Properties

Label 4019.2.a.b.1.11
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.59341 q^{2}\) \(+1.69325 q^{3}\) \(+4.72575 q^{4}\) \(-3.22826 q^{5}\) \(-4.39129 q^{6}\) \(-0.750732 q^{7}\) \(-7.06898 q^{8}\) \(-0.132895 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.59341 q^{2}\) \(+1.69325 q^{3}\) \(+4.72575 q^{4}\) \(-3.22826 q^{5}\) \(-4.39129 q^{6}\) \(-0.750732 q^{7}\) \(-7.06898 q^{8}\) \(-0.132895 q^{9}\) \(+8.37219 q^{10}\) \(-1.90047 q^{11}\) \(+8.00190 q^{12}\) \(+3.93841 q^{13}\) \(+1.94695 q^{14}\) \(-5.46626 q^{15}\) \(+8.88124 q^{16}\) \(-5.08204 q^{17}\) \(+0.344651 q^{18}\) \(-5.14799 q^{19}\) \(-15.2560 q^{20}\) \(-1.27118 q^{21}\) \(+4.92868 q^{22}\) \(+0.476522 q^{23}\) \(-11.9696 q^{24}\) \(+5.42167 q^{25}\) \(-10.2139 q^{26}\) \(-5.30478 q^{27}\) \(-3.54778 q^{28}\) \(-8.68999 q^{29}\) \(+14.1762 q^{30}\) \(+2.91651 q^{31}\) \(-8.89469 q^{32}\) \(-3.21797 q^{33}\) \(+13.1798 q^{34}\) \(+2.42356 q^{35}\) \(-0.628029 q^{36}\) \(-3.88758 q^{37}\) \(+13.3508 q^{38}\) \(+6.66873 q^{39}\) \(+22.8205 q^{40}\) \(+3.93068 q^{41}\) \(+3.29668 q^{42}\) \(+11.6403 q^{43}\) \(-8.98114 q^{44}\) \(+0.429020 q^{45}\) \(-1.23581 q^{46}\) \(+6.60193 q^{47}\) \(+15.0382 q^{48}\) \(-6.43640 q^{49}\) \(-14.0606 q^{50}\) \(-8.60518 q^{51}\) \(+18.6120 q^{52}\) \(-12.6826 q^{53}\) \(+13.7575 q^{54}\) \(+6.13520 q^{55}\) \(+5.30691 q^{56}\) \(-8.71685 q^{57}\) \(+22.5367 q^{58}\) \(+1.95762 q^{59}\) \(-25.8322 q^{60}\) \(-7.61692 q^{61}\) \(-7.56369 q^{62}\) \(+0.0997685 q^{63}\) \(+5.30505 q^{64}\) \(-12.7142 q^{65}\) \(+8.34551 q^{66}\) \(+6.12890 q^{67}\) \(-24.0165 q^{68}\) \(+0.806872 q^{69}\) \(-6.28527 q^{70}\) \(+13.0944 q^{71}\) \(+0.939432 q^{72}\) \(+0.368318 q^{73}\) \(+10.0821 q^{74}\) \(+9.18025 q^{75}\) \(-24.3281 q^{76}\) \(+1.42674 q^{77}\) \(-17.2947 q^{78}\) \(-2.29585 q^{79}\) \(-28.6710 q^{80}\) \(-8.58365 q^{81}\) \(-10.1938 q^{82}\) \(+5.89811 q^{83}\) \(-6.00728 q^{84}\) \(+16.4061 q^{85}\) \(-30.1881 q^{86}\) \(-14.7144 q^{87}\) \(+13.4344 q^{88}\) \(-9.35226 q^{89}\) \(-1.11262 q^{90}\) \(-2.95669 q^{91}\) \(+2.25192 q^{92}\) \(+4.93839 q^{93}\) \(-17.1215 q^{94}\) \(+16.6191 q^{95}\) \(-15.0610 q^{96}\) \(+0.838216 q^{97}\) \(+16.6922 q^{98}\) \(+0.252563 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59341 −1.83381 −0.916907 0.399100i \(-0.869323\pi\)
−0.916907 + 0.399100i \(0.869323\pi\)
\(3\) 1.69325 0.977600 0.488800 0.872396i \(-0.337435\pi\)
0.488800 + 0.872396i \(0.337435\pi\)
\(4\) 4.72575 2.36288
\(5\) −3.22826 −1.44372 −0.721861 0.692038i \(-0.756713\pi\)
−0.721861 + 0.692038i \(0.756713\pi\)
\(6\) −4.39129 −1.79274
\(7\) −0.750732 −0.283750 −0.141875 0.989885i \(-0.545313\pi\)
−0.141875 + 0.989885i \(0.545313\pi\)
\(8\) −7.06898 −2.49926
\(9\) −0.132895 −0.0442983
\(10\) 8.37219 2.64752
\(11\) −1.90047 −0.573012 −0.286506 0.958078i \(-0.592494\pi\)
−0.286506 + 0.958078i \(0.592494\pi\)
\(12\) 8.00190 2.30995
\(13\) 3.93841 1.09232 0.546160 0.837681i \(-0.316089\pi\)
0.546160 + 0.837681i \(0.316089\pi\)
\(14\) 1.94695 0.520345
\(15\) −5.46626 −1.41138
\(16\) 8.88124 2.22031
\(17\) −5.08204 −1.23258 −0.616288 0.787521i \(-0.711364\pi\)
−0.616288 + 0.787521i \(0.711364\pi\)
\(18\) 0.344651 0.0812349
\(19\) −5.14799 −1.18103 −0.590515 0.807027i \(-0.701075\pi\)
−0.590515 + 0.807027i \(0.701075\pi\)
\(20\) −15.2560 −3.41134
\(21\) −1.27118 −0.277394
\(22\) 4.92868 1.05080
\(23\) 0.476522 0.0993616 0.0496808 0.998765i \(-0.484180\pi\)
0.0496808 + 0.998765i \(0.484180\pi\)
\(24\) −11.9696 −2.44328
\(25\) 5.42167 1.08433
\(26\) −10.2139 −2.00311
\(27\) −5.30478 −1.02091
\(28\) −3.54778 −0.670467
\(29\) −8.68999 −1.61369 −0.806846 0.590762i \(-0.798827\pi\)
−0.806846 + 0.590762i \(0.798827\pi\)
\(30\) 14.1762 2.58821
\(31\) 2.91651 0.523821 0.261910 0.965092i \(-0.415648\pi\)
0.261910 + 0.965092i \(0.415648\pi\)
\(32\) −8.89469 −1.57237
\(33\) −3.21797 −0.560177
\(34\) 13.1798 2.26032
\(35\) 2.42356 0.409656
\(36\) −0.628029 −0.104671
\(37\) −3.88758 −0.639114 −0.319557 0.947567i \(-0.603534\pi\)
−0.319557 + 0.947567i \(0.603534\pi\)
\(38\) 13.3508 2.16579
\(39\) 6.66873 1.06785
\(40\) 22.8205 3.60824
\(41\) 3.93068 0.613869 0.306935 0.951731i \(-0.400697\pi\)
0.306935 + 0.951731i \(0.400697\pi\)
\(42\) 3.29668 0.508689
\(43\) 11.6403 1.77513 0.887567 0.460679i \(-0.152394\pi\)
0.887567 + 0.460679i \(0.152394\pi\)
\(44\) −8.98114 −1.35396
\(45\) 0.429020 0.0639545
\(46\) −1.23581 −0.182211
\(47\) 6.60193 0.962990 0.481495 0.876449i \(-0.340094\pi\)
0.481495 + 0.876449i \(0.340094\pi\)
\(48\) 15.0382 2.17057
\(49\) −6.43640 −0.919486
\(50\) −14.0606 −1.98847
\(51\) −8.60518 −1.20497
\(52\) 18.6120 2.58102
\(53\) −12.6826 −1.74209 −0.871043 0.491208i \(-0.836556\pi\)
−0.871043 + 0.491208i \(0.836556\pi\)
\(54\) 13.7575 1.87215
\(55\) 6.13520 0.827271
\(56\) 5.30691 0.709166
\(57\) −8.71685 −1.15458
\(58\) 22.5367 2.95921
\(59\) 1.95762 0.254860 0.127430 0.991848i \(-0.459327\pi\)
0.127430 + 0.991848i \(0.459327\pi\)
\(60\) −25.8322 −3.33492
\(61\) −7.61692 −0.975247 −0.487623 0.873054i \(-0.662136\pi\)
