Properties

Label 6047.2.a.a.1.6
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.67338 q^{2}\) \(-1.23035 q^{3}\) \(+5.14695 q^{4}\) \(+0.526879 q^{5}\) \(+3.28919 q^{6}\) \(-0.672464 q^{7}\) \(-8.41297 q^{8}\) \(-1.48624 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.67338 q^{2}\) \(-1.23035 q^{3}\) \(+5.14695 q^{4}\) \(+0.526879 q^{5}\) \(+3.28919 q^{6}\) \(-0.672464 q^{7}\) \(-8.41297 q^{8}\) \(-1.48624 q^{9}\) \(-1.40855 q^{10}\) \(-0.433333 q^{11}\) \(-6.33255 q^{12}\) \(-2.99709 q^{13}\) \(+1.79775 q^{14}\) \(-0.648246 q^{15}\) \(+12.1972 q^{16}\) \(-1.32515 q^{17}\) \(+3.97327 q^{18}\) \(+5.07313 q^{19}\) \(+2.71182 q^{20}\) \(+0.827367 q^{21}\) \(+1.15846 q^{22}\) \(-8.17389 q^{23}\) \(+10.3509 q^{24}\) \(-4.72240 q^{25}\) \(+8.01236 q^{26}\) \(+5.51965 q^{27}\) \(-3.46114 q^{28}\) \(+3.97740 q^{29}\) \(+1.73301 q^{30}\) \(-4.72593 q^{31}\) \(-15.7817 q^{32}\) \(+0.533151 q^{33}\) \(+3.54262 q^{34}\) \(-0.354308 q^{35}\) \(-7.64958 q^{36}\) \(+0.599199 q^{37}\) \(-13.5624 q^{38}\) \(+3.68748 q^{39}\) \(-4.43262 q^{40}\) \(+11.3768 q^{41}\) \(-2.21187 q^{42}\) \(-3.60497 q^{43}\) \(-2.23034 q^{44}\) \(-0.783067 q^{45}\) \(+21.8519 q^{46}\) \(+11.3917 q^{47}\) \(-15.0068 q^{48}\) \(-6.54779 q^{49}\) \(+12.6248 q^{50}\) \(+1.63040 q^{51}\) \(-15.4259 q^{52}\) \(+10.3472 q^{53}\) \(-14.7561 q^{54}\) \(-0.228314 q^{55}\) \(+5.65743 q^{56}\) \(-6.24173 q^{57}\) \(-10.6331 q^{58}\) \(+10.3827 q^{59}\) \(-3.33649 q^{60}\) \(-6.63089 q^{61}\) \(+12.6342 q^{62}\) \(+0.999441 q^{63}\) \(+17.7960 q^{64}\) \(-1.57911 q^{65}\) \(-1.42531 q^{66}\) \(+0.165526 q^{67}\) \(-6.82047 q^{68}\) \(+10.0568 q^{69}\) \(+0.947198 q^{70}\) \(+8.38727 q^{71}\) \(+12.5037 q^{72}\) \(+8.04160 q^{73}\) \(-1.60189 q^{74}\) \(+5.81021 q^{75}\) \(+26.1111 q^{76}\) \(+0.291401 q^{77}\) \(-9.85802 q^{78}\) \(+10.6596 q^{79}\) \(+6.42643 q^{80}\) \(-2.33239 q^{81}\) \(-30.4146 q^{82}\) \(-5.72195 q^{83}\) \(+4.25842 q^{84}\) \(-0.698193 q^{85}\) \(+9.63745 q^{86}\) \(-4.89360 q^{87}\) \(+3.64562 q^{88}\) \(+5.57967 q^{89}\) \(+2.09343 q^{90}\) \(+2.01544 q^{91}\) \(-42.0706 q^{92}\) \(+5.81456 q^{93}\) \(-30.4542 q^{94}\) \(+2.67293 q^{95}\) \(+19.4170 q^{96}\) \(+11.1527 q^{97}\) \(+17.5047 q^{98}\) \(+0.644035 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67338 −1.89036 −0.945182 0.326545i \(-0.894115\pi\)
−0.945182 + 0.326545i \(0.894115\pi\)
\(3\) −1.23035 −0.710344 −0.355172 0.934801i \(-0.615578\pi\)
−0.355172 + 0.934801i \(0.615578\pi\)
\(4\) 5.14695 2.57347
\(5\) 0.526879 0.235628 0.117814 0.993036i \(-0.462411\pi\)
0.117814 + 0.993036i \(0.462411\pi\)
\(6\) 3.28919 1.34281
\(7\) −0.672464 −0.254168 −0.127084 0.991892i \(-0.540562\pi\)
−0.127084 + 0.991892i \(0.540562\pi\)
\(8\) −8.41297 −2.97444
\(9\) −1.48624 −0.495412
\(10\) −1.40855 −0.445422
\(11\) −0.433333 −0.130655 −0.0653274 0.997864i \(-0.520809\pi\)
−0.0653274 + 0.997864i \(0.520809\pi\)
\(12\) −6.33255 −1.82805
\(13\) −2.99709 −0.831244 −0.415622 0.909537i \(-0.636436\pi\)
−0.415622 + 0.909537i \(0.636436\pi\)
\(14\) 1.79775 0.480469
\(15\) −0.648246 −0.167377
\(16\) 12.1972 3.04929
\(17\) −1.32515 −0.321396 −0.160698 0.987004i \(-0.551374\pi\)
−0.160698 + 0.987004i \(0.551374\pi\)
\(18\) 3.97327 0.936509
\(19\) 5.07313 1.16386 0.581928 0.813240i \(-0.302299\pi\)
0.581928 + 0.813240i \(0.302299\pi\)
\(20\) 2.71182 0.606381
\(21\) 0.827367 0.180546
\(22\) 1.15846 0.246985
\(23\) −8.17389 −1.70437 −0.852187 0.523238i \(-0.824724\pi\)
−0.852187 + 0.523238i \(0.824724\pi\)
\(24\) 10.3509 2.11287
\(25\) −4.72240 −0.944480
\(26\) 8.01236 1.57135
\(27\) 5.51965 1.06226
\(28\) −3.46114 −0.654094
\(29\) 3.97740 0.738585 0.369292 0.929313i \(-0.379600\pi\)
0.369292 + 0.929313i \(0.379600\pi\)
\(30\) 1.73301 0.316402
\(31\) −4.72593 −0.848803 −0.424401 0.905474i \(-0.639515\pi\)
−0.424401 + 0.905474i \(0.639515\pi\)
\(32\) −15.7817 −2.78983
\(33\) 0.533151 0.0928097
\(34\) 3.54262 0.607554
\(35\) −0.354308 −0.0598889
\(36\) −7.64958 −1.27493
\(37\) 0.599199 0.0985077 0.0492539 0.998786i \(-0.484316\pi\)
0.0492539 + 0.998786i \(0.484316\pi\)
\(38\) −13.5624 −2.20011
\(39\) 3.68748 0.590469
\(40\) −4.43262 −0.700859
\(41\) 11.3768 1.77676 0.888382 0.459105i \(-0.151830\pi\)
0.888382 + 0.459105i \(0.151830\pi\)
\(42\) −2.21187 −0.341298
\(43\) −3.60497 −0.549753 −0.274877 0.961479i \(-0.588637\pi\)
−0.274877 + 0.961479i \(0.588637\pi\)
\(44\) −2.23034 −0.336236
\(45\) −0.783067 −0.116733
\(46\) 21.8519 3.22188
\(47\) 11.3917 1.66165 0.830823 0.556537i \(-0.187870\pi\)
0.830823 + 0.556537i \(0.187870\pi\)
\(48\) −15.0068 −2.16604
\(49\) −6.54779 −0.935399
\(50\) 12.6248 1.78541
\(51\) 1.63040 0.228301
\(52\) −15.4259 −2.13918
\(53\) 10.3472 1.42130 0.710652 0.703544i \(-0.248400\pi\)
0.710652 + 0.703544i \(0.248400\pi\)
\(54\) −14.7561 −2.00805
\(55\) −0.228314 −0.0307858
\(56\) 5.65743 0.756005
\(57\) −6.24173 −0.826738
\(58\) −10.6331 −1.39619
\(59\) 10.3827 1.35172 0.675859 0.737031i \(-0.263773\pi\)
0.675859 + 0.737031i \(0.263773\pi\)
\(60\) −3.33649 −0.430739
\(61\) −6.63089 −0.848999 −0.424499 0.905428i \(-0.639550\pi\)
