	25782.5	0.971048
$891$	−2564.57	−0.0964270
$892$	34209.0	1.28408
$893$	2348.77	0.0880162
$894$	−46576.1	−1.74243
$895$	24147.6	0.901861
$896$	2447.63	0.0912606
$897$	1021.00	0.0380045
$898$	63009.1	2.34147
$899$	−1397.60	−0.0518494
$900$	6335.29	0.234640
$901$	5010.74	0.185274
$902$	−31439.7	−1.16056
$903$	1331.55	0.0490712
$904$	−6009.48	−0.221098
$905$	11326.9	0.416042
$906$	−27897.8	−1.02301
$907$	19106.4	0.699468	0.349734	−	0.936849i	$-0.386272\pi$
$907$	19106.4	0.699468	0.349734	+	0.936849i	$0.386272\pi$
$908$	−23345.2	−0.853237
$909$	9626.12	0.351241
$910$	−984.545	−0.0358652
$911$	25088.5	0.912425	0.456212	−	0.889871i	$-0.349206\pi$
$911$	25088.5	0.912425	0.456212	+	0.889871i	$0.349206\pi$
$912$	−208.705	−0.00757777
$913$	−44085.6	−1.59805
$914$	−10967.8	−0.396919
$915$	8227.32	0.297254
$916$	47534.1	1.71460
$917$	−2142.36	−0.0771506
$918$	−10065.1	−0.361872
$919$	−7156.42	−0.256875	−0.128438	−	0.991718i	$-0.540996\pi$
$919$	−7156.42	−0.256875	−0.128438	+	0.991718i	$0.540996\pi$
$920$	−6527.16	−0.233907
$921$	28762.1	1.02904
$922$	9620.78	0.343648
$923$	−8546.87	−0.304793
$924$	−1308.67	−0.0465932
$925$	−15331.9	−0.544984
$926$	−292.170	−0.0103686
$927$	1782.66	0.0631610
$928$	−5588.27	−0.197677
$929$	45807.7	1.61776	0.808882	−	0.587971i	$-0.200073\pi$
$929$	45807.7	1.61776	0.808882	+	0.587971i	$0.200073\pi$
$930$	−8830.05	−0.311343
$931$	−4541.96	−0.159889
$932$	−43464.6	−1.52761
$933$	−7182.80	−0.252041
$934$	−74835.7	−2.62173
$935$	−34913.5	−1.22117
$936$	−2811.78	−0.0981902
$937$	3562.81	0.124218	0.0621088	−	0.998069i	$-0.480217\pi$
$937$	3562.81	0.124218	0.0621088	+	0.998069i	$0.480217\pi$
$938$	−5180.33	−0.180324
$939$	4425.83	0.153814
$940$	30046.4	1.04256
$941$	−29952.6	−1.03765	−0.518824	−	0.854881i	$-0.673630\pi$
$941$	−29952.6	−1.03765	−0.518824	+	0.854881i	$0.673630\pi$
$942$	−41017.7	−1.41871
$943$	−5026.32	−0.173573
$944$	1483.21	0.0511380
$945$	395.366	0.0136098
$946$	58612.3	2.01443
$947$	−8938.51	−0.306719	−0.153359	−	0.988170i	$-0.549009\pi$
$947$	−8938.51	−0.306719	−0.153359	+	0.988170i	$0.549009\pi$
$948$	−16812.2	−0.575985
$949$	14054.4	0.480744
$950$	−3360.68	−0.114774
$951$	27443.8	0.935778
$952$	−1887.12	−0.0642457
$953$	7221.62	0.245468	0.122734	−	0.992440i	$-0.460834\pi$
$953$	7221.62	0.245468	0.122734	+	0.992440i	$0.460834\pi$
$954$	−2497.69	−0.0847649
$955$	−49916.0	−1.69136
$956$	−19951.5	−0.674977
$957$	2754.54	0.0930426
$958$	84091.3	2.83598
$959$	571.111	0.0192306
$960$	−33617.8	−1.13022
$961$	−27468.4	−0.922037
$962$	18520.3	0.620704
$963$	6129.22	0.205100
$964$	−84458.1	−2.82180
$965$	−6479.69	−0.216154
$966$	−341.569	−0.0113766
$967$	−9803.75	−0.326026	−0.163013	−	0.986624i	$-0.552121\pi$
$967$	−9803.75	−0.326026	−0.163013	+	0.986624i	$0.552121\pi$
$968$	6937.01	0.230335
$969$	3270.44	0.108423
$970$	−51728.1	−1.71226
$971$	40030.1	1.32300	0.661498	−	0.749947i	$-0.269921\pi$
$971$	40030.1	1.32300	0.661498	+	0.749947i	$0.269921\pi$
$972$	3073.14	0.101410
$973$	−954.446	−0.0314472
$974$	−77492.9	−2.54931
$975$	2470.84	0.0811592
$976$	−1068.23	−0.0350339
$977$	2518.17	0.0824599	0.0412300	−	0.999150i	$-0.486872\pi$
$977$	2518.17	0.0824599	0.0412300	+	0.999150i	$0.486872\pi$
$978$	26676.2	0.872199
$979$	13365.9	0.436340
$980$	−58102.6	−1.89390
$981$	18313.9	0.596042
$982$	−37586.0	−1.22140
$983$	46770.8	1.51756	0.758778	−	0.651350i	$-0.225797\pi$
$983$	46770.8	1.51756	0.758778	+	0.651350i	$0.225797\pi$
$984$	13842.3	0.448452
$985$	−68876.0	−2.22799
$986$	10810.7	0.349171
$987$	577.711	0.0186310
$988$	2486.59	0.0800699
$989$	9370.47	0.301278
$990$	17403.2	0.558697
$991$	14465.1	0.463673	0.231837	−	0.972755i	$-0.425526\pi$
$991$	14465.1	0.463673	0.231837	+	0.972755i	$0.425526\pi$
$992$	9286.77	0.297233
$993$	21190.3	0.677193
$994$	2859.31	0.0912392
$995$	58574.3	1.86626
$996$	52827.8	1.68064
$997$	−54679.8	−1.73694	−0.868468	−	0.495745i	$-0.834895\pi$
$997$	−54679.8	−1.73694	−0.868468	+	0.495745i	$0.834895\pi$
$998$	34458.0	1.09294
$999$	−7437.23	−0.235539