−0.487623 + 0.873054i \(0.662136\pi\)
\(62\) −7.56369 −0.960590
\(63\) 0.0997685 0.0125697
\(64\) 5.30505 0.663132
\(65\) −12.7142 −1.57701
\(66\) 8.34551 1.02726
\(67\) 6.12890 0.748764 0.374382 0.927275i \(-0.377855\pi\)
0.374382 + 0.927275i \(0.377855\pi\)
\(68\) −24.0165 −2.91242
\(69\) 0.806872 0.0971359
\(70\) −6.28527 −0.751234
\(71\) 13.0944 1.55401 0.777007 0.629492i \(-0.216737\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(72\) 0.939432 0.110713
\(73\) 0.368318 0.0431084 0.0215542 0.999768i \(-0.493139\pi\)
0.0215542 + 0.999768i \(0.493139\pi\)
\(74\) 10.0821 1.17202
\(75\) 9.18025 1.06004
\(76\) −24.3281 −2.79063
\(77\) 1.42674 0.162592
\(78\) −17.2947 −1.95824
\(79\) −2.29585 −0.258303 −0.129151 0.991625i \(-0.541225\pi\)
−0.129151 + 0.991625i \(0.541225\pi\)
\(80\) −28.6710 −3.20551
\(81\) −8.58365 −0.953739
\(82\) −10.1938 −1.12572
\(83\) 5.89811 0.647402 0.323701 0.946159i \(-0.395073\pi\)
0.323701 + 0.946159i \(0.395073\pi\)
\(84\) −6.00728 −0.655448
\(85\) 16.4061 1.77950
\(86\) −30.1881 −3.25527
\(87\) −14.7144 −1.57754
\(88\) 13.4344 1.43211
\(89\) −9.35226 −0.991338 −0.495669 0.868512i \(-0.665077\pi\)
−0.495669 + 0.868512i \(0.665077\pi\)
\(90\) −1.11262 −0.117281
\(91\) −2.95669 −0.309946
\(92\) 2.25192 0.234779
\(93\) 4.93839 0.512087
\(94\) −17.1215 −1.76595
\(95\) 16.6191 1.70508
\(96\) −15.0610 −1.53715
\(97\) 0.838216 0.0851080 0.0425540 0.999094i \(-0.486451\pi\)
0.0425540 + 0.999094i \(0.486451\pi\)
\(98\) 16.6922 1.68617
\(99\) 0.252563 0.0253835
\(100\) 25.6215 2.56215
\(101\) −8.14134 −0.810094 −0.405047 0.914296i \(-0.632745\pi\)
−0.405047 + 0.914296i \(0.632745\pi\)
\(102\) 22.3167 2.20968
\(103\) −2.23795 −0.220512 −0.110256 0.993903i \(-0.535167\pi\)
−0.110256 + 0.993903i \(0.535167\pi\)
\(104\) −27.8406 −2.72999
\(105\) 4.10370 0.400480
\(106\) 32.8911 3.19466
\(107\) −1.68194 −0.162599 −0.0812997 0.996690i \(-0.525907\pi\)
−0.0812997 + 0.996690i \(0.525907\pi\)
\(108\) −25.0691 −2.41227
\(109\) 5.44772 0.521796 0.260898 0.965366i \(-0.415981\pi\)
0.260898 + 0.965366i \(0.415981\pi\)
\(110\) −15.9111 −1.51706
\(111\) −6.58266 −0.624798
\(112\) −6.66743 −0.630013
\(113\) 3.89333 0.366253 0.183127 0.983089i \(-0.441378\pi\)
0.183127 + 0.983089i \(0.441378\pi\)
\(114\) 22.6063 2.11728
\(115\) −1.53834 −0.143451
\(116\) −41.0668 −3.81295
\(117\) −0.523395 −0.0483879
\(118\) −5.07689 −0.467366
\(119\) 3.81525 0.349743
\(120\) 38.6409 3.52742
\(121\) −7.38822 −0.671657
\(122\) 19.7538 1.78842
\(123\) 6.65563 0.600118
\(124\) 13.7827 1.23772
\(125\) −1.36125 −0.121754
\(126\) −0.258740 −0.0230504
\(127\) −11.1026 −0.985195 −0.492597 0.870257i \(-0.663952\pi\)
−0.492597 + 0.870257i \(0.663952\pi\)
\(128\) 4.03122 0.356313
\(129\) 19.7100 1.73537
\(130\) 32.9732 2.89194
\(131\) 22.0662 1.92793 0.963967 0.266021i \(-0.0857092\pi\)
0.963967 + 0.266021i \(0.0857092\pi\)
\(132\) −15.2073 −1.32363
\(133\) 3.86476 0.335117
\(134\) −15.8947 −1.37309
\(135\) 17.1252 1.47390
\(136\) 35.9249 3.08053
\(137\) −3.02361 −0.258324 −0.129162 0.991623i \(-0.541229\pi\)
−0.129162 + 0.991623i \(0.541229\pi\)
\(138\) −2.09255 −0.178129
\(139\) 13.0157 1.10397 0.551987 0.833853i \(-0.313870\pi\)
0.551987 + 0.833853i \(0.313870\pi\)
\(140\) 11.4531 0.967967
\(141\) 11.1787 0.941419
\(142\) −33.9590 −2.84977
\(143\) −7.48483 −0.625913
\(144\) −1.18027 −0.0983560
\(145\) 28.0536 2.32972
\(146\) −0.955199 −0.0790529
\(147\) −10.8985 −0.898889
\(148\) −18.3718 −1.51015
\(149\) 12.8203 1.05028 0.525141 0.851015i \(-0.324013\pi\)
0.525141 + 0.851015i \(0.324013\pi\)
\(150\) −23.8081 −1.94392
\(151\) 8.05227 0.655284 0.327642 0.944802i \(-0.393746\pi\)
0.327642 + 0.944802i \(0.393746\pi\)
\(152\) 36.3911 2.95171
\(153\) 0.675377 0.0546010
\(154\) −3.70012 −0.298164
\(155\) −9.41526 −0.756252
\(156\) 31.5148 2.52320
\(157\) 11.1112 0.886767 0.443383 0.896332i \(-0.353778\pi\)
0.443383 + 0.896332i \(0.353778\pi\)
\(158\) 5.95406 0.473679
\(159\) −21.4748 −1.70306
\(160\) 28.7144 2.27007
\(161\) −0.357740 −0.0281939
\(162\) 22.2609 1.74898
\(163\) −17.6950 −1.38598 −0.692990 0.720947i \(-0.743707\pi\)
−0.692990 + 0.720947i \(0.743707\pi\)
\(164\) 18.5754 1.45050
\(165\) 10.3885 0.808740
\(166\) −15.2962 −1.18722
\(167\) 13.1943 1.02101 0.510504 0.859876i \(-0.329459\pi\)
0.510504 + 0.859876i \(0.329459\pi\)
\(168\) 8.98595 0.693281
\(169\) 2.51111 0.193162
\(170\) −42.5478 −3.26327
\(171\) 0.684142 0.0523177
\(172\) 55.0093 4.19442
\(173\) −13.3258 −1.01315 −0.506573 0.862197i \(-0.669088\pi\)
−0.506573 + 0.862197i \(0.669088\pi\)
\(174\) 38.1603 2.89292
\(175\) −4.07022 −0.307680
\(176\) −16.8785 −1.27227
\(177\) 3.31474 0.249151
\(178\) 24.2542 1.81793
\(179\) 2.92950 0.218961 0.109481 0.993989i \(-0.465081\pi\)
0.109481 + 0.993989i \(0.465081\pi\)
\(180\) 2.02744 0.151117
\(181\) 14.5296 1.07997 0.539987 0.841673i \(-0.318429\pi\)
0.539987 + 0.841673i \(0.318429\pi\)
\(182\) 7.66791 0.568383
\(183\) −12.8974 −0.953401
\(184\) −3.36852 −0.248331
\(185\) 12.5501 0.922704
\(186\) −12.8072 −0.939073
\(187\) 9.65825 0.706281
\(188\) 31.1991 2.27543