−0.424499 + 0.905428i \(0.639550\pi\)
\(62\) 12.6342 1.60455
\(63\) 0.999441 0.125918
\(64\) 17.7960 2.22450
\(65\) −1.57911 −0.195864
\(66\) −1.42531 −0.175444
\(67\) 0.165526 0.0202222 0.0101111 0.999949i \(-0.496781\pi\)
0.0101111 + 0.999949i \(0.496781\pi\)
\(68\) −6.82047 −0.827103
\(69\) 10.0568 1.21069
\(70\) 0.947198 0.113212
\(71\) 8.38727 0.995386 0.497693 0.867353i \(-0.334181\pi\)
0.497693 + 0.867353i \(0.334181\pi\)
\(72\) 12.5037 1.47357
\(73\) 8.04160 0.941198 0.470599 0.882347i \(-0.344038\pi\)
0.470599 + 0.882347i \(0.344038\pi\)
\(74\) −1.60189 −0.186215
\(75\) 5.81021 0.670905
\(76\) 26.1111 2.99515
\(77\) 0.291401 0.0332082
\(78\) −9.85802 −1.11620
\(79\) 10.6596 1.19930 0.599650 0.800263i \(-0.295307\pi\)
0.599650 + 0.800263i \(0.295307\pi\)
\(80\) 6.42643 0.718497
\(81\) −2.33239 −0.259155
\(82\) −30.4146 −3.35873
\(83\) −5.72195 −0.628066 −0.314033 0.949412i \(-0.601680\pi\)
−0.314033 + 0.949412i \(0.601680\pi\)
\(84\) 4.25842 0.464631
\(85\) −0.698193 −0.0757297
\(86\) 9.63745 1.03923
\(87\) −4.89360 −0.524649
\(88\) 3.64562 0.388624
\(89\) 5.57967 0.591444 0.295722 0.955274i \(-0.404440\pi\)
0.295722 + 0.955274i \(0.404440\pi\)
\(90\) 2.09343 0.220667
\(91\) 2.01544 0.211275
\(92\) −42.0706 −4.38616
\(93\) 5.81456 0.602942
\(94\) −30.4542 −3.14111
\(95\) 2.67293 0.274237
\(96\) 19.4170 1.98174
\(97\) 11.1527 1.13239 0.566194 0.824272i \(-0.308415\pi\)
0.566194 + 0.824272i \(0.308415\pi\)
\(98\) 17.5047 1.76824
\(99\) 0.644035 0.0647279
\(100\) −24.3059 −2.43059
\(101\) −9.89164 −0.984255 −0.492128 0.870523i \(-0.663781\pi\)
−0.492128 + 0.870523i \(0.663781\pi\)
\(102\) −4.35867 −0.431572
\(103\) −16.8270 −1.65802 −0.829008 0.559236i \(-0.811095\pi\)
−0.829008 + 0.559236i \(0.811095\pi\)
\(104\) 25.2145 2.47248
\(105\) 0.435923 0.0425417
\(106\) −27.6621 −2.68678
\(107\) −8.54900 −0.826463 −0.413232 0.910626i \(-0.635600\pi\)
−0.413232 + 0.910626i \(0.635600\pi\)
\(108\) 28.4093 2.73369
\(109\) 5.13346 0.491697 0.245848 0.969308i \(-0.420933\pi\)
0.245848 + 0.969308i \(0.420933\pi\)
\(110\) 0.610369 0.0581964
\(111\) −0.737225 −0.0699743
\(112\) −8.20216 −0.775031
\(113\) −3.98187 −0.374582 −0.187291 0.982304i \(-0.559971\pi\)
−0.187291 + 0.982304i \(0.559971\pi\)
\(114\) 16.6865 1.56283
\(115\) −4.30665 −0.401597
\(116\) 20.4715 1.90073
\(117\) 4.45439 0.411808
\(118\) −27.7570 −2.55524
\(119\) 0.891115 0.0816884
\(120\) 5.45368 0.497851
\(121\) −10.8122 −0.982929
\(122\) 17.7269 1.60492
\(123\) −13.9975 −1.26211
\(124\) −24.3241 −2.18437
\(125\) −5.12253 −0.458173
\(126\) −2.67188 −0.238030
\(127\) 7.46274 0.662211 0.331106 0.943594i \(-0.392578\pi\)
0.331106 + 0.943594i \(0.392578\pi\)
\(128\) −16.0122 −1.41529
\(129\) 4.43538 0.390514
\(130\) 4.22155 0.370254
\(131\) −5.24800 −0.458520 −0.229260 0.973365i \(-0.573631\pi\)
−0.229260 + 0.973365i \(0.573631\pi\)
\(132\) 2.74410 0.238843
\(133\) −3.41150 −0.295815
\(134\) −0.442513 −0.0382273
\(135\) 2.90819 0.250297
\(136\) 11.1484 0.955971
\(137\) 9.24843 0.790146 0.395073 0.918650i \(-0.370719\pi\)
0.395073 + 0.918650i \(0.370719\pi\)
\(138\) −26.8855 −2.28864
\(139\) −0.131407 −0.0111458 −0.00557289 0.999984i \(-0.501774\pi\)
−0.00557289 + 0.999984i \(0.501774\pi\)
\(140\) −1.82360 −0.154122
\(141\) −14.0158 −1.18034
\(142\) −22.4223 −1.88164
\(143\) 1.29874 0.108606
\(144\) −18.1279 −1.51066
\(145\) 2.09561 0.174031
\(146\) −21.4982 −1.77921
\(147\) 8.05608 0.664455
\(148\) 3.08405 0.253507
\(149\) 16.5102 1.35257 0.676283 0.736642i \(-0.263590\pi\)
0.676283 + 0.736642i \(0.263590\pi\)
\(150\) −15.5329 −1.26825
\(151\) −17.5087 −1.42484 −0.712418 0.701756i \(-0.752400\pi\)
−0.712418 + 0.701756i \(0.752400\pi\)
\(152\) −42.6801 −3.46181
\(153\) 1.96948 0.159223
\(154\) −0.779024 −0.0627756
\(155\) −2.49000 −0.200001
\(156\) 18.9792 1.51956
\(157\) −10.3196 −0.823596 −0.411798 0.911275i \(-0.635099\pi\)
−0.411798 + 0.911275i \(0.635099\pi\)
\(158\) −28.4972 −2.26711
\(159\) −12.7307 −1.00961
\(160\) −8.31503 −0.657361
\(161\) 5.49665 0.433197
\(162\) 6.23537 0.489897
\(163\) −7.37194 −0.577415 −0.288708 0.957417i \(-0.593226\pi\)
−0.288708 + 0.957417i \(0.593226\pi\)
\(164\) 58.5560 4.57245
\(165\) 0.280906 0.0218685
\(166\) 15.2969 1.18727
\(167\) −13.8761 −1.07377 −0.536884 0.843656i \(-0.680399\pi\)
−0.536884 + 0.843656i \(0.680399\pi\)
\(168\) −6.96062 −0.537024
\(169\) −4.01743 −0.309033
\(170\) 1.86653 0.143157
\(171\) −7.53987 −0.576588
\(172\) −18.5546 −1.41478
\(173\) −19.2753 −1.46548 −0.732738 0.680511i \(-0.761758\pi\)
−0.732738 + 0.680511i \(0.761758\pi\)
\(174\) 13.0824 0.991777
\(175\) 3.17565 0.240056
\(176\) −5.28543 −0.398404
\(177\) −12.7744 −0.960184
\(178\) −14.9166 −1.11804
\(179\) 6.97589 0.521403 0.260701 0.965419i \(-0.416046\pi\)
0.260701 + 0.965419i \(0.416046\pi\)
\(180\) −4.03040 −0.300408
\(181\) 12.8941 0.958412 0.479206 0.877702i \(-0.340925\pi\)
0.479206 + 0.877702i \(0.340925\pi\)
\(182\) −5.38803 −0.399387
\(183\) 8.15833 0.603081
\(184\) 68.7667 5.06955
\(185\) 0.315706 0.0232111
\(186\) −15.5445 −1.13978
\(187\) 0.574230 0.0419919
\(188\) 58.6323 4.27620
