Properties

Label 6034.2.a.n.1.20
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+2.39691 q^{3}\) \(+1.00000 q^{4}\) \(+1.79254 q^{5}\) \(-2.39691 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+2.74520 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+2.39691 q^{3}\) \(+1.00000 q^{4}\) \(+1.79254 q^{5}\) \(-2.39691 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+2.74520 q^{9}\) \(-1.79254 q^{10}\) \(+4.02597 q^{11}\) \(+2.39691 q^{12}\) \(-4.04049 q^{13}\) \(+1.00000 q^{14}\) \(+4.29656 q^{15}\) \(+1.00000 q^{16}\) \(-2.85052 q^{17}\) \(-2.74520 q^{18}\) \(+7.25335 q^{19}\) \(+1.79254 q^{20}\) \(-2.39691 q^{21}\) \(-4.02597 q^{22}\) \(-3.34034 q^{23}\) \(-2.39691 q^{24}\) \(-1.78681 q^{25}\) \(+4.04049 q^{26}\) \(-0.610733 q^{27}\) \(-1.00000 q^{28}\) \(+9.46764 q^{29}\) \(-4.29656 q^{30}\) \(+5.02705 q^{31}\) \(-1.00000 q^{32}\) \(+9.64991 q^{33}\) \(+2.85052 q^{34}\) \(-1.79254 q^{35}\) \(+2.74520 q^{36}\) \(+2.96300 q^{37}\) \(-7.25335 q^{38}\) \(-9.68471 q^{39}\) \(-1.79254 q^{40}\) \(-0.0546808 q^{41}\) \(+2.39691 q^{42}\) \(+2.62861 q^{43}\) \(+4.02597 q^{44}\) \(+4.92087 q^{45}\) \(+3.34034 q^{46}\) \(-5.09558 q^{47}\) \(+2.39691 q^{48}\) \(+1.00000 q^{49}\) \(+1.78681 q^{50}\) \(-6.83247 q^{51}\) \(-4.04049 q^{52}\) \(+6.76559 q^{53}\) \(+0.610733 q^{54}\) \(+7.21670 q^{55}\) \(+1.00000 q^{56}\) \(+17.3857 q^{57}\) \(-9.46764 q^{58}\) \(+2.56502 q^{59}\) \(+4.29656 q^{60}\) \(-5.88046 q^{61}\) \(-5.02705 q^{62}\) \(-2.74520 q^{63}\) \(+1.00000 q^{64}\) \(-7.24272 q^{65}\) \(-9.64991 q^{66}\) \(-7.03088 q^{67}\) \(-2.85052 q^{68}\) \(-8.00651 q^{69}\) \(+1.79254 q^{70}\) \(+11.2544 q^{71}\) \(-2.74520 q^{72}\) \(+16.6187 q^{73}\) \(-2.96300 q^{74}\) \(-4.28284 q^{75}\) \(+7.25335 q^{76}\) \(-4.02597 q^{77}\) \(+9.68471 q^{78}\) \(+10.4282 q^{79}\) \(+1.79254 q^{80}\) \(-9.69948 q^{81}\) \(+0.0546808 q^{82}\) \(+3.21703 q^{83}\) \(-2.39691 q^{84}\) \(-5.10967 q^{85}\) \(-2.62861 q^{86}\) \(+22.6931 q^{87}\) \(-4.02597 q^{88}\) \(-3.96897 q^{89}\) \(-4.92087 q^{90}\) \(+4.04049 q^{91}\) \(-3.34034 q^{92}\) \(+12.0494 q^{93}\) \(+5.09558 q^{94}\) \(+13.0019 q^{95}\) \(-2.39691 q^{96}\) \(+1.99156 q^{97}\) \(-1.00000 q^{98}\) \(+11.0521 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 2.39691 1.38386 0.691930 0.721965i \(-0.256761\pi\)
0.691930 + 0.721965i \(0.256761\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.79254 0.801647 0.400823 0.916155i \(-0.368724\pi\)
