LMFDB - Embedded newform 547.4.a.b.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.54195 q^{2} +10.1442 q^{3} -1.53851 q^{4} +19.6797 q^{5} -25.7861 q^{6} -26.4188 q^{7} +24.2464 q^{8} +75.9054 q^{9} +O(q^{10})$	\(q-2.54195 q^{2} +10.1442 q^{3} -1.53851 q^{4} +19.6797 q^{5} -25.7861 q^{6} -26.4188 q^{7} +24.2464 q^{8} +75.9054 q^{9} -50.0248 q^{10} +45.5338 q^{11} -15.6070 q^{12} +60.7033 q^{13} +67.1552 q^{14} +199.636 q^{15} -49.3249 q^{16} -3.74205 q^{17} -192.947 q^{18} -134.223 q^{19} -30.2775 q^{20} -267.999 q^{21} -115.745 q^{22} -117.498 q^{23} +245.961 q^{24} +262.292 q^{25} -154.305 q^{26} +496.107 q^{27} +40.6456 q^{28} +183.148 q^{29} -507.464 q^{30} +151.099 q^{31} -68.5897 q^{32} +461.906 q^{33} +9.51210 q^{34} -519.915 q^{35} -116.781 q^{36} -168.953 q^{37} +341.187 q^{38} +615.789 q^{39} +477.162 q^{40} -325.095 q^{41} +681.238 q^{42} -15.4780 q^{43} -70.0542 q^{44} +1493.80 q^{45} +298.674 q^{46} -195.023 q^{47} -500.363 q^{48} +354.954 q^{49} -666.733 q^{50} -37.9602 q^{51} -93.3926 q^{52} +171.362 q^{53} -1261.08 q^{54} +896.094 q^{55} -640.561 q^{56} -1361.59 q^{57} -465.553 q^{58} -98.5726 q^{59} -307.141 q^{60} -201.907 q^{61} -384.087 q^{62} -2005.33 q^{63} +568.951 q^{64} +1194.63 q^{65} -1174.14 q^{66} +100.565 q^{67} +5.75718 q^{68} -1191.93 q^{69} +1321.60 q^{70} -408.364 q^{71} +1840.43 q^{72} -49.3758 q^{73} +429.470 q^{74} +2660.75 q^{75} +206.503 q^{76} -1202.95 q^{77} -1565.30 q^{78} +781.289 q^{79} -970.702 q^{80} +2983.18 q^{81} +826.373 q^{82} -148.667 q^{83} +412.318 q^{84} -73.6426 q^{85} +39.3441 q^{86} +1857.90 q^{87} +1104.03 q^{88} +138.929 q^{89} -3797.16 q^{90} -1603.71 q^{91} +180.772 q^{92} +1532.79 q^{93} +495.739 q^{94} -2641.47 q^{95} -695.790 q^{96} -1414.47 q^{97} -902.274 q^{98} +3456.26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.54195	−0.898714	−0.449357	−	0.893352i	$-0.648347\pi$
$2$	−2.54195	−0.898714	−0.449357	+	0.893352i	$0.648347\pi$
$3$	10.1442	1.95226	0.976129	−	0.217192i	$-0.0696897\pi$
$3$	10.1442	1.95226	0.976129	+	0.217192i	$0.0696897\pi$
$4$	−1.53851	−0.192314
$5$	19.6797	1.76021	0.880105	−	0.474779i	$-0.157472\pi$
$5$	19.6797	1.76021	0.880105	+	0.474779i	$0.157472\pi$
$6$	−25.7861	−1.75452
$7$	−26.4188	−1.42648	−0.713241	−	0.700919i	$-0.752773\pi$
$7$	−26.4188	−1.42648	−0.713241	+	0.700919i	$0.752773\pi$
$8$	24.2464	1.07155
$9$	75.9054	2.81131
$10$	−50.0248	−1.58192
$11$	45.5338	1.24809	0.624044	−	0.781389i	$-0.285489\pi$
$11$	45.5338	1.24809	0.624044	+	0.781389i	$0.285489\pi$
$12$	−15.6070	−0.375446
$13$	60.7033	1.29508	0.647541	−	0.762030i	$-0.275797\pi$
$13$	60.7033	1.29508	0.647541	+	0.762030i	$0.275797\pi$
$14$	67.1552	1.28200
$15$	199.636	3.43638
$16$	−49.3249	−0.770702
$17$	−3.74205	−0.0533871	−0.0266936	−	0.999644i	$-0.508498\pi$
$17$	−3.74205	−0.0533871	−0.0266936	+	0.999644i	$0.508498\pi$
$18$	−192.947	−2.52656
$19$	−134.223	−1.62067	−0.810337	−	0.585964i	$-0.800716\pi$
$19$	−134.223	−1.62067	−0.810337	+	0.585964i	$0.800716\pi$
$20$	−30.2775	−0.338512
$21$	−267.999	−2.78486
$22$	−115.745	−1.12167
$23$	−117.498	−1.06522	−0.532610	−	0.846361i	$-0.678789\pi$
$23$	−117.498	−1.06522	−0.532610	+	0.846361i	$0.678789\pi$
$24$	245.961	2.09194
$25$	262.292	2.09834
$26$	−154.305	−1.16391
$27$	496.107	3.53615
$28$	40.6456	0.274332
$29$	183.148	1.17275	0.586375	−	0.810039i	$-0.300554\pi$
$29$	183.148	1.17275	0.586375	+	0.810039i	$0.300554\pi$
$30$	−507.464	−3.08832
$31$	151.099	0.875428	0.437714	−	0.899114i	$-0.355788\pi$
$31$	151.099	0.875428	0.437714	+	0.899114i	$0.355788\pi$
$32$	−68.5897	−0.378908
$33$	461.906	2.43659
$34$	9.51210	0.0479797
$35$	−519.915	−2.51091
$36$	−116.781	−0.540653
$37$	−168.953	−0.750695	−0.375347	−	0.926884i	$-0.622477\pi$
$37$	−168.953	−0.750695	−0.375347	+	0.926884i	$0.622477\pi$
$38$	341.187	1.45652
$39$	615.789	2.52834
$40$	477.162	1.88615
$41$	−325.095	−1.23832	−0.619162	−	0.785264i	$-0.712527\pi$
$41$	−325.095	−1.23832	−0.619162	+	0.785264i	$0.712527\pi$
$42$	681.238	2.50279
$43$	−15.4780	−0.0548922	−0.0274461	−	0.999623i	$-0.508737\pi$
$43$	−15.4780	−0.0548922	−0.0274461	+	0.999623i	$0.508737\pi$
$44$	−70.0542	−0.240024
$45$	1493.80	4.94850
$46$	298.674	0.957327
$47$	−195.023	−0.605257	−0.302629	−	0.953109i	$-0.597864\pi$
$47$	−195.023	−0.605257	−0.302629	+	0.953109i	$0.597864\pi$
$48$	−500.363	−1.50461
$49$	354.954	1.03485
$50$	−666.733	−1.88580
$51$	−37.9602	−0.104225
$52$	−93.3926	−0.249062
$53$	171.362	0.444121	0.222060	−	0.975033i	$-0.428722\pi$
$53$	171.362	0.444121	0.222060	+	0.975033i	$0.428722\pi$
$54$	−1261.08	−3.17798
$55$	896.094	2.19690
$56$	−640.561	−1.52854
$57$	−1361.59	−3.16398
$58$	−465.553	−1.05397
$59$	−98.5726	−0.217510	−0.108755	−	0.994069i	$-0.534686\pi$
$59$	−98.5726	−0.217510	−0.108755	+	0.994069i	$0.534686\pi$
$60$	−307.141	−0.660863
$61$	−201.907	−0.423796	−0.211898	−	0.977292i	$-0.567965\pi$
$61$	−201.907	−0.423796	−0.211898	+	0.977292i	$0.567965\pi$
$62$	−384.087	−0.786759
$63$	−2005.33	−4.01028
$64$	568.951	1.11123
$65$	1194.63	2.27962
$66$	−1174.14	−2.18980
$67$	100.565	0.183373	0.0916865	−	0.995788i	$-0.470774\pi$
$67$	100.565	0.183373	0.0916865	+	0.995788i	$0.470774\pi$
$68$	5.75718	0.0102671
$69$	−1191.93	−2.07958
$70$	1321.60	2.25659
$71$	−408.364	−0.682590	−0.341295	−	0.939956i	$-0.610866\pi$
$71$	−408.364	−0.682590	−0.341295	+	0.939956i	$0.610866\pi$
$72$	1840.43	3.01246
$73$	−49.3758	−0.0791644	−0.0395822	−	0.999216i	$-0.512603\pi$
$73$	−49.3758	−0.0791644	−0.0395822	+	0.999216i	$0.512603\pi$
