LMFDB - Embedded newform 547.4.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,4,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	547.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:	$32.2740447731$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.16082 q^{2} +9.40532 q^{3} +18.6341 q^{4} -10.9794 q^{5} -48.5392 q^{6} -11.5228 q^{7} -54.8805 q^{8} +61.4600 q^{9} +O(q^{10})$	\(q-5.16082 q^{2} +9.40532 q^{3} +18.6341 q^{4} -10.9794 q^{5} -48.5392 q^{6} -11.5228 q^{7} -54.8805 q^{8} +61.4600 q^{9} +56.6629 q^{10} +17.4710 q^{11} +175.259 q^{12} -19.9102 q^{13} +59.4670 q^{14} -103.265 q^{15} +134.156 q^{16} -14.4087 q^{17} -317.184 q^{18} -74.7771 q^{19} -204.591 q^{20} -108.375 q^{21} -90.1648 q^{22} +148.288 q^{23} -516.168 q^{24} -4.45213 q^{25} +102.753 q^{26} +324.107 q^{27} -214.716 q^{28} +179.921 q^{29} +532.932 q^{30} +159.684 q^{31} -253.309 q^{32} +164.321 q^{33} +74.3605 q^{34} +126.513 q^{35} +1145.25 q^{36} -232.998 q^{37} +385.911 q^{38} -187.262 q^{39} +602.556 q^{40} +71.1353 q^{41} +559.306 q^{42} +334.921 q^{43} +325.556 q^{44} -674.796 q^{45} -765.289 q^{46} +415.197 q^{47} +1261.78 q^{48} -210.226 q^{49} +22.9766 q^{50} -135.518 q^{51} -371.007 q^{52} +492.950 q^{53} -1672.66 q^{54} -191.822 q^{55} +632.375 q^{56} -703.303 q^{57} -928.539 q^{58} -261.442 q^{59} -1924.25 q^{60} +607.265 q^{61} -824.102 q^{62} -708.190 q^{63} +234.039 q^{64} +218.602 q^{65} -848.029 q^{66} -315.897 q^{67} -268.492 q^{68} +1394.70 q^{69} -652.913 q^{70} +917.242 q^{71} -3372.95 q^{72} +60.3643 q^{73} +1202.46 q^{74} -41.8737 q^{75} -1393.40 q^{76} -201.315 q^{77} +966.423 q^{78} -193.922 q^{79} -1472.95 q^{80} +1388.91 q^{81} -367.117 q^{82} +625.390 q^{83} -2019.47 q^{84} +158.199 q^{85} -1728.47 q^{86} +1692.21 q^{87} -958.818 q^{88} -1138.97 q^{89} +3482.50 q^{90} +229.420 q^{91} +2763.21 q^{92} +1501.88 q^{93} -2142.76 q^{94} +821.010 q^{95} -2382.46 q^{96} +1207.62 q^{97} +1084.94 q^{98} +1073.77 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) $ 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9} + 120 q^{10} + 139 q^{11} + 309 q^{12} + 343 q^{13} + 239 q^{14} + 194 q^{15} + 1346 q^{16} + 842 q^{17} + 423 q^{18} + 157 q^{19} + 1292 q^{20} + 434 q^{21} + 436 q^{22} + 1004 q^{23} + 935 q^{24} + 2206 q^{25} + 812 q^{26} + 1282 q^{27} + 584 q^{28} + 1459 q^{29} + 146 q^{30} + 582 q^{31} + 1428 q^{32} + 1080 q^{33} + 393 q^{34} + 1006 q^{35} + 2996 q^{36} + 1477 q^{37} + 1873 q^{38} + 626 q^{39} + 1272 q^{40} + 1112 q^{41} + 1812 q^{42} + 833 q^{43} + 1392 q^{44} + 3841 q^{45} + 782 q^{46} + 2484 q^{47} + 2034 q^{48} + 4727 q^{49} + 1248 q^{50} + 932 q^{51} + 2118 q^{52} + 5077 q^{53} + 1537 q^{54} + 1736 q^{55} + 2281 q^{56} + 1426 q^{57} + 992 q^{58} + 2977 q^{59} + 1418 q^{60} + 3363 q^{61} + 3438 q^{62} + 3194 q^{63} + 6138 q^{64} + 4640 q^{65} + 288 q^{66} + 955 q^{67} + 8553 q^{68} + 4440 q^{69} + 2203 q^{70} + 2458 q^{71} + 4495 q^{72} + 3724 q^{73} + 2099 q^{74} + 4491 q^{75} + 2260 q^{76} + 9774 q^{77} + 1057 q^{78} + 1638 q^{79} + 8221 q^{80} + 10151 q^{81} + 1018 q^{82} + 6121 q^{83} + 4847 q^{84} + 3836 q^{85} + 2305 q^{86} + 3894 q^{87} + 5815 q^{88} + 8110 q^{89} + 4951 q^{90} + 2312 q^{91} + 13138 q^{92} + 9250 q^{93} - 813 q^{94} + 4858 q^{95} + 6882 q^{96} + 4486 q^{97} + 4216 q^{98} + 4969 q^{99}+O(q^{100}) \) 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9 + 120 * q^10 + 139 * q^11 + 309 * q^12 + 343 * q^13 + 239 * q^14 + 194 * q^15 + 1346 * q^16 + 842 * q^17 + 423 * q^18 + 157 * q^19 + 1292 * q^20 + 434 * q^21 + 436 * q^22 + 1004 * q^23 + 935 * q^24 + 2206 * q^25 + 812 * q^26 + 1282 * q^27 + 584 * q^28 + 1459 * q^29 + 146 * q^30 + 582 * q^31 + 1428 * q^32 + 1080 * q^33 + 393 * q^34 + 1006 * q^35 + 2996 * q^36 + 1477 * q^37 + 1873 * q^38 + 626 * q^39 + 1272 * q^40 + 1112 * q^41 + 1812 * q^42 + 833 * q^43 + 1392 * q^44 + 3841 * q^45 + 782 * q^46 + 2484 * q^47 + 2034 * q^48 + 4727 * q^49 + 1248 * q^50 + 932 * q^51 + 2118 * q^52 + 5077 * q^53 + 1537 * q^54 + 1736 * q^55 + 2281 * q^56 + 1426 * q^57 + 992 * q^58 + 2977 * q^59 + 1418 * q^60 + 3363 * q^61 + 3438 * q^62 + 3194 * q^63 + 6138 * q^64 + 4640 * q^65 + 288 * q^66 + 955 * q^67 + 8553 * q^68 + 4440 * q^69 + 2203 * q^70 + 2458 * q^71 + 4495 * q^72 + 3724 * q^73 + 2099 * q^74 + 4491 * q^75 + 2260 * q^76 + 9774 * q^77 + 1057 * q^78 + 1638 * q^79 + 8221 * q^80 + 10151 * q^81 + 1018 * q^82 + 6121 * q^83 + 4847 * q^84 + 3836 * q^85 + 2305 * q^86 + 3894 * q^87 + 5815 * q^88 + 8110 * q^89 + 4951 * q^90 + 2312 * q^91 + 13138 * q^92 + 9250 * q^93 - 813 * q^94 + 4858 * q^95 + 6882 * q^96 + 4486 * q^97 + 4216 * q^98 + 4969 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.16082	−1.82463	−0.912313	−	0.409494i	$-0.865705\pi$
$2$	−5.16082	−1.82463	−0.912313	+	0.409494i	$0.865705\pi$
$3$	9.40532	1.81005	0.905027	−	0.425354i	$-0.139850\pi$
$3$	9.40532	1.81005	0.905027	+	0.425354i	$0.139850\pi$
$4$	18.6341	2.32926
$5$	−10.9794	−0.982030	−0.491015	−	0.871151i	$-0.663374\pi$
$5$	−10.9794	−0.982030	−0.491015	+	0.871151i	$0.663374\pi$
$6$	−48.5392	−3.30267
$7$	−11.5228	−0.622171	−0.311086	−	0.950382i	$-0.600693\pi$
$7$	−11.5228	−0.622171	−0.311086	+	0.950382i	$0.600693\pi$
$8$	−54.8805	−2.42540
$9$	61.4600	2.27630
$10$	56.6629	1.79184
$11$	17.4710	0.478883	0.239442	−	0.970911i	$-0.423036\pi$
$11$	17.4710	0.478883	0.239442	+	0.970911i	$0.423036\pi$
$12$	175.259	4.21608
$13$	−19.9102	−0.424776	−0.212388	−	0.977185i	$-0.568124\pi$
$13$	−19.9102	−0.424776	−0.212388	+	0.977185i	$0.568124\pi$
$14$	59.4670	1.13523
$15$	−103.265	−1.77753
$16$	134.156	2.09618
$17$	−14.4087	−0.205565	−0.102783	−	0.994704i	$-0.532775\pi$
$17$	−14.4087	−0.205565	−0.102783	+	0.994704i	$0.532775\pi$
$18$	−317.184	−4.15339
$19$	−74.7771	−0.902898	−0.451449	−	0.892297i	$-0.649093\pi$
$19$	−74.7771	−0.902898	−0.451449	+	0.892297i	$0.649093\pi$
$20$	−204.591	−2.28740
$21$	−108.375	−1.12616
$22$	−90.1648	−0.873782
$23$	148.288	1.34436	0.672179	−	0.740388i	$-0.265358\pi$
$23$	148.288	1.34436	0.672179	+	0.740388i	$0.265358\pi$
$24$	−516.168	−4.39010
$25$	−4.45213	−0.0356170
$26$	102.753	0.775057
$27$	324.107	2.31017