\(189\) −3.71177 −0.269991
\(190\) −7.14574 −0.518407
\(191\) 18.7813 1.35897 0.679484 0.733690i \(-0.262204\pi\)
0.679484 + 0.733690i \(0.262204\pi\)
\(192\) −21.8954 −1.58016
\(193\) −4.36239 −0.314012 −0.157006 0.987598i \(-0.550184\pi\)
−0.157006 + 0.987598i \(0.550184\pi\)
\(194\) −29.8154 −2.14062
\(195\) 1.94286 0.139131
\(196\) −33.7011 −2.40722
\(197\) −12.4815 −0.889269 −0.444635 0.895712i \(-0.646667\pi\)
−0.444635 + 0.895712i \(0.646667\pi\)
\(198\) −1.72175 −0.122359
\(199\) 1.45333 0.103024 0.0515118 0.998672i \(-0.483596\pi\)
0.0515118 + 0.998672i \(0.483596\pi\)
\(200\) 39.7294 2.80929
\(201\) −0.203655 −0.0143647
\(202\) 26.4441 1.86060
\(203\) −2.67466 −0.187724
\(204\) 8.39157 0.587527
\(205\) 5.99422 0.418654
\(206\) 44.9850 3.13425
\(207\) 12.1483 0.844367
\(208\) −36.5560 −2.53471
\(209\) −2.19835 −0.152063
\(210\) −1.16539 −0.0804193
\(211\) −11.1832 −0.769885 −0.384943 0.922941i \(-0.625779\pi\)
−0.384943 + 0.922941i \(0.625779\pi\)
\(212\) 53.2567 3.65769
\(213\) −10.3193 −0.707066
\(214\) 22.8547 1.56232
\(215\) −1.89939 −0.129537
\(216\) −46.4366 −3.15961
\(217\) 3.17802 0.215738
\(218\) −13.7237 −0.929485
\(219\) −9.89399 −0.668574
\(220\) −1.17512 −0.0792266
\(221\) 3.97159 0.267158
\(222\) 1.97088 0.132277
\(223\) −0.806602 −0.0540140 −0.0270070 0.999635i \(-0.508598\pi\)
−0.0270070 + 0.999635i \(0.508598\pi\)
\(224\) 10.6126 0.709085
\(225\) 7.01860 0.467907
\(226\) 10.6450 0.708097
\(227\) 2.09576 0.139100 0.0695502 0.997578i \(-0.477844\pi\)
0.0695502 + 0.997578i \(0.477844\pi\)
\(228\) −32.1259 −2.12759
\(229\) 19.4942 1.28821 0.644107 0.764936i \(-0.277229\pi\)
0.644107 + 0.764936i \(0.277229\pi\)
\(230\) 11.5133 0.759165
\(231\) −0.358525 −0.0235892
\(232\) −33.4618 −2.19687
\(233\) 0.782606 0.0512702 0.0256351 0.999671i \(-0.491839\pi\)
0.0256351 + 0.999671i \(0.491839\pi\)
\(234\) −11.9083 −0.778467
\(235\) 6.00203 0.391529
\(236\) 53.4394 3.47861
\(237\) −13.1151 −0.851915
\(238\) −2.38229 −0.154421
\(239\) −1.52758 −0.0988108 −0.0494054 0.998779i \(-0.515733\pi\)
−0.0494054 + 0.998779i \(0.515733\pi\)
\(240\) −7.90677 −0.510380
\(241\) −12.7305 −0.820047 −0.410023 0.912075i \(-0.634479\pi\)
−0.410023 + 0.912075i \(0.634479\pi\)
\(242\) 28.9052 1.85809
\(243\) −13.6893 −0.878167
\(244\) −34.1288 −2.18488
\(245\) −3.44990 −0.220406
\(246\) 37.4206 2.38585
\(247\) −15.2046 −0.967449
\(248\) 39.7592 2.52471
\(249\) 7.04001 0.446142
\(250\) 13.6945 0.866113
\(251\) 5.58656 0.352620 0.176310 0.984335i \(-0.443584\pi\)
0.176310 + 0.984335i \(0.443584\pi\)
\(252\) 5.14407 0.324046
\(253\) 3.54201 0.222684
\(254\) −19.9507 −1.25182
\(255\) 0.859023 0.0537941
\(256\) 7.21450 0.450906
\(257\) 7.35478 0.458779 0.229389 0.973335i \(-0.426327\pi\)
0.229389 + 0.973335i \(0.426327\pi\)
\(258\) −11.8575 −0.738213
\(259\) −0.402940 −0.0250375
\(260\) −8.12757 −0.504051
\(261\) −5.91136 −0.365904
\(262\) 14.0299 0.866769
\(263\) −0.542651 −0.0334613 −0.0167307 0.999860i \(-0.505326\pi\)
−0.0167307 + 0.999860i \(0.505326\pi\)
\(264\) −4.48539 −0.276057
\(265\) 5.45175 0.334898
\(266\) 9.12023 0.559197
\(267\) −6.86496 −0.420129
\(268\) 0.851953 0.0520413
\(269\) −10.7367 −0.654628 −0.327314 0.944916i \(-0.606143\pi\)
−0.327314 + 0.944916i \(0.606143\pi\)
\(270\) −7.77468 −0.473152
\(271\) 25.4360 1.54513 0.772565 0.634936i \(-0.218973\pi\)
0.772565 + 0.634936i \(0.218973\pi\)
\(272\) −16.1630 −0.980029
\(273\) −2.47970 −0.150078
\(274\) −24.7245 −1.49366
\(275\) 2.04637 0.123401
\(276\) 51.7616 3.11568
\(277\) 3.52146 0.211584 0.105792 0.994388i \(-0.466262\pi\)
0.105792 + 0.994388i \(0.466262\pi\)
\(278\) 0.351300 0.0210696
\(279\) 7.02385 0.420507
\(280\) 2.98078 0.178136
\(281\) 15.2073 0.907192 0.453596 0.891207i \(-0.350141\pi\)
0.453596 + 0.891207i \(0.350141\pi\)
\(282\) 37.4694 2.23127
\(283\) −1.53754 −0.0913973 −0.0456987 0.998955i \(-0.514551\pi\)
−0.0456987 + 0.998955i \(0.514551\pi\)
\(284\) 43.1688 2.56160
\(285\) −3.28864 −0.194802
\(286\) −3.47202 −0.205305
\(287\) −7.65052 −0.451596
\(288\) 23.4553 1.38212
\(289\) −15.2440 −0.896705
\(290\) −5.60236 −0.328982
\(291\) −13.7218 −0.804384
\(292\) 41.3897 2.42215
\(293\) −6.07418 −0.354857 −0.177429 0.984134i \(-0.556778\pi\)
−0.177429 + 0.984134i \(0.556778\pi\)
\(294\) −21.5369 −1.25606
\(295\) 5.47045 0.318502
\(296\) −5.04105 −0.293005
\(297\) −2.39184 −0.138789
\(298\) −44.1379 −2.55684
\(299\) 24.4979 1.41675
\(300\) 29.9048 1.72656
\(301\) 2.42422 0.139730
\(302\) 46.8073 2.69346
\(303\) 12.1702 0.699159
\(304\) 61.8778 3.54894
\(305\) −3.49368 −0.200047
\(306\) −5.26517 −0.300990
\(307\) 34.2522 1.95487 0.977437 0.211227i \(-0.0677459\pi\)
0.977437 + 0.211227i \(0.0677459\pi\)
\(308\) 1.49982 0.0854604
\(309\) 20.7032 1.17776
\(310\) 6.65670 0.378075
\(311\) −18.5634 −1.05263 −0.526316 0.850289i \(-0.676427\pi\)
−0.526316 + 0.850289i \(0.676427\pi\)
\(312\) −31.0227 −1.75631
\(313\) 0.340296 0.0192347 0.00961733 0.999954i \(-0.496939\pi\)
0.00961733 + 0.999954i \(0.496939\pi\)
\(314\) 27.5883 1.55690
\(315\) 0.526585 0.0296697
\(316\) 54.8644 3.08636
\(317\) 7.62377 0.428194 0.214097 0.976812i \(-0.431319\pi\)