\(189\) 3.98247 0.289682
\(190\) −43.1000 −3.12680
\(191\) 10.7150 0.775307 0.387654 0.921805i \(-0.373286\pi\)
0.387654 + 0.921805i \(0.373286\pi\)
\(192\) 8.98279 0.648277
\(193\) 23.4016 1.68449 0.842243 0.539098i \(-0.181235\pi\)
0.842243 + 0.539098i \(0.181235\pi\)
\(194\) −2.17383 −0.156072
\(195\) −21.5284 −1.54168
\(196\) −30.4168 −2.17263
\(197\) 6.48951 0.462358 0.231179 0.972911i \(-0.425742\pi\)
0.231179 + 0.972911i \(0.425742\pi\)
\(198\) −0.654997 −0.0465486
\(199\) −11.3346 −0.803486 −0.401743 0.915753i \(-0.631595\pi\)
−0.401743 + 0.915753i \(0.631595\pi\)
\(200\) −38.3257 −2.71003
\(201\) 10.3778 0.731992
\(202\) 21.1138 1.48556
\(203\) 6.52386 0.457885
\(204\) −40.6659 −2.84719
\(205\) −12.6893 −0.886256
\(206\) 5.80392 0.404378
\(207\) −0.0633273 −0.00440155
\(208\) 34.9780 2.42529
\(209\) 9.78359 0.676745
\(210\) −10.6426 −0.734406
\(211\) −1.76338 −0.121396 −0.0606981 0.998156i \(-0.519333\pi\)
−0.0606981 + 0.998156i \(0.519333\pi\)
\(212\) −59.9347 −4.11633
\(213\) 22.1721 1.51920
\(214\) 4.36196 0.298177
\(215\) −37.5780 −2.56280
\(216\) 37.4994 2.55151
\(217\) −2.18952 −0.148634
\(218\) −14.1281 −0.956878
\(219\) 0.623656 0.0421428
\(220\) 28.9935 1.95474
\(221\) −20.0152 −1.34637
\(222\) 17.0715 1.14576
\(223\) −21.3538 −1.42996 −0.714979 0.699146i \(-0.753564\pi\)
−0.714979 + 0.699146i \(0.753564\pi\)
\(224\) 6.67753 0.446161
\(225\) −0.720512 −0.0480342
\(226\) −10.0970 −0.671641
\(227\) −24.7642 −1.64366 −0.821830 0.569733i \(-0.807047\pi\)
−0.821830 + 0.569733i \(0.807047\pi\)
\(228\) −41.1937 −2.72812
\(229\) 11.6397 0.769174 0.384587 0.923089i \(-0.374344\pi\)
0.384587 + 0.923089i \(0.374344\pi\)
\(230\) 3.98953 0.263062
\(231\) 2.41583 0.158950
\(232\) 61.4294 4.03304
\(233\) −4.82430 −0.316051 −0.158025 0.987435i \(-0.550513\pi\)
−0.158025 + 0.987435i \(0.550513\pi\)
\(234\) 1.35738 0.0887345
\(235\) −21.3127 −1.39029
\(236\) 9.25121 0.602202
\(237\) −3.88745 −0.252517
\(238\) −9.89449 −0.641365
\(239\) −0.764649 −0.0494610 −0.0247305 0.999694i \(-0.507873\pi\)
−0.0247305 + 0.999694i \(0.507873\pi\)
\(240\) −48.5472 −3.13371
\(241\) −14.4360 −0.929906 −0.464953 0.885335i \(-0.653929\pi\)
−0.464953 + 0.885335i \(0.653929\pi\)
\(242\) 19.1607 1.23169
\(243\) 1.38005 0.0885305
\(244\) −35.9957 −2.30439
\(245\) 20.7784 1.32748
\(246\) −17.2608 −1.10051
\(247\) −20.2749 −1.29006
\(248\) −20.6168 −1.30917
\(249\) 9.98699 0.632900
\(250\) 3.53028 0.223274
\(251\) 29.2242 1.84461 0.922307 0.386459i \(-0.126302\pi\)
0.922307 + 0.386459i \(0.126302\pi\)
\(252\) 0.471481 0.0297005
\(253\) −0.905614 −0.0569355
\(254\) 28.7935 1.80666
\(255\) 27.7798 1.73964
\(256\) −21.0647 −1.31654
\(257\) −17.3034 −1.07936 −0.539679 0.841871i \(-0.681454\pi\)
−0.539679 + 0.841871i \(0.681454\pi\)
\(258\) −51.1161 −3.18235
\(259\) 2.91853 0.181349
\(260\) −60.0843 −3.72627
\(261\) 1.15486 0.0714838
\(262\) −57.2267 −3.53547
\(263\) 12.4461 0.767461 0.383730 0.923445i \(-0.374639\pi\)
0.383730 + 0.923445i \(0.374639\pi\)
\(264\) 22.7478 1.40003
\(265\) 40.9426 2.51509
\(266\) −10.0229 −0.614543
\(267\) −15.8357 −0.969132
\(268\) 28.9637 1.76924
\(269\) −26.1504 −1.59442 −0.797210 0.603702i \(-0.793692\pi\)
−0.797210 + 0.603702i \(0.793692\pi\)
\(270\) −44.4127 −2.70287
\(271\) 9.18322 0.557841 0.278920 0.960314i \(-0.410023\pi\)
0.278920 + 0.960314i \(0.410023\pi\)
\(272\) −45.1348 −2.73670
\(273\) −5.00643 −0.303003
\(274\) 7.84144 0.473719
\(275\) −10.3037 −0.621337
\(276\) 3.81308 0.229520
\(277\) −18.0381 −1.08380 −0.541901 0.840442i \(-0.682295\pi\)
−0.541901 + 0.840442i \(0.682295\pi\)
\(278\) −33.7549 −2.02448
\(279\) −0.387590 −0.0232044
\(280\) −17.1321 −1.02384
\(281\) 15.2901 0.912128 0.456064 0.889947i \(-0.349259\pi\)
0.456064 + 0.889947i \(0.349259\pi\)
\(282\) −28.9910 −1.72639
\(283\) 27.2624 1.62058 0.810291 0.586028i \(-0.199309\pi\)
0.810291 + 0.586028i \(0.199309\pi\)
\(284\) 61.8807 3.67194
\(285\) 28.1403 1.66689
\(286\) 19.4112 1.14781
\(287\) −2.95089 −0.174185
\(288\) 1.18206 0.0696535
\(289\) 8.82712 0.519242
\(290\) −72.7543 −4.27228
\(291\) 1.41931 0.0832015
\(292\) 1.74058 0.101860
\(293\) −12.3434 −0.721109 −0.360554 0.932738i \(-0.617412\pi\)
−0.360554 + 0.932738i \(0.617412\pi\)
\(294\) 28.2641 1.64840
\(295\) −6.31969 −0.367947
\(296\) 27.4813 1.59732
\(297\) 10.0816 0.584992
\(298\) −33.2483 −1.92602
\(299\) 1.87674 0.108535
\(300\) 43.3836 2.50475
\(301\) −8.73877 −0.503694
\(302\) −20.8828 −1.20167
\(303\) −13.7854 −0.791948
\(304\) −45.7205 −2.62225
\(305\) 24.5894 1.40799
\(306\) −1.75153 −0.100128
\(307\) 11.0014 0.627881 0.313941 0.949443i \(-0.398351\pi\)
0.313941 + 0.949443i \(0.398351\pi\)
\(308\) 6.74243 0.384186
\(309\) −3.78942 −0.215572
\(310\) 24.4176 1.38683
\(311\) 16.7087 0.947464 0.473732 0.880669i \(-0.342907\pi\)
0.473732 + 0.880669i \(0.342907\pi\)
\(312\) −47.1412 −2.66884
\(313\) 16.9364 0.957303 0.478651 0.878005i \(-0.341126\pi\)
0.478651 + 0.878005i \(0.341126\pi\)
\(314\) −28.8157 −1.62617
\(315\) −0.322079 −0.0181471
\(316\) −10.8496 −0.610338
\(317\) 11.3436 0.637118 0.318559 0.947903i \(-0.396801\pi\)