$28$	−214.716	−1.44920
$29$	179.921	1.15208	0.576042	−	0.817420i	$-0.304596\pi$
$29$	179.921	1.15208	0.576042	+	0.817420i	$0.304596\pi$
$30$	532.932	3.24332
$31$	159.684	0.925166	0.462583	−	0.886576i	$-0.346923\pi$
$31$	159.684	0.925166	0.462583	+	0.886576i	$0.346923\pi$
$32$	−253.309	−1.39935
$33$	164.321	0.866805
$34$	74.3605	0.375080
$35$	126.513	0.610991
$36$	1145.25	5.30208
$37$	−232.998	−1.03526	−0.517631	−	0.855604i	$-0.673186\pi$
$37$	−232.998	−1.03526	−0.517631	+	0.855604i	$0.673186\pi$
$38$	385.911	1.64745
$39$	−187.262	−0.768868
$40$	602.556	2.38181
$41$	71.1353	0.270963	0.135481	−	0.990780i	$-0.456742\pi$
$41$	71.1353	0.270963	0.135481	+	0.990780i	$0.456742\pi$
$42$	559.306	2.05483
$43$	334.921	1.18779	0.593894	−	0.804543i	$-0.297590\pi$
$43$	334.921	1.18779	0.593894	+	0.804543i	$0.297590\pi$
$44$	325.556	1.11544
$45$	−674.796	−2.23539
$46$	−765.289	−2.45295
$47$	415.197	1.28857	0.644284	−	0.764786i	$-0.277155\pi$
$47$	415.197	1.28857	0.644284	+	0.764786i	$0.277155\pi$
$48$	1261.78	3.79420
$49$	−210.226	−0.612903
$50$	22.9766	0.0649877
$51$	−135.518	−0.372085
$52$	−371.007	−0.989413
$53$	492.950	1.27758	0.638792	−	0.769380i	$-0.279435\pi$
$53$	492.950	1.27758	0.638792	+	0.769380i	$0.279435\pi$
$54$	−1672.66	−4.21519
$55$	−191.822	−0.470278
$56$	632.375	1.50901
$57$	−703.303	−1.63429
$58$	−928.539	−2.10212
$59$	−261.442	−0.576895	−0.288448	−	0.957496i	$-0.593139\pi$
$59$	−261.442	−0.576895	−0.288448	+	0.957496i	$0.593139\pi$
$60$	−1924.25	−4.14032
$61$	607.265	1.27463	0.637314	−	0.770604i	$-0.280045\pi$
$61$	607.265	1.27463	0.637314	+	0.770604i	$0.280045\pi$
$62$	−824.102	−1.68808
$63$	−708.190	−1.41625
$64$	234.039	0.457108
$65$	218.602	0.417143
$66$	−848.029	−1.58159
$67$	−315.897	−0.576014	−0.288007	−	0.957628i	$-0.592993\pi$
$67$	−315.897	−0.576014	−0.288007	+	0.957628i	$0.592993\pi$
$68$	−268.492	−0.478815
$69$	1394.70	2.43336
$70$	−652.913	−1.11483
$71$	917.242	1.53319	0.766596	−	0.642130i	$-0.221949\pi$
$71$	917.242	1.53319	0.766596	+	0.642130i	$0.221949\pi$
$72$	−3372.95	−5.52092
$73$	60.3643	0.0967824	0.0483912	−	0.998828i	$-0.484591\pi$
$73$	60.3643	0.0967824	0.0483912	+	0.998828i	$0.484591\pi$
$74$	1202.46	1.88897
$75$	−41.8737	−0.0644687
$76$	−1393.40	−2.10308
$77$	−201.315	−0.297947
$78$	966.423	1.40290
$79$	−193.922	−0.276176	−0.138088	−	0.990420i	$-0.544096\pi$
$79$	−193.922	−0.276176	−0.138088	+	0.990420i	$0.544096\pi$
$80$	−1472.95	−2.05851
$81$	1388.91	1.90523
$82$	−367.117	−0.494406
$83$	625.390	0.827054	0.413527	−	0.910492i	$-0.364297\pi$
$83$	625.390	0.827054	0.413527	+	0.910492i	$0.364297\pi$
$84$	−2019.47	−2.62313
$85$	158.199	0.201871
$86$	−1728.47	−2.16727
$87$	1692.21	2.08534
$88$	−958.818	−1.16148
$89$	−1138.97	−1.35653	−0.678264	−	0.734818i	$-0.737268\pi$
$89$	−1138.97	−1.35653	−0.678264	+	0.734818i	$0.737268\pi$
$90$	3482.50	4.07875
$91$	229.420	0.264284
$92$	2763.21	3.13136
$93$	1501.88	1.67460
$94$	−2142.76	−2.35115
$95$	821.010	0.886672
$96$	−2382.46	−2.53290
$97$	1207.62	1.26408	0.632040	−	0.774936i	$-0.282218\pi$
$97$	1207.62	1.26408	0.632040	+	0.774936i	$0.282218\pi$
$98$	1084.94	1.11832
$99$	1073.77	1.09008
$100$	−82.9612	−0.0829612
$101$	−923.915	−0.910227	−0.455114	−	0.890433i	$-0.650401\pi$
$101$	−923.915	−0.910227	−0.455114	+	0.890433i	$0.650401\pi$
$102$	699.384	0.678915
$103$	1275.15	1.21985	0.609923	−	0.792460i	$-0.291200\pi$
$103$	1275.15	1.21985	0.609923	+	0.792460i	$0.291200\pi$
$104$	1092.68	1.03025
$105$	1189.90	1.10593
$106$	−2544.03	−2.33111
$107$	−1320.45	−1.19302	−0.596508	−	0.802607i	$-0.703446\pi$
$107$	−1320.45	−1.19302	−0.596508	+	0.802607i	$0.703446\pi$
$108$	6039.44	5.38097
$109$	−61.3068	−0.0538727	−0.0269364	−	0.999637i	$-0.508575\pi$
$109$	−61.3068	−0.0538727	−0.0269364	+	0.999637i	$0.508575\pi$
$110$	989.959	0.858080
$111$	−2191.42	−1.87388
$112$	−1545.85	−1.30418
$113$	1355.40	1.12837	0.564184	−	0.825649i	$-0.309191\pi$
$113$	1355.40	1.12837	0.564184	+	0.825649i	$0.309191\pi$
$114$	3629.62	2.98197
$115$	−1628.12	−1.32020
$116$	3352.65	2.68350
$117$	−1223.68	−0.966917
$118$	1349.25	1.05262
$119$	166.028	0.127897
$120$	5667.23	4.31121
$121$	−1025.76	−0.770671
$122$	−3133.99	−2.32572
$123$	669.051	0.490457
$124$	2975.57	2.15495
$125$	1421.31	1.01701
$126$	3654.84	2.58412
$127$	−321.947	−0.224946	−0.112473	−	0.993655i	$-0.535877\pi$
$127$	−321.947	−0.224946	−0.112473	+	0.993655i	$0.535877\pi$
$128$	818.642	0.565300
$129$	3150.04	2.14996
$130$	−1128.17	−0.761130
$131$	−1009.76	−0.673462	−0.336731	−	0.941601i	$-0.609321\pi$
$131$	−1009.76	−0.673462	−0.336731	+	0.941601i	$0.609321\pi$
$132$	3061.96	2.01901
$133$	861.640	0.561757
$134$	1630.29	1.05101
$135$	−3558.51	−2.26865
$136$	790.754	0.498578
$137$	2908.99	1.81410	0.907051	−	0.421022i	$-0.138328\pi$
$137$	2908.99	1.81410	0.907051	+	0.421022i	$0.138328\pi$
$138$	−7197.79	−4.43997
$139$	1933.13	1.17961	0.589804	−	0.807546i	$-0.299205\pi$
$139$	1933.13	1.17961	0.589804	+	0.807546i	$0.299205\pi$
$140$	2357.46	1.42315
$141$	3905.06	2.33238
$142$	−4733.72	−2.79750
$143$	−347.851	−0.203418
$144$	8245.21	4.77153
$145$	−1975.43	−1.13138
$146$	−311.530	−0.176592
$147$	−1977.24	−1.10939
$148$	−4341.70	−2.41139
$149$	−443.916	−0.244074	−0.122037	−	0.992526i	$-0.538943\pi$
$149$	−443.916	−0.244074	−0.122037	+	0.992526i	$0.538943\pi$
$150$	216.102	0.117631
$151$	−1761.86	−0.949522	−0.474761	−	0.880115i	$-0.657466\pi$
$151$	−1761.86	−0.949522	−0.474761	+	0.880115i	$0.657466\pi$
$152$	4103.80	2.18988
$153$	−885.556	−0.467928
$154$	1038.95	0.543642
$155$	−1753.24	−0.908541
$156$	−3489.44	−1.79089
$157$	348.732	0.177273	0.0886365	−	0.996064i	$-0.471749\pi$
$157$	348.732	0.177273	0.0886365	+	0.996064i	$0.471749\pi$
$158$	1000.79	0.503918
$159$	4636.35	2.31249
$160$	2781.19	1.37420
$161$	−1708.69	−0.836421
$162$	−7167.93	−3.47633
$163$	3053.22	1.46716	0.733578	−	0.679605i	$-0.237849\pi$
$163$	3053.22	1.46716	0.733578	+	0.679605i	$0.237849\pi$
$164$	1325.54	0.631142
$165$	−1804.15	−0.851228
$166$	−3227.52	−1.50906
$167$	1416.00	0.656129	0.328065	−	0.944655i	$-0.393604\pi$
$167$	1416.00	0.656129	0.328065	+	0.944655i	$0.393604\pi$
$168$	5947.69	2.73139
$169$	−1800.58	−0.819565
