LMFDB - Embedded newform 547.4.a.b.1.9

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			1.9
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)

$f(q)$	$=$	$q-4.65518 q^{2} -5.82218 q^{3} +13.6707 q^{4} -6.25020 q^{5} +27.1033 q^{6} -2.07510 q^{7} -26.3983 q^{8} +6.89779 q^{9} +O(q^{10})$	\(q-4.65518 q^{2} -5.82218 q^{3} +13.6707 q^{4} -6.25020 q^{5} +27.1033 q^{6} -2.07510 q^{7} -26.3983 q^{8} +6.89779 q^{9} +29.0958 q^{10} +28.4381 q^{11} -79.5935 q^{12} -10.0197 q^{13} +9.65997 q^{14} +36.3898 q^{15} +13.5231 q^{16} +49.9768 q^{17} -32.1105 q^{18} +39.6087 q^{19} -85.4448 q^{20} +12.0816 q^{21} -132.385 q^{22} +32.6995 q^{23} +153.696 q^{24} -85.9350 q^{25} +46.6437 q^{26} +117.039 q^{27} -28.3681 q^{28} -295.810 q^{29} -169.401 q^{30} +154.709 q^{31} +148.234 q^{32} -165.572 q^{33} -232.651 q^{34} +12.9698 q^{35} +94.2978 q^{36} -108.599 q^{37} -184.386 q^{38} +58.3367 q^{39} +164.995 q^{40} -318.474 q^{41} -56.2421 q^{42} -356.645 q^{43} +388.770 q^{44} -43.1126 q^{45} -152.222 q^{46} -238.748 q^{47} -78.7339 q^{48} -338.694 q^{49} +400.043 q^{50} -290.974 q^{51} -136.977 q^{52} +692.392 q^{53} -544.837 q^{54} -177.744 q^{55} +54.7791 q^{56} -230.609 q^{57} +1377.05 q^{58} -645.656 q^{59} +497.475 q^{60} -725.081 q^{61} -720.200 q^{62} -14.3136 q^{63} -798.241 q^{64} +62.6254 q^{65} +770.768 q^{66} +841.082 q^{67} +683.219 q^{68} -190.383 q^{69} -60.3768 q^{70} +895.017 q^{71} -182.090 q^{72} -53.0211 q^{73} +505.550 q^{74} +500.329 q^{75} +541.479 q^{76} -59.0119 q^{77} -271.568 q^{78} -1213.75 q^{79} -84.5220 q^{80} -867.661 q^{81} +1482.56 q^{82} +387.503 q^{83} +165.164 q^{84} -312.365 q^{85} +1660.25 q^{86} +1722.26 q^{87} -750.718 q^{88} +919.894 q^{89} +200.697 q^{90} +20.7919 q^{91} +447.026 q^{92} -900.746 q^{93} +1111.41 q^{94} -247.562 q^{95} -863.045 q^{96} +1267.13 q^{97} +1576.68 q^{98} +196.160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.65518	−1.64586	−0.822928	−	0.568146i	$-0.807661\pi$
$2$	−4.65518	−1.64586	−0.822928	+	0.568146i	$0.807661\pi$
$3$	−5.82218	−1.12048	−0.560240	−	0.828331i	$-0.689291\pi$
$3$	−5.82218	−1.12048	−0.560240	+	0.828331i	$0.689291\pi$
$4$	13.6707	1.70884
$5$	−6.25020	−0.559035	−0.279518	−	0.960141i	$-0.590175\pi$
$5$	−6.25020	−0.559035	−0.279518	+	0.960141i	$0.590175\pi$
$6$	27.1033	1.84415
$7$	−2.07510	−0.112045	−0.0560224	−	0.998430i	$-0.517842\pi$
$7$	−2.07510	−0.112045	−0.0560224	+	0.998430i	$0.517842\pi$
$8$	−26.3983	−1.16665
$9$	6.89779	0.255474
$10$	29.0958	0.920091
$11$	28.4381	0.779493	0.389746	−	0.920922i	$-0.372563\pi$
$11$	28.4381	0.779493	0.389746	+	0.920922i	$0.372563\pi$
$12$	−79.5935	−1.91472
$13$	−10.0197	−0.213767	−0.106884	−	0.994272i	$-0.534087\pi$
$13$	−10.0197	−0.213767	−0.106884	+	0.994272i	$0.534087\pi$
$14$	9.65997	0.184410
$15$	36.3898	0.626387
$16$	13.5231	0.211298
$17$	49.9768	0.713009	0.356504	−	0.934294i	$-0.383968\pi$
$17$	49.9768	0.713009	0.356504	+	0.934294i	$0.383968\pi$
$18$	−32.1105	−0.420473
$19$	39.6087	0.478255	0.239128	−	0.970988i	$-0.423139\pi$
$19$	39.6087	0.478255	0.239128	+	0.970988i	$0.423139\pi$
$20$	−85.4448	−0.955302
$21$	12.0816	0.125544
$22$	−132.385	−1.28293
$23$	32.6995	0.296449	0.148224	−	0.988954i	$-0.452644\pi$
$23$	32.6995	0.296449	0.148224	+	0.988954i	$0.452644\pi$
$24$	153.696	1.30721
$25$	−85.9350	−0.687480
$26$	46.6437	0.351830
$27$	117.039	0.834226
$28$	−28.3681	−0.191467
$29$	−295.810	−1.89416	−0.947078	−	0.321002i	$-0.895980\pi$
$29$	−295.810	−1.89416	−0.947078	+	0.321002i	$0.895980\pi$
$30$	−169.401	−1.03094
$31$	154.709	0.896343	0.448171	−	0.893948i	$-0.352075\pi$
$31$	154.709	0.896343	0.448171	+	0.893948i	$0.352075\pi$
$32$	148.234	0.818885
$33$	−165.572	−0.873405
$34$	−232.651	−1.17351
$35$	12.9698	0.0626370
$36$	94.2978	0.436564
$37$	−108.599	−0.482530	−0.241265	−	0.970459i	$-0.577562\pi$
$37$	−108.599	−0.482530	−0.241265	+	0.970459i	$0.577562\pi$
$38$	−184.386	−0.787139
$39$	58.3367	0.239522
$40$	164.995	0.652199
$41$	−318.474	−1.21310	−0.606552	−	0.795044i	$-0.707448\pi$
$41$	−318.474	−1.21310	−0.606552	+	0.795044i	$0.707448\pi$
$42$	−56.2421	−0.206627
$43$	−356.645	−1.26483	−0.632416	−	0.774629i	$-0.717937\pi$
$43$	−356.645	−1.26483	−0.632416	+	0.774629i	$0.717937\pi$
$44$	388.770	1.33203
$45$	−43.1126	−0.142819
$46$	−152.222	−0.487912
$47$	−238.748	−0.740955	−0.370478	−	0.928841i	$-0.620806\pi$
$47$	−238.748	−0.740955	−0.370478	+	0.928841i	$0.620806\pi$
$48$	−78.7339	−0.236755
$49$	−338.694	−0.987446
$50$	400.043	1.13149
$51$	−290.974	−0.798912
$52$	−136.977	−0.365294
$53$	692.392	1.79448	0.897239	−	0.441546i	$-0.145570\pi$
$53$	692.392	1.79448	0.897239	+	0.441546i	$0.145570\pi$
$54$	−544.837	−1.37302
$55$	−177.744	−0.435764
$56$	54.7791	0.130717
$57$	−230.609	−0.535875
$58$	1377.05	3.11751
$59$	−645.656	−1.42470	−0.712350	−	0.701825i	$-0.752369\pi$
$59$	−645.656	−1.42470	−0.712350	+	0.701825i	$0.752369\pi$
$60$	497.475	1.07040
$61$	−725.081	−1.52192	−0.760960	−	0.648799i	$-0.775272\pi$
$61$	−725.081	−1.52192	−0.760960	+	0.648799i	$0.775272\pi$
$62$	−720.200	−1.47525
$63$	−14.3136	−0.0286245
$64$	−798.241	−1.55906
$65$	62.6254	0.119503
$66$	770.768	1.43750
$67$	841.082	1.53365	0.766825	−	0.641856i	$-0.221835\pi$
$67$	841.082	1.53365	0.766825	+	0.641856i	$0.221835\pi$
$68$	683.219	1.21842
$69$	−190.383	−0.332165
$70$	−60.3768	−0.103091
$71$	895.017	1.49604	0.748021	−	0.663675i	$-0.231004\pi$
$71$	895.017	1.49604	0.748021	+	0.663675i	$0.231004\pi$
$72$	−182.090	−0.298049