$74$	429.470	0.674660
$75$	2660.75	4.09650
$76$	206.503	0.311678
$77$	−1202.95	−1.78037
$78$	−1565.30	−2.27225
$79$	781.289	1.11268	0.556341	−	0.830954i	$-0.312205\pi$
$79$	781.289	1.11268	0.556341	+	0.830954i	$0.312205\pi$
$80$	−970.702	−1.35660
$81$	2983.18	4.09216
$82$	826.373	1.11290
$83$	−148.667	−0.196606	−0.0983032	−	0.995157i	$-0.531342\pi$
$83$	−148.667	−0.196606	−0.0983032	+	0.995157i	$0.531342\pi$
$84$	412.318	0.535567
$85$	−73.6426	−0.0939725
$86$	39.3441	0.0493324
$87$	1857.90	2.28951
$88$	1104.03	1.33739
$89$	138.929	0.165466	0.0827330	−	0.996572i	$-0.473635\pi$
$89$	138.929	0.165466	0.0827330	+	0.996572i	$0.473635\pi$
$90$	−3797.16	−4.44728
$91$	−1603.71	−1.84741
$92$	180.772	0.204856
$93$	1532.79	1.70906
$94$	495.739	0.543953
$95$	−2641.47	−2.85273
$96$	−695.790	−0.739727
$97$	−1414.47	−1.48059	−0.740297	−	0.672280i	$-0.765315\pi$
$97$	−1414.47	−1.48059	−0.740297	+	0.672280i	$0.765315\pi$
$98$	−902.274	−0.930035
$99$	3456.26	3.50876
$100$	−403.539	−0.403539
$101$	−1055.10	−1.03947	−0.519735	−	0.854327i	$-0.673969\pi$
$101$	−1055.10	−1.03947	−0.519735	+	0.854327i	$0.673969\pi$
$102$	96.4929	0.0936688
$103$	982.056	0.939465	0.469732	−	0.882809i	$-0.344350\pi$
$103$	982.056	0.939465	0.469732	+	0.882809i	$0.344350\pi$
$104$	1471.84	1.38774
$105$	−5274.14	−4.90194
$106$	−435.593	−0.399138
$107$	1557.14	1.40686	0.703431	−	0.710764i	$-0.251651\pi$
$107$	1557.14	1.40686	0.703431	+	0.710764i	$0.251651\pi$
$108$	−763.266	−0.680049
$109$	1046.99	0.920031	0.460016	−	0.887911i	$-0.347844\pi$
$109$	1046.99	0.920031	0.460016	+	0.887911i	$0.347844\pi$
$110$	−2277.82	−1.97438
$111$	−1713.90	−1.46555
$112$	1303.11	1.09939
$113$	561.461	0.467414	0.233707	−	0.972307i	$-0.424914\pi$
$113$	561.461	0.467414	0.233707	+	0.972307i	$0.424914\pi$
$114$	3461.08	2.84351
$115$	−2312.33	−1.87501
$116$	−281.775	−0.225536
$117$	4607.71	3.64088
$118$	250.566	0.195479
$119$	98.8606	0.0761558
$120$	4840.45	3.68225
$121$	742.330	0.557724
$122$	513.237	0.380872
$123$	−3297.84	−2.41753
$124$	−232.468	−0.168357
$125$	2701.88	1.93330
$126$	5097.44	3.60410
$127$	−636.281	−0.444574	−0.222287	−	0.974981i	$-0.571352\pi$
$127$	−636.281	−0.444574	−0.222287	+	0.974981i	$0.571352\pi$
$128$	−897.524	−0.619771
$129$	−157.012	−0.107164
$130$	−3036.67	−2.04872
$131$	−1725.70	−1.15096	−0.575478	−	0.817817i	$-0.695184\pi$
$131$	−1725.70	−1.15096	−0.575478	+	0.817817i	$0.695184\pi$
$132$	−710.646	−0.468589
$133$	3546.01	2.31186
$134$	−255.631	−0.164800
$135$	9763.27	6.22436
$136$	−90.7312	−0.0572069
$137$	1804.68	1.12543	0.562715	−	0.826651i	$-0.309757\pi$
$137$	1804.68	1.12543	0.562715	+	0.826651i	$0.309757\pi$
$138$	3029.82	1.86895
$139$	−2036.76	−1.24285	−0.621424	−	0.783475i	$-0.713445\pi$
$139$	−2036.76	−1.24285	−0.621424	+	0.783475i	$0.713445\pi$
$140$	799.895	0.482882
$141$	−1978.36	−1.18162
$142$	1038.04	0.613453
$143$	2764.06	1.61638
$144$	−3744.03	−2.16668
$145$	3604.31	2.06429
$146$	125.511	0.0711461
$147$	3600.73	2.02030
$148$	259.936	0.144369
$149$	−1339.32	−0.736387	−0.368194	−	0.929749i	$-0.620024\pi$
$149$	−1339.32	−0.736387	−0.368194	+	0.929749i	$0.620024\pi$
$150$	−6763.49	−3.68158
$151$	−1119.73	−0.603458	−0.301729	−	0.953394i	$-0.597564\pi$
$151$	−1119.73	−0.603458	−0.301729	+	0.953394i	$0.597564\pi$
$152$	−3254.42	−1.73663
$153$	−284.042	−0.150088
$154$	3057.83	1.60005
$155$	2973.60	1.54094
$156$	−947.396	−0.486233
$157$	3259.24	1.65679	0.828393	−	0.560148i	$-0.189256\pi$
$157$	3259.24	1.65679	0.828393	+	0.560148i	$0.189256\pi$
$158$	−1985.99	−0.999982
$159$	1738.34	0.867038
$160$	−1349.83	−0.666958
$161$	3104.16	1.51952
$162$	−7583.09	−3.67768
$163$	360.770	0.173360	0.0866801	−	0.996236i	$-0.472374\pi$
$163$	360.770	0.173360	0.0866801	+	0.996236i	$0.472374\pi$
$164$	500.161	0.238146
$165$	9090.18	4.28891
$166$	377.904	0.176693
$167$	−3573.53	−1.65585	−0.827927	−	0.560835i	$-0.810480\pi$
$167$	−3573.53	−1.65585	−0.827927	+	0.560835i	$0.810480\pi$
$168$	−6497.99	−2.98411
$169$	1487.89	0.677239
$170$	187.196	0.0844544
$171$	−10188.2	−4.55622
$172$	23.8130	0.0105565
$173$	2879.47	1.26544	0.632722	−	0.774379i	$-0.281937\pi$
$173$	2879.47	1.26544	0.632722	+	0.774379i	$0.281937\pi$
$174$	−4722.68	−2.05762
$175$	−6929.45	−2.99324
$176$	−2245.95	−0.961904
$177$	−999.943	−0.424635
$178$	−353.151	−0.148707
$179$	3146.48	1.31385	0.656925	−	0.753956i	$-0.271857\pi$
$179$	3146.48	1.31385	0.656925	+	0.753956i	$0.271857\pi$
$180$	−2298.22	−0.951663
$181$	1774.94	0.728898	0.364449	−	0.931223i	$-0.381257\pi$
$181$	1774.94	0.728898	0.364449	+	0.931223i	$0.381257\pi$
$182$	4076.55	1.66029
$183$	−2048.19	−0.827360
$184$	−2848.90	−1.14143
$185$	−3324.95	−1.32138
$186$	−3896.26	−1.53596
$187$	−170.390	−0.0666318
$188$	300.045	0.116399
$189$	−13106.6	−5.04425
$190$	6714.47	2.56379
$191$	893.274	0.338404	0.169202	−	0.985581i	$-0.445881\pi$
$191$	893.274	0.338404	0.169202	+	0.985581i	$0.445881\pi$
$192$	5771.57	2.16941
$193$	2277.26	0.849331	0.424666	−	0.905350i	$-0.360392\pi$
$193$	2277.26	0.849331	0.424666	+	0.905350i	$0.360392\pi$
$194$	3595.50	1.33063
$195$	12118.6	4.45040
$196$	−546.100	−0.199016
$197$	2482.05	0.897657	0.448828	−	0.893618i	$-0.351841\pi$
$197$	2482.05	0.897657	0.448828	+	0.893618i	$0.351841\pi$
$198$	−8785.64	−3.15337
$199$	−5271.88	−1.87796	−0.938979	−	0.343975i	$-0.888226\pi$
$199$	−5271.88	−1.87796	−0.938979	+	0.343975i	$0.888226\pi$
$200$	6359.64	2.24847
$201$	1020.16	0.357992
$202$	2682.01	0.934186
