LMFDB - Embedded newform 2001.4.a.g.1.22

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:	$43$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0945400 q^{2} +3.00000 q^{3} -7.99106 q^{4} -7.33331 q^{5} -0.283620 q^{6} -11.3676 q^{7} +1.51180 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.0945400 q^{2} +3.00000 q^{3} -7.99106 q^{4} -7.33331 q^{5} -0.283620 q^{6} -11.3676 q^{7} +1.51180 q^{8} +9.00000 q^{9} +0.693291 q^{10} -14.8721 q^{11} -23.9732 q^{12} -78.4868 q^{13} +1.07469 q^{14} -21.9999 q^{15} +63.7856 q^{16} -16.7229 q^{17} -0.850860 q^{18} -106.817 q^{19} +58.6009 q^{20} -34.1027 q^{21} +1.40601 q^{22} -23.0000 q^{23} +4.53539 q^{24} -71.2226 q^{25} +7.42014 q^{26} +27.0000 q^{27} +90.8391 q^{28} +29.0000 q^{29} +2.07987 q^{30} -195.809 q^{31} -18.1246 q^{32} -44.6163 q^{33} +1.58098 q^{34} +83.3620 q^{35} -71.9196 q^{36} -289.055 q^{37} +10.0985 q^{38} -235.460 q^{39} -11.0865 q^{40} +151.730 q^{41} +3.22407 q^{42} +61.6307 q^{43} +118.844 q^{44} -65.9998 q^{45} +2.17442 q^{46} -116.924 q^{47} +191.357 q^{48} -213.778 q^{49} +6.73338 q^{50} -50.1688 q^{51} +627.193 q^{52} -288.811 q^{53} -2.55258 q^{54} +109.062 q^{55} -17.1855 q^{56} -320.451 q^{57} -2.74166 q^{58} -196.219 q^{59} +175.803 q^{60} +230.634 q^{61} +18.5118 q^{62} -102.308 q^{63} -508.571 q^{64} +575.568 q^{65} +4.21802 q^{66} -736.105 q^{67} +133.634 q^{68} -69.0000 q^{69} -7.88104 q^{70} +933.079 q^{71} +13.6062 q^{72} -733.212 q^{73} +27.3273 q^{74} -213.668 q^{75} +853.581 q^{76} +169.060 q^{77} +22.2604 q^{78} +615.502 q^{79} -467.759 q^{80} +81.0000 q^{81} -14.3445 q^{82} -1044.43 q^{83} +272.517 q^{84} +122.634 q^{85} -5.82657 q^{86} +87.0000 q^{87} -22.4836 q^{88} +1368.95 q^{89} +6.23962 q^{90} +892.205 q^{91} +183.794 q^{92} -587.428 q^{93} +11.0540 q^{94} +783.322 q^{95} -54.3739 q^{96} +479.427 q^{97} +20.2106 q^{98} -133.849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9}+O(q^{10}) $ 43 * q + 2 * q^2 + 129 * q^3 + 210 * q^4 + 25 * q^5 + 6 * q^6 + 106 * q^7 + 27 * q^8 + 387 * q^9	\( 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9} + 32 q^{10} + 109 q^{11} + 630 q^{12} + 235 q^{13} + 205 q^{14} + 75 q^{15} + 1190 q^{16} + 228 q^{17} + 18 q^{18} + 291 q^{19} + 407 q^{20} + 318 q^{21} + 808 q^{22} - 989 q^{23} + 81 q^{24} + 1656 q^{25} - 289 q^{26} + 1161 q^{27} + 1831 q^{28} + 1247 q^{29} + 96 q^{30} + 694 q^{31} + 88 q^{32} + 327 q^{33} + 1158 q^{34} - 43 q^{35} + 1890 q^{36} + 1167 q^{37} + 35 q^{38} + 705 q^{39} + 1117 q^{40} + 977 q^{41} + 615 q^{42} + 1361 q^{43} + 798 q^{44} + 225 q^{45} - 46 q^{46} + 684 q^{47} + 3570 q^{48} + 3417 q^{49} + 267 q^{50} + 684 q^{51} + 3054 q^{52} + 1344 q^{53} + 54 q^{54} + 1072 q^{55} + 1741 q^{56} + 873 q^{57} + 58 q^{58} - 313 q^{59} + 1221 q^{60} + 3162 q^{61} - 1010 q^{62} + 954 q^{63} + 8795 q^{64} + 370 q^{65} + 2424 q^{66} + 2699 q^{67} + 2799 q^{68} - 2967 q^{69} + 443 q^{70} + 2140 q^{71} + 243 q^{72} + 922 q^{73} + 2281 q^{74} + 4968 q^{75} + 2237 q^{76} + 879 q^{77} - 867 q^{78} + 5078 q^{79} + 5377 q^{80} + 3483 q^{81} + 1045 q^{82} + 2670 q^{83} + 5493 q^{84} - 1087 q^{85} + 3249 q^{86} + 3741 q^{87} + 8305 q^{88} + 1893 q^{89} + 288 q^{90} + 6847 q^{91} - 4830 q^{92} + 2082 q^{93} - 1128 q^{94} + 6973 q^{95} + 264 q^{96} + 3040 q^{97} + 2581 q^{98} + 981 q^{99}+O(q^{100}) \) 43 * q + 2 * q^2 + 129 * q^3 + 210 * q^4 + 25 * q^5 + 6 * q^6 + 106 * q^7 + 27 * q^8 + 387 * q^9 + 32 * q^10 + 109 * q^11 + 630 * q^12 + 235 * q^13 + 205 * q^14 + 75 * q^15 + 1190 * q^16 + 228 * q^17 + 18 * q^18 + 291 * q^19 + 407 * q^20 + 318 * q^21 + 808 * q^22 - 989 * q^23 + 81 * q^24 + 1656 * q^25 - 289 * q^26 + 1161 * q^27 + 1831 * q^28 + 1247 * q^29 + 96 * q^30 + 694 * q^31 + 88 * q^32 + 327 * q^33 + 1158 * q^34 - 43 * q^35 + 1890 * q^36 + 1167 * q^37 + 35 * q^38 + 705 * q^39 + 1117 * q^40 + 977 * q^41 + 615 * q^42 + 1361 * q^43 + 798 * q^44 + 225 * q^45 - 46 * q^46 + 684 * q^47 + 3570 * q^48 + 3417 * q^49 + 267 * q^50 + 684 * q^51 + 3054 * q^52 + 1344 * q^53 + 54 * q^54 + 1072 * q^55 + 1741 * q^56 + 873 * q^57 + 58 * q^58 - 313 * q^59 + 1221 * q^60 + 3162 * q^61 - 1010 * q^62 + 954 * q^63 + 8795 * q^64 + 370 * q^65 + 2424 * q^66 + 2699 * q^67 + 2799 * q^68 - 2967 * q^69 + 443 * q^70 + 2140 * q^71 + 243 * q^72 + 922 * q^73 + 2281 * q^74 + 4968 * q^75 + 2237 * q^76 + 879 * q^77 - 867 * q^78 + 5078 * q^79 + 5377 * q^80 + 3483 * q^81 + 1045 * q^82 + 2670 * q^83 + 5493 * q^84 - 1087 * q^85 + 3249 * q^86 + 3741 * q^87 + 8305 * q^88 + 1893 * q^89 + 288 * q^90 + 6847 * q^91 - 4830 * q^92 + 2082 * q^93 - 1128 * q^94 + 6973 * q^95 + 264 * q^96 + 3040 * q^97 + 2581 * q^98 + 981 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.0945400	−0.0334249	−0.0167125	−	0.999860i	$-0.505320\pi$
$2$	−0.0945400	−0.0334249	−0.0167125	+	0.999860i	$0.505320\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.99106	−0.998883
$5$	−7.33331	−0.655911	−0.327956	−	0.944693i	$-0.606360\pi$
$5$	−7.33331	−0.655911	−0.327956	+	0.944693i	$0.606360\pi$
$6$	−0.283620	−0.0192979
$7$	−11.3676	−0.613792	−0.306896	−	0.951743i	$-0.599290\pi$
$7$	−11.3676	−0.613792	−0.306896	+	0.951743i	$0.599290\pi$
$8$	1.51180	0.0668125
$9$	9.00000	0.333333
$10$	0.693291	0.0219238
$11$	−14.8721	−0.407646	−0.203823	−	0.979008i	$-0.565337\pi$
$11$	−14.8721	−0.407646	−0.203823	+	0.979008i	$0.565337\pi$
$12$	−23.9732	−0.576705
$13$	−78.4868	−1.67449	−0.837243	−	0.546831i	$-0.815834\pi$
$13$	−78.4868	−1.67449	−0.837243	+	0.546831i	$0.815834\pi$
$14$	1.07469	0.0205160
$15$	−21.9999	−0.378690
$16$	63.7856	0.996650
$17$	−16.7229	−0.238583	−0.119291	−	0.992859i	$-0.538062\pi$
$17$	−16.7229	−0.238583	−0.119291	+	0.992859i	$0.538062\pi$
$18$	−0.850860	−0.0111416
$19$	−106.817	−1.28976	−0.644881	−	0.764283i	$-0.723093\pi$
$19$	−106.817	−1.28976	−0.644881	+	0.764283i	$0.723093\pi$
$20$	58.6009	0.655178
$21$	−34.1027	−0.354373
$22$	1.40601	0.0136255
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	4.53539	0.0385742
$25$	−71.2226	−0.569781
$26$	7.42014	0.0559696
$27$	27.0000	0.192450
$28$	90.8391	0.613106
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	2.07987	0.0126577
$31$	−195.809	−1.13446	−0.567232	−	0.823558i	$-0.691986\pi$
$31$	−195.809	−1.13446	−0.567232	+	0.823558i	$0.691986\pi$