$73$	−53.0211	−0.0850089	−0.0425044	−	0.999096i	$-0.513534\pi$
$73$	−53.0211	−0.0850089	−0.0425044	+	0.999096i	$0.513534\pi$
$74$	505.550	0.794175
$75$	500.329	0.770307
$76$	541.479	0.817263
$77$	−59.0119	−0.0873381
$78$	−271.568	−0.394218
$79$	−1213.75	−1.72858	−0.864291	−	0.502992i	$-0.832232\pi$
$79$	−1213.75	−1.72858	−0.864291	+	0.502992i	$0.832232\pi$
$80$	−84.5220	−0.118123
$81$	−867.661	−1.19021
$82$	1482.56	1.99660
$83$	387.503	0.512457	0.256229	−	0.966616i	$-0.417520\pi$
$83$	387.503	0.512457	0.256229	+	0.966616i	$0.417520\pi$
$84$	165.164	0.214535
$85$	−312.365	−0.398597
$86$	1660.25	2.08173
$87$	1722.26	2.12236
$88$	−750.718	−0.909396
$89$	919.894	1.09560	0.547801	−	0.836609i	$-0.315465\pi$
$89$	919.894	1.09560	0.547801	+	0.836609i	$0.315465\pi$
$90$	200.697	0.235059
$91$	20.7919	0.0239515
$92$	447.026	0.506584
$93$	−900.746	−1.00433
$94$	1111.41	1.21951
$95$	−247.562	−0.267361
$96$	−863.045	−0.917543
$97$	1267.13	1.32637	0.663184	−	0.748456i	$-0.269205\pi$
$97$	1267.13	1.32637	0.663184	+	0.748456i	$0.269205\pi$
$98$	1576.68	1.62519
$99$	196.160	0.199140
$100$	−1174.79	−1.17479
$101$	107.442	0.105851	0.0529253	−	0.998598i	$-0.483145\pi$
$101$	107.442	0.105851	0.0529253	+	0.998598i	$0.483145\pi$
$102$	1354.54	1.31489
$103$	−479.236	−0.458452	−0.229226	−	0.973373i	$-0.573619\pi$
$103$	−479.236	−0.458452	−0.229226	+	0.973373i	$0.573619\pi$
$104$	264.504	0.249392
$105$	−75.5125	−0.0701834
$106$	−3223.21	−2.95345
$107$	181.087	0.163611	0.0818054	−	0.996648i	$-0.473931\pi$
$107$	181.087	0.163611	0.0818054	+	0.996648i	$0.473931\pi$
$108$	1600.00	1.42556
$109$	1791.78	1.57451	0.787255	−	0.616628i	$-0.211502\pi$
$109$	1791.78	1.57451	0.787255	+	0.616628i	$0.211502\pi$
$110$	827.431	0.717204
$111$	632.285	0.540665
$112$	−28.0617	−0.0236749
$113$	925.988	0.770881	0.385441	−	0.922733i	$-0.374049\pi$
$113$	925.988	0.770881	0.385441	+	0.922733i	$0.374049\pi$
$114$	1073.53	0.881973
$115$	−204.379	−0.165725
$116$	−4043.94	−3.23681
$117$	−69.1140	−0.0546119
$118$	3005.65	2.34485
$119$	−103.707	−0.0798890
$120$	−960.629	−0.730775
$121$	−522.273	−0.392391
$122$	3375.38	2.50486
$123$	1854.21	1.35926
$124$	2114.99	1.53171
$125$	1318.39	0.943360
$126$	66.6324	0.0471118
$127$	−922.401	−0.644487	−0.322244	−	0.946657i	$-0.604437\pi$
$127$	−922.401	−0.644487	−0.322244	+	0.946657i	$0.604437\pi$
$128$	2530.09	1.74711
$129$	2076.45	1.41722
$130$	−291.533	−0.196685
$131$	2541.44	1.69501	0.847505	−	0.530788i	$-0.178104\pi$
$131$	2541.44	1.69501	0.847505	+	0.530788i	$0.178104\pi$
$132$	−2263.49	−1.49251
$133$	−82.1919	−0.0535860
$134$	−3915.39	−2.52417
$135$	−731.516	−0.466362
$136$	−1319.30	−0.831833
$137$	1590.39	0.991798	0.495899	−	0.868380i	$-0.334839\pi$
$137$	1590.39	0.991798	0.495899	+	0.868380i	$0.334839\pi$
$138$	886.266	0.546695
$139$	−1402.82	−0.856011	−0.428006	−	0.903776i	$-0.640784\pi$
$139$	−1402.82	−0.856011	−0.428006	+	0.903776i	$0.640784\pi$
$140$	177.307	0.107037
$141$	1390.03	0.830225
$142$	−4166.47	−2.46227
$143$	−284.943	−0.166630
$144$	93.2794	0.0539811
$145$	1848.87	1.05890
$146$	246.823	0.139912
$147$	1971.94	1.10641
$148$	−1484.63	−0.824568
$149$	1713.90	0.942336	0.471168	−	0.882043i	$-0.343833\pi$
$149$	1713.90	0.942336	0.471168	+	0.882043i	$0.343833\pi$
$150$	−2329.12	−1.26781
$151$	−1430.99	−0.771208	−0.385604	−	0.922664i	$-0.626007\pi$
$151$	−1430.99	−0.771208	−0.385604	+	0.922664i	$0.626007\pi$
$152$	−1045.60	−0.557957
$153$	344.729	0.182155
$154$	274.711	0.143746
$155$	−966.965	−0.501087
$156$	797.506	0.409305
$157$	−2749.60	−1.39772	−0.698861	−	0.715258i	$-0.746309\pi$
$157$	−2749.60	−1.39772	−0.698861	+	0.715258i	$0.746309\pi$
$158$	5650.25	2.84500
$159$	−4031.23	−2.01067
$160$	−926.492	−0.457785
$161$	−67.8548	−0.0332156
$162$	4039.12	1.95891
$163$	−2432.09	−1.16869	−0.584344	−	0.811506i	$-0.698648\pi$
$163$	−2432.09	−1.16869	−0.584344	+	0.811506i	$0.698648\pi$
$164$	−4353.77	−2.07300
$165$	1034.86	0.488264
$166$	−1803.90	−0.843431
$167$	−981.820	−0.454943	−0.227471	−	0.973785i	$-0.573046\pi$
$167$	−981.820	−0.454943	−0.227471	+	0.973785i	$0.573046\pi$
$168$	−318.934	−0.146466
$169$	−2096.60	−0.954304
$170$	1454.12	0.656033
$171$	273.212	0.122182
$172$	−4875.59	−2.16140
$173$	−808.375	−0.355258	−0.177629	−	0.984098i	$-0.556843\pi$
$173$	−808.375	−0.355258	−0.177629	+	0.984098i	$0.556843\pi$
$174$	−8017.43	−3.49310
$175$	178.324	0.0770286
$176$	384.571	0.164705
$177$	3759.13	1.59635
$178$	−4282.28	−1.80320
$179$	−1405.14	−0.586730	−0.293365	−	0.956000i	$-0.594775\pi$
$179$	−1405.14	−0.586730	−0.293365	+	0.956000i	$0.594775\pi$
$180$	−589.381	−0.244055
$181$	2937.74	1.20641	0.603205	−	0.797586i	$-0.293890\pi$
$181$	2937.74	1.20641	0.603205	+	0.797586i	$0.293890\pi$
$182$	−96.7903	−0.0394207
$183$	4221.55	1.70528
$184$	−863.212	−0.345852
$185$	678.768	0.269751
$186$	4193.14	1.65299
$187$	1421.25	0.555785
$188$	−3263.85	−1.26618
$189$	−242.867	−0.0934707
$190$	1152.45	0.440038
$191$	4551.87	1.72441	0.862203	−	0.506564i	$-0.169084\pi$
$191$	4551.87	1.72441	0.862203	+	0.506564i	$0.169084\pi$
$192$	4647.50	1.74690
$193$	3367.42	1.25592	0.627960	−	0.778246i	$-0.283890\pi$
$193$	3367.42	1.25592	0.627960	+	0.778246i	$0.283890\pi$
$194$	−5898.73	−2.18301
$195$	−364.616	−0.133901
$196$	−4630.19	−1.68739
$197$	526.977	0.190587	0.0952934	−	0.995449i	$-0.469621\pi$
$197$	526.977	0.190587	0.0952934	+	0.995449i	$0.469621\pi$
$198$	−913.162	−0.327756
$199$	862.544	0.307257	0.153628	−	0.988129i	$-0.450904\pi$
$199$	862.544	0.307257	0.153628	+	0.988129i	$0.450904\pi$