$203$	−4838.56	−1.67291
$204$	58.4022	0.0200440
$205$	−6397.78	−2.17971
$206$	−2496.33	−0.844310
$207$	−8918.74	−2.99466
$208$	−2994.19	−0.998123
$209$	−6111.68	−2.02274
$210$	13406.6	4.40544
$211$	257.449	0.0839976	0.0419988	−	0.999118i	$-0.486627\pi$
$211$	257.449	0.0839976	0.0419988	+	0.999118i	$0.486627\pi$
$212$	−263.642	−0.0854105
$213$	−4142.54	−1.33259
$214$	−3958.16	−1.26437
$215$	−304.602	−0.0966218
$216$	12028.8	3.78915
$217$	−3991.87	−1.24878
$218$	−2661.39	−0.826845
$219$	−500.879	−0.154549
$220$	−1378.65	−0.422493
$221$	−227.155	−0.0691407
$222$	4356.64	1.31711
$223$	−3711.96	−1.11467	−0.557335	−	0.830288i	$-0.688176\pi$
$223$	−3711.96	−1.11467	−0.557335	+	0.830288i	$0.688176\pi$
$224$	1812.06	0.540506
$225$	19909.4	5.89908
$226$	−1427.20	−0.420072
$227$	1358.14	0.397106	0.198553	−	0.980090i	$-0.436376\pi$
$227$	1358.14	0.397106	0.198553	+	0.980090i	$0.436376\pi$
$228$	2094.81	0.608475
$229$	3258.81	0.940385	0.470192	−	0.882564i	$-0.344185\pi$
$229$	3258.81	0.940385	0.470192	+	0.882564i	$0.344185\pi$
$230$	5877.82	1.68510
$231$	−12203.0	−3.47575
$232$	4440.68	1.25666
$233$	−5161.66	−1.45129	−0.725647	−	0.688067i	$-0.758459\pi$
$233$	−5161.66	−1.45129	−0.725647	+	0.688067i	$0.758459\pi$
$234$	−11712.6	−3.27211
$235$	−3838.01	−1.06538
$236$	151.655	0.0418301
$237$	7925.57	2.17224
$238$	−251.298	−0.0684422
$239$	−4873.28	−1.31894	−0.659469	−	0.751732i	$-0.729219\pi$
$239$	−4873.28	−1.31894	−0.659469	+	0.751732i	$0.729219\pi$
$240$	−9847.02	−2.64843
$241$	505.325	0.135066	0.0675328	−	0.997717i	$-0.478487\pi$
$241$	505.325	0.135066	0.0675328	+	0.997717i	$0.478487\pi$
$242$	−1886.96	−0.501234
$243$	16867.2	4.45280
$244$	310.636	0.0815018
$245$	6985.40	1.82155
$246$	8382.92	2.17266
$247$	−8147.77	−2.09891
$248$	3663.61	0.938063
$249$	−1508.11	−0.383827
$250$	−6868.02	−1.73749
$251$	−3363.19	−0.845747	−0.422873	−	0.906189i	$-0.638978\pi$
$251$	−3363.19	−0.845747	−0.422873	+	0.906189i	$0.638978\pi$
$252$	3085.22	0.771232
$253$	−5350.14	−1.32949
$254$	1617.39	0.399544
$255$	−747.048	−0.183459
$256$	−2270.15	−0.554235
$257$	−7592.76	−1.84289	−0.921446	−	0.388506i	$-0.872991\pi$
$257$	−7592.76	−1.84289	−0.921446	+	0.388506i	$0.872991\pi$
$258$	399.116	0.0963096
$259$	4463.54	1.07085
$260$	−1837.94	−0.438401
$261$	13901.9	3.29697
$262$	4386.64	1.03438
$263$	−4624.06	−1.08415	−0.542076	−	0.840330i	$-0.682361\pi$
$263$	−4624.06	−1.08415	−0.542076	+	0.840330i	$0.682361\pi$
$264$	11199.5	2.61092
$265$	3372.36	0.781746
$266$	−9013.76	−2.07770
$267$	1409.33	0.323032
$268$	−154.720	−0.0352651
$269$	3302.68	0.748580	0.374290	−	0.927312i	$-0.377886\pi$
$269$	3302.68	0.748580	0.374290	+	0.927312i	$0.377886\pi$
$270$	−24817.7	−5.59392
$271$	5586.57	1.25225	0.626125	−	0.779723i	$-0.284640\pi$
$271$	5586.57	1.25225	0.626125	+	0.779723i	$0.284640\pi$
$272$	184.576	0.0411455
$273$	−16268.4	−3.60662
$274$	−4587.39	−1.01144
$275$	11943.2	2.61891
$276$	1833.79	0.399932
$277$	676.629	0.146768	0.0733839	−	0.997304i	$-0.476620\pi$
$277$	676.629	0.146768	0.0733839	+	0.997304i	$0.476620\pi$
$278$	5177.34	1.11696
$279$	11469.3	2.46110
$280$	−12606.1	−2.69056
$281$	−2696.71	−0.572499	−0.286249	−	0.958155i	$-0.592409\pi$
$281$	−2696.71	−0.572499	−0.286249	+	0.958155i	$0.592409\pi$
$282$	5028.89	1.06194
$283$	−3137.21	−0.658967	−0.329484	−	0.944161i	$-0.606875\pi$
$283$	−3137.21	−0.658967	−0.329484	+	0.944161i	$0.606875\pi$
$284$	628.272	0.131271
$285$	−26795.7	−5.56926
$286$	−7026.08	−1.45266
$287$	8588.62	1.76645
$288$	−5206.33	−1.06523
$289$	−4899.00	−0.997150
$290$	−9161.96	−1.85520
$291$	−14348.7	−2.89050
$292$	75.9651	0.0152244
$293$	−3967.92	−0.791154	−0.395577	−	0.918433i	$-0.629455\pi$
$293$	−3967.92	−0.791154	−0.395577	+	0.918433i	$0.629455\pi$
$294$	−9152.87	−1.81567
$295$	−1939.88	−0.382862
$296$	−4096.50	−0.804406
$297$	22589.7	4.41342
$298$	3404.49	0.661802
$299$	−7132.53	−1.37955
$300$	−4093.59	−0.787812
$301$	408.909	0.0783028
$302$	2846.29	0.542336
$303$	−10703.2	−2.02931
$304$	6620.53	1.24906
$305$	−3973.48	−0.745970
$306$	722.019	0.134886
$307$	−1629.73	−0.302975	−0.151488	−	0.988459i	$-0.548406\pi$
$307$	−1629.73	−0.302975	−0.151488	+	0.988459i	$0.548406\pi$
$308$	1850.75	0.342390
$309$	9962.21	1.83408
$310$	−7558.72	−1.38486
$311$	4044.14	0.737370	0.368685	−	0.929554i	$-0.379808\pi$
$311$	4044.14	0.737370	0.368685	+	0.929554i	$0.379808\pi$
$312$	14930.6	2.70923
$313$	−2004.94	−0.362064	−0.181032	−	0.983477i	$-0.557944\pi$
$313$	−2004.94	−0.362064	−0.181032	+	0.983477i	$0.557944\pi$
$314$	−8284.80	−1.48898
$315$	−39464.4	−7.05894
$316$	−1202.02	−0.213984
$317$	2366.21	0.419241	0.209621	−	0.977783i	$-0.432777\pi$
$317$	2366.21	0.419241	0.209621	+	0.977783i	$0.432777\pi$
$318$	−4418.76	−0.779219
$319$	8339.44	1.46370
$320$	11196.8	1.95600
$321$	15796.0	2.74656
$322$	−7890.61	−1.36561
$323$	502.269	0.0865231
$324$	−4589.65	−0.786978
$325$	15922.0	2.71752
$326$	−917.058	−0.155801
$327$	10620.9	1.79614
$328$	−7882.37	−1.32692
$329$	5152.29	0.863388
$330$	−23106.8	−3.85450
$331$	−1633.45	−0.271246	−0.135623	−	0.990761i	$-0.543304\pi$
$331$	−1633.45	−0.271246	−0.135623	+	0.990761i	$0.543304\pi$
$332$	228.726	0.0378101
$333$	−12824.4	−2.11044
$334$	9083.71	1.48814
$335$	1979.10	0.322775
$336$	13219.0	2.14630
$337$	−9376.46	−1.51563	−0.757817	−	0.652468i	$-0.773734\pi$
$337$	−9376.46	−1.51563	−0.757817	+	0.652468i	$0.773734\pi$
$338$	−3782.15	−0.608644
$339$	5695.59	0.912513
$340$	113.300	0.0180722
$341$	6880.13	1.09261