$170$	−816.436	−0.368340
$171$	−4595.80	−2.05526
$172$	6240.93	2.76667
$173$	1785.77	0.784795	0.392397	−	0.919796i	$-0.371646\pi$
$173$	1785.77	0.784795	0.392397	+	0.919796i	$0.371646\pi$
$174$	−8733.20	−3.80496
$175$	51.3008	0.0221599
$176$	2343.84	1.00383
$177$	−2458.94	−1.04421
$178$	5878.04	2.47516
$179$	3872.95	1.61719	0.808597	−	0.588364i	$-0.200228\pi$
$179$	3872.95	1.61719	0.808597	+	0.588364i	$0.200228\pi$
$180$	−12574.2	−5.20680
$181$	2746.29	1.12779	0.563896	−	0.825846i	$-0.309302\pi$
$181$	2746.29	1.12779	0.563896	+	0.825846i	$0.309302\pi$
$182$	−1184.00	−0.482218
$183$	5711.52	2.30715
$184$	−8138.13	−3.26060
$185$	2558.19	1.01666
$186$	−7750.94	−3.05552
$187$	−251.734	−0.0984418
$188$	7736.80	3.00141
$189$	−3734.62	−1.43732
$190$	−4237.09	−1.61784
$191$	−2554.38	−0.967688	−0.483844	−	0.875154i	$-0.660760\pi$
$191$	−2554.38	−0.967688	−0.483844	+	0.875154i	$0.660760\pi$
$192$	2201.21	0.827390
$193$	−2044.03	−0.762345	−0.381172	−	0.924504i	$-0.624480\pi$
$193$	−2044.03	−0.762345	−0.381172	+	0.924504i	$0.624480\pi$
$194$	−6232.33	−2.30647
$195$	2056.03	0.755051
$196$	−3917.36	−1.42761
$197$	−2896.35	−1.04749	−0.523747	−	0.851874i	$-0.675466\pi$
$197$	−2896.35	−1.04749	−0.523747	+	0.851874i	$0.675466\pi$
$198$	−5541.53	−1.98899
$199$	3977.24	1.41678	0.708390	−	0.705821i	$-0.249422\pi$
$199$	3977.24	1.41678	0.708390	+	0.705821i	$0.249422\pi$
$200$	244.335	0.0863854
$201$	−2971.11	−1.04262
$202$	4768.16	1.66082
$203$	−2073.19	−0.716794
$204$	−2525.25	−0.866681
$205$	−781.026	−0.266094
$206$	−6580.82	−2.22576
$207$	9113.80	3.06016
$208$	−2671.06	−0.890408
$209$	−1306.43	−0.432382
$210$	−6140.86	−2.01790
$211$	1066.62	0.348007	0.174003	−	0.984745i	$-0.444330\pi$
$211$	1066.62	0.348007	0.174003	+	0.984745i	$0.444330\pi$
$212$	9185.66	2.97582
$213$	8626.96	2.77516
$214$	6814.60	2.17681
$215$	−3677.24	−1.16644
$216$	−17787.2	−5.60307
$217$	−1840.01	−0.575612
$218$	316.393	0.0982976
$219$	567.746	0.175181
$220$	−3574.42	−1.09540
$221$	286.879	0.0873193
$222$	11309.5	3.41913
$223$	−984.300	−0.295577	−0.147788	−	0.989019i	$-0.547215\pi$
$223$	−984.300	−0.295577	−0.147788	+	0.989019i	$0.547215\pi$
$224$	2918.83	0.870635
$225$	−273.628	−0.0810749
$226$	−6994.99	−2.05885
$227$	24.5083	0.00716597	0.00358299	−	0.999994i	$-0.498859\pi$
$227$	24.5083	0.00716597	0.00358299	+	0.999994i	$0.498859\pi$
$228$	−13105.4	−3.80669
$229$	2676.84	0.772448	0.386224	−	0.922405i	$-0.373779\pi$
$229$	2676.84	0.772448	0.386224	+	0.922405i	$0.373779\pi$
$230$	8402.44	2.40887
$231$	−1893.43	−0.539301
$232$	−9874.14	−2.79426
$233$	−3629.44	−1.02048	−0.510241	−	0.860031i	$-0.670444\pi$
$233$	−3629.44	−1.02048	−0.510241	+	0.860031i	$0.670444\pi$
$234$	6315.19	1.76426
$235$	−4558.63	−1.26541
$236$	−4871.72	−1.34374
$237$	−1823.90	−0.499893
$238$	−856.839	−0.233364
$239$	7355.64	1.99078	0.995391	−	0.0958970i	$-0.0305720\pi$
$239$	7355.64	1.99078	0.995391	+	0.0958970i	$0.0305720\pi$
$240$	−13853.6	−3.72602
$241$	−3580.40	−0.956986	−0.478493	−	0.878091i	$-0.658817\pi$
$241$	−3580.40	−0.956986	−0.478493	+	0.878091i	$0.658817\pi$
$242$	5293.78	1.40619
$243$	4312.27	1.13840
$244$	11315.8	2.96894
$245$	2308.16	0.601889
$246$	−3452.85	−0.894901
$247$	1488.83	0.383529
$248$	−8763.55	−2.24389
$249$	5881.99	1.49701
$250$	−7335.13	−1.85566
$251$	243.973	0.0613523	0.0306762	−	0.999529i	$-0.490234\pi$
$251$	243.973	0.0613523	0.0306762	+	0.999529i	$0.490234\pi$
$252$	−13196.5	−3.29880
$253$	2590.75	0.643791
$254$	1661.51	0.410443
$255$	1487.91	0.365398
$256$	−6097.18	−1.48857
$257$	1822.17	0.442271	0.221135	−	0.975243i	$-0.429024\pi$
$257$	1822.17	0.442271	0.221135	+	0.975243i	$0.429024\pi$
$258$	−16256.8	−3.92288
$259$	2684.79	0.644110
$260$	4073.45	0.971633
$261$	11057.9	2.62249
$262$	5211.21	1.22882
$263$	−252.006	−0.0590849	−0.0295425	−	0.999564i	$-0.509405\pi$
$263$	−252.006	−0.0590849	−0.0295425	+	0.999564i	$0.509405\pi$
$264$	−9017.99	−2.10234
$265$	−5412.31	−1.25462
$266$	−4446.77	−1.02500
$267$	−10712.4	−2.45539
$268$	−5886.44	−1.34168
$269$	−8783.75	−1.99091	−0.995455	−	0.0952321i	$-0.969641\pi$
$269$	−8783.75	−1.99091	−0.995455	+	0.0952321i	$0.969641\pi$
$270$	18364.9	4.13944
$271$	−2255.92	−0.505672	−0.252836	−	0.967509i	$-0.581363\pi$
$271$	−2255.92	−0.505672	−0.252836	+	0.967509i	$0.581363\pi$
$272$	−1933.00	−0.430903
$273$	2157.77	0.478368
$274$	−15012.8	−3.31005
$275$	−77.7833	−0.0170564
$276$	25988.9	5.66793
$277$	5302.19	1.15010	0.575050	−	0.818118i	$-0.304983\pi$
$277$	5302.19	1.15010	0.575050	+	0.818118i	$0.304983\pi$
$278$	−9976.51	−2.15234
$279$	9814.20	2.10595
$280$	−6943.12	−1.48189
$281$	−104.410	−0.0221657	−0.0110828	−	0.999939i	$-0.503528\pi$
$281$	−104.410	−0.0221657	−0.0110828	+	0.999939i	$0.503528\pi$
$282$	−20153.3	−4.25572
$283$	1435.34	0.301492	0.150746	−	0.988573i	$-0.451832\pi$
$283$	1435.34	0.301492	0.150746	+	0.988573i	$0.451832\pi$
$284$	17091.9	3.57120
$285$	7721.86	1.60493
$286$	1795.20	0.371162
$287$	−819.677	−0.168585
$288$	−15568.4	−3.18534
$289$	−4705.39	−0.957743
$290$	10194.8	2.06435
$291$	11358.1	2.28805
$292$	1124.83	0.225431
$293$	−1058.77	−0.211105	−0.105553	−	0.994414i	$-0.533661\pi$
$293$	−1058.77	−0.211105	−0.105553	+	0.994414i	$0.533661\pi$
$294$	10204.2	2.02422
$295$	2870.48	0.566528
$296$	12787.1	2.51092
$297$	5662.49	1.10630
$298$	2290.97	0.445344
$299$	−2952.45	−0.571052
$300$	−780.276	−0.150164
$301$	−3859.21	−0.739008
$302$	9092.62	1.73252
$303$	−8689.71	−1.64756
$304$	−10031.8	−1.89264
$305$	−6667.42	−1.25172
$306$	4570.20	0.853793
$307$	−7499.75	−1.39424	−0.697122	−	0.716952i	$-0.745537\pi$
$307$	−7499.75	−1.39424	−0.697122	+	0.716952i	$0.745537\pi$
$308$	−3751.31	−0.693996
$309$	11993.2	2.20799
$310$	9048.17	1.65775
$311$	6185.52	1.12781	0.563905	−	0.825840i	$-0.309298\pi$
$311$	6185.52	1.12781	0.563905	+	0.825840i	$0.309298\pi$
$312$	10277.0	1.86481
$313$	−973.602	−0.175819	−0.0879093	−	0.996128i	$-0.528019\pi$
$313$	−973.602	−0.175819	−0.0879093	+	0.996128i	$0.528019\pi$
$314$	−1799.74	−0.323457
$315$	7775.52	1.39080
$316$	−3613.55	−0.643285
$317$	−26.9378	−0.00477280	−0.00238640	−	0.999997i	$-0.500760\pi$
$317$	−26.9378	−0.00477280	−0.00238640	+	0.999997i	$0.500760\pi$