$200$	2268.54	0.802049
$201$	−4896.93	−1.71842
$202$	−500.164	−0.174215
$203$	613.835	0.212230
$204$	−3977.83	−1.36521
$205$	1990.53	0.678168
$206$	2230.93	0.754546
$207$	225.554	0.0757349
$208$	−135.498	−0.0451686
$209$	1126.40	0.372796
$210$	351.524	0.115512
$211$	1948.89	0.635863	0.317931	−	0.948114i	$-0.397012\pi$
$211$	1948.89	0.635863	0.317931	+	0.948114i	$0.397012\pi$
$212$	9465.50	3.06648
$213$	−5210.95	−1.67628
$214$	−842.994	−0.269280
$215$	2229.10	0.707086
$216$	−3089.62	−0.973251
$217$	−321.037	−0.100431
$218$	−8341.07	−2.59142
$219$	308.698	0.0952507
$220$	−2429.89	−0.744651
$221$	−500.754	−0.152418
$222$	−2943.40	−0.889857
$223$	−3460.35	−1.03911	−0.519557	−	0.854436i	$-0.673903\pi$
$223$	−3460.35	−1.03911	−0.519557	+	0.854436i	$0.673903\pi$
$224$	−307.600	−0.0917518
$225$	−592.761	−0.175633
$226$	−4310.64	−1.26876
$227$	−4710.68	−1.37735	−0.688676	−	0.725069i	$-0.741808\pi$
$227$	−4710.68	−1.37735	−0.688676	+	0.725069i	$0.741808\pi$
$228$	−3152.59	−0.915726
$229$	5134.46	1.48164	0.740818	−	0.671706i	$-0.234438\pi$
$229$	5134.46	1.48164	0.740818	+	0.671706i	$0.234438\pi$
$230$	951.420	0.272760
$231$	343.578	0.0978606
$232$	7808.88	2.20982
$233$	−2936.28	−0.825590	−0.412795	−	0.910824i	$-0.635447\pi$
$233$	−2936.28	−0.825590	−0.412795	+	0.910824i	$0.635447\pi$
$234$	321.738	0.0898833
$235$	1492.22	0.414220
$236$	−8826.59	−2.43459
$237$	7066.69	1.93684
$238$	482.774	0.131486
$239$	2338.44	0.632891	0.316446	−	0.948611i	$-0.397511\pi$
$239$	2338.44	0.632891	0.316446	+	0.948611i	$0.397511\pi$
$240$	492.102	0.132354
$241$	−3996.15	−1.06811	−0.534056	−	0.845449i	$-0.679333\pi$
$241$	−3996.15	−1.06811	−0.534056	+	0.845449i	$0.679333\pi$
$242$	2431.28	0.645819
$243$	1891.63	0.499376
$244$	−9912.39	−2.60072
$245$	2116.91	0.552017
$246$	−8631.70	−2.23714
$247$	−396.868	−0.102235
$248$	−4084.06	−1.04572
$249$	−2256.11	−0.574198
$250$	−6137.33	−1.55264
$251$	4125.47	1.03744	0.518720	−	0.854944i	$-0.326409\pi$
$251$	4125.47	1.03744	0.518720	+	0.854944i	$0.326409\pi$
$252$	−195.677	−0.0489148
$253$	929.913	0.231080
$254$	4293.95	1.06073
$255$	1818.65	0.446620
$256$	−5392.09	−1.31643
$257$	−2582.85	−0.626902	−0.313451	−	0.949604i	$-0.601485\pi$
$257$	−2582.85	−0.626902	−0.313451	+	0.949604i	$0.601485\pi$
$258$	−9666.25	−2.33254
$259$	225.354	0.0540650
$260$	856.135	0.204212
$261$	−2040.44	−0.483907
$262$	−11830.8	−2.78974
$263$	7961.95	1.86675	0.933374	−	0.358905i	$-0.116850\pi$
$263$	7961.95	1.86675	0.933374	+	0.358905i	$0.116850\pi$
$264$	4370.82	1.01896
$265$	−4327.59	−1.00318
$266$	382.618	0.0881949
$267$	−5355.79	−1.22760
$268$	11498.2	2.62077
$269$	−4881.25	−1.10638	−0.553188	−	0.833056i	$-0.686589\pi$
$269$	−4881.25	−1.10638	−0.553188	+	0.833056i	$0.686589\pi$
$270$	3405.34	0.767564
$271$	3974.50	0.890900	0.445450	−	0.895307i	$-0.353044\pi$
$271$	3974.50	0.890900	0.445450	+	0.895307i	$0.353044\pi$
$272$	675.840	0.150658
$273$	−121.054	−0.0268372
$274$	−7403.56	−1.63236
$275$	−2443.83	−0.535885
$276$	−2602.67	−0.567617
$277$	1661.52	0.360402	0.180201	−	0.983630i	$-0.442325\pi$
$277$	1661.52	0.360402	0.180201	+	0.983630i	$0.442325\pi$
$278$	6530.38	1.40887
$279$	1067.15	0.228992
$280$	−342.380	−0.0730755
$281$	−2594.28	−0.550753	−0.275376	−	0.961336i	$-0.588803\pi$
$281$	−2594.28	−0.550753	−0.275376	+	0.961336i	$0.588803\pi$
$282$	−6470.85	−1.36643
$283$	5442.93	1.14328	0.571641	−	0.820504i	$-0.306307\pi$
$283$	5442.93	1.14328	0.571641	+	0.820504i	$0.306307\pi$
$284$	12235.5	2.55650
$285$	1441.35	0.299573
$286$	1326.46	0.274249
$287$	660.865	0.135922
$288$	1022.49	0.209204
$289$	−2415.32	−0.491618
$290$	−8606.84	−1.74280
$291$	−7377.47	−1.48617
$292$	−724.837	−0.145267
$293$	−5424.35	−1.08155	−0.540775	−	0.841167i	$-0.681869\pi$
$293$	−5424.35	−1.08155	−0.540775	+	0.841167i	$0.681869\pi$
$294$	−9179.73	−1.82100
$295$	4035.48	0.796457
$296$	2866.84	0.562944
$297$	3328.36	0.650273
$298$	−7978.51	−1.55095
$299$	−327.641	−0.0633710
$300$	6839.86	1.31633
$301$	740.073	0.141718
$302$	6661.53	1.26930
$303$	−625.549	−0.118603
$304$	535.631	0.101054
$305$	4531.90	0.850806
$306$	−1604.78	−0.299801
$307$	6073.68	1.12913	0.564565	−	0.825388i	$-0.309044\pi$
$307$	6073.68	1.12913	0.564565	+	0.825388i	$0.309044\pi$
$308$	−806.737	−0.149247
$309$	2790.20	0.513686
$310$	4501.40	0.824717
$311$	−6641.43	−1.21093	−0.605467	−	0.795870i	$-0.707014\pi$
$311$	−6641.43	−1.21093	−0.605467	+	0.795870i	$0.707014\pi$
$312$	−1539.99	−0.279438
$313$	10436.2	1.88463	0.942317	−	0.334723i	$-0.108643\pi$
$313$	10436.2	1.88463	0.942317	+	0.334723i	$0.108643\pi$
$314$	12799.9	2.30045
$315$	89.4629	0.0160021
$316$	−16592.9	−2.95387
$317$	6760.54	1.19782	0.598911	−	0.800815i	$-0.295600\pi$
$317$	6760.54	1.19782	0.598911	+	0.800815i	$0.295600\pi$
$318$	18766.1	3.30928
$319$	−8412.28	−1.47648
$320$	4989.17	0.871572
$321$	−1054.32	−0.183322
$322$	315.876	0.0546680
$323$	1979.51	0.341000
$324$	−11861.6	−2.03388
$325$	861.046	0.146961
$326$	11321.8	1.92349
$327$	−10432.1	−1.76420
$328$	8407.18	1.41527
$329$	495.425	0.0830202
$330$	−4817.45	−0.803612
$331$	2678.08	0.444716	0.222358	−	0.974965i	$-0.428625\pi$
$331$	2678.08	0.444716	0.222358	+	0.974965i	$0.428625\pi$
$332$	5297.45	0.875708
$333$	−749.095	−0.123274
$334$	4570.55	0.748771
$335$	−5256.93	−0.857364
$336$	163.381	0.0265272
$337$	10149.0	1.64051	0.820257	−	0.571995i	$-0.193830\pi$
$337$	10149.0	1.64051	0.820257	+	0.571995i	$0.193830\pi$
$338$	9760.08	1.57065
$339$	−5391.27	−0.863757
$340$	−4270.26	−0.681139