$32$	−18.1246	−0.100125
$33$	−44.6163	−0.235355
$34$	1.58098	0.00797461
$35$	83.3620	0.402593
$36$	−71.9196	−0.332961
$37$	−289.055	−1.28433	−0.642167	−	0.766565i	$-0.721964\pi$
$37$	−289.055	−1.28433	−0.642167	+	0.766565i	$0.721964\pi$
$38$	10.0985	0.0431102
$39$	−235.460	−0.966765
$40$	−11.0865	−0.0438231
$41$	151.730	0.577957	0.288978	−	0.957336i	$-0.406684\pi$
$41$	151.730	0.577957	0.288978	+	0.957336i	$0.406684\pi$
$42$	3.22407	0.0118449
$43$	61.6307	0.218572	0.109286	−	0.994010i	$-0.465144\pi$
$43$	61.6307	0.218572	0.109286	+	0.994010i	$0.465144\pi$
$44$	118.844	0.407191
$45$	−65.9998	−0.218637
$46$	2.17442	0.00696958
$47$	−116.924	−0.362876	−0.181438	−	0.983402i	$-0.558075\pi$
$47$	−116.924	−0.362876	−0.181438	+	0.983402i	$0.558075\pi$
$48$	191.357	0.575416
$49$	−213.778	−0.623260
$50$	6.73338	0.0190449
$51$	−50.1688	−0.137746
$52$	627.193	1.67261
$53$	−288.811	−0.748515	−0.374258	−	0.927325i	$-0.622102\pi$
$53$	−288.811	−0.748515	−0.374258	+	0.927325i	$0.622102\pi$
$54$	−2.55258	−0.00643263
$55$	109.062	0.267380
$56$	−17.1855	−0.0410090
$57$	−320.451	−0.744645
$58$	−2.74166	−0.00620686
$59$	−196.219	−0.432976	−0.216488	−	0.976285i	$-0.569460\pi$
$59$	−196.219	−0.432976	−0.216488	+	0.976285i	$0.569460\pi$
$60$	175.803	0.378267
$61$	230.634	0.484093	0.242047	−	0.970265i	$-0.422181\pi$
$61$	230.634	0.484093	0.242047	+	0.970265i	$0.422181\pi$
$62$	18.5118	0.0379194
$63$	−102.308	−0.204597
$64$	−508.571	−0.993303
$65$	575.568	1.09831
$66$	4.21802	0.00786671
$67$	−736.105	−1.34223	−0.671116	−	0.741352i	$-0.734185\pi$
$67$	−736.105	−1.34223	−0.671116	+	0.741352i	$0.734185\pi$
$68$	133.634	0.238316
$69$	−69.0000	−0.120386
$70$	−7.88104	−0.0134566
$71$	933.079	1.55966	0.779832	−	0.625989i	$-0.215305\pi$
$71$	933.079	1.55966	0.779832	+	0.625989i	$0.215305\pi$
$72$	13.6062	0.0222708
$73$	−733.212	−1.17556	−0.587780	−	0.809021i	$-0.699998\pi$
$73$	−733.212	−1.17556	−0.587780	+	0.809021i	$0.699998\pi$
$74$	27.3273	0.0429288
$75$	−213.668	−0.328963
$76$	853.581	1.28832
$77$	169.060	0.250210
$78$	22.2604	0.0323141
$79$	615.502	0.876574	0.438287	−	0.898835i	$-0.355585\pi$
$79$	615.502	0.876574	0.438287	+	0.898835i	$0.355585\pi$
$80$	−467.759	−0.653713
$81$	81.0000	0.111111
$82$	−14.3445	−0.0193182
$83$	−1044.43	−1.38122	−0.690611	−	0.723227i	$-0.742658\pi$
$83$	−1044.43	−1.38122	−0.690611	+	0.723227i	$0.742658\pi$
$84$	272.517	0.353977
$85$	122.634	0.156489
$86$	−5.82657	−0.00730576
$87$	87.0000	0.107211
$88$	−22.4836	−0.0272359
$89$	1368.95	1.63043	0.815216	−	0.579157i	$-0.196618\pi$
$89$	1368.95	1.63043	0.815216	+	0.579157i	$0.196618\pi$
$90$	6.23962	0.00730793
$91$	892.205	1.02779
$92$	183.794	0.208281
$93$	−587.428	−0.654983
$94$	11.0540	0.0121291
$95$	783.322	0.845970
$96$	−54.3739	−0.0578075
$97$	479.427	0.501839	0.250920	−	0.968008i	$-0.419267\pi$
$97$	479.427	0.501839	0.250920	+	0.968008i	$0.419267\pi$
$98$	20.2106	0.0208324
$99$	−133.849	−0.135882
$100$	569.144	0.569144
$101$	−857.794	−0.845086	−0.422543	−	0.906343i	$-0.638862\pi$
$101$	−857.794	−0.845086	−0.422543	+	0.906343i	$0.638862\pi$
$102$	4.74295	0.00460414
$103$	574.337	0.549428	0.274714	−	0.961526i	$-0.411417\pi$
$103$	574.337	0.549428	0.274714	+	0.961526i	$0.411417\pi$
$104$	−118.656	−0.111877
$105$	250.086	0.232437
$106$	27.3042	0.0250191
$107$	−1898.47	−1.71525	−0.857625	−	0.514275i	$-0.828061\pi$
$107$	−1898.47	−1.71525	−0.857625	+	0.514275i	$0.828061\pi$
$108$	−215.759	−0.192235
$109$	−1978.32	−1.73843	−0.869216	−	0.494433i	$-0.835376\pi$
$109$	−1978.32	−1.73843	−0.869216	+	0.494433i	$0.835376\pi$
$110$	−10.3107	−0.00893715
$111$	−867.165	−0.741510
$112$	−725.088	−0.611735
$113$	1608.32	1.33892	0.669462	−	0.742847i	$-0.266525\pi$
$113$	1608.32	1.33892	0.669462	+	0.742847i	$0.266525\pi$
$114$	30.2954	0.0248897
$115$	168.666	0.136767
$116$	−231.741	−0.185488
$117$	−706.381	−0.558162
$118$	18.5506	0.0144722
$119$	190.099	0.146440
$120$	−33.2594	−0.0253013
$121$	−1109.82	−0.833825
$122$	−21.8042	−0.0161808
$123$	455.190	0.333684
$124$	1564.72	1.13320
$125$	1438.96	1.02964
$126$	9.67222	0.00683865
$127$	198.489	0.138686	0.0693428	−	0.997593i	$-0.477910\pi$
$127$	198.489	0.138686	0.0693428	+	0.997593i	$0.477910\pi$
$128$	193.078	0.133327
$129$	184.892	0.126193
$130$	−54.4142	−0.0367111
$131$	−1339.00	−0.893045	−0.446523	−	0.894772i	$-0.647338\pi$
$131$	−1339.00	−0.893045	−0.446523	+	0.894772i	$0.647338\pi$
$132$	356.532	0.235092
$133$	1214.25	0.791646
$134$	69.5914	0.0448640
$135$	−197.999	−0.126230
$136$	−25.2816	−0.0159403
$137$	375.847	0.234385	0.117193	−	0.993109i	$-0.462610\pi$
$137$	375.847	0.234385	0.117193	+	0.993109i	$0.462610\pi$
$138$	6.52326	0.00402389
$139$	2198.04	1.34126	0.670630	−	0.741792i	$-0.266024\pi$
$139$	2198.04	1.34126	0.670630	+	0.741792i	$0.266024\pi$
$140$	−666.151	−0.402143
$141$	−350.773	−0.209506
$142$	−88.2133	−0.0521316
$143$	1167.26	0.682597
$144$	574.070	0.332217
$145$	−212.666	−0.121800
$146$	69.3178	0.0392930
$147$	−641.334	−0.359839
$148$	2309.86	1.28290
$149$	482.727	0.265413	0.132706	−	0.991155i	$-0.457633\pi$
$149$	482.727	0.265413	0.132706	+	0.991155i	$0.457633\pi$
$150$	20.2001	0.0109956
$151$	−2107.76	−1.13594	−0.567971	−	0.823049i	$-0.692271\pi$
$151$	−2107.76	−1.13594	−0.567971	+	0.823049i	$0.692271\pi$
$152$	−161.485	−0.0861723
$153$	−150.506	−0.0795275
$154$	−15.9829	−0.00836325
$155$	1435.93	0.744108
$156$	1881.58	0.965685
$157$	−1670.91	−0.849381	−0.424691	−	0.905339i	$-0.639617\pi$
$157$	−1670.91	−0.849381	−0.424691	+	0.905339i	$0.639617\pi$
$158$	−58.1896	−0.0292994
$159$	−866.434	−0.432155
$160$	132.914	0.0656734
$161$	261.454	0.127984
$162$	−7.65774	−0.00371388
$163$	−1845.67	−0.886896	−0.443448	−	0.896300i	$-0.646245\pi$
$163$	−1845.67	−0.886896	−0.443448	+	0.896300i	$0.646245\pi$
$164$	−1212.48	−0.577311
$165$	327.185	0.154372
$166$	98.7406	0.0461672
$167$	2597.89	1.20378	0.601889	−	0.798580i	$-0.294415\pi$
$167$	2597.89	1.20378	0.601889	+	0.798580i	$0.294415\pi$
$168$	−51.5564	−0.0236765
$169$	3963.17	1.80390
$170$	−11.5938	−0.00523063
$171$	−961.353	−0.429921
$172$	−492.495	−0.218328
$173$	3547.17	1.55888	0.779440	−	0.626477i	$-0.215504\pi$
$173$	3547.17	1.55888	0.779440	+	0.626477i	$0.215504\pi$
$174$	−8.22498	−0.00358353
$175$	809.629	0.349727