0.318559 + 0.947903i \(0.396801\pi\)
\(318\) 55.6929 3.12310
\(319\) 16.5150 0.924665
\(320\) −17.1261 −0.957378
\(321\) −2.84795 −0.158957
\(322\) 0.927765 0.0517023
\(323\) 26.1623 1.45571
\(324\) −40.5642 −2.25357
\(325\) 21.3528 1.18444
\(326\) 45.8904 2.54163
\(327\) 9.22436 0.510108
\(328\) −27.7859 −1.53422
\(329\) −4.95628 −0.273249
\(330\) −26.9415 −1.48308
\(331\) 31.8616 1.75127 0.875635 0.482974i \(-0.160443\pi\)
0.875635 + 0.482974i \(0.160443\pi\)
\(332\) 27.8730 1.52973
\(333\) 0.516640 0.0283117
\(334\) −34.2182 −1.87234
\(335\) −19.7857 −1.08101
\(336\) −11.2896 −0.615901
\(337\) −13.7083 −0.746741 −0.373370 0.927682i \(-0.621798\pi\)
−0.373370 + 0.927682i \(0.621798\pi\)
\(338\) −6.51233 −0.354224
\(339\) 6.59239 0.358049
\(340\) 77.5314 4.20473
\(341\) −5.54273 −0.300156
\(342\) −1.77426 −0.0959409
\(343\) 10.0871 0.544654
\(344\) −82.2853 −4.43653
\(345\) −2.60479 −0.140237
\(346\) 34.5593 1.85792
\(347\) 34.3853 1.84590 0.922949 0.384923i \(-0.125772\pi\)
0.922949 + 0.384923i \(0.125772\pi\)
\(348\) −69.5364 −3.72754
\(349\) −19.1978 −1.02763 −0.513817 0.857900i \(-0.671769\pi\)
−0.513817 + 0.857900i \(0.671769\pi\)
\(350\) 10.5557 0.564228
\(351\) −20.8924 −1.11516
\(352\) 16.9041 0.900989
\(353\) 23.1527 1.23230 0.616148 0.787631i \(-0.288692\pi\)
0.616148 + 0.787631i \(0.288692\pi\)
\(354\) −8.59646 −0.456897
\(355\) −42.2720 −2.24356
\(356\) −44.1965 −2.34241
\(357\) 6.46018 0.341909
\(358\) −7.59739 −0.401535
\(359\) −4.55174 −0.240232 −0.120116 0.992760i \(-0.538327\pi\)
−0.120116 + 0.992760i \(0.538327\pi\)
\(360\) −3.03273 −0.159839
\(361\) 7.50181 0.394832
\(362\) −37.6811 −1.98047
\(363\) −12.5101 −0.656612
\(364\) −13.9726 −0.732364
\(365\) −1.18903 −0.0622366
\(366\) 33.4481 1.74836
\(367\) 9.77515 0.510259 0.255129 0.966907i \(-0.417882\pi\)
0.255129 + 0.966907i \(0.417882\pi\)
\(368\) 4.23210 0.220614
\(369\) −0.522368 −0.0271934
\(370\) −32.5476 −1.69207
\(371\) 9.52121 0.494317
\(372\) 23.3376 1.21000
\(373\) 10.6942 0.553724 0.276862 0.960910i \(-0.410706\pi\)
0.276862 + 0.960910i \(0.410706\pi\)
\(374\) −25.0478 −1.29519
\(375\) −2.30494 −0.119027
\(376\) −46.6689 −2.40677
\(377\) −34.2248 −1.76267
\(378\) −10.3282 −0.531223
\(379\) −10.4880 −0.538735 −0.269367 0.963037i \(-0.586815\pi\)
−0.269367 + 0.963037i \(0.586815\pi\)
\(380\) 78.5376 4.02889
\(381\) −18.7995 −0.963126
\(382\) −27.7882 −1.42177
\(383\) −18.8764 −0.964540 −0.482270 0.876023i \(-0.660188\pi\)
−0.482270 + 0.876023i \(0.660188\pi\)
\(384\) 6.82587 0.348331
\(385\) −4.60590 −0.234738
\(386\) −60.6899 −3.08904
\(387\) −1.54694 −0.0786354
\(388\) 3.96120 0.201100
\(389\) 37.3675 1.89461 0.947303 0.320340i \(-0.103797\pi\)
0.947303 + 0.320340i \(0.103797\pi\)
\(390\) 55.8319 2.82716
\(391\) −2.42170 −0.122471
\(392\) 45.4988 2.29804
\(393\) 37.3637 1.88475
\(394\) −16.8299 −0.847879
\(395\) 7.41159 0.372917
\(396\) 1.19355 0.0599781
\(397\) −0.903344 −0.0453376 −0.0226688 0.999743i \(-0.507216\pi\)
−0.0226688 + 0.999743i \(0.507216\pi\)
\(398\) 29.3951 1.47344
\(399\) 6.54402 0.327611
\(400\) 48.1511 2.40756
\(401\) −26.8156 −1.33911 −0.669555 0.742763i \(-0.733515\pi\)
−0.669555 + 0.742763i \(0.733515\pi\)
\(402\) −26.9138 −1.34234
\(403\) 11.4864 0.572180
\(404\) −38.4740 −1.91415
\(405\) 27.7103 1.37693
\(406\) −16.9190 −0.839676
\(407\) 7.38822 0.366221
\(408\) 60.8299 3.01153
\(409\) −12.5241 −0.619275 −0.309637 0.950855i \(-0.600208\pi\)
−0.309637 + 0.950855i \(0.600208\pi\)
\(410\) 32.9084 1.62523
\(411\) −5.11973 −0.252538
\(412\) −10.5760 −0.521043
\(413\) −1.46964 −0.0723165
\(414\) 0.164233 0.00807163
\(415\) −19.0406 −0.934668
\(416\) −35.0310 −1.71753
\(417\) 22.0388 1.07924
\(418\) −25.3728 −1.24103
\(419\) 27.6385 1.35023 0.675114 0.737713i \(-0.264094\pi\)
0.675114 + 0.737713i \(0.264094\pi\)
\(420\) 19.3931 0.946285
\(421\) 23.0022 1.12106 0.560530 0.828134i \(-0.310597\pi\)
0.560530 + 0.828134i \(0.310597\pi\)
\(422\) 4.57316 0.222618
\(423\) −0.877363 −0.0426589
\(424\) 89.6529 4.35393
\(425\) −27.5531 −1.33652
\(426\) −57.5011 −2.78594
\(427\) 5.71827 0.276726
\(428\) −7.94844 −0.384202
\(429\) −12.6737 −0.611892
\(430\) 97.4550 4.69970
\(431\) 11.5806 0.557816 0.278908 0.960318i \(-0.410028\pi\)
0.278908 + 0.960318i \(0.410028\pi\)
\(432\) −47.1130 −2.26673
\(433\) −18.0607 −0.867943 −0.433972 0.900926i \(-0.642888\pi\)
−0.433972 + 0.900926i \(0.642888\pi\)
\(434\) 5.67831 0.272568
\(435\) 47.5018 2.27754
\(436\) 25.7446 1.23294
\(437\) −2.45313 −0.117349
\(438\) −1.61739 −0.0772821
\(439\) 27.9317 1.33311 0.666554 0.745457i \(-0.267769\pi\)
0.666554 + 0.745457i \(0.267769\pi\)
\(440\) −43.3697 −2.06757
\(441\) 0.855365 0.0407317
\(442\) 51.9075 2.46899
\(443\) −32.5806 −1.54795 −0.773975 0.633216i \(-0.781735\pi\)
−0.773975 + 0.633216i \(0.781735\pi\)
\(444\) −31.1080 −1.47632
\(445\) 30.1915 1.43122
\(446\) 55.3792 2.62228
\(447\) 21.7080 1.02676
\(448\) −3.98267 −0.188164
\(449\) −14.7323 −0.695261 −0.347630 0.937632i \(-0.613014\pi\)
−0.347630 + 0.937632i \(0.613014\pi\)
\(450\) 1.86858 0.0880857