0.400823 + 0.916155i \(0.368724\pi\)
\(6\) −2.39691 −0.978536
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 2.74520 0.915067
\(10\) −1.79254 −0.566850
\(11\) 4.02597 1.21388 0.606938 0.794749i \(-0.292398\pi\)
0.606938 + 0.794749i \(0.292398\pi\)
\(12\) 2.39691 0.691930
\(13\) −4.04049 −1.12063 −0.560315 0.828280i \(-0.689320\pi\)
−0.560315 + 0.828280i \(0.689320\pi\)
\(14\) 1.00000 0.267261
\(15\) 4.29656 1.10937
\(16\) 1.00000 0.250000
\(17\) −2.85052 −0.691354 −0.345677 0.938354i \(-0.612351\pi\)
−0.345677 + 0.938354i \(0.612351\pi\)
\(18\) −2.74520 −0.647050
\(19\) 7.25335 1.66403 0.832016 0.554751i \(-0.187187\pi\)
0.832016 + 0.554751i \(0.187187\pi\)
\(20\) 1.79254 0.400823
\(21\) −2.39691 −0.523050
\(22\) −4.02597 −0.858340
\(23\) −3.34034 −0.696509 −0.348254 0.937400i \(-0.613225\pi\)
−0.348254 + 0.937400i \(0.613225\pi\)
\(24\) −2.39691 −0.489268
\(25\) −1.78681 −0.357363
\(26\) 4.04049 0.792405
\(27\) −0.610733 −0.117536
\(28\) −1.00000 −0.188982
\(29\) 9.46764 1.75810 0.879049 0.476732i \(-0.158179\pi\)
0.879049 + 0.476732i \(0.158179\pi\)
\(30\) −4.29656 −0.784440
\(31\) 5.02705 0.902885 0.451442 0.892300i \(-0.350910\pi\)
0.451442 + 0.892300i \(0.350910\pi\)
\(32\) −1.00000 −0.176777
\(33\) 9.64991 1.67983
\(34\) 2.85052 0.488861
\(35\) −1.79254 −0.302994
\(36\) 2.74520 0.457533
\(37\) 2.96300 0.487114 0.243557 0.969887i \(-0.421686\pi\)
0.243557 + 0.969887i \(0.421686\pi\)
\(38\) −7.25335 −1.17665
\(39\) −9.68471 −1.55079
\(40\) −1.79254 −0.283425
\(41\) −0.0546808 −0.00853971 −0.00426985 0.999991i \(-0.501359\pi\)
−0.00426985 + 0.999991i \(0.501359\pi\)
\(42\) 2.39691 0.369852
\(43\) 2.62861 0.400860 0.200430 0.979708i \(-0.435766\pi\)
0.200430 + 0.979708i \(0.435766\pi\)
\(44\) 4.02597 0.606938
\(45\) 4.92087 0.733560
\(46\) 3.34034 0.492506
\(47\) −5.09558 −0.743267 −0.371633 0.928380i \(-0.621202\pi\)
−0.371633 + 0.928380i \(0.621202\pi\)
\(48\) 2.39691 0.345965
\(49\) 1.00000 0.142857
\(50\) 1.78681 0.252693
\(51\) −6.83247 −0.956736
\(52\) −4.04049 −0.560315
\(53\) 6.76559 0.929326 0.464663 0.885488i \(-0.346176\pi\)
0.464663 + 0.885488i \(0.346176\pi\)
\(54\) 0.610733 0.0831102
\(55\) 7.21670 0.973100
\(56\) 1.00000 0.133631
\(57\) 17.3857 2.30279
\(58\) −9.46764 −1.24316
\(59\) 2.56502 0.333937 0.166969 0.985962i \(-0.446602\pi\)
0.166969 + 0.985962i \(0.446602\pi\)
\(60\) 4.29656 0.554683
\(61\) −5.88046 −0.752915 −0.376458 0.926434i \(-0.622858\pi\)