$176$	−948.625	−0.406280
$177$	−588.658	−0.249979
$178$	−129.421	−0.0544971
$179$	3069.64	1.28176	0.640881	−	0.767640i	$-0.278569\pi$
$179$	3069.64	1.28176	0.640881	+	0.767640i	$0.278569\pi$
$180$	527.408	0.218393
$181$	165.228	0.0678526	0.0339263	−	0.999424i	$-0.489199\pi$
$181$	165.228	0.0678526	0.0339263	+	0.999424i	$0.489199\pi$
$182$	−84.3491	−0.0343537
$183$	691.903	0.279491
$184$	−34.7713	−0.0139314
$185$	2119.73	0.842408
$186$	55.5355	0.0218928
$187$	248.705	0.0972572
$188$	934.349	0.362470
$189$	−306.925	−0.118124
$190$	−74.0553	−0.0282765
$191$	1670.64	0.632898	0.316449	−	0.948610i	$-0.397509\pi$
$191$	1670.64	0.632898	0.316449	+	0.948610i	$0.397509\pi$
$192$	−1525.71	−0.573484
$193$	7.61476	0.00284001	0.00142001	−	0.999999i	$-0.499548\pi$
$193$	7.61476	0.00284001	0.00142001	+	0.999999i	$0.499548\pi$
$194$	−45.3250	−0.0167739
$195$	1726.70	0.634112
$196$	1708.31	0.622563
$197$	−3031.97	−1.09654	−0.548272	−	0.836300i	$-0.684714\pi$
$197$	−3031.97	−1.09654	−0.548272	+	0.836300i	$0.684714\pi$
$198$	12.6541	0.00454185
$199$	5514.32	1.96432	0.982160	−	0.188045i	$-0.0602151\pi$
$199$	5514.32	1.96432	0.982160	+	0.188045i	$0.0602151\pi$
$200$	−107.674	−0.0380685
$201$	−2208.32	−0.774938
$202$	81.0958	0.0282469
$203$	−329.660	−0.113978
$204$	400.902	0.137592
$205$	−1112.68	−0.379088
$206$	−54.2978	−0.0183646
$207$	−207.000	−0.0695048
$208$	−5006.32	−1.66888
$209$	1588.59	0.525767
$210$	−23.6431	−0.00776920
$211$	−925.988	−0.302121	−0.151061	−	0.988524i	$-0.548269\pi$
$211$	−925.988	−0.302121	−0.151061	+	0.988524i	$0.548269\pi$
$212$	2307.91	0.747679
$213$	2799.24	0.900472
$214$	179.481	0.0573321
$215$	−451.957	−0.143364
$216$	40.8185	0.0128581
$217$	2225.88	0.696325
$218$	187.031	0.0581070
$219$	−2199.63	−0.678710
$220$	−871.519	−0.267081
$221$	1312.53	0.399503
$222$	81.9818	0.0247849
$223$	4833.55	1.45147	0.725737	−	0.687972i	$-0.241499\pi$
$223$	4833.55	1.45147	0.725737	+	0.687972i	$0.241499\pi$
$224$	206.033	0.0614562
$225$	−641.003	−0.189927
$226$	−152.051	−0.0447534
$227$	−2339.81	−0.684135	−0.342067	−	0.939675i	$-0.611127\pi$
$227$	−2339.81	−0.684135	−0.342067	+	0.939675i	$0.611127\pi$
$228$	2560.74	0.743813
$229$	−1697.71	−0.489904	−0.244952	−	0.969535i	$-0.578772\pi$
$229$	−1697.71	−0.489904	−0.244952	+	0.969535i	$0.578772\pi$
$230$	−15.9457	−0.00457143
$231$	507.179	0.144459
$232$	43.8421	0.0124068
$233$	348.692	0.0980410	0.0490205	−	0.998798i	$-0.484390\pi$
$233$	348.692	0.0980410	0.0490205	+	0.998798i	$0.484390\pi$
$234$	66.7813	0.0186565
$235$	857.442	0.238014
$236$	1568.00	0.432492
$237$	1846.51	0.506091
$238$	−17.9720	−0.00489475
$239$	−2174.86	−0.588619	−0.294310	−	0.955710i	$-0.595090\pi$
$239$	−2174.86	−0.588619	−0.294310	+	0.955710i	$0.595090\pi$
$240$	−1403.28	−0.377422
$241$	5841.44	1.56133	0.780664	−	0.624951i	$-0.214881\pi$
$241$	5841.44	1.56133	0.780664	+	0.624951i	$0.214881\pi$
$242$	104.922	0.0278705
$243$	243.000	0.0641500
$244$	−1843.01	−0.483552
$245$	1567.70	0.408803
$246$	−43.0336	−0.0111534
$247$	8383.72	2.15969
$248$	−296.024	−0.0757965
$249$	−3133.30	−0.797448
$250$	−136.039	−0.0344155
$251$	3088.58	0.776691	0.388346	−	0.921514i	$-0.373047\pi$
$251$	3088.58	0.776691	0.388346	+	0.921514i	$0.373047\pi$
$252$	817.552	0.204369
$253$	342.058	0.0850001
$254$	−18.7652	−0.00463556
$255$	367.903	0.0903489
$256$	4050.32	0.988846
$257$	2881.94	0.699497	0.349748	−	0.936844i	$-0.386267\pi$
$257$	2881.94	0.699497	0.349748	+	0.936844i	$0.386267\pi$
$258$	−17.4797	−0.00421798
$259$	3285.86	0.788313
$260$	−4599.40	−1.09709
$261$	261.000	0.0618984
$262$	126.589	0.0298500
$263$	−3148.47	−0.738186	−0.369093	−	0.929393i	$-0.620332\pi$
$263$	−3148.47	−0.738186	−0.369093	+	0.929393i	$0.620332\pi$
$264$	−67.4507	−0.0157246
$265$	2117.94	0.490959
$266$	−114.795	−0.0264607
$267$	4106.85	0.941331
$268$	5882.26	1.34073
$269$	−3292.89	−0.746361	−0.373180	−	0.927759i	$-0.621733\pi$
$269$	−3292.89	−0.746361	−0.373180	+	0.927759i	$0.621733\pi$
$270$	18.7189	0.00421923
$271$	−4475.57	−1.00321	−0.501607	−	0.865095i	$-0.667258\pi$
$271$	−4475.57	−1.00321	−0.501607	+	0.865095i	$0.667258\pi$
$272$	−1066.68	−0.237783
$273$	2676.61	0.593392
$274$	−35.5326	−0.00783432
$275$	1059.23	0.232269
$276$	551.383	0.120251
$277$	−600.175	−0.130184	−0.0650921	−	0.997879i	$-0.520734\pi$
$277$	−600.175	−0.130184	−0.0650921	+	0.997879i	$0.520734\pi$
$278$	−207.803	−0.0448315
$279$	−1762.28	−0.378155
$280$	126.026	0.0268982
$281$	7286.73	1.54694	0.773469	−	0.633834i	$-0.218520\pi$
$281$	7286.73	1.54694	0.773469	+	0.633834i	$0.218520\pi$
$282$	33.1621	0.00700274
$283$	−2230.19	−0.468449	−0.234225	−	0.972183i	$-0.575255\pi$
$283$	−2230.19	−0.468449	−0.234225	+	0.972183i	$0.575255\pi$
$284$	−7456.29	−1.55792
$285$	2349.97	0.488421
$286$	−110.353	−0.0228158
$287$	−1724.80	−0.354745
$288$	−163.122	−0.0333752
$289$	−4633.34	−0.943078
$290$	20.1054	0.00407115
$291$	1438.28	0.289737
$292$	5859.14	1.17425
$293$	−2991.11	−0.596391	−0.298196	−	0.954505i	$-0.596385\pi$
$293$	−2991.11	−0.596391	−0.298196	+	0.954505i	$0.596385\pi$
$294$	60.6317	0.0120276
$295$	1438.94	0.283994
$296$	−436.992	−0.0858096
$297$	−401.547	−0.0784515
$298$	−45.6370	−0.00887141
$299$	1805.20	0.349154
$300$	1707.43	0.328595
$301$	−700.592	−0.134158
$302$	199.268	0.0379688
$303$	−2573.38	−0.487911
$304$	−6813.38	−1.28544
$305$	−1691.31	−0.317522
$306$	14.2289	0.00265820
$307$	−6730.10	−1.25116	−0.625582	−	0.780159i	$-0.715138\pi$
$307$	−6730.10	−1.25116	−0.625582	+	0.780159i	$0.715138\pi$
$308$	−1350.97	−0.249930
$309$	1723.01	0.317213
$310$	−135.753	−0.0248718
$311$	9968.38	1.81754	0.908770	−	0.417297i	$-0.137023\pi$
$311$	9968.38	1.81754	0.908770	+	0.417297i	$0.137023\pi$
$312$	−355.968	−0.0645920
$313$	−6530.00	−1.17922	−0.589612	−	0.807687i	$-0.700719\pi$
$313$	−6530.00	−1.17922	−0.589612	+	0.807687i	$0.700719\pi$
$314$	157.967	0.0283905
$315$	750.258	0.134198
$316$	−4918.51	−0.875595
$317$	142.112	0.0251791	0.0125896	−	0.999921i	$-0.495993\pi$
$317$	142.112	0.0251791	0.0125896	+	0.999921i	$0.495993\pi$
$318$	81.9127	0.0144448
$319$	−431.291	−0.0756980
$320$	3729.51	0.651518
$321$	−5695.40	−0.990300
$322$	−24.7179	−0.00427787
$323$	1786.29	0.307715
$324$	−647.276	−0.110987
$325$	5590.03	0.954090
$326$	174.490	0.0296444