\(451\) −7.47013 −0.351755
\(452\) 18.3989 0.865412
\(453\) 13.6345 0.640606
\(454\) 64.2237 3.01417
\(455\) 9.54498 0.447476
\(456\) 61.6193 2.88559
\(457\) −10.5137 −0.491811 −0.245906 0.969294i \(-0.579085\pi\)
−0.245906 + 0.969294i \(0.579085\pi\)
\(458\) −30.1865 −1.41052
\(459\) 26.9591 1.25834
\(460\) −7.26980 −0.338956
\(461\) −0.897127 −0.0417834 −0.0208917 0.999782i \(-0.506651\pi\)
−0.0208917 + 0.999782i \(0.506651\pi\)
\(462\) −6.26524 −0.291485
\(463\) 32.7247 1.52085 0.760423 0.649428i \(-0.224992\pi\)
0.760423 + 0.649428i \(0.224992\pi\)
\(464\) −77.1779 −3.58289
\(465\) −15.9424 −0.739311
\(466\) 12.5114 0.579578
\(467\) −31.8393 −1.47335 −0.736675 0.676247i \(-0.763605\pi\)
−0.736675 + 0.676247i \(0.763605\pi\)
\(468\) −2.47344 −0.114335
\(469\) −4.60116 −0.212462
\(470\) 55.2726 2.54954
\(471\) 18.8140 0.866903
\(472\) −13.8384 −0.636962
\(473\) −22.1221 −1.01717
\(474\) 10.0817 0.463069
\(475\) −27.9107 −1.28063
\(476\) 18.0299 0.826401
\(477\) 1.68545 0.0771714
\(478\) 1.98304 0.0907023
\(479\) 13.6228 0.622442 0.311221 0.950338i \(-0.399262\pi\)
0.311221 + 0.950338i \(0.399262\pi\)
\(480\) 48.6207 2.21922
\(481\) −15.3109 −0.698117
\(482\) 37.4385 1.70528
\(483\) −0.605745 −0.0275623
\(484\) −34.9149 −1.58704
\(485\) −2.70598 −0.122872
\(486\) −3.57904 −0.162348
\(487\) −20.2084 −0.915732 −0.457866 0.889021i \(-0.651386\pi\)
−0.457866 + 0.889021i \(0.651386\pi\)
\(488\) 53.8439 2.43740
\(489\) −29.9621 −1.35493
\(490\) −53.8868 −2.43436
\(491\) −1.34490 −0.0606947 −0.0303473 0.999539i \(-0.509661\pi\)
−0.0303473 + 0.999539i \(0.509661\pi\)
\(492\) 31.4529 1.41801
\(493\) 44.1629 1.98900
\(494\) 52.5811 2.36574
\(495\) −0.815338 −0.0366467
\(496\) 25.9022 1.16304
\(497\) −9.83035 −0.440952
\(498\) −25.9003 −1.16062
\(499\) 14.3490 0.642350 0.321175 0.947020i \(-0.395922\pi\)
0.321175 + 0.947020i \(0.395922\pi\)
\(500\) −6.43294 −0.287690
\(501\) 22.3413 0.998137
\(502\) −75.7901 −3.38268
\(503\) −3.24888 −0.144860 −0.0724301 0.997373i \(-0.523075\pi\)
−0.0724301 + 0.997373i \(0.523075\pi\)
\(504\) −0.705262 −0.0314149
\(505\) 26.2824 1.16955
\(506\) 2.34862 0.104409
\(507\) 4.25194 0.188835
\(508\) −52.4681 −2.32789
\(509\) 6.33035 0.280588 0.140294 0.990110i \(-0.455195\pi\)
0.140294 + 0.990110i \(0.455195\pi\)
\(510\) −72.0442 −3.19017
\(511\) −0.276509 −0.0122320
\(512\) 46.5668 2.05798
\(513\) 27.3090 1.20572
\(514\) 44.8748 1.97934
\(515\) 7.22469 0.318358
\(516\) 93.1447 4.10047
\(517\) −12.5468 −0.551805
\(518\) −7.56894 −0.332560
\(519\) −22.5640 −0.990451
\(520\) 89.8767 3.94135
\(521\) −2.89812 −0.126969 −0.0634844 0.997983i \(-0.520221\pi\)
−0.0634844 + 0.997983i \(0.520221\pi\)
\(522\) −2.99501 −0.131088
\(523\) −32.0569 −1.40175 −0.700875 0.713284i \(-0.747207\pi\)
−0.700875 + 0.713284i \(0.747207\pi\)
\(524\) 104.279 4.55547
\(525\) −6.89191 −0.300788
\(526\) −32.2778 −1.40738
\(527\) −14.8218 −0.645649
\(528\) −28.5796 −1.24377
\(529\) −22.7729 −0.990127
\(530\) −106.181 −4.61220
\(531\) −0.260157 −0.0112899
\(532\) 18.2639 0.791841
\(533\) 15.4806 0.670541
\(534\) 41.0685 1.77721
\(535\) 5.42975 0.234748
\(536\) −43.3251 −1.87136
\(537\) 4.96039 0.214057
\(538\) 67.8187 2.92387
\(539\) 12.2322 0.526877
\(540\) 80.9296 3.48265
\(541\) 45.6333 1.96193 0.980964 0.194190i \(-0.0622079\pi\)
0.980964 + 0.194190i \(0.0622079\pi\)
\(542\) −23.8158 −1.02298
\(543\) 24.6022 1.05578
\(544\) 45.2031 1.93807
\(545\) −17.5866 −0.753329
\(546\) 12.9837 0.555651
\(547\) 14.3464 0.613407 0.306704 0.951805i \(-0.400774\pi\)
0.306704 + 0.951805i \(0.400774\pi\)
\(548\) −14.2888 −0.610388
\(549\) 1.01225 0.0432018
\(550\) 26.7217 1.13942
\(551\) 44.7360 1.90582
\(552\) −5.70376 −0.242768
\(553\) 1.72357 0.0732934
\(554\) 46.7800 1.98749
\(555\) 21.2505 0.902035
\(556\) 61.5088 2.60855
\(557\) 4.44027 0.188140 0.0940702 0.995566i \(-0.470012\pi\)
0.0940702 + 0.995566i \(0.470012\pi\)
\(558\) 1.00518 0.0425525
\(559\) 45.8444 1.93901
\(560\) 21.5242 0.909564
\(561\) 16.3539 0.690460
\(562\) −39.6533 −1.67267
\(563\) 37.2623 1.57042 0.785209 0.619231i \(-0.212555\pi\)
0.785209 + 0.619231i \(0.212555\pi\)
\(564\) 52.8279 2.22446
\(565\) −12.5687 −0.528768
\(566\) −70.7025 −2.97185
\(567\) 6.44403 0.270624
\(568\) −92.5638 −3.88389
\(569\) 25.5184 1.06978 0.534892 0.844920i \(-0.320352\pi\)
0.534892 + 0.844920i \(0.320352\pi\)
\(570\) −72.9791 −3.05676
\(571\) −13.8242 −0.578526 −0.289263 0.957250i \(-0.593410\pi\)
−0.289263 + 0.957250i \(0.593410\pi\)
\(572\) −35.3715 −1.47895
\(573\) 18.1431 0.757940
\(574\) 7.65285 0.319424
\(575\) 2.58354 0.107741
\(576\) −0.705015 −0.0293756
\(577\) 24.5403 1.02163 0.510813 0.859692i \(-0.329344\pi\)
0.510813 + 0.859692i \(0.329344\pi\)
\(578\) −22.8923 −0.952194
\(579\) 39.6249 1.64675
\(580\) 132.574 5.50485
\(581\) −4.42790 −0.183700
\(582\) −3.68085 −0.152576
\(583\) 24.1028 0.998236
\(584\) −2.60364 −0.107739
\(585\) 1.68966 0.0698587
\(586\) 32.0114 1.32238
\(587\) −10.6040 −0.437675 −0.218838 0.975761i \(-0.570227\pi\)
−0.218838 + 0.975761i \(0.570227\pi\)
\(588\) −51.5034 −2.12396
\(589\) −15.0142 −0.618648