0.214097 + 0.976812i \(0.431319\pi\)
\(318\) 34.0341 1.90854
\(319\) −1.72354 −0.0964996
\(320\) 9.37636 0.524154
\(321\) 10.5183 0.587073
\(322\) −14.6946 −0.818899
\(323\) −6.72265 −0.374058
\(324\) −12.0047 −0.666928
\(325\) 14.1535 0.785093
\(326\) 19.7080 1.09152
\(327\) −6.31596 −0.349273
\(328\) −95.7131 −5.28487
\(329\) −7.66049 −0.422337
\(330\) −0.750969 −0.0413395
\(331\) −6.00859 −0.330262 −0.165131 0.986272i \(-0.552805\pi\)
−0.165131 + 0.986272i \(0.552805\pi\)
\(332\) −29.4506 −1.61631
\(333\) −0.890551 −0.0488019
\(334\) 37.0961 2.02981
\(335\) 0.0872122 0.00476491
\(336\) 10.0915 0.550538
\(337\) 8.21681 0.447598 0.223799 0.974635i \(-0.428154\pi\)
0.223799 + 0.974635i \(0.428154\pi\)
\(338\) 10.7401 0.584185
\(339\) 4.89909 0.266082
\(340\) −3.59356 −0.194888
\(341\) 2.04790 0.110900
\(342\) 20.1569 1.08996
\(343\) 9.11041 0.491916
\(344\) 30.3286 1.63521
\(345\) 5.29869 0.285272
\(346\) 51.5302 2.77028
\(347\) 10.1869 0.546860 0.273430 0.961892i \(-0.411842\pi\)
0.273430 + 0.961892i \(0.411842\pi\)
\(348\) −25.1871 −1.35017
\(349\) −17.9854 −0.962735 −0.481367 0.876519i \(-0.659860\pi\)
−0.481367 + 0.876519i \(0.659860\pi\)
\(350\) −8.48970 −0.453793
\(351\) −16.5429 −0.882994
\(352\) 6.83871 0.364505
\(353\) 8.36468 0.445207 0.222603 0.974909i \(-0.428544\pi\)
0.222603 + 0.974909i \(0.428544\pi\)
\(354\) 34.1508 1.81510
\(355\) 4.41908 0.234540
\(356\) 28.7183 1.52207
\(357\) −1.09638 −0.0580268
\(358\) −18.6492 −0.985641
\(359\) 1.55402 0.0820182 0.0410091 0.999159i \(-0.486943\pi\)
0.0410091 + 0.999159i \(0.486943\pi\)
\(360\) 6.58792 0.347214
\(361\) 6.73665 0.354561
\(362\) −34.4708 −1.81175
\(363\) 13.3028 0.698218
\(364\) 10.3734 0.543712
\(365\) 4.23695 0.221772
\(366\) −21.8103 −1.14004
\(367\) −20.9455 −1.09335 −0.546674 0.837346i \(-0.684106\pi\)
−0.546674 + 0.837346i \(0.684106\pi\)
\(368\) −99.6982 −5.19713
\(369\) −16.9087 −0.880230
\(370\) −0.844000 −0.0438775
\(371\) −6.95815 −0.361249
\(372\) 29.9272 1.55165
\(373\) −12.1408 −0.628627 −0.314314 0.949319i \(-0.601774\pi\)
−0.314314 + 0.949319i \(0.601774\pi\)
\(374\) −1.53513 −0.0793799
\(375\) 6.30251 0.325460
\(376\) −95.8378 −4.94246
\(377\) −11.9206 −0.613944
\(378\) 9.92295 0.510381
\(379\) 20.5420 1.05517 0.527586 0.849502i \(-0.323097\pi\)
0.527586 + 0.849502i \(0.323097\pi\)
\(380\) 13.7574 0.705740
\(381\) −9.18179 −0.470397
\(382\) −50.2096 −2.56894
\(383\) −13.8888 −0.709685 −0.354843 0.934926i \(-0.615466\pi\)
−0.354843 + 0.934926i \(0.615466\pi\)
\(384\) 19.7006 1.00534
\(385\) 0.153533 0.00782477
\(386\) 11.6623 0.593596
\(387\) 5.35784 0.272354
\(388\) 57.4025 2.91417
\(389\) 16.7265 0.848067 0.424034 0.905646i \(-0.360614\pi\)
0.424034 + 0.905646i \(0.360614\pi\)
\(390\) −5.19398 −0.263008
\(391\) 10.8316 0.547778
\(392\) 55.0864 2.78228
\(393\) 6.45688 0.325706
\(394\) 33.3677 1.68104
\(395\) 5.61632 0.282588
\(396\) 3.31481 0.166576
\(397\) −2.59425 −0.130202 −0.0651008 0.997879i \(-0.520737\pi\)
−0.0651008 + 0.997879i \(0.520737\pi\)
\(398\) −3.88529 −0.194752
\(399\) 4.19734 0.210130
\(400\) −57.5999 −2.87999
\(401\) −28.4494 −1.42069 −0.710347 0.703851i \(-0.751462\pi\)
−0.710347 + 0.703851i \(0.751462\pi\)
\(402\) 0.544447 0.0271545
\(403\) 14.1641 0.705563
\(404\) −50.9117 −2.53295
\(405\) −1.22889 −0.0610640
\(406\) 7.15038 0.354867
\(407\) −0.259653 −0.0128705
\(408\) −13.7165 −0.679068
\(409\) 2.46492 0.121882 0.0609412 0.998141i \(-0.480590\pi\)
0.0609412 + 0.998141i \(0.480590\pi\)
\(410\) −16.0248 −0.791409
\(411\) −11.3788 −0.561275
\(412\) −86.6078 −4.26686
\(413\) −6.98202 −0.343563
\(414\) −32.4771 −1.59616
\(415\) −3.01478 −0.147990
\(416\) 47.2991 2.31903
\(417\) 0.161677 0.00791734
\(418\) 5.87703 0.287455
\(419\) −32.3609 −1.58094 −0.790468 0.612504i \(-0.790162\pi\)
−0.790468 + 0.612504i \(0.790162\pi\)
\(420\) 2.24367 0.109480
\(421\) −31.1219 −1.51679 −0.758394 0.651796i \(-0.774016\pi\)
−0.758394 + 0.651796i \(0.774016\pi\)
\(422\) 29.8970 1.45536
\(423\) −16.9307 −0.823199
\(424\) −87.0511 −4.22758
\(425\) 6.25788 0.303552
\(426\) 27.5873 1.33661
\(427\) 4.45904 0.215788
\(428\) −44.0013 −2.12688
\(429\) −1.59790 −0.0771476
\(430\) 5.07777 0.244872
\(431\) 37.1718 1.79050 0.895252 0.445561i \(-0.146996\pi\)
0.895252 + 0.445561i \(0.146996\pi\)
\(432\) 67.3240 3.23913
\(433\) −19.5183 −0.937989 −0.468994 0.883201i \(-0.655384\pi\)
−0.468994 + 0.883201i \(0.655384\pi\)
\(434\) −8.49605 −0.407824
\(435\) −2.57834 −0.123622
\(436\) 26.4217 1.26537
\(437\) −41.4672 −1.98365
\(438\) 26.4504 1.26385
\(439\) −19.2408 −0.918313 −0.459157 0.888355i \(-0.651848\pi\)
−0.459157 + 0.888355i \(0.651848\pi\)
\(440\) 1.92080 0.0915705
\(441\) 9.73156 0.463408
\(442\) −10.6176 −0.505026
\(443\) 20.2916 0.964084 0.482042 0.876148i \(-0.339895\pi\)
0.482042 + 0.876148i \(0.339895\pi\)
\(444\) −3.79446 −0.180077
\(445\) 2.93981 0.139361
\(446\) 2.15635 0.102106
\(447\) −20.3133 −0.960787
\(448\) −11.9672 −0.565397
\(449\) −37.5653 −1.77282 −0.886409 0.462903i \(-0.846808\pi\)
−0.886409 + 0.462903i \(0.846808\pi\)
\(450\) −18.7634 −0.884513
\(451\) −4.92996 −0.232143