$342$	25897.9	4.09474
$343$	−315.805	−0.0497140
$344$	−375.284	−0.0588197
$345$	−23456.8	−3.66050
$346$	−7319.45	−1.13727
$347$	−886.146	−0.137092	−0.0685458	−	0.997648i	$-0.521836\pi$
$347$	−886.146	−0.137092	−0.0685458	+	0.997648i	$0.521836\pi$
$348$	−2858.39	−0.440304
$349$	−2452.39	−0.376141	−0.188071	−	0.982156i	$-0.560223\pi$
$349$	−2452.39	−0.376141	−0.188071	+	0.982156i	$0.560223\pi$
$350$	17614.3	2.69007
$351$	30115.4	4.57960
$352$	−3123.15	−0.472911
$353$	−5958.19	−0.898363	−0.449182	−	0.893440i	$-0.648284\pi$
$353$	−5958.19	−0.898363	−0.449182	+	0.893440i	$0.648284\pi$
$354$	2541.80	0.381625
$355$	−8036.50	−1.20150
$356$	−213.744	−0.0318214
$357$	1002.86	0.148676
$358$	−7998.19	−1.18077
$359$	−2460.46	−0.361721	−0.180861	−	0.983509i	$-0.557888\pi$
$359$	−2460.46	−0.361721	−0.180861	+	0.983509i	$0.557888\pi$
$360$	36219.2	5.30255
$361$	11156.8	1.62659
$362$	−4511.81	−0.655070
$363$	7530.37	1.08882
$364$	2467.32	0.355282
$365$	−971.703	−0.139346
$366$	5206.40	0.743559
$367$	−6776.58	−0.963855	−0.481927	−	0.876211i	$-0.660063\pi$
$367$	−6776.58	−0.963855	−0.481927	+	0.876211i	$0.660063\pi$
$368$	5795.58	0.820967
$369$	−24676.4	−3.48131
$370$	8451.85	1.18754
$371$	−4527.19	−0.633530
$372$	−2358.21	−0.328676
$373$	−13180.5	−1.82965	−0.914825	−	0.403851i	$-0.867671\pi$
$373$	−13180.5	−1.82965	−0.914825	+	0.403851i	$0.867671\pi$
$374$	433.122	0.0598829
$375$	27408.4	3.77431
$376$	−4728.61	−0.648562
$377$	11117.7	1.51881
$378$	33316.2	4.53333
$379$	−10738.3	−1.45538	−0.727691	−	0.685905i	$-0.759407\pi$
$379$	−10738.3	−1.45538	−0.727691	+	0.685905i	$0.759407\pi$
$380$	4063.92	0.548618
$381$	−6454.58	−0.867922
$382$	−2270.66	−0.304128
$383$	5010.95	0.668532	0.334266	−	0.942479i	$-0.391512\pi$
$383$	5010.95	0.668532	0.334266	+	0.942479i	$0.391512\pi$
$384$	−9104.69	−1.20995
$385$	−23673.7	−3.13383
$386$	−5788.68	−0.763306
$387$	−1174.86	−0.154319
$388$	2176.17	0.284738
$389$	5112.94	0.666418	0.333209	−	0.942853i	$-0.391869\pi$
$389$	5112.94	0.666418	0.333209	+	0.942853i	$0.391869\pi$
$390$	−30804.7	−3.99964
$391$	439.684	0.0568690
$392$	8606.34	1.10889
$393$	−17505.9	−2.24696
$394$	−6309.23	−0.806737
$395$	15375.6	1.95855
$396$	−5317.49	−0.674783
$397$	6766.45	0.855411	0.427706	−	0.903918i	$-0.359322\pi$
$397$	6766.45	0.855411	0.427706	+	0.903918i	$0.359322\pi$
$398$	13400.8	1.68775
$399$	35971.5	4.51335
$400$	−12937.5	−1.61719
$401$	5634.38	0.701665	0.350832	−	0.936438i	$-0.385899\pi$
$401$	5634.38	0.701665	0.350832	+	0.936438i	$0.385899\pi$
$402$	−2593.18	−0.321732
$403$	9172.24	1.13375
$404$	1623.28	0.199904
$405$	58708.3	7.20305
$406$	12299.4	1.50347
$407$	−7693.08	−0.936933
$408$	−920.398	−0.111683
$409$	−13288.3	−1.60652	−0.803259	−	0.595630i	$-0.796902\pi$
$409$	−13288.3	−1.60652	−0.803259	+	0.595630i	$0.796902\pi$
$410$	16262.8	1.95893
$411$	18307.1	2.19713
$412$	−1510.90	−0.180672
$413$	2604.17	0.310273
$414$	22671.0	2.69134
$415$	−2925.73	−0.346069
$416$	−4163.62	−0.490718
$417$	−20661.4	−2.42636
$418$	15535.6	1.81787
$419$	1696.58	0.197812	0.0989062	−	0.995097i	$-0.468466\pi$
$419$	1696.58	0.197812	0.0989062	+	0.995097i	$0.468466\pi$
$420$	8114.31	0.942709
$421$	10328.2	1.19564	0.597820	−	0.801631i	$-0.296034\pi$
$421$	10328.2	1.19564	0.597820	+	0.801631i	$0.296034\pi$
$422$	−654.420	−0.0754898
$423$	−14803.3	−1.70157
$424$	4154.91	0.475897
$425$	−981.511	−0.112024
$426$	10530.1	1.19762
$427$	5334.15	0.604538
$428$	−2395.67	−0.270559
$429$	28039.2	3.15559
$430$	774.282	0.0868354
$431$	−14009.1	−1.56565	−0.782826	−	0.622241i	$-0.786223\pi$
$431$	−14009.1	−1.56565	−0.782826	+	0.622241i	$0.786223\pi$
$432$	−24470.5	−2.72531
$433$	3772.62	0.418708	0.209354	−	0.977840i	$-0.432864\pi$
$433$	3772.62	0.418708	0.209354	+	0.977840i	$0.432864\pi$
$434$	10147.1	1.12230
$435$	36562.9	4.03002
$436$	−1610.80	−0.176935
$437$	15770.9	1.72637
$438$	1273.21	0.138896
$439$	11405.2	1.23996	0.619980	−	0.784618i	$-0.287141\pi$
$439$	11405.2	1.23996	0.619980	+	0.784618i	$0.287141\pi$
$440$	21727.0	2.35408
$441$	26942.9	2.90929
$442$	577.416	0.0621377
$443$	−12807.6	−1.37360	−0.686802	−	0.726844i	$-0.740986\pi$
$443$	−12807.6	−1.37360	−0.686802	+	0.726844i	$0.740986\pi$
$444$	2636.85	0.281845
$445$	2734.09	0.291255
$446$	9435.60	1.00177
$447$	−13586.4	−1.43762
$448$	−15031.0	−1.58515
$449$	1949.93	0.204951	0.102476	−	0.994736i	$-0.467324\pi$
$449$	1949.93	0.204951	0.102476	+	0.994736i	$0.467324\pi$
$450$	−50608.6	−5.30158
$451$	−14802.8	−1.54554
$452$	−863.813	−0.0898901
$453$	−11358.8	−1.17811
$454$	−3452.32	−0.356884
$455$	−31560.6	−3.25183
$456$	−33013.5	−3.39035
$457$	−9752.85	−0.998291	−0.499145	−	0.866518i	$-0.666353\pi$
$457$	−9752.85	−0.998291	−0.499145	+	0.866518i	$0.666353\pi$
$458$	−8283.72	−0.845137
$459$	−1856.46	−0.188785
$460$	3557.54	0.360590
$461$	−9074.77	−0.916820	−0.458410	−	0.888741i	$-0.651581\pi$
$461$	−9074.77	−0.916820	−0.458410	+	0.888741i	$0.651581\pi$
$462$	31019.4	3.12371
$463$	8559.09	0.859125	0.429562	−	0.903037i	$-0.358668\pi$
$463$	8559.09	0.859125	0.429562	+	0.903037i	$0.358668\pi$
$464$	−9033.77	−0.903841
$465$	30164.9	3.00830
$466$	13120.7	1.30430
$467$	−910.481	−0.0902185	−0.0451092	−	0.998982i	$-0.514364\pi$
$467$	−910.481	−0.0902185	−0.0451092	+	0.998982i	$0.514364\pi$
$468$	−7089.00	−0.700191
$469$	−2656.81	−0.261578
$470$	9756.01	0.957471
$471$	33062.4	3.23447
$472$	−2390.03	−0.233072
$473$	−704.771	−0.0685103
$474$	−20146.4	−1.95222
$475$	−35205.6	−3.40072
$476$	−152.098	−0.0146458
$477$	13007.3	1.24856