$327$	−5934.97	−1.00368
$328$	229.385	0.0386148
$329$	1329.15	0.222730
$330$	−30.9321	−0.00515986
$331$	−10028.4	−1.66528	−0.832641	−	0.553813i	$-0.813172\pi$
$331$	−10028.4	−1.66528	−0.832641	+	0.553813i	$0.813172\pi$
$332$	8346.12	1.37968
$333$	−2601.49	−0.428111
$334$	−245.605	−0.0402362
$335$	5398.09	0.880385
$336$	−2175.26	−0.353186
$337$	5921.03	0.957090	0.478545	−	0.878063i	$-0.341164\pi$
$337$	5921.03	0.957090	0.478545	+	0.878063i	$0.341164\pi$
$338$	−374.678	−0.0602953
$339$	4824.97	0.773028
$340$	−979.978	−0.156314
$341$	2912.10	0.462460
$342$	90.8863	0.0143701
$343$	6329.22	0.996343
$344$	93.1730	0.0146033
$345$	505.998	0.0789624
$346$	−335.349	−0.0521055
$347$	−5327.01	−0.824118	−0.412059	−	0.911157i	$-0.635190\pi$
$347$	−5327.01	−0.824118	−0.412059	+	0.911157i	$0.635190\pi$
$348$	−695.222	−0.107091
$349$	−4227.35	−0.648381	−0.324191	−	0.945992i	$-0.605092\pi$
$349$	−4227.35	−0.648381	−0.324191	+	0.945992i	$0.605092\pi$
$350$	−76.5423	−0.0116896
$351$	−2119.14	−0.322255
$352$	269.552	0.0408158
$353$	−3506.25	−0.528665	−0.264332	−	0.964432i	$-0.585152\pi$
$353$	−3506.25	−0.528665	−0.264332	+	0.964432i	$0.585152\pi$
$354$	55.6517	0.00835553
$355$	−6842.56	−1.02300
$356$	−10939.4	−1.62861
$357$	570.297	0.0845472
$358$	−290.203	−0.0428428
$359$	−13150.8	−1.93335	−0.966676	−	0.256003i	$-0.917594\pi$
$359$	−13150.8	−1.93335	−0.966676	+	0.256003i	$0.917594\pi$
$360$	−99.7781	−0.0146077
$361$	4550.87	0.663488
$362$	−15.6207	−0.00226797
$363$	−3329.46	−0.481409
$364$	−7129.66	−1.02664
$365$	5376.87	0.771063
$366$	−65.4125	−0.00934198
$367$	−7637.46	−1.08630	−0.543150	−	0.839635i	$-0.682769\pi$
$367$	−7637.46	−1.08630	−0.543150	+	0.839635i	$0.682769\pi$
$368$	−1467.07	−0.207816
$369$	1365.57	0.192652
$370$	−200.399	−0.0281575
$371$	3283.09	0.459432
$372$	4694.17	0.654252
$373$	−543.980	−0.0755127	−0.0377563	−	0.999287i	$-0.512021\pi$
$373$	−543.980	−0.0755127	−0.0377563	+	0.999287i	$0.512021\pi$
$374$	−23.5126	−0.00325082
$375$	4316.88	0.594461
$376$	−176.766	−0.0242446
$377$	−2276.12	−0.310944
$378$	29.0167	0.00394830
$379$	9670.05	1.31060	0.655300	−	0.755369i	$-0.272542\pi$
$379$	9670.05	1.31060	0.655300	+	0.755369i	$0.272542\pi$
$380$	−6259.57	−0.845025
$381$	595.468	0.0800702
$382$	−157.943	−0.0211546
$383$	10709.3	1.42877	0.714385	−	0.699753i	$-0.246707\pi$
$383$	10709.3	1.42877	0.714385	+	0.699753i	$0.246707\pi$
$384$	579.233	0.0769761
$385$	−1239.77	−0.164115
$386$	−0.719900	−9.49273e−5 0
$387$	554.676	0.0728573
$388$	−3831.13	−0.501279
$389$	−7239.99	−0.943656	−0.471828	−	0.881691i	$-0.656406\pi$
$389$	−7239.99	−0.943656	−0.471828	+	0.881691i	$0.656406\pi$
$390$	−163.243	−0.0211951
$391$	384.627	0.0497479
$392$	−323.189	−0.0416416
$393$	−4017.00	−0.515600
$394$	286.643	0.0366519
$395$	−4513.67	−0.574955
$396$	1069.59	0.135730
$397$	−1947.00	−0.246138	−0.123069	−	0.992398i	$-0.539274\pi$
$397$	−1947.00	−0.246138	−0.123069	+	0.992398i	$0.539274\pi$
$398$	−521.324	−0.0656573
$399$	3642.75	0.457057
$400$	−4542.97	−0.567872
$401$	−11405.4	−1.42035	−0.710174	−	0.704026i	$-0.751384\pi$
$401$	−11405.4	−1.42035	−0.710174	+	0.704026i	$0.751384\pi$
$402$	208.774	0.0259023
$403$	15368.4	1.89964
$404$	6854.69	0.844142
$405$	−593.998	−0.0728790
$406$	31.1660	0.00380972
$407$	4298.85	0.523553
$408$	−75.8449	−0.00920314
$409$	12632.5	1.52722	0.763612	−	0.645675i	$-0.223424\pi$
$409$	12632.5	1.52722	0.763612	+	0.645675i	$0.223424\pi$
$410$	105.193	0.0126710
$411$	1127.54	0.135322
$412$	−4589.56	−0.548815
$413$	2230.54	0.265757
$414$	19.5698	0.00232319
$415$	7659.15	0.905958
$416$	1422.55	0.167659
$417$	6594.11	0.774377
$418$	−150.186	−0.0175737
$419$	−13897.8	−1.62041	−0.810204	−	0.586147i	$-0.800644\pi$
$419$	−13897.8	−1.62041	−0.810204	+	0.586147i	$0.800644\pi$
$420$	−1998.45	−0.232177
$421$	15055.2	1.74286	0.871432	−	0.490516i	$-0.163192\pi$
$421$	15055.2	1.74286	0.871432	+	0.490516i	$0.163192\pi$
$422$	87.5429	0.0100984
$423$	−1052.32	−0.120959
$424$	−436.624	−0.0500102
$425$	1191.05	0.135940
$426$	−264.640	−0.0300982
$427$	−2621.75	−0.297132
$428$	15170.8	1.71333
$429$	3501.79	0.394098
$430$	42.7280	0.00479193
$431$	−12378.6	−1.38343	−0.691713	−	0.722173i	$-0.743144\pi$
$431$	−12378.6	−1.38343	−0.691713	+	0.722173i	$0.743144\pi$
$432$	1722.21	0.191805
$433$	−4525.85	−0.502306	−0.251153	−	0.967947i	$-0.580810\pi$
$433$	−4525.85	−0.502306	−0.251153	+	0.967947i	$0.580810\pi$
$434$	−210.435	−0.0232746
$435$	−637.998	−0.0703210
$436$	15808.9	1.73649
$437$	2456.79	0.268934
$438$	207.953	0.0226858
$439$	16197.9	1.76101	0.880507	−	0.474034i	$-0.157203\pi$
$439$	16197.9	1.76101	0.880507	+	0.474034i	$0.157203\pi$
$440$	164.879	0.0178643
$441$	−1924.00	−0.207753
$442$	−124.086	−0.0133534
$443$	1903.12	0.204108	0.102054	−	0.994779i	$-0.467459\pi$
$443$	1903.12	0.204108	0.102054	+	0.994779i	$0.467459\pi$
$444$	6929.57	0.740682
$445$	−10038.9	−1.06942
$446$	−456.964	−0.0485154
$447$	1448.18	0.153236
$448$	5781.22	0.609681
$449$	−3174.79	−0.333691	−0.166846	−	0.985983i	$-0.553358\pi$
$449$	−3174.79	−0.333691	−0.166846	+	0.985983i	$0.553358\pi$
$450$	60.6004	0.00634829
$451$	−2256.54	−0.235602
$452$	−12852.2	−1.33743
$453$	−6323.28	−0.655836
$454$	221.206	0.0228672
$455$	−6542.81	−0.674136
$456$	−484.456	−0.0497516
$457$	−1272.49	−0.130250	−0.0651252	−	0.997877i	$-0.520745\pi$
$457$	−1272.49	−0.130250	−0.0651252	+	0.997877i	$0.520745\pi$
$458$	160.502	0.0163750
$459$	−451.519	−0.0459152
$460$	−1347.82	−0.136614
$461$	8035.07	0.811780	0.405890	−	0.913922i	$-0.366962\pi$
$461$	8035.07	0.811780	0.405890	+	0.913922i	$0.366962\pi$
$462$	−47.9487	−0.00482852
$463$	−17685.9	−1.77523	−0.887615	−	0.460586i	$-0.847639\pi$
$463$	−17685.9	−1.77523	−0.887615	+	0.460586i	$0.847639\pi$
$464$	1849.78	0.185073
$465$	4307.79	0.429611
$466$	−32.9653	−0.00327701
$467$	15791.3	1.56474	0.782372	−	0.622811i	$-0.214010\pi$
$467$	15791.3	1.56474	0.782372	+	0.622811i	$0.214010\pi$
$468$	5644.73	0.557538
$469$	8367.74	0.823851
$470$	−81.0625	−0.00795561
$471$	−5012.72	−0.490390
$472$	−296.643	−0.0289282
$473$	−916.578	−0.0891000
$474$	−174.569	−0.0169160
$475$	7607.78	0.734882
$476$	−1519.09	−0.146276
$477$	−2599.30	−0.249505
$478$	205.611	0.0196746
$479$	1517.39	0.144742	0.0723710	−	0.997378i	$-0.476943\pi$