\(590\) 16.3895 0.674746
\(591\) 10.9884 0.452001
\(592\) −34.5265 −1.41903
\(593\) −19.6125 −0.805388 −0.402694 0.915335i \(-0.631926\pi\)
−0.402694 + 0.915335i \(0.631926\pi\)
\(594\) −26.1456 −1.07277
\(595\) −12.3166 −0.504932
\(596\) 60.5857 2.48169
\(597\) −19.1923 −0.785488
\(598\) −4.86715 −0.199033
\(599\) −22.1832 −0.906379 −0.453190 0.891414i \(-0.649714\pi\)
−0.453190 + 0.891414i \(0.649714\pi\)
\(600\) −64.8951 −2.64933
\(601\) −16.5455 −0.674905 −0.337453 0.941343i \(-0.609565\pi\)
−0.337453 + 0.941343i \(0.609565\pi\)
\(602\) 22.6632 0.923682
\(603\) −0.814500 −0.0331690
\(604\) 38.0530 1.54836
\(605\) 23.8511 0.969686
\(606\) 35.7510 1.45229
\(607\) 21.1646 0.859044 0.429522 0.903056i \(-0.358682\pi\)
0.429522 + 0.903056i \(0.358682\pi\)
\(608\) 45.7898 1.85702
\(609\) 11.0465 0.447628
\(610\) −63.7703 −2.58198
\(611\) 26.0011 1.05189
\(612\) 3.19167 0.129015
\(613\) 43.8957 1.77293 0.886464 0.462797i \(-0.153154\pi\)
0.886464 + 0.462797i \(0.153154\pi\)
\(614\) −28.5310 −1.15142
\(615\) −21.4861 −0.866404
\(616\) −10.0856 −0.406361
\(617\) −35.8634 −1.44381 −0.721904 0.691993i \(-0.756733\pi\)
−0.721904 + 0.691993i \(0.756733\pi\)
\(618\) 9.82750 0.395320
\(619\) −1.70051 −0.0683494 −0.0341747 0.999416i \(-0.510880\pi\)
−0.0341747 + 0.999416i \(0.510880\pi\)
\(620\) −44.4942 −1.78693
\(621\) −2.52784 −0.101439
\(622\) −43.3325 −1.73747
\(623\) 7.02104 0.281292
\(624\) 59.2266 2.37096
\(625\) −22.7139 −0.908554
\(626\) −43.9230 −1.75552
\(627\) 16.5661 0.661586
\(628\) 52.5086 2.09532
\(629\) 19.7568 0.787757
\(630\) 0.835281 0.0332784
\(631\) 11.5062 0.458053 0.229026 0.973420i \(-0.426446\pi\)
0.229026 + 0.973420i \(0.426446\pi\)
\(632\) 16.2293 0.645567
\(633\) −2.98585 −0.118677
\(634\) −29.4185 −1.16836
\(635\) 35.8420 1.42235
\(636\) −101.485 −4.02413
\(637\) −25.3492 −1.00437
\(638\) −42.8302 −1.69566
\(639\) −1.74017 −0.0688402
\(640\) −13.0138 −0.514417
\(641\) 25.4406 1.00484 0.502421 0.864623i \(-0.332443\pi\)
0.502421 + 0.864623i \(0.332443\pi\)
\(642\) 7.38590 0.291498
\(643\) 18.2160 0.718367 0.359183 0.933267i \(-0.383055\pi\)
0.359183 + 0.933267i \(0.383055\pi\)
\(644\) −1.69059 −0.0666187
\(645\) −63.6291 −2.50539
\(646\) −67.8494 −2.66950
\(647\) 30.0129 1.17993 0.589964 0.807430i \(-0.299142\pi\)
0.589964 + 0.807430i \(0.299142\pi\)
\(648\) 60.6777 2.38365
\(649\) −3.72038 −0.146038
\(650\) −55.3764 −2.17204
\(651\) −3.70741 −0.145305
\(652\) −83.6223 −3.27490
\(653\) 0.146955 0.00575079 0.00287540 0.999996i \(-0.499085\pi\)
0.00287540 + 0.999996i \(0.499085\pi\)
\(654\) −23.9225 −0.935444
\(655\) −71.2355 −2.78340
\(656\) 34.9093 1.36298
\(657\) −0.0489477 −0.00190963
\(658\) 12.8536 0.501087
\(659\) 20.0542 0.781199 0.390600 0.920561i \(-0.372268\pi\)
0.390600 + 0.920561i \(0.372268\pi\)
\(660\) 49.0933 1.91095
\(661\) 11.5108 0.447717 0.223858 0.974622i \(-0.428135\pi\)
0.223858 + 0.974622i \(0.428135\pi\)
\(662\) −82.6299 −3.21150
\(663\) −33.8908 −1.31621
\(664\) −41.6937 −1.61803
\(665\) −12.4765 −0.483816
\(666\) −1.33986 −0.0519184
\(667\) −4.14097 −0.160339
\(668\) 62.3531 2.41252
\(669\) −36.1574 −1.39793
\(670\) 51.3123 1.98237
\(671\) 14.4757 0.558829
\(672\) 11.3067 0.436167
\(673\) −6.35746 −0.245062 −0.122531 0.992465i \(-0.539101\pi\)
−0.122531 + 0.992465i \(0.539101\pi\)
\(674\) 35.5513 1.36938
\(675\) −28.7608 −1.10700
\(676\) 11.8669 0.456419
\(677\) 28.0154 1.07672 0.538360 0.842715i \(-0.319044\pi\)
0.538360 + 0.842715i \(0.319044\pi\)
\(678\) −17.0967 −0.656596
\(679\) −0.629276 −0.0241494
\(680\) −115.975 −4.44743
\(681\) −41.9321 −1.60684
\(682\) 14.3746 0.550430
\(683\) 51.6176 1.97509 0.987547 0.157325i \(-0.0502869\pi\)
0.987547 + 0.157325i \(0.0502869\pi\)
\(684\) 3.23309 0.123620
\(685\) 9.76099 0.372948
\(686\) −26.1600 −0.998795
\(687\) 19.7090 0.751945
\(688\) 103.381 3.94135
\(689\) −49.9492 −1.90291
\(690\) 6.75528 0.257169
\(691\) 9.58150 0.364497 0.182249 0.983252i \(-0.441662\pi\)
0.182249 + 0.983252i \(0.441662\pi\)
\(692\) −62.9747 −2.39394
\(693\) −0.189607 −0.00720257
\(694\) −89.1749 −3.38503
\(695\) −42.0179 −1.59383
\(696\) 104.016 3.94270
\(697\) −19.9759 −0.756640
\(698\) 49.7877 1.88449
\(699\) −8.16876 −0.308971
\(700\) −19.2349 −0.727009
\(701\) 9.19586 0.347323 0.173661 0.984805i \(-0.444440\pi\)
0.173661 + 0.984805i \(0.444440\pi\)
\(702\) 54.1826 2.04499
\(703\) 20.0132 0.754813
\(704\) −10.0821 −0.379983
\(705\) −36.0879 −1.35915
\(706\) −60.0444 −2.25980
\(707\) 6.11197 0.229864
\(708\) 15.6646 0.588713
\(709\) −37.4936 −1.40810 −0.704051 0.710149i \(-0.748628\pi\)
−0.704051 + 0.710149i \(0.748628\pi\)
\(710\) 109.628 4.11428
\(711\) 0.305106 0.0114424
\(712\) 66.1110 2.47761
\(713\) 1.38978 0.0520477
\(714\) −16.7539 −0.626998
\(715\) 24.1630 0.903644
\(716\) 13.8441 0.517379
\(717\) −1.29474 −0.0483531
\(718\) 11.8045 0.440540
\(719\) 5.12401 0.191093 0.0955466 0.995425i \(-0.469540\pi\)
0.0955466 + 0.995425i \(0.469540\pi\)
\(720\) 3.81023 0.141999
\(721\) 1.68010 0.0625703
\(722\) −19.4552 −0.724049
\(723\) −24.4438 −0.909077
\(724\) 68.6632 2.55185