\(452\) −20.4944 −0.963978
\(453\) 21.5418 1.01212
\(454\) −5.60276 −0.262950
\(455\) 1.06189 0.0497823
\(456\) 52.5115 2.45908
\(457\) −10.3715 −0.485157 −0.242578 0.970132i \(-0.577993\pi\)
−0.242578 + 0.970132i \(0.577993\pi\)
\(458\) −52.1154 −2.43519
\(459\) −7.31435 −0.341405
\(460\) −22.1661 −1.03350
\(461\) −23.5141 −1.09516 −0.547581 0.836753i \(-0.684451\pi\)
−0.547581 + 0.836753i \(0.684451\pi\)
\(462\) 0.958473 0.0445922
\(463\) 37.5071 1.74310 0.871552 0.490303i \(-0.163114\pi\)
0.871552 + 0.490303i \(0.163114\pi\)
\(464\) 48.5130 2.25216
\(465\) 3.06357 0.142070
\(466\) −2.09220 −0.0969193
\(467\) −25.2513 −1.16849 −0.584245 0.811578i \(-0.698609\pi\)
−0.584245 + 0.811578i \(0.698609\pi\)
\(468\) 22.9265 1.05978
\(469\) −0.111310 −0.00513983
\(470\) −16.0457 −0.740133
\(471\) 12.6968 0.585036
\(472\) −87.3497 −4.02060
\(473\) 1.56215 0.0718279
\(474\) 35.0615 1.61043
\(475\) −23.9573 −1.09924
\(476\) 4.58652 0.210223
\(477\) −15.3784 −0.704131
\(478\) 4.08379 0.186788
\(479\) 30.0023 1.37084 0.685420 0.728148i \(-0.259619\pi\)
0.685420 + 0.728148i \(0.259619\pi\)
\(480\) 10.2304 0.466952
\(481\) −1.79586 −0.0818840
\(482\) 34.0336 1.55019
\(483\) −6.76281 −0.307718
\(484\) −55.6499 −2.52954
\(485\) 5.87614 0.266822
\(486\) 36.5966 1.66006
\(487\) −16.4354 −0.744761 −0.372381 0.928080i \(-0.621458\pi\)
−0.372381 + 0.928080i \(0.621458\pi\)
\(488\) 55.7855 2.52529
\(489\) 9.07008 0.410163
\(490\) 9.22287 0.416647
\(491\) 1.97718 0.0892290 0.0446145 0.999004i \(-0.485794\pi\)
0.0446145 + 0.999004i \(0.485794\pi\)
\(492\) −72.0444 −3.24801
\(493\) −5.27065 −0.237378
\(494\) 40.6478 1.82883
\(495\) 0.339328 0.0152517
\(496\) −57.6430 −2.58825
\(497\) −5.64014 −0.252995
\(498\) −18.8206 −0.843371
\(499\) −17.8941 −0.801048 −0.400524 0.916286i \(-0.631172\pi\)
−0.400524 + 0.916286i \(0.631172\pi\)
\(500\) −26.3654 −1.17910
\(501\) 17.0725 0.762744
\(502\) −14.9350 −0.666581
\(503\) 19.0804 0.850752 0.425376 0.905017i \(-0.360142\pi\)
0.425376 + 0.905017i \(0.360142\pi\)
\(504\) −8.40827 −0.374534
\(505\) −5.21170 −0.231918
\(506\) −9.46914 −0.420954
\(507\) 4.94285 0.219520
\(508\) 38.4103 1.70418
\(509\) 35.6708 1.58108 0.790541 0.612409i \(-0.209799\pi\)
0.790541 + 0.612409i \(0.209799\pi\)
\(510\) −2.29649 −0.101690
\(511\) −5.40769 −0.239222
\(512\) 12.7373 0.562913
\(513\) 28.0019 1.23631
\(514\) −19.6621 −0.867259
\(515\) −8.86581 −0.390674
\(516\) 22.8287 1.00498
\(517\) −4.93638 −0.217102
\(518\) 1.07721 0.0473299
\(519\) 23.7154 1.04099
\(520\) 13.2850 0.582585
\(521\) −38.8027 −1.69998 −0.849988 0.526802i \(-0.823391\pi\)
−0.849988 + 0.526802i \(0.823391\pi\)
\(522\) 15.8033 0.691691
\(523\) −13.6674 −0.597633 −0.298816 0.954311i \(-0.596592\pi\)
−0.298816 + 0.954311i \(0.596592\pi\)
\(524\) −27.0112 −1.17999
\(525\) −3.90716 −0.170522
\(526\) 1.45071 0.0632540
\(527\) 6.26256 0.272802
\(528\) 6.50293 0.283004
\(529\) 43.8124 1.90489
\(530\) −14.5746 −0.633079
\(531\) −15.4312 −0.669657
\(532\) −17.5588 −0.761271
\(533\) −34.0975 −1.47692
\(534\) 18.3526 0.794195
\(535\) −4.50429 −0.194737
\(536\) −1.39257 −0.0601497
\(537\) −8.58280 −0.370375
\(538\) 28.7032 1.23748
\(539\) 2.83737 0.122214
\(540\) 14.9683 0.644132
\(541\) −8.50269 −0.365559 −0.182780 0.983154i \(-0.558509\pi\)
−0.182780 + 0.983154i \(0.558509\pi\)
\(542\) −68.0002 −2.92086
\(543\) −15.8643 −0.680802
\(544\) 20.9130 0.896640
\(545\) 2.70471 0.115857
\(546\) 6.62917 0.283702
\(547\) −23.8810 −1.02108 −0.510538 0.859855i \(-0.670554\pi\)
−0.510538 + 0.859855i \(0.670554\pi\)
\(548\) 47.6012 2.03342
\(549\) 9.85507 0.420604
\(550\) −5.47072 −0.233272
\(551\) 20.1779 0.859606
\(552\) −84.6072 −3.60112
\(553\) −7.16821 −0.304823
\(554\) −9.41420 −0.399971
\(555\) −0.388429 −0.0164879
\(556\) −0.676344 −0.0286834
\(557\) −33.6876 −1.42739 −0.713695 0.700457i \(-0.752980\pi\)
−0.713695 + 0.700457i \(0.752980\pi\)
\(558\) −18.7774 −0.794911
\(559\) 10.8044 0.456979
\(560\) −4.32155 −0.182619
\(561\) −0.706505 −0.0298286
\(562\) −40.6549 −1.71492
\(563\) −18.1592 −0.765318 −0.382659 0.923890i \(-0.624992\pi\)
−0.382659 + 0.923890i \(0.624992\pi\)
\(564\) −72.1383 −3.03757
\(565\) −2.09796 −0.0882619
\(566\) 4.11043 0.172774
\(567\) 1.56845 0.0658688
\(568\) −70.5619 −2.96071
\(569\) 11.4372 0.479471 0.239735 0.970838i \(-0.422939\pi\)
0.239735 + 0.970838i \(0.422939\pi\)
\(570\) 8.79177 0.368247
\(571\) −22.2829 −0.932511 −0.466255 0.884650i \(-0.654397\pi\)
−0.466255 + 0.884650i \(0.654397\pi\)
\(572\) 6.68454 0.279495
\(573\) −23.1076 −0.965335
\(574\) 20.4527 0.853680
\(575\) 38.6004 1.60975
\(576\) −26.4491 −1.10205
\(577\) 27.9761 1.16466 0.582331 0.812952i \(-0.302141\pi\)
0.582331 + 0.812952i \(0.302141\pi\)
\(578\) 40.7529 1.69510
\(579\) 5.36727 0.223056
\(580\) 10.7860 0.447864
\(581\) 3.84781 0.159634
\(582\) 36.6835 1.52058
\(583\) −4.48380 −0.185700
\(584\) −67.6538 −2.79953
\(585\) 2.34692 0.0970334
\(586\) 16.2386 0.670809
\(587\) 22.8350 0.942501 0.471250 0.881999i \(-0.343803\pi\)
0.471250 + 0.881999i \(0.343803\pi\)
\(588\) 41.4642 1.70996
\(589\) −23.9753 −0.987884