$479$	1517.39	0.144742	0.0723710	+	0.997378i	$0.476943\pi$
$480$	398.741	0.0379166
$481$	22687.0	2.15060
$482$	−552.250	−0.0521873
$483$	784.363	0.0738918
$484$	8868.65	0.832893
$485$	−3515.78	−0.329162
$486$	−22.9732	−0.00214421
$487$	−10966.3	−1.02039	−0.510194	−	0.860060i	$-0.670426\pi$
$487$	−10966.3	−1.02039	−0.510194	+	0.860060i	$0.670426\pi$
$488$	348.672	0.0323435
$489$	−5537.01	−0.512050
$490$	−148.210	−0.0136642
$491$	2414.86	0.221958	0.110979	−	0.993823i	$-0.464601\pi$
$491$	2414.86	0.221958	0.110979	+	0.993823i	$0.464601\pi$
$492$	−3637.45	−0.333311
$493$	−484.965	−0.0443037
$494$	−792.597	−0.0721875
$495$	981.555	0.0891265
$496$	−12489.8	−1.13066
$497$	−10606.9	−0.957308
$498$	296.222	0.0266547
$499$	17330.2	1.55472	0.777359	−	0.629057i	$-0.216559\pi$
$499$	17330.2	1.55472	0.777359	+	0.629057i	$0.216559\pi$
$500$	−11498.8	−1.02849
$501$	7793.67	0.695001
$502$	−291.994	−0.0259608
$503$	16945.8	1.50214	0.751069	−	0.660224i	$-0.229539\pi$
$503$	16945.8	1.50214	0.751069	+	0.660224i	$0.229539\pi$
$504$	−154.669	−0.0136697
$505$	6290.47	0.554301
$506$	−32.3382	−0.00284112
$507$	11889.5	1.04148
$508$	−1586.14	−0.138531
$509$	−3736.68	−0.325394	−0.162697	−	0.986676i	$-0.552019\pi$
$509$	−3736.68	−0.325394	−0.162697	+	0.986676i	$0.552019\pi$
$510$	−34.7815	−0.00301991
$511$	8334.84	0.721549
$512$	−1927.54	−0.166379
$513$	−2884.06	−0.248215
$514$	−272.459	−0.0233806
$515$	−4211.79	−0.360376
$516$	−1477.48	−0.126052
$517$	1738.91	0.147925
$518$	−310.645	−0.0263493
$519$	10641.5	0.900020
$520$	870.140	0.0733811
$521$	−4851.30	−0.407945	−0.203972	−	0.978977i	$-0.565385\pi$
$521$	−4851.30	−0.407945	−0.203972	+	0.978977i	$0.565385\pi$
$522$	−24.6749	−0.00206895
$523$	−16806.2	−1.40513	−0.702565	−	0.711620i	$-0.747962\pi$
$523$	−16806.2	−1.40513	−0.702565	+	0.711620i	$0.747962\pi$
$524$	10700.0	0.892048
$525$	2428.89	0.201915
$526$	297.656	0.0246738
$527$	3274.50	0.270663
$528$	−2845.88	−0.234566
$529$	529.000	0.0434783
$530$	−200.230	−0.0164103
$531$	−1765.97	−0.144325
$532$	−9703.15	−0.790761
$533$	−11908.8	−0.967781
$534$	−388.262	−0.0314639
$535$	13922.1	1.12505
$536$	−1112.84	−0.0896780
$537$	9208.91	0.740026
$538$	311.310	0.0249471
$539$	3179.33	0.254069
$540$	1582.23	0.126089
$541$	5911.60	0.469796	0.234898	−	0.972020i	$-0.424524\pi$
$541$	5911.60	0.469796	0.234898	+	0.972020i	$0.424524\pi$
$542$	423.120	0.0335324
$543$	495.685	0.0391747
$544$	303.097	0.0238882
$545$	14507.7	1.14026
$546$	−253.047	−0.0198341
$547$	−23375.8	−1.82720	−0.913599	−	0.406616i	$-0.866709\pi$
$547$	−23375.8	−1.82720	−0.913599	+	0.406616i	$0.866709\pi$
$548$	−3003.42	−0.234123
$549$	2075.71	0.161364
$550$	−100.140	−0.00776357
$551$	−3097.69	−0.239503
$552$	−104.314	−0.00804328
$553$	−6996.77	−0.538034
$554$	56.7405	0.00435140
$555$	6359.19	0.486365
$556$	−17564.7	−1.33976
$557$	10829.1	0.823778	0.411889	−	0.911234i	$-0.364869\pi$
$557$	10829.1	0.823778	0.411889	+	0.911234i	$0.364869\pi$
$558$	166.606	0.0126398
$559$	−4837.20	−0.365996
$560$	5317.29	0.401244
$561$	746.115	0.0561515
$562$	−688.887	−0.0517063
$563$	−12005.7	−0.898720	−0.449360	−	0.893351i	$-0.648348\pi$
$563$	−12005.7	−0.898720	−0.449360	+	0.893351i	$0.648348\pi$
$564$	2803.05	0.209272
$565$	−11794.3	−0.878215
$566$	210.842	0.0156579
$567$	−920.774	−0.0681991
$568$	1410.62	0.104205
$569$	6202.01	0.456945	0.228472	−	0.973550i	$-0.426627\pi$
$569$	6202.01	0.456945	0.228472	+	0.973550i	$0.426627\pi$
$570$	−222.166	−0.0163254
$571$	9747.60	0.714403	0.357202	−	0.934027i	$-0.383731\pi$
$571$	9747.60	0.714403	0.357202	+	0.934027i	$0.383731\pi$
$572$	−9327.67	−0.681835
$573$	5011.93	0.365404
$574$	163.063	0.0118573
$575$	1638.12	0.118807
$576$	−4577.14	−0.331101
$577$	6456.68	0.465850	0.232925	−	0.972495i	$-0.425170\pi$
$577$	6456.68	0.465850	0.232925	+	0.972495i	$0.425170\pi$
$578$	438.036	0.0315223
$579$	22.8443	0.00163968
$580$	1699.43	0.121664
$581$	11872.7	0.847782
$582$	−135.975	−0.00968444
$583$	4295.23	0.305129
$584$	−1108.47	−0.0785422
$585$	5180.11	0.366105
$586$	282.780	0.0199343
$587$	−8536.28	−0.600221	−0.300111	−	0.953904i	$-0.597024\pi$
$587$	−8536.28	−0.600221	−0.300111	+	0.953904i	$0.597024\pi$
$588$	5124.94	0.359437
$589$	20915.8	1.46319
$590$	−136.037	−0.00949247
$591$	−9095.92	−0.633090
$592$	−18437.5	−1.28003
$593$	−22685.9	−1.57099	−0.785495	−	0.618868i	$-0.787592\pi$
$593$	−22685.9	−1.57099	−0.785495	+	0.618868i	$0.787592\pi$
$594$	37.9622	0.00262224
$595$	−1394.06	−0.0960516
$596$	−3857.50	−0.265116
$597$	16543.0	1.13410
$598$	−170.663	−0.0116705
$599$	5739.64	0.391512	0.195756	−	0.980653i	$-0.437284\pi$
$599$	5739.64	0.391512	0.195756	+	0.980653i	$0.437284\pi$
$600$	−323.022	−0.0219789
$601$	−21046.5	−1.42846	−0.714230	−	0.699911i	$-0.753223\pi$
$601$	−21046.5	−1.42846	−0.714230	+	0.699911i	$0.753223\pi$
$602$	66.2340	0.00448421
$603$	−6624.95	−0.447411
$604$	16843.2	1.13467
$605$	8138.66	0.546915
$606$	243.288	0.0163084
$607$	−10476.5	−0.700544	−0.350272	−	0.936648i	$-0.613911\pi$
$607$	−10476.5	−0.700544	−0.350272	+	0.936648i	$0.613911\pi$
$608$	1936.02	0.129138
$609$	−988.980	−0.0658054
$610$	159.897	0.0106132
$611$	9177.01	0.607630
$612$	1202.70	0.0794387
$613$	−10942.4	−0.720974	−0.360487	−	0.932764i	$-0.617390\pi$
$613$	−10942.4	−0.720974	−0.360487	+	0.932764i	$0.617390\pi$
$614$	636.264	0.0418201
$615$	−3338.05	−0.218867
$616$	255.584	0.0167172
$617$	−28783.3	−1.87807	−0.939037	−	0.343815i	$-0.888281\pi$
$617$	−28783.3	−1.87807	−0.939037	+	0.343815i	$0.888281\pi$
$618$	−162.894	−0.0106028
$619$	−15491.8	−1.00593	−0.502964	−	0.864307i	$-0.667757\pi$
$619$	−15491.8	−1.00593	−0.502964	+	0.864307i	$0.667757\pi$
$620$	−11474.6	−0.743277
$621$	−621.000	−0.0401286
$622$	−942.411	−0.0607512
$623$	−15561.7	−1.00075
$624$	−15019.0	−0.963526
$625$	−1649.52	−0.105569
$626$	617.346	0.0394155
$627$	4765.78	0.303552
$628$	13352.3	0.848432
$629$	4833.84	0.306419
$630$	−70.9294	−0.00448555
$631$	23876.7	1.50636	0.753181	−	0.657813i	$-0.228518\pi$
$631$	23876.7	1.50636	0.753181	+	0.657813i	$0.228518\pi$
$632$	930.513	0.0585662
$633$	−2777.96	−0.174430
$634$	−13.4352	−0.000841610 0
$635$	−1455.58	−0.0909655
$636$	6923.73	0.431673
$637$	16778.7	1.04364
$638$	40.7742	0.00253020
$639$	8397.71	0.519888
$640$	−1415.90	−0.0874504