$478$	12387.6	1.18535
$479$	−13177.8	−1.25701	−0.628506	−	0.777805i	$-0.716333\pi$
$479$	−13177.8	−1.25701	−0.628506	+	0.777805i	$0.716333\pi$
$480$	−13693.0	−1.30207
$481$	−10256.0	−0.972212
$482$	−1284.51	−0.121385
$483$	31489.3	2.96649
$484$	−1142.08	−0.107258
$485$	−27836.4	−2.60615
$486$	−42875.5	−4.00179
$487$	618.787	0.0575768	0.0287884	−	0.999586i	$-0.490835\pi$
$487$	618.787	0.0575768	0.0287884	+	0.999586i	$0.490835\pi$
$488$	−4895.52	−0.454118
$489$	3659.73	0.338444
$490$	−17756.5	−1.63706
$491$	−16033.2	−1.47366	−0.736832	−	0.676076i	$-0.763679\pi$
$491$	−16033.2	−1.47366	−0.736832	+	0.676076i	$0.763679\pi$
$492$	5073.75	0.464923
$493$	−685.350	−0.0626098
$494$	20711.2	1.88632
$495$	68018.4	6.17616
$496$	−7452.97	−0.674694
$497$	10788.5	0.973703
$498$	3833.54	0.344950
$499$	3542.78	0.317829	0.158914	−	0.987292i	$-0.449201\pi$
$499$	3542.78	0.317829	0.158914	+	0.987292i	$0.449201\pi$
$500$	−4156.86	−0.371801
$501$	−36250.7	−3.23266
$502$	8549.04	0.760084
$503$	795.590	0.0705241	0.0352620	−	0.999378i	$-0.488773\pi$
$503$	795.590	0.0705241	0.0352620	+	0.999378i	$0.488773\pi$
$504$	−48622.0	−4.29721
$505$	−20764.1	−1.82969
$506$	13599.8	1.19483
$507$	15093.5	1.32215
$508$	978.925	0.0854976
$509$	7445.08	0.648325	0.324162	−	0.946001i	$-0.394918\pi$
$509$	7445.08	0.648325	0.324162	+	0.946001i	$0.394918\pi$
$510$	1898.95	0.164877
$511$	1304.45	0.112927
$512$	12950.8	1.11787
$513$	−66588.9	−5.73094
$514$	19300.4	1.65623
$515$	19326.6	1.65366
$516$	241.564	0.0206091
$517$	−8880.16	−0.755414
$518$	−11346.1	−0.962390
$519$	29210.0	2.47047
$520$	28965.4	2.44272
$521$	−9558.83	−0.803800	−0.401900	−	0.915684i	$-0.631650\pi$
$521$	−9558.83	−0.803800	−0.401900	+	0.915684i	$0.631650\pi$
$522$	−35338.0	−2.96303
$523$	11354.5	0.949329	0.474665	−	0.880167i	$-0.342569\pi$
$523$	11354.5	0.949329	0.474665	+	0.880167i	$0.342569\pi$
$524$	2655.01	0.221345
$525$	−70293.9	−5.84358
$526$	11754.1	0.974341
$527$	−565.422	−0.0467365
$528$	−22783.5	−1.87788
$529$	1638.80	0.134693
$530$	−8572.37	−0.702566
$531$	−7482.19	−0.611487
$532$	−5455.56	−0.444603
$533$	−19734.3	−1.60373
$534$	−3582.44	−0.290314
$535$	30644.1	2.47637
$536$	2438.34	0.196493
$537$	31918.6	2.56497
$538$	−8395.24	−0.672759
$539$	16162.4	1.29158
$540$	−15020.9	−1.19703
$541$	−13017.5	−1.03450	−0.517249	−	0.855835i	$-0.673044\pi$
$541$	−13017.5	−1.03450	−0.517249	+	0.855835i	$0.673044\pi$
$542$	−14200.8	−1.12541
$543$	18005.4	1.42300
$544$	256.666	0.0202288
$545$	20604.5	1.61945
$546$	41353.4	3.24132
$547$	−547.000	−0.0427569
$547$	−547.000	−0.0427569
$548$	−2776.51	−0.216436
$549$	−15325.8	−1.19142
$550$	−30358.9	−2.35365
$551$	−24582.7	−1.90065
$552$	−28899.9	−2.22837
$553$	−20640.7	−1.58722
$554$	−1719.96	−0.131902
$555$	−33729.1	−2.57968
$556$	3133.58	0.239017
$557$	10318.8	0.784956	0.392478	−	0.919761i	$-0.371618\pi$
$557$	10318.8	0.784956	0.392478	+	0.919761i	$0.371618\pi$
$558$	−29154.2	−2.21182
$559$	−939.564	−0.0710900
$560$	25644.8	1.93516
$561$	−1728.48	−0.130082
$562$	6854.89	0.514513
$563$	15032.3	1.12529	0.562644	−	0.826699i	$-0.309784\pi$
$563$	15032.3	1.12529	0.562644	+	0.826699i	$0.309784\pi$
$564$	3043.73	0.227241
$565$	11049.4	0.822747
$566$	7974.62	0.592223
$567$	−78812.1	−5.83739
$568$	−9901.35	−0.731429
$569$	9487.29	0.698994	0.349497	−	0.936937i	$-0.386352\pi$
$569$	9487.29	0.698994	0.349497	+	0.936937i	$0.386352\pi$
$570$	68113.2	5.00517
$571$	9846.78	0.721672	0.360836	−	0.932629i	$-0.382491\pi$
$571$	9846.78	0.721672	0.360836	+	0.932629i	$0.382491\pi$
$572$	−4252.52	−0.310851
$573$	9061.58	0.660651
$574$	−21831.8	−1.58753
$575$	−30818.8	−2.23519
$576$	43186.4	3.12402
$577$	11087.2	0.799942	0.399971	−	0.916528i	$-0.369020\pi$
$577$	11087.2	0.799942	0.399971	+	0.916528i	$0.369020\pi$
$578$	12453.0	0.896152
$579$	23101.1	1.65811
$580$	−5545.26	−0.396991
$581$	3927.61	0.280456
$582$	36473.6	2.59773
$583$	7802.78	0.554302
$584$	−1197.18	−0.0848285
$585$	90678.5	6.40871
$586$	10086.2	0.711021
$587$	−535.110	−0.0376258	−0.0188129	−	0.999823i	$-0.505989\pi$
$587$	−535.110	−0.0376258	−0.0188129	+	0.999823i	$0.505989\pi$
$588$	−5539.76	−0.388530
$589$	−20281.0	−1.41878
$590$	4931.08	0.344084
$591$	25178.4	1.75246
$592$	8333.60	0.578562
$593$	−4040.97	−0.279836	−0.139918	−	0.990163i	$-0.544684\pi$
$593$	−4040.97	−0.279836	−0.139918	+	0.990163i	$0.544684\pi$
$594$	−57421.7	−3.96640
$595$	1945.55	0.134050
$596$	2060.56	0.141617
$597$	−53479.1	−3.66626
$598$	18130.5	1.23982
$599$	19276.6	1.31489	0.657447	−	0.753501i	$-0.271636\pi$
$599$	19276.6	1.31489	0.657447	+	0.753501i	$0.271636\pi$
$600$	64513.6	4.38959
$601$	15077.7	1.02335	0.511676	−	0.859179i	$-0.329025\pi$
$601$	15077.7	1.02335	0.511676	+	0.859179i	$0.329025\pi$
$602$	−1039.43	−0.0703718
$603$	7633.44	0.515519
$604$	1722.71	0.116053
$605$	14608.9	0.981710
$606$	27206.9	1.82377
$607$	17198.9	1.15005	0.575025	−	0.818136i	$-0.304992\pi$
$607$	17198.9	1.15005	0.575025	+	0.818136i	$0.304992\pi$
$608$	9206.30	0.614087
$609$	−49083.5	−3.26595
$610$	10100.4	0.670414
$611$	−11838.6	−0.783858
$612$	437.001	0.0288639
$613$	1292.21	0.0851415	0.0425708	−	0.999093i	$-0.486445\pi$
$613$	1292.21	0.0851415	0.0425708	+	0.999093i	$0.486445\pi$
$614$	4142.68	0.272288
$615$	−64900.5	−4.25535
$616$	−29167.2	−1.90776
$617$	−15329.2	−1.00021	−0.500107	−	0.865964i	$-0.666706\pi$
$617$	−15329.2	−1.00021	−0.500107	+	0.865964i	$0.666706\pi$
$618$	−25323.4	−1.64831
$619$	8162.70	0.530027	0.265013	−	0.964245i	$-0.414624\pi$