$318$	−23927.4	−4.21944
$319$	3143.40	0.551714
$320$	−2569.62	−0.448893
$321$	−12419.2	−2.15942
$322$	8818.25	1.52616
$323$	1077.44	0.185605
$324$	25881.1	4.43777
$325$	88.6426	0.0151293
$326$	−15757.1	−2.67701
$327$	−576.610	−0.0975126
$328$	−3903.94	−0.657192
$329$	−4784.22	−0.801710
$330$	9310.88	1.55317
$331$	10167.9	1.68845	0.844224	−	0.535991i	$-0.180062\pi$
$331$	10167.9	1.68845	0.844224	+	0.535991i	$0.180062\pi$
$332$	11653.6	1.92642
$333$	−14320.1	−2.35656
$334$	−7307.74	−1.19719
$335$	3468.37	0.565663
$336$	−14539.2	−2.36064
$337$	−5731.20	−0.926405	−0.463203	−	0.886252i	$-0.653300\pi$
$337$	−5731.20	−0.926405	−0.463203	+	0.886252i	$0.653300\pi$
$338$	9292.49	1.49540
$339$	12748.0	2.04241
$340$	2947.89	0.470210
$341$	2789.85	0.443046
$342$	23718.1	3.75008
$343$	6374.69	1.00350
$344$	−18380.6	−2.88086
$345$	−15313.0	−2.38964
$346$	−9216.03	−1.43196
$347$	−9937.23	−1.53734	−0.768672	−	0.639643i	$-0.779082\pi$
$347$	−9937.23	−1.53734	−0.768672	+	0.639643i	$0.779082\pi$
$348$	31532.8	4.85728
$349$	−12445.2	−1.90882	−0.954408	−	0.298506i	$-0.903512\pi$
$349$	−12445.2	−1.90882	−0.954408	+	0.298506i	$0.903512\pi$
$350$	−264.754	−0.0404335
$351$	−6453.04	−0.981304
$352$	−4425.58	−0.670125
$353$	444.462	0.0670151	0.0335076	−	0.999438i	$-0.489332\pi$
$353$	444.462	0.0670151	0.0335076	+	0.999438i	$0.489332\pi$
$354$	12690.2	1.90529
$355$	−10070.8	−1.50564
$356$	−21223.7	−3.15970
$357$	1561.54	0.231500
$358$	−19987.6	−2.95077
$359$	−2430.75	−0.357355	−0.178677	−	0.983908i	$-0.557182\pi$
$359$	−2430.75	−0.357355	−0.178677	+	0.983908i	$0.557182\pi$
$360$	37033.1	5.42171
$361$	−1267.38	−0.184776
$362$	−14173.1	−2.05780
$363$	−9647.63	−1.39496
$364$	4275.03	0.615584
$365$	−662.766	−0.0950432
$366$	−29476.1	−4.20968
$367$	−5364.38	−0.762992	−0.381496	−	0.924370i	$-0.624591\pi$
$367$	−5364.38	−0.762992	−0.381496	+	0.924370i	$0.624591\pi$
$368$	19893.7	2.81802
$369$	4371.98	0.616792
$370$	−13202.4	−1.85502
$371$	−5680.15	−0.794875
$372$	27986.2	3.90058
$373$	7142.58	0.991498	0.495749	−	0.868466i	$-0.334894\pi$
$373$	7142.58	0.991498	0.495749	+	0.868466i	$0.334894\pi$
$374$	1299.15	0.179619
$375$	13367.9	1.84084
$376$	−22786.2	−3.12529
$377$	−3582.26	−0.489378
$378$	19273.7	2.62257
$379$	10512.1	1.42472	0.712361	−	0.701813i	$-0.247626\pi$
$379$	10512.1	1.42472	0.712361	+	0.701813i	$0.247626\pi$
$380$	15298.8	2.06529
$381$	−3028.02	−0.407165
$382$	13182.7	1.76567
$383$	−5484.38	−0.731694	−0.365847	−	0.930675i	$-0.619221\pi$
$383$	−5484.38	−0.731694	−0.365847	+	0.930675i	$0.619221\pi$
$384$	7699.59	1.02322
$385$	2210.32	0.292593
$386$	10548.9	1.39099
$387$	20584.2	2.70376
$388$	22502.9	2.94437
$389$	−7003.98	−0.912894	−0.456447	−	0.889751i	$-0.650878\pi$
$389$	−7003.98	−0.912894	−0.456447	+	0.889751i	$0.650878\pi$
$390$	−10610.8	−1.37769
$391$	−2136.64	−0.276354
$392$	11537.3	1.48653
$393$	−9497.16	−1.21900
$394$	14947.5	1.91128
$395$	2129.15	0.271213
$396$	20008.7	2.53908
$397$	−5797.15	−0.732873	−0.366437	−	0.930443i	$-0.619422\pi$
$397$	−5797.15	−0.732873	−0.366437	+	0.930443i	$0.619422\pi$
$398$	−20525.8	−2.58509
$399$	8104.00	1.01681
$400$	−597.278	−0.0746597
$401$	−13051.7	−1.62537	−0.812683	−	0.582706i	$-0.801994\pi$
$401$	−13051.7	−1.62537	−0.812683	+	0.582706i	$0.801994\pi$
$402$	15333.4	1.90238
$403$	−3179.34	−0.392989
$404$	−17216.3	−2.12015
$405$	−15249.5	−1.87099
$406$	10699.3	1.30788
$407$	−4070.72	−0.495770
$408$	7437.29	0.902453
$409$	5937.69	0.717848	0.358924	−	0.933367i	$-0.383144\pi$
$409$	5937.69	0.717848	0.358924	+	0.933367i	$0.383144\pi$
$410$	4030.73	0.485521
$411$	27360.0	3.28362
$412$	23761.2	2.84134
$413$	3012.53	0.358928
$414$	−47034.7	−5.58364
$415$	−6866.42	−0.812192
$416$	5043.44	0.594411
$417$	18181.7	2.13516
$418$	6742.27	0.788936
$419$	−14945.0	−1.74250	−0.871252	−	0.490836i	$-0.836691\pi$
$419$	−14945.0	−1.74250	−0.871252	+	0.490836i	$0.836691\pi$
$420$	22172.7	2.57599
$421$	−2919.94	−0.338027	−0.169013	−	0.985614i	$-0.554058\pi$
$421$	−2919.94	−0.338027	−0.169013	+	0.985614i	$0.554058\pi$
$422$	−5504.65	−0.634982
$423$	25518.0	2.93316
$424$	−27053.3	−3.09865
$425$	64.1492	0.00732163
$426$	−44522.2	−5.06363
$427$	−6997.38	−0.793037
$428$	−24605.3	−2.77884
$429$	−3271.65	−0.368198
$430$	18977.6	2.12832
$431$	10866.1	1.21439	0.607195	−	0.794553i	$-0.292295\pi$
$431$	10866.1	1.21439	0.607195	+	0.794553i	$0.292295\pi$
$432$	43480.8	4.84253
$433$	3584.67	0.397848	0.198924	−	0.980015i	$-0.436255\pi$
$433$	3584.67	0.397848	0.198924	+	0.980015i	$0.436255\pi$
$434$	9495.94	1.05028
$435$	−18579.5	−2.04786
$436$	−1142.39	−0.125483
$437$	−11088.6	−1.21382
$438$	−2930.03	−0.319640
$439$	−8720.89	−0.948121	−0.474061	−	0.880492i	$-0.657212\pi$
$439$	−8720.89	−0.948121	−0.474061	+	0.880492i	$0.657212\pi$
$440$	10527.3	1.14061
$441$	−12920.5	−1.39515
$442$	−1480.53	−0.159325
$443$	5433.52	0.582741	0.291371	−	0.956610i	$-0.405889\pi$
$443$	5433.52	0.582741	0.291371	+	0.956610i	$0.405889\pi$
$444$	−40835.1	−4.36475
$445$	12505.3	1.33215
$446$	5079.80	0.539317
$447$	−4175.17	−0.441787
$448$	−2696.78	−0.284399
$449$	12180.1	1.28021	0.640107	−	0.768286i	$-0.278890\pi$
$449$	12180.1	1.28021	0.640107	+	0.768286i	$0.278890\pi$
$450$	1412.14	0.147931
$451$	1242.81	0.129760
$452$	25256.7	2.62826
$453$	−16570.8	−1.71869
$454$	−126.483	−0.0130752
$455$	−2518.91	−0.259534
$456$	38597.6	3.96381
$457$	−14523.6	−1.48662	−0.743312	−	0.668945i	$-0.766746\pi$
$457$	−14523.6	−1.48662	−0.743312	+	0.668945i	$0.766746\pi$
$458$	−13814.7	−1.40943
$459$	−4669.95	−0.474890
$460$	−30338.5	−3.07509
$461$	−5143.78	−0.519674	−0.259837	−	0.965653i	$-0.583669\pi$
$461$	−5143.78	−0.519674	−0.259837	+	0.965653i	$0.583669\pi$
$462$	9771.65	0.984022
$463$	−10448.9	−1.04882	−0.524409	−	0.851467i	$-0.675714\pi$
$463$	−10448.9	−1.04882	−0.524409	+	0.851467i	$0.675714\pi$
$464$	24137.4	2.41498
$465$	−16489.8	−1.64451
$466$	18730.9	1.86200
$467$	18599.1	1.84297	0.921483	−	0.388419i	$-0.126979\pi$
$467$	18599.1	1.84297	0.921483	+	0.388419i	$0.126979\pi$
$468$	−22802.1	−2.25220
$469$	3640.01	0.358379
$470$	23526.2	2.30890
$471$	3279.94	0.320874
$472$	14348.0	1.39920
$473$	5851.41	0.568812