\(725\) −47.1143 −1.74978
\(726\) 32.4438 1.20410
\(727\) −2.64598 −0.0981341 −0.0490671 0.998795i \(-0.515625\pi\)
−0.0490671 + 0.998795i \(0.515625\pi\)
\(728\) 20.9008 0.774636
\(729\) 28.0877 1.04029
\(730\) 3.08363 0.114130
\(731\) −59.1566 −2.18799
\(732\) −60.9498 −2.25277
\(733\) −30.7659 −1.13637 −0.568183 0.822902i \(-0.692353\pi\)
−0.568183 + 0.822902i \(0.692353\pi\)
\(734\) −25.3509 −0.935720
\(735\) 35.1831 1.29775
\(736\) −4.23851 −0.156234
\(737\) −11.6478 −0.429051
\(738\) 1.35471 0.0498676
\(739\) 24.4851 0.900699 0.450350 0.892852i \(-0.351299\pi\)
0.450350 + 0.892852i \(0.351299\pi\)
\(740\) 59.3088 2.18023
\(741\) −34.3306 −1.26117
\(742\) −24.6924 −0.906485
\(743\) 8.46018 0.310374 0.155187 0.987885i \(-0.450402\pi\)
0.155187 + 0.987885i \(0.450402\pi\)
\(744\) −34.9094 −1.27984
\(745\) −41.3873 −1.51632
\(746\) −27.7344 −1.01543
\(747\) −0.783829 −0.0286788
\(748\) 45.6425 1.66886
\(749\) 1.26269 0.0461376
\(750\) 5.97765 0.218273
\(751\) −42.8284 −1.56283 −0.781415 0.624012i \(-0.785502\pi\)
−0.781415 + 0.624012i \(0.785502\pi\)
\(752\) 58.6333 2.13814
\(753\) 49.4839 1.80329
\(754\) 88.7588 3.23240
\(755\) −25.9948 −0.946048
\(756\) 18.8202 0.684483
\(757\) −53.6680 −1.95060 −0.975298 0.220894i \(-0.929103\pi\)
−0.975298 + 0.220894i \(0.929103\pi\)
\(758\) 27.1998 0.987940
\(759\) −1.53343 −0.0556601
\(760\) −117.480 −4.26144
\(761\) 6.35272 0.230286 0.115143 0.993349i \(-0.463267\pi\)
0.115143 + 0.993349i \(0.463267\pi\)
\(762\) 48.7547 1.76620
\(763\) −4.08978 −0.148060
\(764\) 50.6363 1.83196
\(765\) −2.18029 −0.0788287
\(766\) 48.9542 1.76879
\(767\) 7.70990 0.278388
\(768\) −35.6678 −1.28705
\(769\) −8.05600 −0.290507 −0.145253 0.989394i \(-0.546400\pi\)
−0.145253 + 0.989394i \(0.546400\pi\)
\(770\) 11.9450 0.430466
\(771\) −29.2991 −1.05518
\(772\) 110.590 3.98023
\(773\) −13.5121 −0.485997 −0.242998 0.970027i \(-0.578131\pi\)
−0.242998 + 0.970027i \(0.578131\pi\)
\(774\) 4.01184 0.144203
\(775\) 15.8123 0.567996
\(776\) −5.92534 −0.212707
\(777\) 4.94181 0.177287
\(778\) −96.9090 −3.47436
\(779\) −20.2351 −0.724998
\(780\) −101.738 −3.64280
\(781\) −24.8854 −0.890469
\(782\) 6.28046 0.224589
\(783\) 46.0985 1.64743
\(784\) −57.1632 −2.04154
\(785\) −35.8697 −1.28024
\(786\) −96.8992 −3.45628
\(787\) 26.2460 0.935569 0.467784 0.883843i \(-0.345052\pi\)
0.467784 + 0.883843i \(0.345052\pi\)
\(788\) 30.6678 1.09250
\(789\) 21.0744 0.750270
\(790\) −19.2213 −0.683862
\(791\) −2.92285 −0.103924
\(792\) −1.78536 −0.0634400
\(793\) −29.9986 −1.06528
\(794\) 2.34274 0.0831407
\(795\) 69.3262 2.45875
\(796\) −53.5643 −1.89854
\(797\) −35.9770 −1.27437 −0.637185 0.770711i \(-0.719901\pi\)
−0.637185 + 0.770711i \(0.719901\pi\)
\(798\) −16.9713 −0.600778
\(799\) −33.5513 −1.18696
\(800\) −48.2240 −1.70498
\(801\) 1.24287 0.0439146
\(802\) 69.5438 2.45568
\(803\) −0.699977 −0.0247017
\(804\) 49.0428 1.72961
\(805\) 1.15488 0.0407041
\(806\) −29.7890 −1.04927
\(807\) −44.2793 −1.55871
\(808\) 57.5510 2.02464
\(809\) 15.6571 0.550473 0.275236 0.961377i \(-0.411244\pi\)
0.275236 + 0.961377i \(0.411244\pi\)
\(810\) −71.8640 −2.52504
\(811\) 5.90148 0.207229 0.103614 0.994618i \(-0.466959\pi\)
0.103614 + 0.994618i \(0.466959\pi\)
\(812\) 30.8301 1.08193
\(813\) 15.5495 0.545345
\(814\) −19.1607 −0.671581
\(815\) 57.1241 2.00097
\(816\) −76.4246 −2.67540
\(817\) −59.9243 −2.09649
\(818\) 32.4800 1.13564
\(819\) 0.392930 0.0137301
\(820\) −59.9663 −2.09411
\(821\) 31.0639 1.08414 0.542068 0.840335i \(-0.317641\pi\)
0.542068 + 0.840335i \(0.317641\pi\)
\(822\) 13.2775 0.463107
\(823\) 27.1781 0.947369 0.473685 0.880695i \(-0.342924\pi\)
0.473685 + 0.880695i \(0.342924\pi\)
\(824\) 15.8200 0.551117
\(825\) −17.4468 −0.607419
\(826\) 3.81139 0.132615
\(827\) −53.9201 −1.87499 −0.937493 0.348004i \(-0.886859\pi\)
−0.937493 + 0.348004i \(0.886859\pi\)
\(828\) −0.299269 −0.0104003
\(829\) 51.5068 1.78890 0.894452 0.447164i \(-0.147566\pi\)
0.894452 + 0.447164i \(0.147566\pi\)
\(830\) 49.3801 1.71401
\(831\) −30.5430 −1.05953
\(832\) 20.8935 0.724352
\(833\) 32.7100 1.13334
\(834\) −57.1555 −1.97913
\(835\) −42.5947 −1.47405
\(836\) 46.2348 1.59907
\(837\) −15.4715 −0.534772
\(838\) −71.6778 −2.47607
\(839\) −23.2282 −0.801926 −0.400963 0.916094i \(-0.631324\pi\)
−0.400963 + 0.916094i \(0.631324\pi\)
\(840\) −29.0090 −1.00090
\(841\) 46.5160 1.60400
\(842\) −59.6541 −2.05582
\(843\) 25.8899 0.891697
\(844\) −8.33331 −0.286844
\(845\) −8.10652 −0.278873
\(846\) 2.27536 0.0782284
\(847\) 5.54658 0.190583
\(848\) −112.637 −3.86797
\(849\) 46.1621 1.58428
\(850\) 71.4564 2.45094
\(851\) −1.85252 −0.0635035
\(852\) 104.780 3.58969
\(853\) 10.3715 0.355114 0.177557 0.984111i \(-0.443181\pi\)
0.177557 + 0.984111i \(0.443181\pi\)
\(854\) −14.8298 −0.507465
\(855\) −2.20859 −0.0755322
\(856\) 11.8896 0.406379
\(857\) 6.06354 0.207126 0.103563 0.994623i \(-0.466976\pi\)
0.103563 + 0.994623i \(0.466976\pi\)
\(858\) 32.8681 1.12210
\(859\) −41.1329 −1.40344 −0.701718 0.712455i \(-0.747583\pi\)
−0.701718 + 0.712455i \(0.747583\pi\)
\(860\) −177.584 −6.05558