−0.376458 + 0.926434i \(0.622858\pi\)
\(62\) −5.02705 −0.638436
\(63\) −2.74520 −0.345863
\(64\) 1.00000 0.125000
\(65\) −7.24272 −0.898349
\(66\) −9.64991 −1.18782
\(67\) −7.03088 −0.858958 −0.429479 0.903077i \(-0.641303\pi\)
−0.429479 + 0.903077i \(0.641303\pi\)
\(68\) −2.85052 −0.345677
\(69\) −8.00651 −0.963870
\(70\) 1.79254 0.214249
\(71\) 11.2544 1.33566 0.667829 0.744315i \(-0.267224\pi\)
0.667829 + 0.744315i \(0.267224\pi\)
\(72\) −2.74520 −0.323525
\(73\) 16.6187 1.94507 0.972536 0.232751i \(-0.0747728\pi\)
0.972536 + 0.232751i \(0.0747728\pi\)
\(74\) −2.96300 −0.344442
\(75\) −4.28284 −0.494540
\(76\) 7.25335 0.832016
\(77\) −4.02597 −0.458802
\(78\) 9.68471 1.09658
\(79\) 10.4282 1.17326 0.586631 0.809854i \(-0.300454\pi\)
0.586631 + 0.809854i \(0.300454\pi\)
\(80\) 1.79254 0.200412
\(81\) −9.69948 −1.07772
\(82\) 0.0546808 0.00603849
\(83\) 3.21703 0.353114 0.176557 0.984290i \(-0.443504\pi\)
0.176557 + 0.984290i \(0.443504\pi\)
\(84\) −2.39691 −0.261525
\(85\) −5.10967 −0.554222
\(86\) −2.62861 −0.283451
\(87\) 22.6931 2.43296
\(88\) −4.02597 −0.429170
\(89\) −3.96897 −0.420709 −0.210355 0.977625i \(-0.567462\pi\)
−0.210355 + 0.977625i \(0.567462\pi\)
\(90\) −4.92087 −0.518705
\(91\) 4.04049 0.423558
\(92\) −3.34034 −0.348254
\(93\) 12.0494 1.24947
\(94\) 5.09558 0.525569
\(95\) 13.0019 1.33397
\(96\) −2.39691 −0.244634
\(97\) 1.99156 0.202213 0.101106 0.994876i \(-0.467762\pi\)
0.101106 + 0.994876i \(0.467762\pi\)
\(98\) −1.00000 −0.101015
\(99\) 11.0521 1.11078
\(100\) −1.78681 −0.178681
\(101\) 12.6691 1.26062 0.630311 0.776342i \(-0.282927\pi\)
0.630311 + 0.776342i \(0.282927\pi\)
\(102\) 6.83247 0.676515
\(103\) 2.70526 0.266557 0.133279 0.991079i \(-0.457449\pi\)
0.133279 + 0.991079i \(0.457449\pi\)
\(104\) 4.04049 0.396202
\(105\) −4.29656 −0.419301
\(106\) −6.76559 −0.657132
\(107\) −4.64585 −0.449131 −0.224565 0.974459i \(-0.572096\pi\)
−0.224565 + 0.974459i \(0.572096\pi\)
\(108\) −0.610733 −0.0587678
\(109\) −4.88199 −0.467610 −0.233805 0.972283i \(-0.575118\pi\)
−0.233805 + 0.972283i \(0.575118\pi\)
\(110\) −7.21670 −0.688085
\(111\) 7.10206 0.674097
\(112\) −1.00000 −0.0944911
\(113\) 5.58515 0.525406 0.262703 0.964877i \(-0.415386\pi\)
0.262703 + 0.964877i \(0.415386\pi\)
\(114\) −17.3857 −1.62832
\(115\) −5.98768 −0.558354
\(116\) 9.46764 0.879049
\(117\) −11.0920 −1.02545
\(118\) −2.56502 −0.236129
\(119\) 2.85052 0.261307
\(120\) −4.29656 −0.392220
\(121\) 5.20844 0.473495