$474$	9412.80	0.912118
$475$	332.917	0.0321585
$476$	3093.77	0.297905
$477$	30296.7	2.90816
$478$	−37961.1	−3.63243
$479$	10180.8	0.971135	0.485568	−	0.874199i	$-0.338613\pi$
$479$	10180.8	0.971135	0.485568	+	0.874199i	$0.338613\pi$
$480$	26158.0	2.48738
$481$	4639.04	0.439755
$482$	18477.8	1.74614
$483$	−16070.8	−1.51397
$484$	−19114.1	−1.79509
$485$	−13259.0	−1.24136
$486$	−22254.9	−2.07716
$487$	−14593.7	−1.35791	−0.678954	−	0.734180i	$-0.737567\pi$
$487$	−14593.7	−1.35791	−0.678954	+	0.734180i	$0.737567\pi$
$488$	−33327.0	−3.09148
$489$	28716.5	2.65563
$490$	−11912.0	−1.09822
$491$	20199.6	1.85661	0.928307	−	0.371815i	$-0.121264\pi$
$491$	20199.6	1.85661	0.928307	+	0.371815i	$0.121264\pi$
$492$	12467.1	1.14240
$493$	−2592.42	−0.236829
$494$	−7683.56	−0.699797
$495$	−11789.4	−1.07049
$496$	21422.6	1.93932
$497$	−10569.2	−0.953908
$498$	−30355.9	−2.73149
$499$	−15468.0	−1.38766	−0.693831	−	0.720138i	$-0.744079\pi$
$499$	−15468.0	−1.38766	−0.693831	+	0.720138i	$0.744079\pi$
$500$	26484.8	2.36887
$501$	13318.0	1.18763
$502$	−1259.10	−0.111945
$503$	21104.9	1.87082	0.935408	−	0.353569i	$-0.115032\pi$
$503$	21104.9	1.87082	0.935408	+	0.353569i	$0.115032\pi$
$504$	38865.8	3.43496
$505$	10144.1	0.893871
$506$	−13370.4	−1.17468
$507$	−16935.1	−1.48346
$508$	−5999.18	−0.523958
$509$	1924.59	0.167595	0.0837974	−	0.996483i	$-0.473295\pi$
$509$	1924.59	0.167595	0.0837974	+	0.996483i	$0.473295\pi$
$510$	−7678.84	−0.666715
$511$	−695.565	−0.0602152
$512$	24917.3	2.15078
$513$	−24235.8	−2.08584
$514$	−9403.87	−0.806979
$515$	−14000.4	−1.19793
$516$	58697.9	5.00782
$517$	7253.92	0.617074
$518$	−13855.7	−1.17526
$519$	16795.7	1.42052
$520$	−11997.0	−1.01174
$521$	−13615.5	−1.14493	−0.572464	−	0.819930i	$-0.694012\pi$
$521$	−13615.5	−1.14493	−0.572464	+	0.819930i	$0.694012\pi$
$522$	−57068.0	−4.78506
$523$	2489.94	0.208179	0.104089	−	0.994568i	$-0.466807\pi$
$523$	2489.94	0.208179	0.104089	+	0.994568i	$0.466807\pi$
$524$	−18816.0	−1.56867
$525$	482.501	0.0401106
$526$	1300.56	0.107808
$527$	−2300.84	−0.190182
$528$	22044.5	1.81698
$529$	9822.43	0.807301
$530$	27932.0	2.28922
$531$	−16068.2	−1.31318
$532$	16055.9	1.30848
$533$	−1416.32	−0.115099
$534$	55284.9	4.48017
$535$	14497.8	1.17158
$536$	17336.6	1.39706
$537$	36426.3	2.92721
$538$	45331.4	3.63266
$539$	−3672.86	−0.293509
$540$	−66309.6	−5.28428
$541$	−23139.8	−1.83893	−0.919463	−	0.393176i	$-0.871376\pi$
$541$	−23139.8	−1.83893	−0.919463	+	0.393176i	$0.871376\pi$
$542$	11642.4	0.922663
$543$	25829.8	2.04137
$544$	3649.85	0.287658
$545$	673.114	0.0529046
$546$	−11135.9	−0.872842
$547$	−547.000	−0.0427569
$547$	−547.000	−0.0427569
$548$	54206.3	4.22551
$549$	37322.5	2.90143
$550$	401.425	0.0311215
$551$	−13454.0	−1.04021
$552$	−76541.7	−5.90187
$553$	2234.52	0.171829
$554$	−27363.6	−2.09850
$555$	24060.6	1.84021
$556$	36022.0	2.74761
$557$	8042.30	0.611783	0.305891	−	0.952066i	$-0.401046\pi$
$557$	8042.30	0.611783	0.305891	+	0.952066i	$0.401046\pi$
$558$	−50649.3	−3.84257
$559$	−6668.33	−0.504544
$560$	16972.5	1.28075
$561$	−2367.64	−0.178185
$562$	538.839	0.0404440
$563$	−16102.5	−1.20540	−0.602699	−	0.797968i	$-0.705908\pi$
$563$	−16102.5	−1.20540	−0.602699	+	0.797968i	$0.705908\pi$
$564$	72767.1	5.43271
$565$	−14881.6	−1.10809
$566$	−7407.55	−0.550110
$567$	−16004.1	−1.18538
$568$	−50338.7	−3.71860
$569$	−23047.5	−1.69807	−0.849036	−	0.528336i	$-0.822816\pi$
$569$	−23047.5	−1.69807	−0.849036	+	0.528336i	$0.822816\pi$
$570$	−39851.1	−2.92839
$571$	−4171.01	−0.305694	−0.152847	−	0.988250i	$-0.548844\pi$
$571$	−4171.01	−0.305694	−0.152847	+	0.988250i	$0.548844\pi$
$572$	−6481.88	−0.473813
$573$	−24024.8	−1.75157
$574$	4230.20	0.307605
$575$	−660.198	−0.0478820
$576$	14384.0	1.04051
$577$	−13265.2	−0.957081	−0.478540	−	0.878066i	$-0.658834\pi$
$577$	−13265.2	−0.957081	−0.478540	+	0.878066i	$0.658834\pi$
$578$	24283.7	1.74752
$579$	−19224.8	−1.37989
$580$	−36810.2	−2.63528
$581$	−7206.23	−0.514569
$582$	−58617.1	−4.17484
$583$	8612.35	0.611813
$584$	−3312.82	−0.234736
$585$	13435.3	0.949541
$586$	5464.11	0.385188
$587$	−20444.2	−1.43752	−0.718759	−	0.695260i	$-0.755289\pi$
$587$	−20444.2	−1.43752	−0.718759	+	0.695260i	$0.755289\pi$
$588$	−36844.0	−2.58405
$589$	−11940.7	−0.835330
$590$	−14814.0	−1.03370
$591$	−27241.1	−1.89602
$592$	−31258.0	−2.17010
$593$	−4478.00	−0.310100	−0.155050	−	0.987907i	$-0.549554\pi$
$593$	−4478.00	−0.310100	−0.155050	+	0.987907i	$0.549554\pi$
$594$	−29223.1	−2.01858
$595$	−1822.89	−0.125599
$596$	−8271.96	−0.568511
$597$	37407.3	2.56445
$598$	15237.0	1.04196
$599$	−25794.5	−1.75949	−0.879747	−	0.475442i	$-0.842288\pi$
$599$	−25794.5	−1.75949	−0.879747	+	0.475442i	$0.842288\pi$
$600$	2298.05	0.156362
$601$	−27295.7	−1.85261	−0.926303	−	0.376779i	$-0.877032\pi$
$601$	−27295.7	−1.85261	−0.926303	+	0.376779i	$0.877032\pi$
$602$	19916.7	1.34841
$603$	−19415.0	−1.31118
$604$	−32830.5	−2.21168
$605$	11262.3	0.756822
$606$	44846.0	3.00618
$607$	479.074	0.0320346	0.0160173	−	0.999872i	$-0.494901\pi$
$607$	479.074	0.0320346	0.0160173	+	0.999872i	$0.494901\pi$
$608$	18941.8	1.26347
$609$	−19499.0	−1.29744
$610$	34409.4	2.28393
$611$	−8266.65	−0.547353
$612$	−16501.5	−1.08992
$613$	−307.433	−0.0202563	−0.0101282	−	0.999949i	$-0.503224\pi$
$613$	−307.433	−0.0202563	−0.0101282	+	0.999949i	$0.503224\pi$
$614$	38704.8	2.54397
$615$	−7345.79	−0.481644
$616$	11048.2	0.722640
$617$	−8005.69	−0.522361	−0.261181	−	0.965290i	$-0.584112\pi$
$617$	−8005.69	−0.522361	−0.261181	+	0.965290i	$0.584112\pi$
$618$	−61894.7	−4.02875
$619$	9500.92	0.616921	0.308461	−	0.951237i	$-0.400186\pi$
$619$	9500.92	0.616921	0.308461	+	0.951237i	$0.400186\pi$
$620$	−32670.0	−2.11623
$621$	48061.3	3.10569
$622$	−31922.4	−2.05783
$623$	13124.1	0.843993
$624$	−25122.2	−1.61169
$625$	−15048.7	−0.963114
$626$	5024.59	0.320803
$627$	−12287.4	−0.782636
$628$	6498.29	0.412914
$629$	3357.19	0.212814
$630$	−40128.1	−2.53768
$631$	20938.5	1.32099	0.660497	−	0.750828i	$-0.270345\pi$
$631$	20938.5	1.32099	0.660497	+	0.750828i	$0.270345\pi$
$632$	10642.5	0.669836
$633$	10031.9	0.629911
$634$	139.021	0.00870858
$635$	3534.80	0.220904
$636$	86394.1	5.38640