$619$	8162.70	0.530027	0.265013	+	0.964245i	$0.414624\pi$
$620$	−4574.91	−0.296343
$621$	−58291.7	−3.76677
$622$	−10280.0	−0.662685
$623$	−3670.35	−0.236034
$624$	−30373.7	−1.94859
$625$	20385.7	1.30468
$626$	5096.46	0.325392
$627$	−61998.3	−3.94892
$628$	−5014.36	−0.318622
$629$	632.231	0.0400774
$630$	100316.	6.34397
$631$	20986.4	1.32402	0.662009	−	0.749496i	$-0.269704\pi$
$631$	20986.4	1.32402	0.662009	+	0.749496i	$0.269704\pi$
$632$	18943.4	1.19229
$633$	2611.62	0.163985
$634$	−6014.77	−0.376778
$635$	−12521.9	−0.782543
$636$	−2674.45	−0.166743
$637$	21546.9	1.34022
$638$	−21198.4	−1.31544
$639$	−30997.0	−1.91897
$640$	−17663.0	−1.09093
$641$	−15091.4	−0.929913	−0.464956	−	0.885334i	$-0.653930\pi$
$641$	−15091.4	−0.929913	−0.464956	+	0.885334i	$0.653930\pi$
$642$	−40152.5	−2.46837
$643$	−14955.6	−0.917251	−0.458625	−	0.888630i	$-0.651658\pi$
$643$	−14955.6	−0.917251	−0.458625	+	0.888630i	$0.651658\pi$
$644$	−4775.78	−0.292224
$645$	−3089.95	−0.188631
$646$	−1276.74	−0.0777595
$647$	3131.11	0.190258	0.0951288	−	0.995465i	$-0.469674\pi$
$647$	3131.11	0.190258	0.0951288	+	0.995465i	$0.469674\pi$
$648$	72331.4	4.38495
$649$	−4488.39	−0.271471
$650$	−40472.9	−2.44227
$651$	−40494.4	−2.43794
$652$	−555.048	−0.0333395
$653$	12614.5	0.755964	0.377982	−	0.925813i	$-0.376618\pi$
$653$	12614.5	0.755964	0.377982	+	0.925813i	$0.376618\pi$
$654$	−26997.8	−1.61421
$655$	−33961.4	−2.02592
$656$	16035.3	0.954378
$657$	−3747.89	−0.222556
$658$	−13096.8	−0.775939
$659$	18041.4	1.06646	0.533228	−	0.845971i	$-0.320979\pi$
$659$	18041.4	1.06646	0.533228	+	0.845971i	$0.320979\pi$
$660$	−13985.3	−0.824815
$661$	14068.3	0.827828	0.413914	−	0.910316i	$-0.364161\pi$
$661$	14068.3	0.827828	0.413914	+	0.910316i	$0.364161\pi$
$662$	4152.13	0.243772
$663$	−2304.31	−0.134981
$664$	−3604.64	−0.210673
$665$	69784.5	4.06936
$666$	32599.1	1.89668
$667$	−21519.6	−1.24924
$668$	5497.90	0.318443
$669$	−37655.0	−2.17612
$670$	−5030.76	−0.290082
$671$	−9193.61	−0.528935
$672$	18381.9	1.05521
$673$	22277.0	1.27595	0.637976	−	0.770056i	$-0.279772\pi$
$673$	22277.0	1.27595	0.637976	+	0.770056i	$0.279772\pi$
$674$	23834.5	1.36212
$675$	130125.	7.42003
$676$	−2289.14	−0.130242
$677$	16243.8	0.922154	0.461077	−	0.887360i	$-0.347463\pi$
$677$	16243.8	0.922154	0.461077	+	0.887360i	$0.347463\pi$
$678$	−14477.9	−0.820088
$679$	37368.6	2.11204
$680$	−1785.57	−0.100696
$681$	13777.3	0.775253
$682$	−17488.9	−0.981944
$683$	−3485.21	−0.195253	−0.0976266	−	0.995223i	$-0.531125\pi$
$683$	−3485.21	−0.195253	−0.0976266	+	0.995223i	$0.531125\pi$
$684$	15674.7	0.876223
$685$	35515.6	1.98099
$686$	802.760	0.0446786
$687$	33058.1	1.83587
$688$	763.449	0.0423056
$689$	10402.3	0.575173
$690$	59626.0	3.28974
$691$	3698.94	0.203638	0.101819	−	0.994803i	$-0.467534\pi$
$691$	3698.94	0.203638	0.101819	+	0.994803i	$0.467534\pi$
$692$	−4430.09	−0.243362
$693$	−91310.4	−5.00519
$694$	2252.54	0.123206
$695$	−40082.9	−2.18767
$696$	45047.3	2.45332
$697$	1216.52	0.0661105
$698$	6233.84	0.338043
$699$	−52361.0	−2.83330
$700$	10661.0	0.575641
$701$	−7177.37	−0.386713	−0.193356	−	0.981129i	$-0.561937\pi$
$701$	−7177.37	−0.386713	−0.193356	+	0.981129i	$0.561937\pi$
$702$	−76551.7	−4.11575
$703$	22677.4	1.21663
$704$	25906.5	1.38692
$705$	−38933.6	−2.07990
$706$	15145.4	0.807372
$707$	27874.5	1.48279
$708$	1538.42	0.0816630
$709$	−5941.59	−0.314727	−0.157363	−	0.987541i	$-0.550299\pi$
$709$	−5941.59	−0.314727	−0.157363	+	0.987541i	$0.550299\pi$
$710$	20428.4	1.07981
$711$	59304.0	3.12809
$712$	3368.53	0.177305
$713$	−17753.9	−0.932522
$714$	−2549.23	−0.133617
$715$	54395.9	2.84516
$716$	−4840.89	−0.252671
$717$	−49435.6	−2.57491
$718$	6254.35	0.325084
$719$	−4517.86	−0.234336	−0.117168	−	0.993112i	$-0.537382\pi$
$719$	−4517.86	−0.234336	−0.117168	+	0.993112i	$0.537382\pi$
$720$	−73681.5	−3.81382
$721$	−25944.8	−1.34013
$722$	−28359.9	−1.46184
$723$	5126.13	0.263683
$724$	−2730.77	−0.140177
$725$	48038.4	2.46083
$726$	−19141.8	−0.978538
$727$	−10016.1	−0.510970	−0.255485	−	0.966813i	$-0.582235\pi$
$727$	−10016.1	−0.510970	−0.255485	+	0.966813i	$0.582235\pi$
$728$	−38884.2	−1.97959
$729$	90558.7	4.60086
$730$	2470.02	0.125232
$731$	57.9193	0.00293054
$732$	3151.16	0.159113
$733$	23472.3	1.18277	0.591383	−	0.806391i	$-0.298582\pi$
$733$	23472.3	1.18277	0.591383	+	0.806391i	$0.298582\pi$
$734$	17225.7	0.866229
$735$	70861.5	3.55614
$736$	8059.16	0.403620
$737$	4579.12	0.228866
$738$	62726.2	3.12870
$739$	−37625.5	−1.87291	−0.936453	−	0.350793i	$-0.885912\pi$
$739$	−37625.5	−1.87291	−0.936453	+	0.350793i	$0.885912\pi$
$740$	5115.47	0.254119
$741$	−82652.9	−4.09761
$742$	11507.9	0.569363
$743$	25029.5	1.23586	0.617930	−	0.786233i	$-0.287971\pi$
$743$	25029.5	1.23586	0.617930	+	0.786233i	$0.287971\pi$
$744$	37164.5	1.83134
$745$	−26357.6	−1.29620
$746$	33504.1	1.64433
$747$	−11284.6	−0.552722
$748$	262.146	0.0128142
$749$	−41137.7	−2.00686
$750$	−69670.8	−3.39202
$751$	−19956.0	−0.969647	−0.484823	−	0.874612i	$-0.661116\pi$
$751$	−19956.0	−0.969647	−0.484823	+	0.874612i	$0.661116\pi$
$752$	9619.51	0.466473
$753$	−34116.9	−1.65112
$754$	−28260.6	−1.36497
$755$	−22036.0	−1.06221
$756$	20164.6	0.970078
$757$	16443.2	0.789483	0.394741	−	0.918792i	$-0.370834\pi$
$757$	16443.2	0.789483	0.394741	+	0.918792i	$0.370834\pi$
$758$	27296.2	1.30797
$759$	−54273.0	−2.59550
$760$	−64046.1	−3.05684
$761$	19070.5	0.908418	0.454209	−	0.890895i	$-0.349922\pi$
$761$	19070.5	0.908418	0.454209	+	0.890895i	$0.349922\pi$