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.h.1.7	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.h.1.7	✓	44	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)

\(f(q)\)	\(=\)	\(q-4.54386 q^{2} +3.00000 q^{3} +12.6466 q^{4} +13.4410 q^{5} -13.6316 q^{6} +1.08944 q^{7} -21.1137 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.54386 q^{2} +3.00000 q^{3} +12.6466 q^{4} +13.4410 q^{5} -13.6316 q^{6} +1.08944 q^{7} -21.1137 q^{8} +9.00000 q^{9} -61.0740 q^{10} -31.6614 q^{11} +37.9399 q^{12} +14.7970 q^{13} -4.95027 q^{14} +40.3230 q^{15} -5.23550 q^{16} +82.0410 q^{17} -40.8947 q^{18} +13.2878 q^{19} +169.984 q^{20} +3.26832 q^{21} +143.865 q^{22} +23.0000 q^{23} -63.3411 q^{24} +55.6607 q^{25} -67.2357 q^{26} +27.0000 q^{27} +13.7778 q^{28} -29.0000 q^{29} -183.222 q^{30} +48.1932 q^{31} +192.699 q^{32} -94.9842 q^{33} -372.783 q^{34} +14.6432 q^{35} +113.820 q^{36} -275.453 q^{37} -60.3781 q^{38} +44.3911 q^{39} -283.789 q^{40} -218.536 q^{41} -14.8508 q^{42} +407.412 q^{43} -400.411 q^{44} +120.969 q^{45} -104.509 q^{46} +176.761 q^{47} -15.7065 q^{48} -341.813 q^{49} -252.914 q^{50} +246.123 q^{51} +187.133 q^{52} +61.0761 q^{53} -122.684 q^{54} -425.561 q^{55} -23.0021 q^{56} +39.8635 q^{57} +131.772 q^{58} -283.298 q^{59} +509.951 q^{60} +204.035 q^{61} -218.983 q^{62} +9.80497 q^{63} -833.713 q^{64} +198.887 q^{65} +431.595 q^{66} +1046.48 q^{67} +1037.54 q^{68} +69.0000 q^{69} -66.5366 q^{70} -577.607 q^{71} -190.023 q^{72} +949.814 q^{73} +1251.62 q^{74} +166.982 q^{75} +168.047 q^{76} -34.4933 q^{77} -201.707 q^{78} -443.126 q^{79} -70.3704 q^{80} +81.0000 q^{81} +992.996 q^{82} +1392.41 q^{83} +41.3334 q^{84} +1102.71 q^{85} -1851.22 q^{86} -87.0000 q^{87} +668.490 q^{88} -422.152 q^{89} -549.666 q^{90} +16.1205 q^{91} +290.873 q^{92} +144.579 q^{93} -803.175 q^{94} +178.602 q^{95} +578.097 q^{96} +846.974 q^{97} +1553.15 q^{98} -284.953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * q^99

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