$637$	4185.63	0.260347
$638$	−16222.5	−1.00667
$639$	56373.7	3.49000
$640$	−8988.22	−0.555142
$641$	−4808.96	−0.296322	−0.148161	−	0.988963i	$-0.547335\pi$
$641$	−4808.96	−0.296322	−0.148161	+	0.988963i	$0.547335\pi$
$642$	64093.5	3.94014
$643$	29539.0	1.81167	0.905836	−	0.423629i	$-0.139244\pi$
$643$	29539.0	1.81167	0.905836	+	0.423629i	$0.139244\pi$
$644$	−31839.9	−1.94824
$645$	−34585.6	−2.11133
$646$	−5560.46	−0.338659
$647$	5445.44	0.330885	0.165442	−	0.986219i	$-0.447095\pi$
$647$	5445.44	0.330885	0.165442	+	0.986219i	$0.447095\pi$
$648$	−76224.2	−4.62094
$649$	−4567.66	−0.276265
$650$	−457.469	−0.0276052
$651$	−17305.8	−1.04189
$652$	56893.9	3.41739
$653$	−5089.78	−0.305020	−0.152510	−	0.988302i	$-0.548736\pi$
$653$	−5089.78	−0.305020	−0.152510	+	0.988302i	$0.548736\pi$
$654$	2975.78	0.177924
$655$	11086.6	0.661360
$656$	9543.21	0.567987
$657$	3709.99	0.220305
$658$	24690.5	1.46282
$659$	8022.32	0.474211	0.237106	−	0.971484i	$-0.423801\pi$
$659$	8022.32	0.474211	0.237106	+	0.971484i	$0.423801\pi$
$660$	−33618.6	−1.98273
$661$	−5447.55	−0.320552	−0.160276	−	0.987072i	$-0.551238\pi$
$661$	−5447.55	−0.320552	−0.160276	+	0.987072i	$0.551238\pi$
$662$	−52474.5	−3.08078
$663$	2698.19	0.158053
$664$	−34321.7	−2.00593
$665$	−9460.32	−0.551662
$666$	73903.4	4.29985
$667$	26680.2	1.54882
$668$	26385.9	1.52829
$669$	−9257.66	−0.535010
$670$	−17899.6	−1.03212
$671$	10609.5	0.610398
$672$	27452.5	1.57590
$673$	8075.80	0.462555	0.231277	−	0.972888i	$-0.425710\pi$
$673$	8075.80	0.462555	0.231277	+	0.972888i	$0.425710\pi$
$674$	29577.7	1.69034
$675$	−1442.97	−0.0822812
$676$	−33552.2	−1.90898
$677$	29066.0	1.65007	0.825036	−	0.565080i	$-0.191155\pi$
$677$	29066.0	1.65007	0.825036	+	0.565080i	$0.191155\pi$
$678$	−65790.1	−3.72663
$679$	−13915.2	−0.786474
$680$	−8682.02	−0.489618
$681$	230.509	0.0129708
$682$	−14397.9	−0.808394
$683$	−17530.8	−0.982136	−0.491068	−	0.871121i	$-0.663393\pi$
$683$	−17530.8	−0.982136	−0.491068	+	0.871121i	$0.663393\pi$
$684$	−85638.5	−4.78724
$685$	−31939.1	−1.78150
$686$	−32898.6	−1.83101
$687$	25176.5	1.39817
$688$	44931.5	2.48982
$689$	−9814.72	−0.542687
$690$	79027.6	4.36019
$691$	22423.5	1.23449	0.617243	−	0.786773i	$-0.288250\pi$
$691$	22423.5	1.23449	0.617243	+	0.786773i	$0.288250\pi$
$692$	33276.1	1.82799
$693$	−12372.8	−0.678217
$694$	51284.3	2.80508
$695$	−21224.6	−1.15841
$696$	−92869.4	−5.05777
$697$	−1024.96	−0.0557006
$698$	64227.5	3.48287
$699$	−34136.0	−1.84713
$700$	955.943	0.0516161
$701$	20618.4	1.11091	0.555454	−	0.831547i	$-0.312544\pi$
$701$	20618.4	1.11091	0.555454	+	0.831547i	$0.312544\pi$
$702$	33303.0	1.79051
$703$	17423.0	0.934736
$704$	4088.90	0.218901
$705$	−42875.3	−2.29047
$706$	−2293.79	−0.122277
$707$	10646.1	0.566317
$708$	−45820.1	−2.43224
$709$	21610.4	1.14470	0.572351	−	0.820009i	$-0.306031\pi$
$709$	21610.4	1.14470	0.572351	+	0.820009i	$0.306031\pi$
$710$	51973.6	2.74723
$711$	−11918.4	−0.628658
$712$	62507.4	3.29012
$713$	23679.3	1.24376
$714$	−8058.84	−0.422401
$715$	3819.21	0.199763
$716$	72168.7	3.76686
$717$	69182.2	3.60342
$718$	12544.7	0.652038
$719$	−7972.16	−0.413507	−0.206753	−	0.978393i	$-0.566290\pi$
$719$	−7972.16	−0.413507	−0.206753	+	0.978393i	$0.566290\pi$
$720$	−90527.7	−4.68579
$721$	−14693.3	−0.758954
$722$	6540.71	0.337147
$723$	−33674.8	−1.73220
$724$	51174.6	2.62692
$725$	−801.030	−0.0410338
$726$	49789.7	2.54527
$727$	−3059.99	−0.156105	−0.0780527	−	0.996949i	$-0.524870\pi$
$727$	−3059.99	−0.156105	−0.0780527	+	0.996949i	$0.524870\pi$
$728$	−12590.7	−0.640992
$729$	3057.62	0.155343
$730$	3420.42	0.173418
$731$	−4825.76	−0.244168
$732$	106429.	5.37394
$733$	18824.6	0.948572	0.474286	−	0.880371i	$-0.342706\pi$
$733$	18824.6	0.948572	0.474286	+	0.880371i	$0.342706\pi$
$734$	27684.6	1.39218
$735$	21709.0	1.08945
$736$	−37562.8	−1.88123
$737$	−5519.04	−0.275843
$738$	−22563.0	−1.12541
$739$	8315.74	0.413937	0.206968	−	0.978348i	$-0.433640\pi$
$739$	8315.74	0.413937	0.206968	+	0.978348i	$0.433640\pi$
$740$	47669.4	2.36806
$741$	14002.9	0.694209
$742$	29314.2	1.45035
$743$	21915.2	1.08209	0.541045	−	0.840994i	$-0.318029\pi$
$743$	21915.2	1.08209	0.541045	+	0.840994i	$0.318029\pi$
$744$	−82424.0	−4.06157
$745$	4873.95	0.239688
$746$	−36861.6	−1.80911
$747$	38436.5	1.88262
$748$	−4690.83	−0.229296
$749$	15215.2	0.742260
$750$	−68989.2	−3.35884
$751$	−12654.0	−0.614847	−0.307423	−	0.951573i	$-0.599467\pi$
$751$	−12654.0	−0.614847	−0.307423	+	0.951573i	$0.599467\pi$
$752$	55701.0	2.70107
$753$	2294.64	0.111051
$754$	18487.4	0.892932
$755$	19344.2	0.932459
$756$	−69591.1	−3.34789
$757$	7358.43	0.353298	0.176649	−	0.984274i	$-0.443474\pi$
$757$	7358.43	0.353298	0.176649	+	0.984274i	$0.443474\pi$
$758$	−54251.0	−2.59958
$759$	24366.8	1.16530
$760$	−45057.4	−2.15053
$761$	−15255.4	−0.726687	−0.363343	−	0.931655i	$-0.618365\pi$
$761$	−15255.4	−0.726687	−0.363343	+	0.931655i	$0.618365\pi$
$762$	15627.0	0.742924
$763$	706.425	0.0335181
$764$	−47598.5	−2.25399
$765$	9722.90	0.459519
$766$	28303.9	1.33507
$767$	5205.35	0.245051
$768$	−57345.9	−2.69439
$769$	18610.9	0.872725	0.436362	−	0.899771i	$-0.356267\pi$
$769$	18610.9	0.872725	0.436362	+	0.899771i	$0.356267\pi$
$770$	−11407.1	−0.533873
$771$	17138.1	0.800535
$772$	−38088.6	−1.77570
$773$	36599.1	1.70295	0.851473	−	0.524398i	$-0.175710\pi$
$773$	36599.1	1.70295	0.851473	+	0.524398i	$0.175710\pi$
$774$	−106231.	−4.93335
$775$	−710.935	−0.0329517
$776$	−66275.0	−3.06589
$777$	25251.3	1.16587
$778$	36146.3	1.66569
$779$	−5319.30	−0.244652
$780$	38312.1	1.75871
$781$	16025.2	0.734220
$782$	11026.8	0.504242
$783$	58313.7	2.66151
$784$	−28203.0	−1.28476
$785$	−3828.88	−0.174087
$786$	49013.1	2.22422
$787$	21383.7	0.968548	0.484274	−	0.874916i	$-0.339084\pi$
$787$	21383.7	0.968548	0.484274	+	0.874916i	$0.339084\pi$
$788$	−53970.8	−2.43988
$789$	−2370.19	−0.106947
$790$	−10988.2	−0.494862
$791$	−15618.0	−0.702038
$792$	−58929.0	−2.64388
$793$	−12090.8	−0.541432
$794$	29918.0	1.33722
$795$	−50904.5	−2.27094
$796$	74112.2	3.30005
$797$	34420.1	1.52976	0.764882	−	0.644171i	$-0.222797\pi$
$797$	34420.1	1.52976	0.764882	+	0.644171i	$0.222797\pi$
$798$	−41823.3	−1.85530