$762$	16407.2	0.780014
$763$	−27660.2	−1.31241
$764$	−1374.31	−0.0650796
$765$	−5589.87	−0.264186
$766$	−12737.6	−0.600818
$767$	−5983.69	−0.281693
$768$	−23028.9	−1.08201
$769$	29180.5	1.36837	0.684184	−	0.729309i	$-0.260158\pi$
$769$	29180.5	1.36837	0.684184	+	0.729309i	$0.260158\pi$
$770$	60177.4	2.81642
$771$	−77022.7	−3.59780
$772$	−3503.59	−0.163338
$773$	5996.68	0.279024	0.139512	−	0.990220i	$-0.455447\pi$
$773$	5996.68	0.279024	0.139512	+	0.990220i	$0.455447\pi$
$774$	2986.43	0.138689
$775$	39632.2	1.83694
$776$	−34295.8	−1.58653
$777$	45279.2	2.09058
$778$	−12996.8	−0.598919
$779$	43635.1	2.00692
$780$	−18644.5	−0.855873
$781$	−18594.4	−0.851933
$782$	−1117.65	−0.0511089
$783$	90861.2	4.14702
$784$	−17508.1	−0.797561
$785$	64140.9	2.91629
$786$	44499.1	2.01938
$787$	25637.6	1.16122	0.580611	−	0.814181i	$-0.302814\pi$
$787$	25637.6	1.16122	0.580611	+	0.814181i	$0.302814\pi$
$788$	−3818.65	−0.172632
$789$	−46907.5	−2.11654
$790$	−39083.8	−1.76018
$791$	−14833.1	−0.666758
$792$	83801.9	3.75981
$793$	−12256.4	−0.548851
$794$	−17199.9	−0.768770
$795$	34210.0	1.52617
$796$	8110.83	0.361157
$797$	−33108.5	−1.47147	−0.735737	−	0.677267i	$-0.763164\pi$
$797$	−33108.5	−1.47147	−0.735737	+	0.677267i	$0.763164\pi$
$798$	−91437.7	−4.05621
$799$	729.788	0.0323129
$800$	−17990.6	−0.795078
$801$	10545.5	0.465176
$802$	−14322.3	−0.630596
$803$	−2248.27	−0.0988041
$804$	−1569.52	−0.0688466
$805$	61089.1	2.67467
$806$	−23315.3	−1.01892
$807$	33503.2	1.46142
$808$	−25582.4	−1.11384
$809$	−1040.52	−0.0452196	−0.0226098	−	0.999744i	$-0.507198\pi$
$809$	−1040.52	−0.0452196	−0.0226098	+	0.999744i	$0.507198\pi$
$810$	−149233.	−6.47348
$811$	24306.0	1.05240	0.526202	−	0.850360i	$-0.323616\pi$
$811$	24306.0	1.05240	0.526202	+	0.850360i	$0.323616\pi$
$812$	7444.17	0.321723
$813$	56671.4	2.44472
$814$	19555.4	0.842035
$815$	7099.86	0.305150
$816$	1872.39	0.0803267
$817$	2077.49	0.0889625
$818$	33778.2	1.44380
$819$	−121730.	−5.19365
$820$	9843.04	0.419188
$821$	−6347.39	−0.269824	−0.134912	−	0.990858i	$-0.543075\pi$
$821$	−6347.39	−0.269824	−0.134912	+	0.990858i	$0.543075\pi$
$822$	−46535.6	−1.97459
$823$	−35895.9	−1.52035	−0.760177	−	0.649716i	$-0.774888\pi$
$823$	−35895.9	−1.52035	−0.760177	+	0.649716i	$0.774888\pi$
$824$	23811.3	1.00668
$825$	121154.	5.11279
$826$	−6619.67	−0.278847
$827$	−28060.5	−1.17988	−0.589939	−	0.807448i	$-0.700848\pi$
$827$	−28060.5	−1.17988	−0.589939	+	0.807448i	$0.700848\pi$
$828$	13721.6	0.575914
$829$	−2333.92	−0.0977809	−0.0488904	−	0.998804i	$-0.515569\pi$
$829$	−2333.92	−0.0977809	−0.0488904	+	0.998804i	$0.515569\pi$
$830$	7437.05	0.311017
$831$	6863.88	0.286529
$832$	34537.2	1.43914
$833$	−1328.26	−0.0552477
$834$	52520.1	2.18060
$835$	−70326.1	−2.91465
$836$	9402.87	0.389001
$837$	74961.5	3.09564
$838$	−4312.62	−0.177777
$839$	−9144.68	−0.376292	−0.188146	−	0.982141i	$-0.560248\pi$
$839$	−9144.68	−0.376292	−0.188146	+	0.982141i	$0.560248\pi$
$840$	−127879.	−5.25267
$841$	9154.28	0.375345
$842$	−26253.7	−1.07454
$843$	−27356.0	−1.11767
$844$	−396.087	−0.0161539
$845$	29281.4	1.19208
$846$	37629.3	1.52922
$847$	−19611.5	−0.795583
$848$	−8452.43	−0.342285
$849$	−31824.6	−1.28647
$850$	2494.95	0.100678
$851$	19851.7	0.799655
$852$	6373.33	0.256276
$853$	−26484.8	−1.06310	−0.531549	−	0.847028i	$-0.678390\pi$
$853$	−26484.8	−1.06310	−0.531549	+	0.847028i	$0.678390\pi$
$854$	−13559.1	−0.543306
$855$	−200502.	−8.01990
$856$	37754.9	1.50752
$857$	−8686.13	−0.346222	−0.173111	−	0.984902i	$-0.555382\pi$
$857$	−8686.13	−0.346222	−0.173111	+	0.984902i	$0.555382\pi$
$858$	−71274.2	−2.83597
$859$	20164.2	0.800925	0.400462	−	0.916313i	$-0.368850\pi$
$859$	20164.2	0.800925	0.400462	+	0.916313i	$0.368850\pi$
$860$	468.633	0.0185817
$861$	87124.9	3.44856
$862$	35610.5	1.40707
$863$	−21611.3	−0.852441	−0.426220	−	0.904619i	$-0.640155\pi$
$863$	−21611.3	−0.852441	−0.426220	+	0.904619i	$0.640155\pi$
$864$	−34027.9	−1.33987
$865$	56667.2	2.22745
$866$	−9589.81	−0.376299
$867$	−49696.5	−1.94669
$868$	6141.52	0.240158
$869$	35575.1	1.38872
$870$	−92941.1	−3.62184
$871$	6104.64	0.237483
$872$	25385.7	0.985858
$873$	−107366.	−4.16241
$874$	−40088.8	−1.55152
$875$	−71380.3	−2.75782
$876$	770.607	0.0297219
$877$	1977.68	0.0761476	0.0380738	−	0.999275i	$-0.487878\pi$
$877$	1977.68	0.0761476	0.0380738	+	0.999275i	$0.487878\pi$
$878$	−28991.5	−1.11437
$879$	−40251.5	−1.54454
$880$	−44199.8	−1.69315
$881$	6911.76	0.264317	0.132158	−	0.991229i	$-0.457809\pi$
$881$	6911.76	0.264317	0.132158	+	0.991229i	$0.457809\pi$
$882$	−68487.4	−2.61462
$883$	2976.74	0.113449	0.0567243	−	0.998390i	$-0.481934\pi$
$883$	2976.74	0.113449	0.0567243	+	0.998390i	$0.481934\pi$
$884$	349.480	0.0132967
$885$	−19678.6	−0.747446
$886$	32556.2	1.23448
$887$	−544.869	−0.0206256	−0.0103128	−	0.999947i	$-0.503283\pi$
$887$	−544.869	−0.0206256	−0.0103128	+	0.999947i	$0.503283\pi$
$888$	−41555.8	−1.57041
$889$	16809.8	0.634176
$890$	−6949.92	−0.261755
$891$	135836.	5.10737
$892$	5710.88	0.214366
$893$	26176.6	0.980925
$894$	34535.9	1.29201
$895$	61921.9	2.31265
$896$	23711.5	0.884092
$897$	−72354.0	−2.69323
$898$	−4956.63	−0.184192
$899$	27673.6	1.02666
$900$	−30630.8	−1.13447
$901$	−641.246	−0.0237103
$902$	37627.9	1.38899
$903$	4148.07	0.152867
$904$	13613.4	0.500857
$905$	34930.4	1.28301
$906$	28873.4	1.05878
$907$	−14682.9	−0.537528	−0.268764	−	0.963206i	$-0.586615\pi$
$907$	−14682.9	−0.537528	−0.268764	+	0.963206i	$0.586615\pi$
$908$	−2089.51	−0.0763688