$341$	4399.64	0.698692
$342$	−1271.85	−0.201093
$343$	1414.58	0.222683
$344$	9414.81	1.47562
$345$	1189.93	0.185692
$346$	3763.13	0.584703
$347$	−3448.54	−0.533509	−0.266754	−	0.963765i	$-0.585951\pi$
$347$	−3448.54	−0.533509	−0.266754	+	0.963765i	$0.585951\pi$
$348$	23544.6	3.62678
$349$	3834.12	0.588069	0.294034	−	0.955795i	$-0.405002\pi$
$349$	3834.12	0.588069	0.294034	+	0.955795i	$0.405002\pi$
$350$	−830.129	−0.126778
$351$	−1172.70	−0.178330
$352$	4215.50	0.638315
$353$	7285.84	1.09854	0.549272	−	0.835644i	$-0.314905\pi$
$353$	7285.84	1.09854	0.549272	+	0.835644i	$0.314905\pi$
$354$	−17499.4	−2.62736
$355$	−5594.04	−0.836340
$356$	12575.6	1.87221
$357$	603.800	0.0895139
$358$	6541.16	0.965674
$359$	8966.24	1.31816	0.659081	−	0.752072i	$-0.270945\pi$
$359$	8966.24	1.31816	0.659081	+	0.752072i	$0.270945\pi$
$360$	1138.10	0.166620
$361$	−5290.15	−0.771272
$362$	−13675.7	−1.98558
$363$	3040.77	0.439666
$364$	284.241	0.0409294
$365$	331.393	0.0475230
$366$	−19652.1	−2.80664
$367$	6247.84	0.888650	0.444325	−	0.895866i	$-0.353443\pi$
$367$	6247.84	0.888650	0.444325	+	0.895866i	$0.353443\pi$
$368$	442.198	0.0626391
$369$	−2196.77	−0.309916
$370$	−3159.79	−0.443972
$371$	−1436.78	−0.201062
$372$	−12313.9	−1.71625
$373$	9510.55	1.32021	0.660104	−	0.751174i	$-0.270512\pi$
$373$	9510.55	1.32021	0.660104	+	0.751174i	$0.270512\pi$
$374$	−6616.16	−0.914742
$375$	−7675.88	−1.05702
$376$	6302.53	0.864437
$377$	2963.94	0.404909
$378$	1130.59	0.153839
$379$	−4680.58	−0.634367	−0.317183	−	0.948364i	$-0.602737\pi$
$379$	−4680.58	−0.634367	−0.317183	+	0.948364i	$0.602737\pi$
$380$	−3384.36	−0.456878
$381$	5370.39	0.722135
$382$	−21189.8	−2.83812
$383$	−4208.90	−0.561527	−0.280763	−	0.959777i	$-0.590588\pi$
$383$	−4208.90	−0.561527	−0.280763	+	0.959777i	$0.590588\pi$
$384$	−14730.6	−1.95760
$385$	368.837	0.0488251
$386$	−15676.0	−2.06706
$387$	−2460.06	−0.323131
$388$	17322.6	2.26655
$389$	10525.3	1.37186	0.685930	−	0.727668i	$-0.259396\pi$
$389$	10525.3	1.37186	0.685930	+	0.727668i	$0.259396\pi$
$390$	1697.36	0.220382
$391$	1634.22	0.211371
$392$	8940.95	1.15201
$393$	−14796.7	−1.89922
$394$	−2453.18	−0.313678
$395$	7586.20	0.966338
$396$	2681.65	0.340298
$397$	5244.56	0.663015	0.331508	−	0.943453i	$-0.392443\pi$
$397$	5244.56	0.663015	0.331508	+	0.943453i	$0.392443\pi$
$398$	−4015.30	−0.505700
$399$	478.536	0.0600420
$400$	−1162.11	−0.145263
$401$	−12796.8	−1.59362	−0.796812	−	0.604228i	$-0.793482\pi$
$401$	−12796.8	−1.59362	−0.796812	+	0.604228i	$0.793482\pi$
$402$	22796.1	2.82828
$403$	−1550.15	−0.191609
$404$	1468.82	0.180882
$405$	5423.06	0.665367
$406$	−2857.52	−0.349301
$407$	−3088.36	−0.376129
$408$	7681.22	0.932051
$409$	−7140.55	−0.863271	−0.431635	−	0.902048i	$-0.642063\pi$
$409$	−7140.55	−0.863271	−0.431635	+	0.902048i	$0.642063\pi$
$410$	−9266.27	−1.11617
$411$	−9259.54	−1.11129
$412$	−6551.51	−0.783422
$413$	1339.80	0.159630
$414$	−1050.00	−0.124649
$415$	−2421.97	−0.286482
$416$	−1485.27	−0.175051
$417$	8167.47	0.959143
$418$	−5243.58	−0.613569
$419$	−10530.5	−1.22780	−0.613899	−	0.789385i	$-0.710400\pi$
$419$	−10530.5	−1.22780	−0.613899	+	0.789385i	$0.710400\pi$
$420$	−1032.31	−0.119932
$421$	−2230.50	−0.258214	−0.129107	−	0.991631i	$-0.541211\pi$
$421$	−2230.50	−0.258214	−0.129107	+	0.991631i	$0.541211\pi$
$422$	−9072.43	−1.04654
$423$	−1646.83	−0.189295
$424$	−18278.0	−2.09353
$425$	−4294.75	−0.490179
$426$	24257.9	2.75892
$427$	1504.61	0.170523
$428$	2475.59	0.279585
$429$	1658.99	0.186705
$430$	−10376.9	−1.16376
$431$	6720.53	0.751083	0.375541	−	0.926806i	$-0.377457\pi$
$431$	6720.53	0.751083	0.375541	+	0.926806i	$0.377457\pi$
$432$	1582.72	0.176271
$433$	−6517.86	−0.723391	−0.361695	−	0.932296i	$-0.617802\pi$
$433$	−6517.86	−0.723391	−0.361695	+	0.932296i	$0.617802\pi$
$434$	1494.49	0.165294
$435$	−10764.5	−1.18648
$436$	24495.0	2.69059
$437$	1295.18	0.141778
$438$	−1437.05	−0.156769
$439$	−6673.45	−0.725527	−0.362764	−	0.931881i	$-0.618167\pi$
$439$	−6673.45	−0.725527	−0.362764	+	0.931881i	$0.618167\pi$
$440$	4692.14	0.508384
$441$	−2336.24	−0.252266
$442$	2331.10	0.250858
$443$	7656.67	0.821172	0.410586	−	0.911822i	$-0.365324\pi$
$443$	7656.67	0.821172	0.410586	+	0.911822i	$0.365324\pi$
$444$	8643.80	0.923911
$445$	−5749.52	−0.612480
$446$	16108.6	1.71023
$447$	−9978.63	−1.05587
$448$	1656.43	0.174685
$449$	5693.51	0.598426	0.299213	−	0.954186i	$-0.403276\pi$
$449$	5693.51	0.598426	0.299213	+	0.954186i	$0.403276\pi$
$450$	2759.41	0.289067
$451$	−9056.81	−0.945606
$452$	12658.9	1.31731
$453$	8331.49	0.864123
$454$	21929.1	2.26692
$455$	−129.954	−0.0133897
$456$	6087.68	0.625179
$457$	11554.4	1.18269	0.591346	−	0.806418i	$-0.298597\pi$
$457$	11554.4	1.18269	0.591346	+	0.806418i	$0.298597\pi$
$458$	−23901.8	−2.43856
$459$	5849.22	0.594811
$460$	−2794.01	−0.283198
$461$	8069.58	0.815267	0.407633	−	0.913146i	$-0.366354\pi$
$461$	8069.58	0.815267	0.407633	+	0.913146i	$0.366354\pi$
$462$	−1599.42	−0.161064
$463$	−2263.83	−0.227234	−0.113617	−	0.993525i	$-0.536244\pi$
$463$	−2263.83	−0.227234	−0.113617	+	0.993525i	$0.536244\pi$
$464$	−4000.26	−0.400232
$465$	5629.84	0.561458
$466$	13668.9	1.35880
$467$	564.825	0.0559679	0.0279839	−	0.999608i	$-0.491091\pi$
$467$	564.825	0.0559679	0.0279839	+	0.999608i	$0.491091\pi$
$468$	−944.839	−0.0933231
$469$	−1745.33	−0.171838
$470$	−6946.56	−0.681747
$471$	16008.7	1.56612
$472$	17044.2	1.66213
$473$	−10142.3	−0.985927
$474$	−32896.8	−3.18776
$475$	−3403.77	−0.328791
$476$	−1417.75	−0.136518