$799$	−5982.43	−0.264885
$800$	1127.77	0.0498407
$801$	−70001.4	−3.08786
$802$	67357.6	2.96568
$803$	1054.63	0.0463474
$804$	−55363.8	−2.42852
$805$	18760.5	0.821391
$806$	16408.0	0.717057
$807$	−82614.0	−3.60366
$808$	50704.9	2.20766
$809$	−1655.29	−0.0719368	−0.0359684	−	0.999353i	$-0.511452\pi$
$809$	−1655.29	−0.0719368	−0.0359684	+	0.999353i	$0.511452\pi$
$810$	78699.8	3.41386
$811$	5190.36	0.224733	0.112366	−	0.993667i	$-0.464157\pi$
$811$	5190.36	0.224733	0.112366	+	0.993667i	$0.464157\pi$
$812$	−38631.9	−1.66960
$813$	−21217.6	−0.915295
$814$	21008.3	0.904594
$815$	−33522.6	−1.44079
$816$	−18180.5	−0.779957
$817$	−25044.4	−1.07245
$818$	−30643.4	−1.30980
$819$	14100.2	0.601588
$820$	−14553.7	−0.619800
$821$	−15261.9	−0.648773	−0.324386	−	0.945925i	$-0.605158\pi$
$821$	−15261.9	−0.648773	−0.324386	+	0.945925i	$0.605158\pi$
$822$	−141200.	−5.99138
$823$	−25125.6	−1.06418	−0.532092	−	0.846686i	$-0.678594\pi$
$823$	−25125.6	−1.06418	−0.532092	+	0.846686i	$0.678594\pi$
$824$	−69980.8	−2.95861
$825$	−731.576	−0.0308730
$826$	−15547.1	−0.654908
$827$	−7786.74	−0.327414	−0.163707	−	0.986509i	$-0.552345\pi$
$827$	−7786.74	−0.327414	−0.163707	+	0.986509i	$0.552345\pi$
$828$	169827.	7.12790
$829$	−26285.4	−1.10124	−0.550622	−	0.834755i	$-0.685609\pi$
$829$	−26285.4	−1.10124	−0.550622	+	0.834755i	$0.685609\pi$
$830$	35436.4	1.48195
$831$	49868.8	2.08174
$832$	−4659.76	−0.194168
$833$	3029.07	0.125992
$834$	−93832.3	−3.89586
$835$	−15546.9	−0.644339
$836$	−24344.2	−1.00713
$837$	51754.9	2.13729
$838$	77128.2	3.17942
$839$	−9107.98	−0.374782	−0.187391	−	0.982285i	$-0.560003\pi$
$839$	−9107.98	−0.374782	−0.187391	+	0.982285i	$0.560003\pi$
$840$	−65302.2	−2.68231
$841$	7982.50	0.327299
$842$	15069.3	0.616772
$843$	−982.005	−0.0401211
$844$	19875.5	0.810597
$845$	19769.4	0.804838
$846$	−131694.	−5.35192
$847$	11819.6	0.479489
$848$	66132.0	2.67805
$849$	13499.9	0.545718
$850$	−331.062	−0.0133592
$851$	−34550.9	−1.39176
$852$	160755.	6.46406
$853$	22537.1	0.904639	0.452320	−	0.891856i	$-0.350597\pi$
$853$	22537.1	0.904639	0.452320	+	0.891856i	$0.350597\pi$
$854$	36112.2	1.44700
$855$	50459.3	2.01833
$856$	72466.9	2.89354
$857$	16061.8	0.640211	0.320106	−	0.947382i	$-0.396282\pi$
$857$	16061.8	0.640211	0.320106	+	0.947382i	$0.396282\pi$
$858$	16884.4	0.671823
$859$	−11949.0	−0.474615	−0.237308	−	0.971435i	$-0.576265\pi$
$859$	−11949.0	−0.474615	−0.237308	+	0.971435i	$0.576265\pi$
$860$	−68521.9	−2.71695
$861$	−7709.32	−0.305149
$862$	−56078.0	−2.21581
$863$	23507.2	0.927224	0.463612	−	0.886038i	$-0.346553\pi$
$863$	23507.2	0.927224	0.463612	+	0.886038i	$0.346553\pi$
$864$	−82099.5	−3.23273
$865$	−19606.7	−0.770692
$866$	−18499.8	−0.725923
$867$	−44255.7	−1.73357
$868$	−34286.8	−1.34075
$869$	−3388.01	−0.132256
$870$	95885.6	3.73658
$871$	6289.56	0.244677
$872$	3364.55	0.130663
$873$	74220.6	2.87742
$874$	57226.1	2.21476
$875$	−16377.4	−0.632753
$876$	10579.4	0.408042
$877$	−18682.1	−0.719328	−0.359664	−	0.933082i	$-0.617109\pi$
$877$	−18682.1	−0.719328	−0.359664	+	0.933082i	$0.617109\pi$
$878$	45006.9	1.72997
$879$	−9958.05	−0.382112
$880$	−25734.0	−0.985787
$881$	37303.1	1.42653	0.713265	−	0.700894i	$-0.247215\pi$
$881$	37303.1	1.42653	0.713265	+	0.700894i	$0.247215\pi$
$882$	66680.2	2.54562
$883$	36080.7	1.37510	0.687550	−	0.726137i	$-0.258686\pi$
$883$	36080.7	1.37510	0.687550	+	0.726137i	$0.258686\pi$
$884$	5345.72	0.203389
$885$	26997.8	1.02545
$886$	−28041.4	−1.06328
$887$	−38732.0	−1.46617	−0.733086	−	0.680136i	$-0.761921\pi$
$887$	−38732.0	−1.46617	−0.733086	+	0.680136i	$0.761921\pi$
$888$	120266.	4.54490
$889$	3709.72	0.139955
$890$	−64537.6	−2.43068
$891$	24265.7	0.912383
$892$	−18341.5	−0.688474
$893$	−31047.2	−1.16345
$894$	21547.3	0.806096
$895$	−42522.7	−1.58813
$896$	−9433.02	−0.351713
$897$	−27768.7	−1.03363
$898$	−62859.4	−2.33591
$899$	28730.5	1.06587
$900$	−5098.80	−0.188844
$901$	−7102.75	−0.262627
$902$	−6413.91	−0.236762
$903$	−36297.1	−1.33764
$904$	−74385.1	−2.73674
$905$	−30152.7	−1.10753
$906$	85519.0	3.13596
$907$	−39943.5	−1.46230	−0.731148	−	0.682219i	$-0.761015\pi$
$907$	−39943.5	−1.46230	−0.731148	+	0.682219i	$0.761015\pi$
$908$	456.690	0.0166914
$909$	−56783.8	−2.07195
$910$	12999.6	0.473553
$911$	−24023.9	−0.873708	−0.436854	−	0.899532i	$-0.643907\pi$
$911$	−24023.9	−0.873708	−0.436854	+	0.899532i	$0.643907\pi$
$912$	−94352.0	−3.42578
$913$	10926.2	0.396062
$914$	74953.9	2.71253
$915$	−62709.2	−2.26569
$916$	49880.4	1.79923
$917$	11635.3	0.419009
$918$	24100.8	0.866497
$919$	27805.0	0.998045	0.499022	−	0.866589i	$-0.333693\pi$
$919$	27805.0	0.998045	0.499022	+	0.866589i	$0.333693\pi$
$920$	89352.0	3.20201
$921$	−70537.5	−2.52366
$922$	26546.1	0.948210
$923$	−18262.5	−0.651264
$924$	−35282.3	−1.25617
$925$	1037.34	0.0368729
$926$	53925.0	1.91370
$927$	78370.7	2.77673
$928$	−45575.6	−1.61217
$929$	15046.2	0.531377	0.265689	−	0.964059i	$-0.414401\pi$
$929$	15046.2	0.531377	0.265689	+	0.964059i	$0.414401\pi$
$930$	85100.9	3.00061
$931$	15720.1	0.553389
$932$	−67631.2	−2.37697
$933$	58176.8	2.04140
$934$	−95986.8	−3.36272
$935$	2763.90	0.0966728
$936$	67156.1	2.34516
$937$	23795.5	0.829632	0.414816	−	0.909905i	$-0.363846\pi$
$937$	23795.5	0.829632	0.414816	+	0.909905i	$0.363846\pi$
$938$	−18785.4	−0.653908
$939$	−9157.04	−0.318241
$940$	−84945.7	−2.94747
$941$	−3289.96	−0.113974	−0.0569871	−	0.998375i	$-0.518149\pi$
$941$	−3289.96	−0.113974	−0.0569871	+	0.998375i	$0.518149\pi$
$942$	−16927.2	−0.585474
$943$	10548.5	0.364271
$944$	−35073.9	−1.20928
$945$	41004.0	1.41149
$946$	−30198.1	−1.03787
$947$	−46160.0	−1.58395	−0.791974	−	0.610555i	$-0.790947\pi$
$947$	−46160.0	−1.58395	−0.791974	+	0.610555i	$0.790947\pi$
$948$	−33986.6	−1.16438
$949$	−1201.87	−0.0411108
$950$	−1718.13	−0.0586772
$951$	−253.359	−0.00863903
$952$	−9111.67	−0.310201
$953$	−18727.4	−0.636559	−0.318280	−	0.947997i	$-0.603105\pi$
$953$	−18727.4	−0.636559	−0.318280	+	0.947997i	$0.603105\pi$
$954$	−156356.	−5.30630
$955$	28045.6	0.950299
$956$	137065.	4.63704
$957$	29564.7	0.998632
$958$	−52541.4	−1.77196
$959$	−33519.6	−1.12868
$960$	−24168.1	−0.812522
$961$	−4291.92	−0.144068