\(861\) −4.99660 −0.170284
\(862\) −30.0331 −1.02293
\(863\) 26.8911 0.915383 0.457691 0.889111i \(-0.348676\pi\)
0.457691 + 0.889111i \(0.348676\pi\)
\(864\) 47.1844 1.60525
\(865\) 43.0193 1.46270
\(866\) 46.8388 1.59165
\(867\) 14.9465 0.507611
\(868\) −10.3471 −0.351204
\(869\) 4.36318 0.148011
\(870\) −123.191 −4.17658
\(871\) 24.1381 0.817890
\(872\) −38.5098 −1.30411
\(873\) −0.111395 −0.00377014
\(874\) 6.36196 0.215197
\(875\) 1.02194 0.0345477
\(876\) 2.94725 0.0995782
\(877\) −16.9538 −0.572488 −0.286244 0.958157i \(-0.592407\pi\)
−0.286244 + 0.958157i \(0.592407\pi\)
\(878\) −72.4382 −2.44467
\(879\) −20.9005 −0.704956
\(880\) 54.4882 1.83680
\(881\) −38.7528 −1.30561 −0.652807 0.757524i \(-0.726409\pi\)
−0.652807 + 0.757524i \(0.726409\pi\)
\(882\) −2.21831 −0.0746944
\(883\) −20.7850 −0.699471 −0.349736 0.936848i \(-0.613729\pi\)
−0.349736 + 0.936848i \(0.613729\pi\)
\(884\) −94.5868 −3.18130
\(885\) −10.7008 −0.359705
\(886\) 84.4947 2.83866
\(887\) −24.8321 −0.833782 −0.416891 0.908957i \(-0.636880\pi\)
−0.416891 + 0.908957i \(0.636880\pi\)
\(888\) 46.5327 1.56154
\(889\) 8.33506 0.279549
\(890\) −78.2989 −2.62459
\(891\) 16.3130 0.546505
\(892\) −100.913 −3.37882
\(893\) −33.9867 −1.13732
\(894\) −56.2978 −1.88288
\(895\) −9.45720 −0.316119
\(896\) −3.02637 −0.101104
\(897\) 3.17780 0.106103
\(898\) 38.2069 1.27498
\(899\) −25.3445 −0.845285
\(900\) −3.40496 −0.113499
\(901\) 64.4533 2.14725
\(902\) 19.3731 0.645053
\(903\) −14.7969 −0.492411
\(904\) −27.5219 −0.915364
\(905\) −46.9053 −1.55918
\(906\) −35.3599 −1.17475
\(907\) −24.4876 −0.813099 −0.406549 0.913629i \(-0.633268\pi\)
−0.406549 + 0.913629i \(0.633268\pi\)
\(908\) −117.030 −3.88377
\(909\) 1.08194 0.0358858
\(910\) −24.7540 −0.820587
\(911\) 19.4839 0.645530 0.322765 0.946479i \(-0.395388\pi\)
0.322765 + 0.946479i \(0.395388\pi\)
\(912\) −77.4164 −2.56351
\(913\) −11.2092 −0.370969
\(914\) 27.2664 0.901891
\(915\) 41.6361 1.37645
\(916\) 55.0065 1.81746
\(917\) −16.5658 −0.547052
\(918\) −69.9159 −2.30757
\(919\) −23.7854 −0.784609 −0.392305 0.919835i \(-0.628322\pi\)
−0.392305 + 0.919835i \(0.628322\pi\)
\(920\) 10.8745 0.358521
\(921\) 18.6281 0.613816
\(922\) 2.32661 0.0766229
\(923\) 51.5710 1.69748
\(924\) 11.4166 0.375580
\(925\) −21.0772 −0.693013
\(926\) −84.8685 −2.78895
\(927\) 0.297413 0.00976831
\(928\) 77.2948 2.53732
\(929\) −21.4773 −0.704649 −0.352324 0.935878i \(-0.614609\pi\)
−0.352324 + 0.935878i \(0.614609\pi\)
\(930\) 41.3451 1.35576
\(931\) 33.1345 1.08594
\(932\) −22.7985 −0.746789
\(933\) 28.2921 0.926241
\(934\) 82.5723 2.70185
\(935\) −31.1793 −1.01967
\(936\) 3.69987 0.120934
\(937\) −28.1170 −0.918544 −0.459272 0.888296i \(-0.651890\pi\)
−0.459272 + 0.888296i \(0.651890\pi\)
\(938\) 11.9327 0.389616
\(939\) 28.6776 0.935859
\(940\) −100.719 −3.28508
\(941\) 20.7050 0.674962 0.337481 0.941332i \(-0.390425\pi\)
0.337481 + 0.941332i \(0.390425\pi\)
\(942\) −48.7923 −1.58974
\(943\) 1.87305 0.0609950
\(944\) 17.3860 0.565868
\(945\) −12.8565 −0.418221
\(946\) 57.3715 1.86531
\(947\) −31.1915 −1.01359 −0.506794 0.862067i \(-0.669169\pi\)
−0.506794 + 0.862067i \(0.669169\pi\)
\(948\) −18.3711 −0.596666
\(949\) 1.45059 0.0470882
\(950\) 72.3838 2.34844
\(951\) 19.2075 0.622847
\(952\) −26.9699 −0.874101
\(953\) −45.7916 −1.48334 −0.741668 0.670767i \(-0.765965\pi\)
−0.741668 + 0.670767i \(0.765965\pi\)
\(954\) −4.37106 −0.141518
\(955\) −34.5907 −1.11933
\(956\) −3.61354 −0.116870
\(957\) 27.9642 0.903953
\(958\) −35.3295 −1.14144
\(959\) 2.26992 0.0732995
\(960\) −28.9988 −0.935932
\(961\) −22.4940 −0.725612
\(962\) 39.7074 1.28022
\(963\) 0.223522 0.00720288
\(964\) −68.2211 −2.19725
\(965\) −75.5466 −2.43193
\(966\) 1.57094 0.0505442
\(967\) 5.94135 0.191061 0.0955304 0.995427i \(-0.469545\pi\)
0.0955304 + 0.995427i \(0.469545\pi\)
\(968\) 52.2272 1.67865
\(969\) 44.2994 1.42310
\(970\) 7.01771 0.225325
\(971\) −15.4255 −0.495027 −0.247513 0.968884i \(-0.579613\pi\)
−0.247513 + 0.968884i \(0.579613\pi\)
\(972\) 6.52179 0.209187
\(973\) −9.77127 −0.313253
\(974\) 52.4087 1.67928
\(975\) 36.1556 1.15791
\(976\) −67.6477 −2.16535
\(977\) −12.2469 −0.391812 −0.195906 0.980623i \(-0.562765\pi\)
−0.195906 + 0.980623i \(0.562765\pi\)
\(978\) 77.7040 2.48470
\(979\) 17.7737 0.568049
\(980\) 98.1935 3.13668
\(981\) −0.723974 −0.0231147
\(982\) 3.48788 0.111303
\(983\) −29.3212 −0.935202 −0.467601 0.883940i \(-0.654882\pi\)
−0.467601 + 0.883940i \(0.654882\pi\)
\(984\) −47.0486 −1.49985
\(985\) −20.9498 −0.667517
\(986\) −114.532 −3.64745
\(987\) −8.39224 −0.267128
\(988\) −95.8143 −3.04826
\(989\) 5.54687 0.176380
\(990\) 2.11450 0.0672033
\(991\) 16.4889 0.523788 0.261894 0.965097i \(-0.415653\pi\)
0.261894 + 0.965097i \(0.415653\pi\)
\(992\) −25.9414 −0.823642
\(993\) 53.9497 1.71204
\(994\) 25.4941 0.808624
\(995\) 36.5909 1.16001
\(996\) 47.1961 1.49546
\(997\) −38.7685 −1.22781 −0.613905 0.789380i \(-0.710402\pi\)
−0.613905 + 0.789380i \(0.710402\pi\)
\(998\) −37.2128 −1.17795
\(999\) 20.6228 0.652476
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 \(a_p\))