$477$	4775.97	0.458442
$478$	−10885.9	−1.04165
$479$	−527.961	−0.0503615	−0.0251807	−	0.999683i	$-0.508016\pi$
$479$	−527.961	−0.0503615	−0.0251807	+	0.999683i	$0.508016\pi$
$480$	5394.21	0.512939
$481$	1088.14	0.103149
$482$	18602.8	1.75796
$483$	395.063	0.0372173
$484$	−7139.85	−0.670535
$485$	−7919.83	−0.741486
$486$	−8805.90	−0.821901
$487$	−1986.20	−0.184812	−0.0924058	−	0.995721i	$-0.529456\pi$
$487$	−1986.20	−0.184812	−0.0924058	+	0.995721i	$0.529456\pi$
$488$	19140.9	1.77555
$489$	14160.1	1.30949
$490$	−9854.58	−0.908540
$491$	−7306.61	−0.671574	−0.335787	−	0.941938i	$-0.609002\pi$
$491$	−7306.61	−0.671574	−0.335787	+	0.941938i	$0.609002\pi$
$492$	25348.5	2.32276
$493$	−14783.6	−1.35055
$494$	1847.49	0.168265
$495$	−1226.04	−0.111326
$496$	2092.15	0.189396
$497$	−1857.25	−0.167624
$498$	10502.6	0.945046
$499$	14771.1	1.32514	0.662572	−	0.748998i	$-0.269465\pi$
$499$	14771.1	1.32514	0.662572	+	0.748998i	$0.269465\pi$
$500$	18023.3	1.61205
$501$	5716.33	0.509754
$502$	−19204.8	−1.70748
$503$	6809.92	0.603657	0.301829	−	0.953362i	$-0.402403\pi$
$503$	6809.92	0.603657	0.301829	+	0.953362i	$0.402403\pi$
$504$	377.855	0.0333948
$505$	−671.537	−0.0591742
$506$	−4328.92	−0.380324
$507$	12206.8	1.06928
$508$	−12609.9	−1.10133
$509$	20267.8	1.76494	0.882469	−	0.470371i	$-0.155880\pi$
$509$	20267.8	1.76494	0.882469	+	0.470371i	$0.155880\pi$
$510$	−8466.13	−0.735072
$511$	110.024	0.00952481
$512$	4860.47	0.419540
$513$	4635.75	0.398973
$514$	12023.6	1.03179
$515$	2995.32	0.256291
$516$	28386.6	2.42180
$517$	−6789.53	−0.577569
$518$	−1049.07	−0.0889832
$519$	4706.50	0.398059
$520$	−1653.20	−0.139419
$521$	17797.3	1.49657	0.748286	−	0.663377i	$-0.230877\pi$
$521$	17797.3	1.49657	0.748286	+	0.663377i	$0.230877\pi$
$522$	9498.60	0.796442
$523$	4722.47	0.394836	0.197418	−	0.980319i	$-0.436744\pi$
$523$	4722.47	0.394836	0.197418	+	0.980319i	$0.436744\pi$
$524$	34743.3	2.89650
$525$	−1038.23	−0.0863089
$526$	−37064.3	−3.07240
$527$	7731.88	0.639100
$528$	−2239.04	−0.184549
$529$	−11097.7	−0.912118
$530$	20145.7	1.65108
$531$	−4453.60	−0.363973
$532$	−1123.62	−0.0915701
$533$	3191.03	0.259322
$534$	24932.2	2.02045
$535$	−1131.83	−0.0914642
$536$	−22203.1	−1.78924
$537$	8180.95	0.657419
$538$	22723.1	1.82094
$539$	−9631.82	−0.769707
$540$	−10000.4	−0.796938
$541$	−873.557	−0.0694217	−0.0347109	−	0.999397i	$-0.511051\pi$
$541$	−873.557	−0.0694217	−0.0347109	+	0.999397i	$0.511051\pi$
$542$	−18502.0	−1.46629
$543$	−17104.0	−1.35176
$544$	7408.26	0.583872
$545$	−11199.0	−0.880206
$546$	563.531	0.0441701
$547$	−547.000	−0.0427569
$547$	−547.000	−0.0427569
$548$	21741.8	1.69483
$549$	−5001.45	−0.388810
$550$	11376.5	0.881990
$551$	−11716.6	−0.905891
$552$	5025.78	0.387520
$553$	2518.66	0.193679
$554$	−7734.69	−0.593169
$555$	−3951.91	−0.302251
$556$	−19177.6	−1.46279
$557$	−14447.5	−1.09903	−0.549515	−	0.835484i	$-0.685187\pi$
$557$	−14447.5	−1.09903	−0.549515	+	0.835484i	$0.685187\pi$
$558$	−4967.79	−0.376888
$559$	3573.48	0.270380
$560$	175.392	0.0132351
$561$	−8274.75	−0.622746
$562$	12076.8	0.906460
$563$	3764.90	0.281832	0.140916	−	0.990022i	$-0.454995\pi$
$563$	3764.90	0.281832	0.140916	+	0.990022i	$0.454995\pi$
$564$	19002.7	1.41872
$565$	−5787.61	−0.430950
$566$	−25337.8	−1.88168
$567$	1800.48	0.133357
$568$	−23626.9	−1.74536
$569$	−2712.48	−0.199847	−0.0999237	−	0.994995i	$-0.531860\pi$
$569$	−2712.48	−0.199847	−0.0999237	+	0.994995i	$0.531860\pi$
$570$	−6709.76	−0.493054
$571$	−21761.1	−1.59487	−0.797436	−	0.603403i	$-0.793811\pi$
$571$	−21761.1	−1.59487	−0.797436	+	0.603403i	$0.793811\pi$
$572$	−3895.37	−0.284744
$573$	−26501.8	−1.93216
$574$	−3076.45	−0.223708
$575$	−2810.03	−0.203803
$576$	−5506.10	−0.398300
$577$	21168.8	1.52733	0.763665	−	0.645613i	$-0.223398\pi$
$577$	21168.8	1.52733	0.763665	+	0.645613i	$0.223398\pi$
$578$	11243.8	0.809133
$579$	−19605.8	−1.40723
$580$	25275.4	1.80949
$581$	−804.107	−0.0574182
$582$	34343.5	2.44602
$583$	19690.3	1.39878
$584$	1399.67	0.0991757
$585$	431.977	0.0305300
$586$	25251.4	1.78007
$587$	3212.94	0.225915	0.112958	−	0.993600i	$-0.463968\pi$
$587$	3212.94	0.225915	0.112958	+	0.993600i	$0.463968\pi$
$588$	26957.8	1.89068
$589$	6127.83	0.428681
$590$	−18785.9	−1.31085
$591$	−3068.16	−0.213548
$592$	−1468.60	−0.101958
$593$	21759.1	1.50681	0.753407	−	0.657554i	$-0.228409\pi$
$593$	21759.1	1.50681	0.753407	+	0.657554i	$0.228409\pi$
$594$	−15494.1	−1.07026
$595$	648.188	0.0446607
$596$	23430.3	1.61030
$597$	−5021.89	−0.344275
$598$	1525.23	0.104300
$599$	−18122.3	−1.23615	−0.618077	−	0.786117i	$-0.712088\pi$
$599$	−18122.3	−1.23615	−0.618077	+	0.786117i	$0.712088\pi$
$600$	−13207.8	−0.898679
$601$	12016.4	0.815570	0.407785	−	0.913078i	$-0.366301\pi$
$601$	12016.4	0.815570	0.407785	+	0.913078i	$0.366301\pi$
$602$	−3445.18	−0.233247
$603$	5801.61	0.391807
$604$	−19562.7	−1.31787
$605$	3264.31	0.219360
$606$	2912.05	0.195204
$607$	−2486.53	−0.166269	−0.0831343	−	0.996538i	$-0.526493\pi$
$607$	−2486.53	−0.166269	−0.0831343	+	0.996538i	$0.526493\pi$
$608$	5871.35	0.391636
$609$	−3573.86	−0.237800
$610$	−21096.8	−1.40030
$611$	2392.19	0.158392
$612$	4712.70	0.311274
$613$	−10925.5	−0.719862	−0.359931	−	0.932979i	$-0.617200\pi$
$613$	−10925.5	−0.719862	−0.359931	+	0.932979i	$0.617200\pi$
$614$	−28274.1	−1.85839
$615$	−11589.2	−0.759873
$616$	1557.82	0.101893
$617$	7914.22	0.516393	0.258196	−	0.966092i	$-0.416872\pi$
$617$	7914.22	0.516393	0.258196	+	0.966092i	$0.416872\pi$
$618$	−12988.9	−0.845453