\(590\) −14.6246 −0.602084
\(591\) 15.3566 0.631687
\(592\) 7.30853 0.300379
\(593\) −9.79407 −0.402194 −0.201097 0.979571i \(-0.564451\pi\)
−0.201097 + 0.979571i \(0.564451\pi\)
\(594\) 6.39430 0.262361
\(595\) 0.469510 0.0192480
\(596\) 84.9770 3.48079
\(597\) −1.78810 −0.0731821
\(598\) −65.4921 −2.67817
\(599\) −7.08905 −0.289651 −0.144825 0.989457i \(-0.546262\pi\)
−0.144825 + 0.989457i \(0.546262\pi\)
\(600\) −48.8811 −1.99556
\(601\) 16.7877 0.684785 0.342392 0.939557i \(-0.388763\pi\)
0.342392 + 0.939557i \(0.388763\pi\)
\(602\) −6.48085 −0.264140
\(603\) −0.246011 −0.0100183
\(604\) −90.1162 −3.66678
\(605\) −5.69674 −0.231605
\(606\) −32.5355 −1.32166
\(607\) 45.5633 1.84936 0.924679 0.380747i \(-0.124333\pi\)
0.924679 + 0.380747i \(0.124333\pi\)
\(608\) −80.0625 −3.24696
\(609\) 3.29077 0.133349
\(610\) 9.33992 0.378162
\(611\) −34.1419 −1.38123
\(612\) 10.1368 0.409757
\(613\) −36.3515 −1.46822 −0.734112 0.679028i \(-0.762401\pi\)
−0.734112 + 0.679028i \(0.762401\pi\)
\(614\) −91.5689 −3.69542
\(615\) −7.37500 −0.297389
\(616\) −2.45155 −0.0987757
\(617\) 15.9257 0.641145 0.320572 0.947224i \(-0.396125\pi\)
0.320572 + 0.947224i \(0.396125\pi\)
\(618\) −55.3474 −2.22640
\(619\) 1.06984 0.0430007 0.0215003 0.999769i \(-0.493156\pi\)
0.0215003 + 0.999769i \(0.493156\pi\)
\(620\) −12.8159 −0.514698
\(621\) −45.1170 −1.81048
\(622\) 49.6269 1.98986
\(623\) −3.75213 −0.150326
\(624\) 44.9768 1.80051
\(625\) 20.9130 0.836522
\(626\) −0.909739 −0.0363605
\(627\) 2.70475 0.108017
\(628\) −53.1146 −2.11950
\(629\) −0.794028 −0.0316600
\(630\) −1.40776 −0.0560865
\(631\) 6.38405 0.254145 0.127073 0.991893i \(-0.459442\pi\)
0.127073 + 0.991893i \(0.459442\pi\)
\(632\) −89.6790 −3.56724
\(633\) 13.7593 0.546883
\(634\) −20.3812 −0.809442
\(635\) 3.93196 0.156035
\(636\) −65.5245 −2.59821
\(637\) 19.6243 0.777545
\(638\) 4.60767 0.182419
\(639\) −12.4655 −0.493126
\(640\) −8.43648 −0.333481
\(641\) −45.2672 −1.78795 −0.893973 0.448121i \(-0.852093\pi\)
−0.893973 + 0.448121i \(0.852093\pi\)
\(642\) −28.1193 −1.10978
\(643\) 0.352953 0.0139191 0.00695955 0.999976i \(-0.497785\pi\)
0.00695955 + 0.999976i \(0.497785\pi\)
\(644\) 28.2910 1.11482
\(645\) 2.33691 0.0920158
\(646\) 17.9722 0.707106
\(647\) −32.3418 −1.27149 −0.635743 0.771901i \(-0.719306\pi\)
−0.635743 + 0.771901i \(0.719306\pi\)
\(648\) 19.6224 0.770840
\(649\) −4.49918 −0.176608
\(650\) −37.8376 −1.48411
\(651\) −3.91008 −0.153248
\(652\) −37.9430 −1.48596
\(653\) 22.4004 0.876596 0.438298 0.898830i \(-0.355581\pi\)
0.438298 + 0.898830i \(0.355581\pi\)
\(654\) 16.8849 0.660254
\(655\) −2.76506 −0.108040
\(656\) 138.765 5.41787
\(657\) −11.9517 −0.466281
\(658\) 20.4794 0.798370
\(659\) 15.6610 0.610066 0.305033 0.952342i \(-0.401332\pi\)
0.305033 + 0.952342i \(0.401332\pi\)
\(660\) 1.44581 0.0562781
\(661\) 10.9165 0.424604 0.212302 0.977204i \(-0.431904\pi\)
0.212302 + 0.977204i \(0.431904\pi\)
\(662\) 16.0632 0.624315
\(663\) −4.88645 −0.189774
\(664\) 48.1386 1.86814
\(665\) −1.79745 −0.0697021
\(666\) 2.38078 0.0922533
\(667\) −32.5108 −1.25882
\(668\) −71.4197 −2.76331
\(669\) 0.992403 0.0383685
\(670\) −0.233151 −0.00900741
\(671\) 2.87338 0.110926
\(672\) −13.0572 −0.503694
\(673\) −4.54143 −0.175059 −0.0875297 0.996162i \(-0.527897\pi\)
−0.0875297 + 0.996162i \(0.527897\pi\)
\(674\) −21.9666 −0.846123
\(675\) −26.0660 −1.00328
\(676\) −20.6775 −0.795288
\(677\) 31.8208 1.22297 0.611486 0.791255i \(-0.290572\pi\)
0.611486 + 0.791255i \(0.290572\pi\)
\(678\) −13.0971 −0.502992
\(679\) −7.49981 −0.287816
\(680\) 5.87388 0.225253
\(681\) −2.57852 −0.0988091
\(682\) −5.47481 −0.209641
\(683\) −39.0354 −1.49365 −0.746823 0.665023i \(-0.768422\pi\)
−0.746823 + 0.665023i \(0.768422\pi\)
\(684\) −38.8073 −1.48383
\(685\) 4.87280 0.186180
\(686\) −24.3556 −0.929900
\(687\) −23.9847 −0.915074
\(688\) −43.9704 −1.67636
\(689\) −31.0117 −1.18145
\(690\) −14.1654 −0.539268
\(691\) −22.0686 −0.839531 −0.419765 0.907633i \(-0.637888\pi\)
−0.419765 + 0.907633i \(0.637888\pi\)
\(692\) −99.2091 −3.77136
\(693\) −0.433090 −0.0164517
\(694\) −27.2333 −1.03376
\(695\) −0.0692355 −0.00262625
\(696\) 41.1697 1.56053
\(697\) −15.0760 −0.571044
\(698\) 48.0817 1.81992
\(699\) −0.962880 −0.0364195
\(700\) 16.3449 0.617778
\(701\) 17.7782 0.671475 0.335737 0.941956i \(-0.391015\pi\)
0.335737 + 0.941956i \(0.391015\pi\)
\(702\) 44.2254 1.66918
\(703\) 3.03982 0.114649
\(704\) −7.71160 −0.290642
\(705\) −7.38461 −0.278120
\(706\) −22.3619 −0.841603
\(707\) 6.65178 0.250166
\(708\) −65.7492 −2.47101
\(709\) 40.3518 1.51544 0.757722 0.652578i \(-0.226313\pi\)
0.757722 + 0.652578i \(0.226313\pi\)
\(710\) −11.8139 −0.443366
\(711\) −15.8427 −0.594147
\(712\) −46.9416 −1.75921
\(713\) 38.6293 1.44668
\(714\) 2.93105 0.109692
\(715\) 0.684278 0.0255906
\(716\) 35.9046 1.34182
\(717\) 1.87946 0.0701896
\(718\) −4.15449 −0.155044
\(719\) −43.6635 −1.62837 −0.814186 0.580603i \(-0.802817\pi\)
−0.814186 + 0.580603i \(0.802817\pi\)
\(720\) −9.55119 −0.355952
\(721\) 11.3156 0.421414
\(722\) −18.0096 −0.670249
\(723\) 15.6630 0.582515
\(724\) 66.3653 2.46645