$641$	−11822.5	−0.728491	−0.364245	−	0.931303i	$-0.618673\pi$
$641$	−11822.5	−0.728491	−0.364245	+	0.931303i	$0.618673\pi$
$642$	538.444	0.0331007
$643$	−23053.4	−1.41390	−0.706951	−	0.707263i	$-0.749930\pi$
$643$	−23053.4	−1.41390	−0.706951	+	0.707263i	$0.749930\pi$
$644$	−2089.30	−0.127841
$645$	−1355.87	−0.0827711
$646$	−168.876	−0.0102854
$647$	−28320.6	−1.72086	−0.860431	−	0.509567i	$-0.829806\pi$
$647$	−28320.6	−1.72086	−0.860431	+	0.509567i	$0.829806\pi$
$648$	122.455	0.00742361
$649$	2918.19	0.176501
$650$	−528.481	−0.0318904
$651$	6677.64	0.402023
$652$	14748.9	0.885905
$653$	16914.9	1.01368	0.506838	−	0.862041i	$-0.330814\pi$
$653$	16914.9	1.01368	0.506838	+	0.862041i	$0.330814\pi$
$654$	561.092	0.0335481
$655$	9819.30	0.585758
$656$	9678.18	0.576021
$657$	−6598.90	−0.391854
$658$	−125.657	−0.00744474
$659$	24242.2	1.43299	0.716496	−	0.697591i	$-0.245745\pi$
$659$	24242.2	1.43299	0.716496	+	0.697591i	$0.245745\pi$
$660$	−2614.56	−0.154199
$661$	6200.90	0.364882	0.182441	−	0.983217i	$-0.441600\pi$
$661$	6200.90	0.364882	0.182441	+	0.983217i	$0.441600\pi$
$662$	948.081	0.0556620
$663$	3937.58	0.230653
$664$	−1578.97	−0.0922829
$665$	−8904.48	−0.519249
$666$	245.945	0.0143096
$667$	−667.000	−0.0387202
$668$	−20759.9	−1.20243
$669$	14500.7	0.838009
$670$	−510.335	−0.0294268
$671$	−3430.02	−0.197339
$672$	618.100	0.0354818
$673$	26177.7	1.49937	0.749686	−	0.661794i	$-0.230205\pi$
$673$	26177.7	1.49937	0.749686	+	0.661794i	$0.230205\pi$
$674$	−559.774	−0.0319907
$675$	−1923.01	−0.109654
$676$	−31670.0	−1.80189
$677$	−31609.2	−1.79445	−0.897223	−	0.441578i	$-0.854419\pi$
$677$	−31609.2	−1.79445	−0.897223	+	0.441578i	$0.854419\pi$
$678$	−456.153	−0.0258384
$679$	−5449.92	−0.308025
$680$	185.398	0.0104554
$681$	−7019.43	−0.394985
$682$	−275.310	−0.0154577
$683$	−12925.1	−0.724108	−0.362054	−	0.932157i	$-0.617924\pi$
$683$	−12925.1	−0.724108	−0.362054	+	0.932157i	$0.617924\pi$
$684$	7682.23	0.429441
$685$	−2756.20	−0.153736
$686$	−598.365	−0.0333027
$687$	−5093.14	−0.282846
$688$	3931.15	0.217840
$689$	22667.9	1.25338
$690$	−47.8371	−0.00263931
$691$	30946.0	1.70368	0.851839	−	0.523803i	$-0.175487\pi$
$691$	30946.0	1.70368	0.851839	+	0.523803i	$0.175487\pi$
$692$	−28345.7	−1.55714
$693$	1521.54	0.0834033
$694$	503.616	0.0275461
$695$	−16118.9	−0.879747
$696$	131.526	0.00716306
$697$	−2537.37	−0.137890
$698$	399.654	0.0216721
$699$	1046.08	0.0566040
$700$	−6469.79	−0.349336
$701$	−12072.5	−0.650457	−0.325228	−	0.945636i	$-0.605441\pi$
$701$	−12072.5	−0.650457	−0.325228	+	0.945636i	$0.605441\pi$
$702$	200.344	0.0107714
$703$	30876.0	1.65649
$704$	7563.52	0.404916
$705$	2572.32	0.137418
$706$	331.481	0.0176706
$707$	9751.04	0.518707
$708$	4704.00	0.249700
$709$	17134.1	0.907594	0.453797	−	0.891105i	$-0.350069\pi$
$709$	17134.1	0.907594	0.453797	+	0.891105i	$0.350069\pi$
$710$	646.895	0.0341937
$711$	5539.52	0.292191
$712$	2069.57	0.108933
$713$	4503.62	0.236552
$714$	−53.9159	−0.00282598
$715$	−8559.90	−0.447723
$716$	−24529.7	−1.28033
$717$	−6524.58	−0.339840
$718$	1243.28	0.0646222
$719$	−8859.41	−0.459528	−0.229764	−	0.973246i	$-0.573795\pi$
$719$	−8859.41	−0.459528	−0.229764	+	0.973246i	$0.573795\pi$
$720$	−4209.83	−0.217904
$721$	−6528.83	−0.337235
$722$	−430.239	−0.0221771
$723$	17524.3	0.901433
$724$	−1320.35	−0.0677768
$725$	−2065.45	−0.105806
$726$	314.767	0.0160911
$727$	20050.0	1.02285	0.511426	−	0.859328i	$-0.329118\pi$
$727$	20050.0	1.02285	0.511426	+	0.859328i	$0.329118\pi$
$728$	1348.83	0.0686690
$729$	729.000	0.0370370
$730$	−508.329	−0.0257727
$731$	−1030.65	−0.0521475
$732$	−5529.04	−0.279179
$733$	5492.20	0.276752	0.138376	−	0.990380i	$-0.455812\pi$
$733$	5492.20	0.276752	0.138376	+	0.990380i	$0.455812\pi$
$734$	722.046	0.0363095
$735$	4703.10	0.236022
$736$	416.867	0.0208776
$737$	10947.4	0.547156
$738$	−129.101	−0.00643939
$739$	−29410.6	−1.46399	−0.731993	−	0.681312i	$-0.761410\pi$
$739$	−29410.6	−1.46399	−0.731993	+	0.681312i	$0.761410\pi$
$740$	−16938.9	−0.841467
$741$	25151.2	1.24690
$742$	−310.383	−0.0153565
$743$	−25363.2	−1.25233	−0.626167	−	0.779689i	$-0.715377\pi$
$743$	−25363.2	−1.25233	−0.626167	+	0.779689i	$0.715377\pi$
$744$	−888.071	−0.0437611
$745$	−3539.98	−0.174087
$746$	51.4279	0.00252401
$747$	−9399.89	−0.460407
$748$	−1987.42	−0.0971486
$749$	21581.0	1.05281
$750$	−408.118	−0.0198698
$751$	−5579.25	−0.271092	−0.135546	−	0.990771i	$-0.543279\pi$
$751$	−5579.25	−0.271092	−0.135546	+	0.990771i	$0.543279\pi$
$752$	−7458.08	−0.361660
$753$	9265.74	0.448423
$754$	215.184	0.0103933
$755$	15456.9	0.745076
$756$	2452.65	0.117992
$757$	10603.3	0.509095	0.254547	−	0.967060i	$-0.418074\pi$
$757$	10603.3	0.509095	0.254547	+	0.967060i	$0.418074\pi$
$758$	−914.207	−0.0438067
$759$	1026.17	0.0490748
$760$	1184.22	0.0565214
$761$	−2258.97	−0.107605	−0.0538027	−	0.998552i	$-0.517134\pi$
$761$	−2258.97	−0.107605	−0.0538027	+	0.998552i	$0.517134\pi$
$762$	−56.2955	−0.00267634
$763$	22488.8	1.06704
$764$	−13350.2	−0.632191
$765$	1103.71	0.0521630
$766$	−1012.46	−0.0477565
$767$	15400.6	0.725012
$768$	12150.9	0.570911
$769$	5524.94	0.259082	0.129541	−	0.991574i	$-0.458650\pi$
$769$	5524.94	0.259082	0.129541	+	0.991574i	$0.458650\pi$
$770$	117.208	0.00548555
$771$	8645.83	0.403855
$772$	−60.8501	−0.00283684
$773$	24971.3	1.16191	0.580954	−	0.813937i	$-0.302680\pi$
$773$	24971.3	1.16191	0.580954	+	0.813937i	$0.302680\pi$
$774$	−52.4391	−0.00243525
$775$	13946.0	0.646396
$776$	724.795	0.0335292
$777$	9857.57	0.455133
$778$	684.469	0.0315416
$779$	−16207.3	−0.745427
$780$	−13798.2	−0.633403
$781$	−13876.8	−0.635791
$782$	−36.3626	−0.00166282
$783$	783.000	0.0357371
$784$	−13636.0	−0.621171
$785$	12253.3	0.557118
$786$	379.767	0.0172339
$787$	−7432.08	−0.336627	−0.168313	−	0.985734i	$-0.553832\pi$
$787$	−7432.08	−0.336627	−0.168313	+	0.985734i	$0.553832\pi$
$788$	24228.7	1.09532
$789$	−9445.40	−0.426192
$790$	426.722	0.0192178
$791$	−18282.7	−0.821820
$792$	−202.352	−0.00907862
$793$	−18101.7	−0.810607
$794$	184.069	0.00822716
$795$	6353.83	0.283455
$796$	−44065.3	−1.96213
$797$	5756.42	0.255838	0.127919	−	0.991785i	$-0.459170\pi$
$797$	5756.42	0.255838	0.127919	+	0.991785i	$0.459170\pi$
$798$	−344.386	−0.0152771
$799$	1955.31	0.0865758
$800$	1290.88	0.0570496