$619$	19964.6	1.29636	0.648178	−	0.761489i	$-0.275531\pi$
$619$	19964.6	1.29636	0.648178	+	0.761489i	$0.275531\pi$
$620$	−13219.1	−0.856278
$621$	3827.11	0.247305
$622$	30917.1	1.99302
$623$	−1908.87	−0.122757
$624$	788.892	0.0506105
$625$	2501.69	0.160108
$626$	−48582.5	−3.10183
$627$	−6558.08	−0.417711
$628$	−37589.1	−2.38848
$629$	−5427.44	−0.344048
$630$	−416.466	−0.0263372
$631$	6764.31	0.426756	0.213378	−	0.976970i	$-0.431553\pi$
$631$	6764.31	0.426756	0.213378	+	0.976970i	$0.431553\pi$
$632$	32041.0	2.01665
$633$	−11346.8	−0.712471
$634$	−31471.6	−1.97144
$635$	5765.19	0.360291
$636$	−55109.9	−3.43592
$637$	3393.62	0.211084
$638$	39160.7	2.43008
$639$	6173.64	0.382199
$640$	−15813.6	−0.976696
$641$	−29129.0	−1.79489	−0.897446	−	0.441124i	$-0.854580\pi$
$641$	−29129.0	−1.79489	−0.897446	+	0.441124i	$0.854580\pi$
$642$	4908.06	0.301722
$643$	−31657.0	−1.94157	−0.970785	−	0.239951i	$-0.922869\pi$
$643$	−31657.0	−1.94157	−0.970785	+	0.239951i	$0.922869\pi$
$644$	−927.624	−0.0567601
$645$	−12978.2	−0.792275
$646$	−9215.00	−0.561237
$647$	11671.8	0.709219	0.354609	−	0.935014i	$-0.384614\pi$
$647$	11671.8	0.709219	0.354609	+	0.935014i	$0.384614\pi$
$648$	22904.8	1.38856
$649$	−18361.3	−1.11054
$650$	−4008.33	−0.241876
$651$	1869.14	0.112530
$652$	−33248.5	−1.99710
$653$	10250.4	0.614287	0.307143	−	0.951663i	$-0.400627\pi$
$653$	10250.4	0.614287	0.307143	+	0.951663i	$0.400627\pi$
$654$	48563.2	2.90363
$655$	−15884.5	−0.947570
$656$	−4306.75	−0.256327
$657$	−365.728	−0.0217175
$658$	−2306.29	−0.136639
$659$	1228.31	0.0726075	0.0363037	−	0.999341i	$-0.488442\pi$
$659$	1228.31	0.0726075	0.0363037	+	0.999341i	$0.488442\pi$
$660$	14147.3	0.834366
$661$	8050.99	0.473748	0.236874	−	0.971540i	$-0.423877\pi$
$661$	8050.99	0.473748	0.236874	+	0.971540i	$0.423877\pi$
$662$	−12467.0	−0.731938
$663$	2915.48	0.170781
$664$	−10229.4	−0.597859
$665$	513.716	0.0299565
$666$	3487.18	0.202891
$667$	−9672.85	−0.561520
$668$	−13422.2	−0.777426
$669$	20146.8	1.16431
$670$	24472.0	1.41110
$671$	−20619.9	−1.18632
$672$	1790.90	0.102806
$673$	−25912.9	−1.48420	−0.742102	−	0.670287i	$-0.766171\pi$
$673$	−25912.9	−1.48420	−0.742102	+	0.670287i	$0.766171\pi$
$674$	−47245.6	−2.70005
$675$	−10057.7	−0.573514
$676$	−28662.1	−1.63075
$677$	−7301.85	−0.414524	−0.207262	−	0.978285i	$-0.566455\pi$
$677$	−7301.85	−0.414524	−0.207262	+	0.978285i	$0.566455\pi$
$678$	25097.3	1.42162
$679$	−2629.42	−0.148613
$680$	8245.91	0.465024
$681$	27426.4	1.54329
$682$	−20481.2	−1.14995
$683$	−16682.3	−0.934598	−0.467299	−	0.884099i	$-0.654773\pi$
$683$	−16682.3	−0.934598	−0.467299	+	0.884099i	$0.654773\pi$
$684$	3735.01	0.208789
$685$	−9940.27	−0.554450
$686$	−6585.14	−0.366504
$687$	−29893.7	−1.66014
$688$	−4822.94	−0.267257
$689$	−6937.58	−0.383600
$690$	−5539.34	−0.305622
$691$	30700.3	1.69015	0.845074	−	0.534649i	$-0.179556\pi$
$691$	30700.3	1.69015	0.845074	+	0.534649i	$0.179556\pi$
$692$	−11051.1	−0.607079
$693$	−407.052	−0.0223126
$694$	16053.6	0.878078
$695$	8767.90	0.478540
$696$	−45464.7	−2.47606
$697$	−15916.3	−0.864954
$698$	−17848.6	−0.967876
$699$	17095.6	0.925056
$700$	2437.81	0.131630
$701$	12488.7	0.672884	0.336442	−	0.941704i	$-0.390776\pi$
$701$	12488.7	0.672884	0.336442	+	0.941704i	$0.390776\pi$
$702$	5459.12	0.293506
$703$	−4301.47	−0.230773
$704$	−22700.5	−1.21528
$705$	−8687.98	−0.464125
$706$	−33916.9	−1.80805
$707$	−222.954	−0.0118600
$708$	51390.0	2.72790
$709$	11988.2	0.635015	0.317507	−	0.948256i	$-0.397154\pi$
$709$	11988.2	0.635015	0.317507	+	0.948256i	$0.397154\pi$
$710$	26041.3	1.37650
$711$	−8372.22	−0.441607
$712$	−24283.6	−1.27819
$713$	5058.92	0.265720
$714$	−2810.80	−0.147327
$715$	1780.95	0.0931520
$716$	−19209.2	−1.00263
$717$	−13614.8	−0.709141
$718$	−41739.5	−2.16950
$719$	−27227.1	−1.41224	−0.706118	−	0.708094i	$-0.749555\pi$
$719$	−27227.1	−1.41224	−0.706118	+	0.708094i	$0.749555\pi$
$720$	−583.015	−0.0301773
$721$	994.463	0.0513672
$722$	24626.6	1.26940
$723$	23266.3	1.19680
$724$	40161.0	2.06156
$725$	25420.4	1.30219
$726$	−14155.3	−0.723627
$727$	30223.5	1.54185	0.770926	−	0.636925i	$-0.219794\pi$
$727$	30223.5	1.54185	0.770926	+	0.636925i	$0.219794\pi$
$728$	−548.872	−0.0279431
$729$	12413.4	0.630667
$730$	−1542.69	−0.0782159
$731$	−17823.9	−0.901837
$732$	57711.7	2.91405
$733$	−12522.0	−0.630982	−0.315491	−	0.948929i	$-0.602169\pi$
$733$	−12522.0	−0.630982	−0.315491	+	0.948929i	$0.602169\pi$
$734$	−29084.8	−1.46259
$735$	−12325.0	−0.618523
$736$	4847.18	0.242757
$737$	23918.8	1.19547
$738$	10226.4	0.510078
$739$	−24241.0	−1.20666	−0.603328	−	0.797493i	$-0.706159\pi$
$739$	−24241.0	−1.20666	−0.603328	+	0.797493i	$0.706159\pi$
$740$	9279.25	0.460962
$741$	2310.64	0.114553
$742$	6688.48	0.330919
$743$	−10309.1	−0.509023	−0.254511	−	0.967070i	$-0.581915\pi$
$743$	−10309.1	−0.509023	−0.254511	+	0.967070i	$0.581915\pi$
$744$	23778.2	1.17171
$745$	−10712.2	−0.526799
$746$	−44273.3	−2.17287
$747$	2672.91	0.130919
$748$	19429.5	0.949749
$749$	−375.774	−0.0183317
$750$	35732.6	1.73970
$751$	−35618.7	−1.73069	−0.865344	−	0.501179i	$-0.832900\pi$
$751$	−35618.7	−1.73069	−0.865344	+	0.501179i	$0.832900\pi$
$752$	−3228.60	−0.156563
$753$	−24019.3	−1.16243
$754$	−13797.7	−0.666421
$755$	8943.99	0.431132
$756$	−3320.17	−0.159727
$757$	−18566.4	−0.891421	−0.445711	−	0.895177i	$-0.647049\pi$
$757$	−18566.4	−0.891421	−0.445711	+	0.895177i	$0.647049\pi$
$758$	21788.9	1.04408
$759$	−5414.12	−0.258920
$760$	6535.22	0.311918
$761$	−9252.01	−0.440716	−0.220358	−	0.975419i	$-0.570723\pi$