\(725\) −18.7829 −0.697578
\(726\) −35.5635 −1.31988
\(727\) 46.6480 1.73008 0.865040 0.501703i \(-0.167293\pi\)
0.865040 + 0.501703i \(0.167293\pi\)
\(728\) −16.9558 −0.628425
\(729\) 23.8398 0.882955
\(730\) −11.3270 −0.419230
\(731\) 4.77712 0.176688
\(732\) 41.9905 1.55201
\(733\) −35.0773 −1.29561 −0.647804 0.761807i \(-0.724312\pi\)
−0.647804 + 0.761807i \(0.724312\pi\)
\(734\) 55.9953 2.06682
\(735\) 4.24458 0.156564
\(736\) 128.998 4.75491
\(737\) −0.0717278 −0.00264213
\(738\) 45.2033 1.66395
\(739\) 13.8722 0.510298 0.255149 0.966902i \(-0.417875\pi\)
0.255149 + 0.966902i \(0.417875\pi\)
\(740\) 1.62492 0.0597332
\(741\) 18.7071 0.687221
\(742\) 18.6018 0.682893
\(743\) −48.7075 −1.78691 −0.893453 0.449156i \(-0.851725\pi\)
−0.893453 + 0.449156i \(0.851725\pi\)
\(744\) −48.9177 −1.79341
\(745\) 8.69887 0.318702
\(746\) 32.4570 1.18833
\(747\) 8.50417 0.311151
\(748\) 2.95553 0.108065
\(749\) 5.74890 0.210060
\(750\) −16.8490 −0.615238
\(751\) 12.0948 0.441344 0.220672 0.975348i \(-0.429175\pi\)
0.220672 + 0.975348i \(0.429175\pi\)
\(752\) 138.946 5.06684
\(753\) −6.87343 −0.250482
\(754\) 31.8684 1.16058
\(755\) −9.22495 −0.335730
\(756\) −19.1043 −0.694815
\(757\) −34.3271 −1.24764 −0.623819 0.781569i \(-0.714420\pi\)
−0.623819 + 0.781569i \(0.714420\pi\)
\(758\) −54.9165 −1.99466
\(759\) −4.35792 −0.158182
\(760\) −22.4873 −0.815699
\(761\) −26.4451 −0.958635 −0.479317 0.877642i \(-0.659116\pi\)
−0.479317 + 0.877642i \(0.659116\pi\)
\(762\) 24.5464 0.889222
\(763\) −3.45207 −0.124973
\(764\) 96.6665 3.49727
\(765\) 1.03768 0.0375174
\(766\) 37.1300 1.34156
\(767\) −31.1180 −1.12361
\(768\) −8.87636 −0.320298
\(769\) −23.7801 −0.857533 −0.428767 0.903415i \(-0.641052\pi\)
−0.428767 + 0.903415i \(0.641052\pi\)
\(770\) −0.410452 −0.0147917
\(771\) −9.04897 −0.325891
\(772\) −22.4530 −0.808100
\(773\) −30.0801 −1.08191 −0.540954 0.841052i \(-0.681937\pi\)
−0.540954 + 0.841052i \(0.681937\pi\)
\(774\) −14.3235 −0.514849
\(775\) 22.3177 0.801677
\(776\) −93.8276 −3.36821
\(777\) 0.495758 0.0177852
\(778\) −44.7163 −1.60316
\(779\) 57.7162 2.06790
\(780\) 9.99977 0.358049
\(781\) −3.63448 −0.130052
\(782\) −28.9570 −1.03550
\(783\) 21.9538 0.784566
\(784\) −79.8645 −2.85230
\(785\) −5.43720 −0.194062
\(786\) −17.2617 −0.615703
\(787\) −12.0057 −0.427957 −0.213978 0.976838i \(-0.568642\pi\)
−0.213978 + 0.976838i \(0.568642\pi\)
\(788\) −64.2416 −2.28851
\(789\) 0.667652 0.0237690
\(790\) −15.0146 −0.534194
\(791\) 2.67766 0.0952067
\(792\) −5.41825 −0.192529
\(793\) 19.8734 0.705725
\(794\) 6.93540 0.246128
\(795\) −6.70756 −0.237893
\(796\) 7.48019 0.265128
\(797\) −5.54371 −0.196368 −0.0981841 0.995168i \(-0.531303\pi\)
−0.0981841 + 0.995168i \(0.531303\pi\)
\(798\) −11.2211 −0.397222
\(799\) −15.0956 −0.534046
\(800\) 74.5273 2.63494
\(801\) −8.29271 −0.293009
\(802\) 76.0560 2.68563
\(803\) −3.48469 −0.122972
\(804\) −1.04820 −0.0369672
\(805\) 2.89607 0.102073
\(806\) −37.8659 −1.33377
\(807\) 13.2099 0.465011
\(808\) 83.2181 2.92760
\(809\) 7.18058 0.252456 0.126228 0.992001i \(-0.459713\pi\)
0.126228 + 0.992001i \(0.459713\pi\)
\(810\) 3.28529 0.115433
\(811\) −55.9250 −1.96379 −0.981896 0.189420i \(-0.939339\pi\)
−0.981896 + 0.189420i \(0.939339\pi\)
\(812\) −13.7663 −0.483104
\(813\) −31.2953 −1.09757
\(814\) 0.694149 0.0243299
\(815\) −3.88412 −0.136055
\(816\) 19.8862 0.696157
\(817\) −18.2885 −0.639834
\(818\) −6.58966 −0.230402
\(819\) −2.99542 −0.104668
\(820\) 30.8519 1.07740
\(821\) −21.4400 −0.748262 −0.374131 0.927376i \(-0.622059\pi\)
−0.374131 + 0.927376i \(0.622059\pi\)
\(822\) 30.4199 1.06101
\(823\) 16.6799 0.581424 0.290712 0.956811i \(-0.406108\pi\)
0.290712 + 0.956811i \(0.406108\pi\)
\(824\) 141.565 4.93166
\(825\) −2.51775 −0.0876569
\(826\) 18.6656 0.649459
\(827\) −28.6145 −0.995025 −0.497512 0.867457i \(-0.665753\pi\)
−0.497512 + 0.867457i \(0.665753\pi\)
\(828\) 62.5268 2.17296
\(829\) −43.4564 −1.50930 −0.754651 0.656127i \(-0.772194\pi\)
−0.754651 + 0.656127i \(0.772194\pi\)
\(830\) 8.05964 0.279754
\(831\) −4.33264 −0.150298
\(832\) −53.3364 −1.84911
\(833\) 8.67679 0.300633
\(834\) −0.432223 −0.0149666
\(835\) −7.31105 −0.253009
\(836\) −11.3148 −0.391331
\(837\) −26.0855 −0.901646
\(838\) 86.5130 2.98854
\(839\) 30.8620 1.06547 0.532737 0.846281i \(-0.321163\pi\)
0.532737 + 0.846281i \(0.321163\pi\)
\(840\) −3.66741 −0.126538
\(841\) −13.1803 −0.454492
\(842\) 83.2006 2.86728
\(843\) −18.7103 −0.644418
\(844\) −57.5595 −1.98128
\(845\) −2.11670 −0.0728167
\(846\) 45.2622 1.55615
\(847\) 7.27084 0.249829
\(848\) 126.207 4.33397
\(849\) 1.89171 0.0649235
\(850\) −16.7297 −0.573823
\(851\) −4.89779 −0.167894
\(852\) −53.1128 −1.81961
\(853\) 34.2011 1.17102 0.585512 0.810664i \(-0.300893\pi\)
0.585512 + 0.810664i \(0.300893\pi\)
\(854\) −11.9207 −0.407918
\(855\) −3.97260 −0.135860
\(856\) 71.9225 2.45826
\(857\) 26.5403 0.906599 0.453300 0.891358i \(-0.350247\pi\)
0.453300 + 0.891358i \(0.350247\pi\)
\(858\) 4.27180 0.145837
\(859\) −54.7593 −1.86836 −0.934182 0.356796i \(-0.883869\pi\)
−0.934182 + 0.356796i \(0.883869\pi\)
\(860\) −9.77604 −0.333360