$801$	12320.6	0.543477
$802$	1078.27	0.0474750
$803$	10904.4	0.479213
$804$	17646.8	0.774073
$805$	−1917.33	−0.0839464
$806$	−1452.93	−0.0634955
$807$	−9878.67	−0.430911
$808$	−1296.81	−0.0564623
$809$	−38794.7	−1.68597	−0.842985	−	0.537937i	$-0.819204\pi$
$809$	−38794.7	−1.68597	−0.842985	+	0.537937i	$0.819204\pi$
$810$	56.1566	0.00243598
$811$	−18232.1	−0.789415	−0.394708	−	0.918807i	$-0.629154\pi$
$811$	−18232.1	−0.789415	−0.394708	+	0.918807i	$0.629154\pi$
$812$	2634.33	0.113851
$813$	−13426.7	−0.579206
$814$	−406.414	−0.0174997
$815$	13534.9	0.581725
$816$	−3200.04	−0.137284
$817$	−6583.21	−0.281906
$818$	−1194.27	−0.0510474
$819$	8029.84	0.342595
$820$	8891.51	0.378665
$821$	33741.0	1.43431	0.717154	−	0.696914i	$-0.245444\pi$
$821$	33741.0	1.43431	0.717154	+	0.696914i	$0.245444\pi$
$822$	−106.598	−0.00452314
$823$	43373.8	1.83708	0.918540	−	0.395328i	$-0.129369\pi$
$823$	43373.8	1.83708	0.918540	+	0.395328i	$0.129369\pi$
$824$	868.280	0.0367087
$825$	3177.69	0.134100
$826$	−210.875	−0.00888292
$827$	20675.5	0.869356	0.434678	−	0.900586i	$-0.356862\pi$
$827$	20675.5	0.869356	0.434678	+	0.900586i	$0.356862\pi$
$828$	1654.15	0.0694272
$829$	−11126.2	−0.466137	−0.233068	−	0.972460i	$-0.574877\pi$
$829$	−11126.2	−0.466137	−0.233068	+	0.972460i	$0.574877\pi$
$830$	−724.096	−0.0302816
$831$	−1800.52	−0.0751618
$832$	39916.1	1.66327
$833$	3574.99	0.148699
$834$	−623.408	−0.0258835
$835$	−19051.1	−0.789571
$836$	−12694.5	−0.525179
$837$	−5286.85	−0.218328
$838$	1313.90	0.0541621
$839$	−28404.8	−1.16882	−0.584411	−	0.811458i	$-0.698674\pi$
$839$	−28404.8	−1.16882	−0.584411	+	0.811458i	$0.698674\pi$
$840$	378.079	0.0155297
$841$	841.000	0.0344828
$842$	−1423.32	−0.0582551
$843$	21860.2	0.893125
$844$	7399.63	0.301784
$845$	−29063.2	−1.18320
$846$	99.4862	0.00404303
$847$	12616.0	0.511795
$848$	−18422.0	−0.746007
$849$	−6690.57	−0.270459
$850$	−112.602	−0.00454378
$851$	6648.26	0.267802
$852$	−22368.9	−0.899466
$853$	−45082.4	−1.80960	−0.904802	−	0.425833i	$-0.859981\pi$
$853$	−45082.4	−1.80960	−0.904802	+	0.425833i	$0.859981\pi$
$854$	247.861	0.00993164
$855$	7049.90	0.281990
$856$	−2870.09	−0.114600
$857$	−42266.7	−1.68472	−0.842359	−	0.538916i	$-0.818834\pi$
$857$	−42266.7	−1.68472	−0.842359	+	0.538916i	$0.818834\pi$
$858$	−331.059	−0.0131727
$859$	−12175.5	−0.483611	−0.241805	−	0.970325i	$-0.577740\pi$
$859$	−12175.5	−0.483611	−0.241805	+	0.970325i	$0.577740\pi$
$860$	3611.62	0.143204
$861$	−5174.41	−0.204812
$862$	1170.27	0.0462409
$863$	−43469.4	−1.71462	−0.857308	−	0.514803i	$-0.827865\pi$
$863$	−43469.4	−1.71462	−0.857308	+	0.514803i	$0.827865\pi$
$864$	−489.366	−0.0192692
$865$	−26012.5	−1.02249
$866$	427.874	0.0167895
$867$	−13900.0	−0.544487
$868$	−17787.1	−0.695547
$869$	−9153.81	−0.357332
$870$	60.3163	0.00235048
$871$	57774.5	2.24755
$872$	−2990.82	−0.116149
$873$	4314.84	0.167280
$874$	−232.265	−0.00898911
$875$	−16357.5	−0.631982
$876$	17577.4	0.677952
$877$	17827.6	0.686426	0.343213	−	0.939258i	$-0.388485\pi$
$877$	17827.6	0.686426	0.343213	+	0.939258i	$0.388485\pi$
$878$	−1531.35	−0.0588618
$879$	−8973.34	−0.344327
$880$	6956.56	0.266484
$881$	−23607.4	−0.902785	−0.451392	−	0.892326i	$-0.649073\pi$
$881$	−23607.4	−0.902785	−0.451392	+	0.892326i	$0.649073\pi$
$882$	181.895	0.00694414
$883$	36572.5	1.39384	0.696922	−	0.717147i	$-0.254553\pi$
$883$	36572.5	1.39384	0.696922	+	0.717147i	$0.254553\pi$
$884$	−10488.5	−0.399057
$885$	4316.81	0.163964
$886$	−179.921	−0.00682230
$887$	−17902.2	−0.677675	−0.338837	−	0.940845i	$-0.610034\pi$
$887$	−17902.2	−0.677675	−0.338837	+	0.940845i	$0.610034\pi$
$888$	−1310.98	−0.0495422
$889$	−2256.34	−0.0851241
$890$	949.081	0.0357453
$891$	−1204.64	−0.0452940
$892$	−38625.2	−1.44985
$893$	12489.5	0.468024
$894$	−136.911	−0.00512191
$895$	−22510.6	−0.840722
$896$	−2194.82	−0.0818348
$897$	5415.59	0.201584
$898$	300.144	0.0111536
$899$	−5678.47	−0.210665
$900$	5122.30	0.189715
$901$	4829.77	0.178583
$902$	213.334	0.00787498
$903$	−2101.78	−0.0774560
$904$	2431.46	0.0894569
$905$	−1211.67	−0.0445053
$906$	597.803	0.0219213
$907$	14682.5	0.537514	0.268757	−	0.963208i	$-0.413387\pi$
$907$	14682.5	0.537514	0.268757	+	0.963208i	$0.413387\pi$
$908$	18697.6	0.683370
$909$	−7720.15	−0.281695
$910$	618.558	0.0225330
$911$	−31826.9	−1.15749	−0.578745	−	0.815509i	$-0.696457\pi$
$911$	−31826.9	−1.15749	−0.578745	+	0.815509i	$0.696457\pi$
$912$	−20440.1	−0.742150
$913$	15532.9	0.563049
$914$	120.301	0.00435361
$915$	−5073.94	−0.183322
$916$	13566.5	0.489357
$917$	15221.2	0.548144
$918$	42.6866	0.00153471
$919$	−207.176	−0.00743648	−0.00371824	−	0.999993i	$-0.501184\pi$
$919$	−207.176	−0.00743648	−0.00371824	+	0.999993i	$0.501184\pi$
$920$	254.989	0.00913774
$921$	−20190.3	−0.722360
$922$	−759.635	−0.0271337
$923$	−73234.3	−2.61163
$924$	−4052.90	−0.144297
$925$	20587.2	0.731788
$926$	1672.02	0.0593370
$927$	5169.03	0.183143
$928$	−525.615	−0.0185928
$929$	−50862.5	−1.79628	−0.898140	−	0.439710i	$-0.855081\pi$
$929$	−50862.5	−1.79628	−0.898140	+	0.439710i	$0.855081\pi$
$930$	−407.259	−0.0143597
$931$	22835.1	0.803857
$932$	−2786.42	−0.0979315
$933$	29905.1	1.04936
$934$	−1492.91	−0.0523015
$935$	−1823.83	−0.0637921
$936$	−1067.90	−0.0372922
$937$	−10753.5	−0.374922	−0.187461	−	0.982272i	$-0.560026\pi$
$937$	−10753.5	−0.374922	−0.187461	+	0.982272i	$0.560026\pi$
$938$	−791.086	−0.0275372
$939$	−19590.0	−0.680825
$940$	−6851.87	−0.237748
$941$	−8650.34	−0.299674	−0.149837	−	0.988711i	$-0.547875\pi$
$941$	−8650.34	−0.299674	−0.149837	+	0.988711i	$0.547875\pi$
$942$	473.902	0.0163913
$943$	−3489.79	−0.120512
$944$	−12516.0	−0.431525
$945$	2250.77	0.0774790
$946$	86.6533	0.00297816
$947$	−10984.3	−0.376920	−0.188460	−	0.982081i	$-0.560350\pi$
$947$	−10984.3	−0.376920	−0.188460	+	0.982081i	$0.560350\pi$
$948$	−14755.5	−0.505525
$949$	57547.4	1.96846
$950$	−719.240	−0.0245634
$951$	426.335	0.0145372
$952$	287.391	0.00978403
$953$	14516.9	0.493440	0.246720	−	0.969087i	$-0.420647\pi$
$953$	14516.9	0.493440	0.246720	+	0.969087i	$0.420647\pi$
$954$	245.738	0.00833969
$955$	−12251.3	−0.415125
$956$	17379.4	0.587962
$957$	−1293.87	−0.0437042
$958$	−143.454	−0.00483799
$959$	−4272.47	−0.143864
$960$	11188.5	0.376154
$961$	8550.31	0.287010
$962$	−2144.83	−0.0718836