$761$	−9252.01	−0.440716	−0.220358	+	0.975419i	$0.570723\pi$
$762$	−25000.1	−1.18853
$763$	−3718.12	−0.176416
$764$	62227.3	2.94674
$765$	−2154.63	−0.101831
$766$	19593.2	0.924193
$767$	6469.30	0.304554
$768$	31393.7	1.47503
$769$	21680.4	1.01666	0.508332	−	0.861161i	$-0.330262\pi$
$769$	21680.4	1.01666	0.508332	+	0.861161i	$0.330262\pi$
$770$	−1717.00	−0.0803590
$771$	15037.8	0.702430
$772$	46035.2	2.14617
$773$	28569.0	1.32931	0.664653	−	0.747152i	$-0.268579\pi$
$773$	28569.0	1.32931	0.664653	+	0.747152i	$0.268579\pi$
$774$	11452.0	0.531828
$775$	−13294.9	−0.616217
$776$	−33450.1	−1.54741
$777$	−1312.05	−0.0605787
$778$	−48997.1	−2.25788
$779$	−12614.3	−0.580174
$780$	−4984.57	−0.228816
$781$	25452.6	1.16615
$782$	−7607.58	−0.347886
$783$	−34621.2	−1.58016
$784$	−4580.19	−0.208646
$785$	17185.6	0.781375
$786$	68881.3	3.12585
$787$	39840.9	1.80454	0.902270	−	0.431170i	$-0.141899\pi$
$787$	39840.9	1.80454	0.902270	+	0.431170i	$0.141899\pi$
$788$	7204.17	0.325683
$789$	−46355.9	−2.09165
$790$	−35315.2	−1.59045
$791$	−1921.52	−0.0863733
$792$	−5178.30	−0.232327
$793$	7265.12	0.325337
$794$	−24414.4	−1.09123
$795$	25196.0	1.12404
$796$	11791.6	0.525053
$797$	−5392.12	−0.239647	−0.119823	−	0.992795i	$-0.538233\pi$
$797$	−5392.12	−0.239647	−0.119823	+	0.992795i	$0.538233\pi$
$798$	−2227.67	−0.0988205
$799$	−11931.8	−0.528308
$800$	−12738.5	−0.562967
$801$	6345.23	0.279897
$802$	59571.6	2.62287
$803$	−1507.82	−0.0662638
$804$	−66944.7	−2.93651
$805$	424.106	0.0185687
$806$	7216.22	0.315360
$807$	28419.5	1.23967
$808$	−2836.30	−0.123491
$809$	32471.8	1.41118	0.705592	−	0.708619i	$-0.250681\pi$
$809$	32471.8	1.41118	0.705592	+	0.708619i	$0.250681\pi$
$810$	−25245.3	−1.09510
$811$	20817.3	0.901349	0.450674	−	0.892688i	$-0.351184\pi$
$811$	20817.3	0.901349	0.450674	+	0.892688i	$0.351184\pi$
$812$	8391.58	0.362668
$813$	−23140.3	−0.998235
$814$	14376.9	0.619054
$815$	15201.1	0.653338
$816$	−3934.86	−0.168809
$817$	−14126.2	−0.604913
$818$	33240.6	1.42082
$819$	143.418	0.00611898
$820$	27212.0	1.15888
$821$	45116.5	1.91788	0.958938	−	0.283615i	$-0.0915337\pi$
$821$	45116.5	1.91788	0.958938	+	0.283615i	$0.0915337\pi$
$822$	43104.9	1.82902
$823$	19180.6	0.812387	0.406194	−	0.913787i	$-0.366856\pi$
$823$	19180.6	0.812387	0.406194	+	0.913787i	$0.366856\pi$
$824$	12651.0	0.534853
$825$	14228.4	0.600449
$826$	−6237.02	−0.262728
$827$	−27245.7	−1.14562	−0.572809	−	0.819689i	$-0.694146\pi$
$827$	−27245.7	−1.14562	−0.572809	+	0.819689i	$0.694146\pi$
$828$	3083.49	0.129419
$829$	37745.9	1.58139	0.790694	−	0.612211i	$-0.209720\pi$
$829$	37745.9	1.58139	0.790694	+	0.612211i	$0.209720\pi$
$830$	11274.7	0.471507
$831$	−9673.69	−0.403823
$832$	7998.16	0.333277
$833$	−16926.8	−0.704058
$834$	−38021.1	−1.57861
$835$	6136.57	0.254329
$836$	15398.7	0.637050
$837$	18107.0	0.747753
$838$	49021.3	2.02078
$839$	−19802.7	−0.814858	−0.407429	−	0.913237i	$-0.633575\pi$
$839$	−19802.7	−0.814858	−0.407429	+	0.913237i	$0.633575\pi$
$840$	1993.40	0.0818796
$841$	63114.6	2.58783
$842$	10383.4	0.424983
$843$	15104.3	0.617107
$844$	26642.7	1.08659
$845$	13104.2	0.533489
$846$	7666.30	0.311552
$847$	1083.77	0.0439654
$848$	9363.27	0.379170
$849$	−31689.7	−1.28102
$850$	19992.9	0.806764
$851$	−3551.15	−0.143045
$852$	−71237.5	−2.86450
$853$	−24798.8	−0.995421	−0.497710	−	0.867343i	$-0.665826\pi$
$853$	−24798.8	−0.995421	−0.497710	+	0.867343i	$0.665826\pi$
$854$	−7004.26	−0.280657
$855$	−1707.63	−0.0683038
$856$	−4780.39	−0.190877
$857$	−18245.9	−0.727267	−0.363633	−	0.931542i	$-0.618464\pi$
$857$	−18245.9	−0.727267	−0.363633	+	0.931542i	$0.618464\pi$
$858$	−7722.89	−0.307290
$859$	26542.2	1.05426	0.527130	−	0.849784i	$-0.323268\pi$
$859$	26542.2	1.05426	0.527130	+	0.849784i	$0.323268\pi$
$860$	30473.4	1.20830
$861$	−3847.68	−0.152298
$862$	−31285.3	−1.23617
$863$	1532.28	0.0604397	0.0302199	−	0.999543i	$-0.490379\pi$
$863$	1532.28	0.0604397	0.0302199	+	0.999543i	$0.490379\pi$
$864$	17349.1	0.683135
$865$	5052.50	0.198602
$866$	30341.8	1.19060
$867$	14062.4	0.550848
$868$	−4388.82	−0.171620
$869$	−34516.9	−1.34742
$870$	50110.6	1.95277
$871$	−8427.42	−0.327844
$872$	−47300.0	−1.83690
$873$	8740.41	0.338852
$874$	−6029.32	−0.233346
$875$	−2735.78	−0.105699
$876$	4220.13	0.162768
$877$	32629.7	1.25636	0.628179	−	0.778069i	$-0.283800\pi$
$877$	32629.7	1.25636	0.628179	+	0.778069i	$0.283800\pi$
$878$	31066.1	1.19411
$879$	31581.6	1.21185
$880$	−2403.65	−0.0920761
$881$	−31710.8	−1.21267	−0.606335	−	0.795209i	$-0.707361\pi$
$881$	−31710.8	−1.21267	−0.606335	+	0.795209i	$0.707361\pi$
$882$	10875.6	0.415194
$883$	−1503.37	−0.0572960	−0.0286480	−	0.999590i	$-0.509120\pi$
$883$	−1503.37	−0.0572960	−0.0286480	+	0.999590i	$0.509120\pi$
$884$	−6845.68	−0.260458
$885$	−23495.3	−0.892413
$886$	−35643.2	−1.35153
$887$	22818.8	0.863787	0.431894	−	0.901925i	$-0.357846\pi$
$887$	22818.8	0.863787	0.431894	+	0.901925i	$0.357846\pi$
$888$	−16691.2	−0.630768
$889$	1914.07	0.0722115
$890$	26765.1	1.00805
$891$	−24674.7	−0.927757
$892$	−47305.6	−1.77568
$893$	−9456.47	−0.354366
$894$	46452.3	1.73781
$895$	8782.38	0.328003
$896$	−5250.18	−0.195755
$897$	1907.58	0.0710059
$898$	−26504.3	−0.984922
$899$	−45764.6	−1.69781
$900$	−8103.48	−0.300129
$901$	34603.5	1.27948
$902$	42161.1	1.55633
$903$	−4308.84	−0.158792
$904$	−24444.5	−0.899350
$905$	−18361.4	−0.674425
$906$	−38784.6	−1.42222
$907$	−24617.3	−0.901217	−0.450609	−	0.892722i	$-0.648793\pi$