\(861\) 9.41283 0.320788
\(862\) −99.3743 −3.38470
\(863\) 17.8293 0.606918 0.303459 0.952845i \(-0.401858\pi\)
0.303459 + 0.952845i \(0.401858\pi\)
\(864\) −87.1092 −2.96352
\(865\) −10.1558 −0.345306
\(866\) 52.1797 1.77314
\(867\) 18.7555 0.636969
\(868\) 16.3571 0.555197
\(869\) −4.61916 −0.156694
\(870\) 6.89287 0.233690
\(871\) −0.496097 −0.0168096
\(872\) −43.1877 −1.46252
\(873\) −16.5756 −0.560998
\(874\) 110.857 3.74981
\(875\) 3.44472 0.116453
\(876\) −50.9239 −1.72056
\(877\) 0.627910 0.0212030 0.0106015 0.999944i \(-0.496625\pi\)
0.0106015 + 0.999944i \(0.496625\pi\)
\(878\) 51.4379 1.73595
\(879\) 7.47337 0.252071
\(880\) −2.78478 −0.0938750
\(881\) −6.26350 −0.211023 −0.105511 0.994418i \(-0.533648\pi\)
−0.105511 + 0.994418i \(0.533648\pi\)
\(882\) −26.0161 −0.876009
\(883\) 18.0996 0.609099 0.304550 0.952496i \(-0.401494\pi\)
0.304550 + 0.952496i \(0.401494\pi\)
\(884\) 20.4416 0.687525
\(885\) −6.73057 −0.226246
\(886\) −54.2472 −1.82247
\(887\) −30.9360 −1.03873 −0.519365 0.854552i \(-0.673832\pi\)
−0.519365 + 0.854552i \(0.673832\pi\)
\(888\) 6.20226 0.208134
\(889\) −5.01843 −0.168313
\(890\) −7.85923 −0.263442
\(891\) 1.01070 0.0338598
\(892\) −4.15153 −0.139004
\(893\) 57.7914 1.93392
\(894\) 54.3052 1.81624
\(895\) 3.67545 0.122857
\(896\) 10.7676 0.359721
\(897\) −30.1410 −1.00638
\(898\) 100.426 3.35127
\(899\) −18.7969 −0.626913
\(900\) 36.1243 1.20414
\(901\) −13.7116 −0.456801
\(902\) 13.1796 0.438834
\(903\) −2.98264 −0.0992560
\(904\) 33.4993 1.11417
\(905\) 6.79364 0.225828
\(906\) −57.5894 −1.91328
\(907\) −45.2965 −1.50405 −0.752023 0.659137i \(-0.770922\pi\)
−0.752023 + 0.659137i \(0.770922\pi\)
\(908\) 10.7868 0.357971
\(909\) 14.7013 0.487612
\(910\) −2.83884 −0.0941066
\(911\) −6.48882 −0.214984 −0.107492 0.994206i \(-0.534282\pi\)
−0.107492 + 0.994206i \(0.534282\pi\)
\(912\) −76.1314 −2.52096
\(913\) 2.47951 0.0820598
\(914\) 27.7268 0.917122
\(915\) 4.29845 0.142102
\(916\) 100.336 3.31518
\(917\) 3.52909 0.116541
\(918\) 19.5540 0.645379
\(919\) −37.9442 −1.25166 −0.625832 0.779958i \(-0.715240\pi\)
−0.625832 + 0.779958i \(0.715240\pi\)
\(920\) 36.2317 1.19453
\(921\) −42.1422 −1.38863
\(922\) 62.8621 2.07025
\(923\) −25.1374 −0.827409
\(924\) −1.84531 −0.0607063
\(925\) −2.82966 −0.0930385
\(926\) −100.271 −3.29510
\(927\) 25.0089 0.821402
\(928\) −62.7700 −2.06053
\(929\) −18.4086 −0.603968 −0.301984 0.953313i \(-0.597649\pi\)
−0.301984 + 0.953313i \(0.597649\pi\)
\(930\) −8.19008 −0.268563
\(931\) −33.2178 −1.08867
\(932\) 4.02803 0.131943
\(933\) 22.8395 0.747731
\(934\) 67.5062 2.20887
\(935\) 0.302550 0.00989444
\(936\) −37.4747 −1.22490
\(937\) 22.8883 0.747728 0.373864 0.927484i \(-0.378033\pi\)
0.373864 + 0.927484i \(0.378033\pi\)
\(938\) 0.297574 0.00971615
\(939\) −0.418683 −0.0136632
\(940\) 30.8921 1.00759
\(941\) −19.6893 −0.641853 −0.320927 0.947104i \(-0.603994\pi\)
−0.320927 + 0.947104i \(0.603994\pi\)
\(942\) −33.9432 −1.10593
\(943\) −92.9930 −3.02827
\(944\) 126.640 4.12178
\(945\) −1.95565 −0.0636174
\(946\) −4.17622 −0.135781
\(947\) 38.2568 1.24318 0.621590 0.783343i \(-0.286487\pi\)
0.621590 + 0.783343i \(0.286487\pi\)
\(948\) −67.5025 −2.19238
\(949\) −24.1014 −0.782366
\(950\) 64.0470 2.07796
\(951\) −9.37992 −0.304165
\(952\) −7.49693 −0.242977
\(953\) 44.2121 1.43217 0.716085 0.698013i \(-0.245932\pi\)
0.716085 + 0.698013i \(0.245932\pi\)
\(954\) 41.1124 1.33106
\(955\) 9.89549 0.320210
\(956\) −7.86236 −0.254287
\(957\) 2.12056 0.0685479
\(958\) −80.2075 −2.59139
\(959\) −6.21924 −0.200830
\(960\) −11.5362 −0.372330
\(961\) −8.66554 −0.279534
\(962\) 4.80100 0.154790
\(963\) 12.7058 0.409440
\(964\) −65.5234 −2.11037
\(965\) −2.29845 −0.0739898
\(966\) 18.0795 0.581700
\(967\) 13.4138 0.431359 0.215680 0.976464i \(-0.430803\pi\)
0.215680 + 0.976464i \(0.430803\pi\)
\(968\) 90.9630 2.92366
\(969\) 8.27122 0.265710
\(970\) −15.7091 −0.504390
\(971\) 54.4020 1.74584 0.872921 0.487861i \(-0.162223\pi\)
0.872921 + 0.487861i \(0.162223\pi\)
\(972\) −70.4580 −2.25994
\(973\) 0.0883665 0.00283290
\(974\) 43.9381 1.40787
\(975\) −17.4137 −0.557686
\(976\) −80.8781 −2.58884
\(977\) −18.6457 −0.596529 −0.298264 0.954483i \(-0.596408\pi\)
−0.298264 + 0.954483i \(0.596408\pi\)
\(978\) −24.2477 −0.775357
\(979\) −2.41785 −0.0772750
\(980\) −17.7564 −0.567208
\(981\) −7.62954 −0.243592
\(982\) −5.28576 −0.168675
\(983\) 5.29232 0.168799 0.0843994 0.996432i \(-0.473103\pi\)
0.0843994 + 0.996432i \(0.473103\pi\)
\(984\) 117.761 3.75407
\(985\) −6.57624 −0.209536
\(986\) 14.0904 0.448731
\(987\) 9.42510 0.300004
\(988\) −78.2575 −2.48970
\(989\) 29.4666 0.936985
\(990\) −0.907153 −0.0288312
\(991\) 33.9976 1.07997 0.539984 0.841675i \(-0.318430\pi\)
0.539984 + 0.841675i \(0.318430\pi\)
\(992\) 74.5831 2.36802
\(993\) 7.39268 0.234600
\(994\) 15.0782 0.478252
\(995\) 0.765727 0.0242752
\(996\) 36.2346 1.14814
\(997\) −25.4203 −0.805068 −0.402534 0.915405i \(-0.631870\pi\)
−0.402534 + 0.915405i \(0.631870\pi\)
\(998\) 47.8376 1.51427
\(999\) 3.30737 0.104640
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 \(a_p\))