$909$	−80087.9	−2.92227
$910$	80225.4	2.92247
$911$	26346.4	0.958173	0.479086	−	0.877768i	$-0.340968\pi$
$911$	26346.4	0.958173	0.479086	+	0.877768i	$0.340968\pi$
$912$	67160.2	2.43848
$913$	−6769.38	−0.245382
$914$	24791.2	0.897178
$915$	−40307.9	−1.45633
$916$	−5013.71	−0.180849
$917$	45591.0	1.64182
$918$	4719.02	0.169663
$919$	9472.87	0.340023	0.170012	−	0.985442i	$-0.445619\pi$
$919$	9472.87	0.340023	0.170012	+	0.985442i	$0.445619\pi$
$920$	−56065.7	−2.00916
$921$	−16532.3	−0.591486
$922$	23067.6	0.823959
$923$	−24789.1	−0.884011
$924$	18774.4	0.668434
$925$	−44315.1	−1.57521
$926$	−21756.8	−0.772107
$927$	74543.4	2.64113
$928$	−12562.1	−0.444365
$929$	−12848.8	−0.453772	−0.226886	−	0.973921i	$-0.572854\pi$
$929$	−12848.8	−0.453772	−0.226886	+	0.973921i	$0.572854\pi$
$930$	−76677.4	−2.70360
$931$	−47642.9	−1.67716
$932$	7941.26	0.279104
$933$	41024.7	1.43954
$934$	2314.39	0.0810806
$935$	−3353.23	−0.117286
$936$	111720.	3.90138
$937$	18438.5	0.642859	0.321429	−	0.946934i	$-0.395837\pi$
$937$	18438.5	0.642859	0.321429	+	0.946934i	$0.395837\pi$
$938$	6753.48	0.235084
$939$	−20338.6	−0.706843
$940$	5904.81	0.204887
$941$	47532.2	1.64666	0.823329	−	0.567564i	$-0.192114\pi$
$941$	47532.2	1.64666	0.823329	+	0.567564i	$0.192114\pi$
$942$	−84042.9	−2.90686
$943$	38198.0	1.31909
$944$	4862.09	0.167635
$945$	−257934.	−8.87893
$946$	1791.49	0.0615712
$947$	−49274.6	−1.69082	−0.845411	−	0.534116i	$-0.820644\pi$
$947$	−49274.6	−1.69082	−0.845411	+	0.534116i	$0.820644\pi$
$948$	−12193.6	−0.417752
$949$	−2997.27	−0.102524
$950$	89490.7	3.05628
$951$	24003.3	0.818467
$952$	2397.01	0.0816046
$953$	43010.7	1.46197	0.730983	−	0.682396i	$-0.239062\pi$
$953$	43010.7	1.46197	0.730983	+	0.682396i	$0.239062\pi$
$954$	−33063.9	−1.12210
$955$	17579.4	0.595661
$956$	7497.58	0.253650
$957$	84597.2	2.85751
$958$	33497.2	1.12969
$959$	−47677.4	−1.60541
$960$	113583.	3.81862
$961$	−6959.97	−0.233627
$962$	26070.2	0.873740
$963$	118195.	3.95512
$964$	−777.446	−0.0259750
$965$	44815.9	1.49500
$966$	−80044.2	−2.66602
$967$	53943.8	1.79391	0.896957	−	0.442118i	$-0.145773\pi$
$967$	53943.8	1.79391	0.896957	+	0.442118i	$0.145773\pi$
$968$	17998.8	0.597628
$969$	5095.13	0.168915
$970$	70758.6	2.34219
$971$	−21756.1	−0.719039	−0.359519	−	0.933138i	$-0.617059\pi$
$971$	−21756.1	−0.719039	−0.359519	+	0.933138i	$0.617059\pi$
$972$	−25950.3	−0.856334
$973$	53808.8	1.77290
$974$	−1572.92	−0.0517451
$975$	161517.	5.30530
$976$	9959.06	0.326621
$977$	−42175.7	−1.38108	−0.690542	−	0.723292i	$-0.742628\pi$
$977$	−42175.7	−1.38108	−0.690542	+	0.723292i	$0.742628\pi$
$978$	−9302.85	−0.304164
$979$	6325.98	0.206516
$980$	−10747.1	−0.350310
$981$	79472.2	2.58649
$982$	40755.6	1.32440
$983$	31351.5	1.01725	0.508625	−	0.860988i	$-0.330154\pi$
$983$	31351.5	1.01725	0.508625	+	0.860988i	$0.330154\pi$
$984$	−79960.6	−2.59050
$985$	48846.0	1.58006
$986$	1742.12	0.0562683
$987$	52266.0	1.68556
$988$	12535.4	0.403649
$989$	1818.63	0.0584723
$990$	−172899.	−5.55060
$991$	−13346.5	−0.427815	−0.213908	−	0.976854i	$-0.568619\pi$
$991$	−13346.5	−0.427815	−0.213908	+	0.976854i	$0.568619\pi$
$992$	−10363.9	−0.331707
$993$	−16570.0	−0.529541
$994$	−27423.8	−0.875080
$995$	−103749.	−3.30560
$996$	2320.25	0.0738151
$997$	−2964.65	−0.0941738	−0.0470869	−	0.998891i	$-0.514994\pi$
$997$	−2964.65	−0.0941738	−0.0470869	+	0.998891i	$0.514994\pi$
$998$	−9005.55	−0.285637
$999$	−83818.9	−2.65457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.b.1.19	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.b.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.54195 q^{2} +10.1442 q^{3} -1.53851 q^{4} +19.6797 q^{5} -25.7861 q^{6} -26.4188 q^{7} +24.2464 q^{8} +75.9054 q^{9} +O(q^{10})\)	\(q-2.54195 q^{2} +10.1442 q^{3} -1.53851 q^{4} +19.6797 q^{5} -25.7861 q^{6} -26.4188 q^{7} +24.2464 q^{8} +75.9054 q^{9} -50.0248 q^{10} +45.5338 q^{11} -15.6070 q^{12} +60.7033 q^{13} +67.1552 q^{14} +199.636 q^{15} -49.3249 q^{16} -3.74205 q^{17} -192.947 q^{18} -134.223 q^{19} -30.2775 q^{20} -267.999 q^{21} -115.745 q^{22} -117.498 q^{23} +245.961 q^{24} +262.292 q^{25} -154.305 q^{26} +496.107 q^{27} +40.6456 q^{28} +183.148 q^{29} -507.464 q^{30} +151.099 q^{31} -68.5897 q^{32} +461.906 q^{33} +9.51210 q^{34} -519.915 q^{35} -116.781 q^{36} -168.953 q^{37} +341.187 q^{38} +615.789 q^{39} +477.162 q^{40} -325.095 q^{41} +681.238 q^{42} -15.4780 q^{43} -70.0542 q^{44} +1493.80 q^{45} +298.674 q^{46} -195.023 q^{47} -500.363 q^{48} +354.954 q^{49} -666.733 q^{50} -37.9602 q^{51} -93.3926 q^{52} +171.362 q^{53} -1261.08 q^{54} +896.094 q^{55} -640.561 q^{56} -1361.59 q^{57} -465.553 q^{58} -98.5726 q^{59} -307.141 q^{60} -201.907 q^{61} -384.087 q^{62} -2005.33 q^{63} +568.951 q^{64} +1194.63 q^{65} -1174.14 q^{66} +100.565 q^{67} +5.75718 q^{68} -1191.93 q^{69} +1321.60 q^{70} -408.364 q^{71} +1840.43 q^{72} -49.3758 q^{73} +429.470 q^{74} +2660.75 q^{75} +206.503 q^{76} -1202.95 q^{77} -1565.30 q^{78} +781.289 q^{79} -970.702 q^{80} +2983.18 q^{81} +826.373 q^{82} -148.667 q^{83} +412.318 q^{84} -73.6426 q^{85} +39.3441 q^{86} +1857.90 q^{87} +1104.03 q^{88} +138.929 q^{89} -3797.16 q^{90} -1603.71 q^{91} +180.772 q^{92} +1532.79 q^{93} +495.739 q^{94} -2641.47 q^{95} -695.790 q^{96} -1414.47 q^{97} -902.274 q^{98} +3456.26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) \) 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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