$962$	−23941.2	−0.802387
$963$	−81154.9	−2.71566
$964$	−66717.3	−2.22907
$965$	22442.3	0.748645
$966$	82938.5	2.76242
$967$	−19987.5	−0.664690	−0.332345	−	0.943158i	$-0.607840\pi$
$967$	−19987.5	−0.664690	−0.332345	+	0.943158i	$0.607840\pi$
$968$	56294.3	1.86918
$969$	10133.6	0.335954
$970$	68427.4	2.26502
$971$	−28324.0	−0.936109	−0.468054	−	0.883700i	$-0.655045\pi$
$971$	−28324.0	−0.936109	−0.468054	+	0.883700i	$0.655045\pi$
$972$	80355.1	2.65164
$973$	−22275.0	−0.733919
$974$	75315.2	2.47767
$975$	833.712	0.0273848
$976$	81468.0	2.67185
$977$	41171.6	1.34820	0.674102	−	0.738638i	$-0.264531\pi$
$977$	41171.6	1.34820	0.674102	+	0.738638i	$0.264531\pi$
$978$	−148201.	−4.84554
$979$	−19899.1	−0.649619
$980$	43010.4	1.40195
$981$	−3767.92	−0.122630
$982$	−104247.	−3.38762
$983$	26494.1	0.859644	0.429822	−	0.902914i	$-0.358576\pi$
$983$	26494.1	0.859644	0.429822	+	0.902914i	$0.358576\pi$
$984$	−36717.8	−1.18955
$985$	31800.3	1.02867
$986$	13379.0	0.432124
$987$	−44997.1	−1.45114
$988$	27742.9	0.893339
$989$	49664.8	1.59681
$990$	60842.9	1.95325
$991$	−34673.3	−1.11144	−0.555718	−	0.831371i	$-0.687557\pi$
$991$	−34673.3	−1.11144	−0.555718	+	0.831371i	$0.687557\pi$
$992$	−40449.5	−1.29463
$993$	95631.9	3.05618
$994$	54545.6	1.74052
$995$	−43667.9	−1.39132
$996$	109605.	3.48693
$997$	−16004.4	−0.508390	−0.254195	−	0.967153i	$-0.581811\pi$
$997$	−16004.4	−0.508390	−0.254195	+	0.967153i	$0.581811\pi$
$998$	79827.6	2.53196
$999$	−75516.5	−2.39163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.b.1.4	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.b.1.4	✓	71	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-5.16082 q^{2} +9.40532 q^{3} +18.6341 q^{4} -10.9794 q^{5} -48.5392 q^{6} -11.5228 q^{7} -54.8805 q^{8} +61.4600 q^{9} +O(q^{10})\)	\(q-5.16082 q^{2} +9.40532 q^{3} +18.6341 q^{4} -10.9794 q^{5} -48.5392 q^{6} -11.5228 q^{7} -54.8805 q^{8} +61.4600 q^{9} +56.6629 q^{10} +17.4710 q^{11} +175.259 q^{12} -19.9102 q^{13} +59.4670 q^{14} -103.265 q^{15} +134.156 q^{16} -14.4087 q^{17} -317.184 q^{18} -74.7771 q^{19} -204.591 q^{20} -108.375 q^{21} -90.1648 q^{22} +148.288 q^{23} -516.168 q^{24} -4.45213 q^{25} +102.753 q^{26} +324.107 q^{27} -214.716 q^{28} +179.921 q^{29} +532.932 q^{30} +159.684 q^{31} -253.309 q^{32} +164.321 q^{33} +74.3605 q^{34} +126.513 q^{35} +1145.25 q^{36} -232.998 q^{37} +385.911 q^{38} -187.262 q^{39} +602.556 q^{40} +71.1353 q^{41} +559.306 q^{42} +334.921 q^{43} +325.556 q^{44} -674.796 q^{45} -765.289 q^{46} +415.197 q^{47} +1261.78 q^{48} -210.226 q^{49} +22.9766 q^{50} -135.518 q^{51} -371.007 q^{52} +492.950 q^{53} -1672.66 q^{54} -191.822 q^{55} +632.375 q^{56} -703.303 q^{57} -928.539 q^{58} -261.442 q^{59} -1924.25 q^{60} +607.265 q^{61} -824.102 q^{62} -708.190 q^{63} +234.039 q^{64} +218.602 q^{65} -848.029 q^{66} -315.897 q^{67} -268.492 q^{68} +1394.70 q^{69} -652.913 q^{70} +917.242 q^{71} -3372.95 q^{72} +60.3643 q^{73} +1202.46 q^{74} -41.8737 q^{75} -1393.40 q^{76} -201.315 q^{77} +966.423 q^{78} -193.922 q^{79} -1472.95 q^{80} +1388.91 q^{81} -367.117 q^{82} +625.390 q^{83} -2019.47 q^{84} +158.199 q^{85} -1728.47 q^{86} +1692.21 q^{87} -958.818 q^{88} -1138.97 q^{89} +3482.50 q^{90} +229.420 q^{91} +2763.21 q^{92} +1501.88 q^{93} -2142.76 q^{94} +821.010 q^{95} -2382.46 q^{96} +1207.62 q^{97} +1084.94 q^{98} +1073.77 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) \) 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9} + 120 q^{10} + 139 q^{11} + 309 q^{12} + 343 q^{13} + 239 q^{14} + 194 q^{15} + 1346 q^{16} + 842 q^{17} + 423 q^{18} + 157 q^{19} + 1292 q^{20} + 434 q^{21} + 436 q^{22} + 1004 q^{23} + 935 q^{24} + 2206 q^{25} + 812 q^{26} + 1282 q^{27} + 584 q^{28} + 1459 q^{29} + 146 q^{30} + 582 q^{31} + 1428 q^{32} + 1080 q^{33} + 393 q^{34} + 1006 q^{35} + 2996 q^{36} + 1477 q^{37} + 1873 q^{38} + 626 q^{39} + 1272 q^{40} + 1112 q^{41} + 1812 q^{42} + 833 q^{43} + 1392 q^{44} + 3841 q^{45} + 782 q^{46} + 2484 q^{47} + 2034 q^{48} + 4727 q^{49} + 1248 q^{50} + 932 q^{51} + 2118 q^{52} + 5077 q^{53} + 1537 q^{54} + 1736 q^{55} + 2281 q^{56} + 1426 q^{57} + 992 q^{58} + 2977 q^{59} + 1418 q^{60} + 3363 q^{61} + 3438 q^{62} + 3194 q^{63} + 6138 q^{64} + 4640 q^{65} + 288 q^{66} + 955 q^{67} + 8553 q^{68} + 4440 q^{69} + 2203 q^{70} + 2458 q^{71} + 4495 q^{72} + 3724 q^{73} + 2099 q^{74} + 4491 q^{75} + 2260 q^{76} + 9774 q^{77} + 1057 q^{78} + 1638 q^{79} + 8221 q^{80} + 10151 q^{81} + 1018 q^{82} + 6121 q^{83} + 4847 q^{84} + 3836 q^{85} + 2305 q^{86} + 3894 q^{87} + 5815 q^{88} + 8110 q^{89} + 4951 q^{90} + 2312 q^{91} + 13138 q^{92} + 9250 q^{93} - 813 q^{94} + 4858 q^{95} + 6882 q^{96} + 4486 q^{97} + 4216 q^{98} + 4969 q^{99}+O(q^{100}) \) 71 * q + 14 * q^2 + 31 * q^3 + 294 * q^4 + 159 * q^5 + 60 * q^6 + 66 * q^7 + 168 * q^8 + 738 * q^9 + 120 * q^10 + 139 * q^11 + 309 * q^12 + 343 * q^13 + 239 * q^14 + 194 * q^15 + 1346 * q^16 + 842 * q^17 + 423 * q^18 + 157 * q^19 + 1292 * q^20 + 434 * q^21 + 436 * q^22 + 1004 * q^23 + 935 * q^24 + 2206 * q^25 + 812 * q^26 + 1282 * q^27 + 584 * q^28 + 1459 * q^29 + 146 * q^30 + 582 * q^31 + 1428 * q^32 + 1080 * q^33 + 393 * q^34 + 1006 * q^35 + 2996 * q^36 + 1477 * q^37 + 1873 * q^38 + 626 * q^39 + 1272 * q^40 + 1112 * q^41 + 1812 * q^42 + 833 * q^43 + 1392 * q^44 + 3841 * q^45 + 782 * q^46 + 2484 * q^47 + 2034 * q^48 + 4727 * q^49 + 1248 * q^50 + 932 * q^51 + 2118 * q^52 + 5077 * q^53 + 1537 * q^54 + 1736 * q^55 + 2281 * q^56 + 1426 * q^57 + 992 * q^58 + 2977 * q^59 + 1418 * q^60 + 3363 * q^61 + 3438 * q^62 + 3194 * q^63 + 6138 * q^64 + 4640 * q^65 + 288 * q^66 + 955 * q^67 + 8553 * q^68 + 4440 * q^69 + 2203 * q^70 + 2458 * q^71 + 4495 * q^72 + 3724 * q^73 + 2099 * q^74 + 4491 * q^75 + 2260 * q^76 + 9774 * q^77 + 1057 * q^78 + 1638 * q^79 + 8221 * q^80 + 10151 * q^81 + 1018 * q^82 + 6121 * q^83 + 4847 * q^84 + 3836 * q^85 + 2305 * q^86 + 3894 * q^87 + 5815 * q^88 + 8110 * q^89 + 4951 * q^90 + 2312 * q^91 + 13138 * q^92 + 9250 * q^93 - 813 * q^94 + 4858 * q^95 + 6882 * q^96 + 4486 * q^97 + 4216 * q^98 + 4969 * q^99

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