$963$	−17086.2	−0.571750
$964$	−46679.3	−1.55958
$965$	−55.8414	−0.00186280
$966$	−74.1537	−0.00246983
$967$	−1582.59	−0.0526295	−0.0263148	−	0.999654i	$-0.508377\pi$
$967$	−1582.59	−0.0526295	−0.0263148	+	0.999654i	$0.508377\pi$
$968$	−1677.82	−0.0557099
$969$	5358.87	0.177659
$970$	332.382	0.0110022
$971$	−43305.4	−1.43124	−0.715622	−	0.698488i	$-0.753857\pi$
$971$	−43305.4	−1.43124	−0.715622	+	0.698488i	$0.753857\pi$
$972$	−1941.83	−0.0640784
$973$	−24986.4	−0.823254
$974$	1036.75	0.0341064
$975$	16770.1	0.550844
$976$	14711.1	0.482471
$977$	6171.57	0.202094	0.101047	−	0.994882i	$-0.467781\pi$
$977$	6171.57	0.202094	0.101047	+	0.994882i	$0.467781\pi$
$978$	523.469	0.0171152
$979$	−20359.2	−0.664639
$980$	−12527.6	−0.408346
$981$	−17804.9	−0.579477
$982$	−228.301	−0.00741892
$983$	28815.8	0.934976	0.467488	−	0.883999i	$-0.345159\pi$
$983$	28815.8	0.934976	0.467488	+	0.883999i	$0.345159\pi$
$984$	688.154	0.0222942
$985$	22234.4	0.719236
$986$	45.8486	0.00148085
$987$	3987.44	0.128593
$988$	−66994.8	−2.15728
$989$	−1417.51	−0.0455754
$990$	−92.7962	−0.00297905
$991$	−29035.6	−0.930724	−0.465362	−	0.885120i	$-0.654076\pi$
$991$	−29035.6	−0.930724	−0.465362	+	0.885120i	$0.654076\pi$
$992$	3548.98	0.113589
$993$	−30085.1	−0.961451
$994$	1002.77	0.0319980
$995$	−40438.2	−1.28842
$996$	25038.4	0.796557
$997$	−56482.6	−1.79420	−0.897102	−	0.441824i	$-0.854332\pi$
$997$	−56482.6	−1.79420	−0.897102	+	0.441824i	$0.854332\pi$
$998$	−1638.39	−0.0519664
$999$	−7804.48	−0.247170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.g.1.22	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.g.1.22	✓	43	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.0945400 q^{2} +3.00000 q^{3} -7.99106 q^{4} -7.33331 q^{5} -0.283620 q^{6} -11.3676 q^{7} +1.51180 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.0945400 q^{2} +3.00000 q^{3} -7.99106 q^{4} -7.33331 q^{5} -0.283620 q^{6} -11.3676 q^{7} +1.51180 q^{8} +9.00000 q^{9} +0.693291 q^{10} -14.8721 q^{11} -23.9732 q^{12} -78.4868 q^{13} +1.07469 q^{14} -21.9999 q^{15} +63.7856 q^{16} -16.7229 q^{17} -0.850860 q^{18} -106.817 q^{19} +58.6009 q^{20} -34.1027 q^{21} +1.40601 q^{22} -23.0000 q^{23} +4.53539 q^{24} -71.2226 q^{25} +7.42014 q^{26} +27.0000 q^{27} +90.8391 q^{28} +29.0000 q^{29} +2.07987 q^{30} -195.809 q^{31} -18.1246 q^{32} -44.6163 q^{33} +1.58098 q^{34} +83.3620 q^{35} -71.9196 q^{36} -289.055 q^{37} +10.0985 q^{38} -235.460 q^{39} -11.0865 q^{40} +151.730 q^{41} +3.22407 q^{42} +61.6307 q^{43} +118.844 q^{44} -65.9998 q^{45} +2.17442 q^{46} -116.924 q^{47} +191.357 q^{48} -213.778 q^{49} +6.73338 q^{50} -50.1688 q^{51} +627.193 q^{52} -288.811 q^{53} -2.55258 q^{54} +109.062 q^{55} -17.1855 q^{56} -320.451 q^{57} -2.74166 q^{58} -196.219 q^{59} +175.803 q^{60} +230.634 q^{61} +18.5118 q^{62} -102.308 q^{63} -508.571 q^{64} +575.568 q^{65} +4.21802 q^{66} -736.105 q^{67} +133.634 q^{68} -69.0000 q^{69} -7.88104 q^{70} +933.079 q^{71} +13.6062 q^{72} -733.212 q^{73} +27.3273 q^{74} -213.668 q^{75} +853.581 q^{76} +169.060 q^{77} +22.2604 q^{78} +615.502 q^{79} -467.759 q^{80} +81.0000 q^{81} -14.3445 q^{82} -1044.43 q^{83} +272.517 q^{84} +122.634 q^{85} -5.82657 q^{86} +87.0000 q^{87} -22.4836 q^{88} +1368.95 q^{89} +6.23962 q^{90} +892.205 q^{91} +183.794 q^{92} -587.428 q^{93} +11.0540 q^{94} +783.322 q^{95} -54.3739 q^{96} +479.427 q^{97} +20.2106 q^{98} -133.849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9}+O(q^{10}) \) 43 * q + 2 * q^2 + 129 * q^3 + 210 * q^4 + 25 * q^5 + 6 * q^6 + 106 * q^7 + 27 * q^8 + 387 * q^9	\( 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9} + 32 q^{10} + 109 q^{11} + 630 q^{12} + 235 q^{13} + 205 q^{14} + 75 q^{15} + 1190 q^{16} + 228 q^{17} + 18 q^{18} + 291 q^{19} + 407 q^{20} + 318 q^{21} + 808 q^{22} - 989 q^{23} + 81 q^{24} + 1656 q^{25} - 289 q^{26} + 1161 q^{27} + 1831 q^{28} + 1247 q^{29} + 96 q^{30} + 694 q^{31} + 88 q^{32} + 327 q^{33} + 1158 q^{34} - 43 q^{35} + 1890 q^{36} + 1167 q^{37} + 35 q^{38} + 705 q^{39} + 1117 q^{40} + 977 q^{41} + 615 q^{42} + 1361 q^{43} + 798 q^{44} + 225 q^{45} - 46 q^{46} + 684 q^{47} + 3570 q^{48} + 3417 q^{49} + 267 q^{50} + 684 q^{51} + 3054 q^{52} + 1344 q^{53} + 54 q^{54} + 1072 q^{55} + 1741 q^{56} + 873 q^{57} + 58 q^{58} - 313 q^{59} + 1221 q^{60} + 3162 q^{61} - 1010 q^{62} + 954 q^{63} + 8795 q^{64} + 370 q^{65} + 2424 q^{66} + 2699 q^{67} + 2799 q^{68} - 2967 q^{69} + 443 q^{70} + 2140 q^{71} + 243 q^{72} + 922 q^{73} + 2281 q^{74} + 4968 q^{75} + 2237 q^{76} + 879 q^{77} - 867 q^{78} + 5078 q^{79} + 5377 q^{80} + 3483 q^{81} + 1045 q^{82} + 2670 q^{83} + 5493 q^{84} - 1087 q^{85} + 3249 q^{86} + 3741 q^{87} + 8305 q^{88} + 1893 q^{89} + 288 q^{90} + 6847 q^{91} - 4830 q^{92} + 2082 q^{93} - 1128 q^{94} + 6973 q^{95} + 264 q^{96} + 3040 q^{97} + 2581 q^{98} + 981 q^{99}+O(q^{100}) \) 43 * q + 2 * q^2 + 129 * q^3 + 210 * q^4 + 25 * q^5 + 6 * q^6 + 106 * q^7 + 27 * q^8 + 387 * q^9 + 32 * q^10 + 109 * q^11 + 630 * q^12 + 235 * q^13 + 205 * q^14 + 75 * q^15 + 1190 * q^16 + 228 * q^17 + 18 * q^18 + 291 * q^19 + 407 * q^20 + 318 * q^21 + 808 * q^22 - 989 * q^23 + 81 * q^24 + 1656 * q^25 - 289 * q^26 + 1161 * q^27 + 1831 * q^28 + 1247 * q^29 + 96 * q^30 + 694 * q^31 + 88 * q^32 + 327 * q^33 + 1158 * q^34 - 43 * q^35 + 1890 * q^36 + 1167 * q^37 + 35 * q^38 + 705 * q^39 + 1117 * q^40 + 977 * q^41 + 615 * q^42 + 1361 * q^43 + 798 * q^44 + 225 * q^45 - 46 * q^46 + 684 * q^47 + 3570 * q^48 + 3417 * q^49 + 267 * q^50 + 684 * q^51 + 3054 * q^52 + 1344 * q^53 + 54 * q^54 + 1072 * q^55 + 1741 * q^56 + 873 * q^57 + 58 * q^58 - 313 * q^59 + 1221 * q^60 + 3162 * q^61 - 1010 * q^62 + 954 * q^63 + 8795 * q^64 + 370 * q^65 + 2424 * q^66 + 2699 * q^67 + 2799 * q^68 - 2967 * q^69 + 443 * q^70 + 2140 * q^71 + 243 * q^72 + 922 * q^73 + 2281 * q^74 + 4968 * q^75 + 2237 * q^76 + 879 * q^77 - 867 * q^78 + 5078 * q^79 + 5377 * q^80 + 3483 * q^81 + 1045 * q^82 + 2670 * q^83 + 5493 * q^84 - 1087 * q^85 + 3249 * q^86 + 3741 * q^87 + 8305 * q^88 + 1893 * q^89 + 288 * q^90 + 6847 * q^91 - 4830 * q^92 + 2082 * q^93 - 1128 * q^94 + 6973 * q^95 + 264 * q^96 + 3040 * q^97 + 2581 * q^98 + 981 * q^99

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