$907$	−24617.3	−0.901217	−0.450609	+	0.892722i	$0.648793\pi$
$908$	−64398.5	−2.35368
$909$	741.115	0.0270421
$910$	604.959	0.0220376
$911$	8572.62	0.311771	0.155886	−	0.987775i	$-0.450177\pi$
$911$	8572.62	0.311771	0.155886	+	0.987775i	$0.450177\pi$
$912$	−3118.54	−0.113229
$913$	11019.9	0.399457
$914$	−53787.7	−1.94654
$915$	−26385.5	−0.953311
$916$	70191.8	2.53188
$917$	−5273.73	−0.189917
$918$	−27229.2	−0.978973
$919$	−25613.0	−0.919364	−0.459682	−	0.888084i	$-0.652037\pi$
$919$	−25613.0	−0.919364	−0.459682	+	0.888084i	$0.652037\pi$
$920$	5395.25	0.193344
$921$	−35362.1	−1.26517
$922$	−37565.4	−1.34181
$923$	−8967.83	−0.319805
$924$	4696.97	0.167228
$925$	9332.48	0.331730
$926$	10538.6	0.373994
$927$	−3305.67	−0.117122
$928$	−43849.1	−1.55110
$929$	−4055.45	−0.143224	−0.0716119	−	0.997433i	$-0.522814\pi$
$929$	−4055.45	−0.143224	−0.0716119	+	0.997433i	$0.522814\pi$
$930$	−26208.0	−0.924078
$931$	−13415.2	−0.472251
$932$	−40141.2	−1.41080
$933$	38667.6	1.35683
$934$	−2629.37	−0.0921151
$935$	−8883.08	−0.310703
$936$	1824.49	0.0637131
$937$	41752.0	1.45569	0.727843	−	0.685744i	$-0.240523\pi$
$937$	41752.0	1.45569	0.727843	+	0.685744i	$0.240523\pi$
$938$	8124.83	0.282820
$939$	−60761.6	−2.11169
$940$	20399.7	0.707836
$941$	46686.4	1.61736	0.808678	−	0.588252i	$-0.200184\pi$
$941$	46686.4	1.61736	0.808678	+	0.588252i	$0.200184\pi$
$942$	−74523.4	−2.57760
$943$	−10413.9	−0.359623
$944$	−8731.26	−0.301036
$945$	1517.97	0.0522534
$946$	47214.3	1.62269
$947$	24803.0	0.851098	0.425549	−	0.904935i	$-0.360081\pi$
$947$	24803.0	0.851098	0.425549	+	0.904935i	$0.360081\pi$
$948$	96606.9	3.30975
$949$	531.257	0.0181721
$950$	15845.2	0.541142
$951$	−39361.1	−1.34214
$952$	2737.68	0.0932026
$953$	35215.3	1.19700	0.598498	−	0.801125i	$-0.295765\pi$
$953$	35215.3	1.19700	0.598498	+	0.801125i	$0.295765\pi$
$954$	−22233.0	−0.754529
$955$	−28450.1	−0.964003
$956$	31968.2	1.08151
$957$	48977.8	1.65437
$958$	2457.75	0.0828877
$959$	−3300.22	−0.111126
$960$	−29047.8	−0.976578
$961$	−5856.01	−0.196570
$962$	−5065.47	−0.169769
$963$	1249.10	0.0417982
$964$	−54630.4	−1.82523
$965$	−21047.1	−0.702103
$966$	−1839.09	−0.0612544
$967$	−15319.2	−0.509444	−0.254722	−	0.967014i	$-0.581984\pi$
$967$	−15319.2	−0.509444	−0.254722	+	0.967014i	$0.581984\pi$
$968$	13787.1	0.457784
$969$	−11525.1	−0.382084
$970$	36868.3	1.22038
$971$	8438.07	0.278878	0.139439	−	0.990231i	$-0.455470\pi$
$971$	8438.07	0.278878	0.139439	+	0.990231i	$0.455470\pi$
$972$	25860.0	0.853354
$973$	2910.99	0.0959117
$974$	9246.12	0.304173
$975$	−5013.16	−0.164666
$976$	−9805.33	−0.321579
$977$	−38999.1	−1.27706	−0.638532	−	0.769595i	$-0.720458\pi$
$977$	−38999.1	−1.27706	−0.638532	+	0.769595i	$0.720458\pi$
$978$	−65917.8	−2.15523
$979$	26160.1	0.854014
$980$	28939.7	0.943309
$981$	12359.3	0.402246
$982$	34013.6	1.10531
$983$	42026.0	1.36360	0.681801	−	0.731538i	$-0.261197\pi$
$983$	42026.0	1.36360	0.681801	+	0.731538i	$0.261197\pi$
$984$	−48948.1	−1.58578
$985$	−3293.72	−0.106545
$986$	68820.5	2.22281
$987$	−2884.45	−0.0930224
$988$	−5425.48	−0.174704
$989$	−11662.1	−0.374958
$990$	5707.45	0.183227
$991$	38074.0	1.22044	0.610222	−	0.792230i	$-0.291080\pi$
$991$	38074.0	1.22044	0.610222	+	0.792230i	$0.291080\pi$
$992$	22933.2	0.734001
$993$	−15592.3	−0.498294
$994$	8645.84	0.275885
$995$	−5391.07	−0.171767
$996$	−30842.7	−0.981213
$997$	19999.1	0.635284	0.317642	−	0.948211i	$-0.397109\pi$
$997$	19999.1	0.635284	0.317642	+	0.948211i	$0.397109\pi$
$998$	−68762.4	−2.18100
$999$	−12710.3	−0.402539

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.b.1.9	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-4.65518 q^{2} -5.82218 q^{3} +13.6707 q^{4} -6.25020 q^{5} +27.1033 q^{6} -2.07510 q^{7} -26.3983 q^{8} +6.89779 q^{9} +O(q^{10})\)	\(q-4.65518 q^{2} -5.82218 q^{3} +13.6707 q^{4} -6.25020 q^{5} +27.1033 q^{6} -2.07510 q^{7} -26.3983 q^{8} +6.89779 q^{9} +29.0958 q^{10} +28.4381 q^{11} -79.5935 q^{12} -10.0197 q^{13} +9.65997 q^{14} +36.3898 q^{15} +13.5231 q^{16} +49.9768 q^{17} -32.1105 q^{18} +39.6087 q^{19} -85.4448 q^{20} +12.0816 q^{21} -132.385 q^{22} +32.6995 q^{23} +153.696 q^{24} -85.9350 q^{25} +46.6437 q^{26} +117.039 q^{27} -28.3681 q^{28} -295.810 q^{29} -169.401 q^{30} +154.709 q^{31} +148.234 q^{32} -165.572 q^{33} -232.651 q^{34} +12.9698 q^{35} +94.2978 q^{36} -108.599 q^{37} -184.386 q^{38} +58.3367 q^{39} +164.995 q^{40} -318.474 q^{41} -56.2421 q^{42} -356.645 q^{43} +388.770 q^{44} -43.1126 q^{45} -152.222 q^{46} -238.748 q^{47} -78.7339 q^{48} -338.694 q^{49} +400.043 q^{50} -290.974 q^{51} -136.977 q^{52} +692.392 q^{53} -544.837 q^{54} -177.744 q^{55} +54.7791 q^{56} -230.609 q^{57} +1377.05 q^{58} -645.656 q^{59} +497.475 q^{60} -725.081 q^{61} -720.200 q^{62} -14.3136 q^{63} -798.241 q^{64} +62.6254 q^{65} +770.768 q^{66} +841.082 q^{67} +683.219 q^{68} -190.383 q^{69} -60.3768 q^{70} +895.017 q^{71} -182.090 q^{72} -53.0211 q^{73} +505.550 q^{74} +500.329 q^{75} +541.479 q^{76} -59.0119 q^{77} -271.568 q^{78} -1213.75 q^{79} -84.5220 q^{80} -867.661 q^{81} +1482.56 q^{82} +387.503 q^{83} +165.164 q^{84} -312.365 q^{85} +1660.25 q^{86} +1722.26 q^{87} -750.718 q^{88} +919.894 q^{89} +200.697 q^{90} +20.7919 q^{91} +447.026 q^{92} -900.746 q^{93} +1111.41 q^{94} -247.562 q^{95} -863.045 q^{96} +1267.13 q^{97} +1576.68 q^{98} +196.160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) \) 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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