\(122\) 5.88046 0.532392
\(123\) −0.131065 −0.0118178
\(124\) 5.02705 0.451442
\(125\) −12.1656 −1.08813
\(126\) 2.74520 0.244562
\(127\) −1.97600 −0.175342 −0.0876708 0.996150i \(-0.527942\pi\)
−0.0876708 + 0.996150i \(0.527942\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 6.30056 0.554734
\(130\) 7.24272 0.635229
\(131\) −2.73266 −0.238753 −0.119377 0.992849i \(-0.538090\pi\)
−0.119377 + 0.992849i \(0.538090\pi\)
\(132\) 9.64991 0.839917
\(133\) −7.25335 −0.628945
\(134\) 7.03088 0.607375
\(135\) −1.09476 −0.0942220
\(136\) 2.85052 0.244430
\(137\) 2.45556 0.209793 0.104897 0.994483i \(-0.466549\pi\)
0.104897 + 0.994483i \(0.466549\pi\)
\(138\) 8.00651 0.681559
\(139\) −15.9287 −1.35105 −0.675526 0.737336i \(-0.736084\pi\)
−0.675526 + 0.737336i \(0.736084\pi\)
\(140\) −1.79254 −0.151497
\(141\) −12.2137 −1.02858
\(142\) −11.2544 −0.944452
\(143\) −16.2669 −1.36031
\(144\) 2.74520 0.228767
\(145\) 16.9711 1.40937
\(146\) −16.6187 −1.37537
\(147\) 2.39691 0.197694
\(148\) 2.96300 0.243557
\(149\) −20.2934 −1.66250 −0.831251 0.555898i \(-0.812375\pi\)
−0.831251 + 0.555898i \(0.812375\pi\)
\(150\) 4.28284 0.349692
\(151\) 4.16224 0.338719 0.169359 0.985554i \(-0.445830\pi\)
0.169359 + 0.985554i \(0.445830\pi\)
\(152\) −7.25335 −0.588324
\(153\) −7.82526 −0.632635
\(154\) 4.02597 0.324422
\(155\) 9.01117 0.723794
\(156\) −9.68471 −0.775397
\(157\) 21.6335 1.72655 0.863273 0.504738i \(-0.168411\pi\)
0.863273 + 0.504738i \(0.168411\pi\)
\(158\) −10.4282 −0.829622
\(159\) 16.2165 1.28606
\(160\) −1.79254 −0.141712
\(161\) 3.34034 0.263255
\(162\) 9.69948 0.762063
\(163\) −5.77547 −0.452370 −0.226185 0.974084i \(-0.572625\pi\)
−0.226185 + 0.974084i \(0.572625\pi\)
\(164\) −0.0546808 −0.00426985
\(165\) 17.2978 1.34663
\(166\) −3.21703 −0.249690
\(167\) −12.7031 −0.982996 −0.491498 0.870879i \(-0.663551\pi\)
−0.491498 + 0.870879i \(0.663551\pi\)
\(168\) 2.39691 0.184926
\(169\) 3.32555 0.255811
\(170\) 5.10967 0.391894
\(171\) 19.9119 1.52270
\(172\) 2.62861 0.200430
\(173\) 6.98665 0.531185 0.265593 0.964085i \(-0.414432\pi\)
0.265593 + 0.964085i \(0.414432\pi\)
\(174\) −22.6931 −1.72036
\(175\) 1.78681 0.135070
\(176\) 4.02597 0.303469
\(177\) 6.14814 0.462122
\(178\) 3.96897 0.297487
\(179\) 0.807690 0.0603696 0.0301848 0.999544i \(-0.490390\pi\)
0.0301848 + 0.999544i \(0.490390\pi\)
\(180\) 4.92087 0.366780
\(181\) 23.9060 1.77692 0.888459 0.458956i \(-0.151776\pi\)
0.888459 + 0.458956i \(0.151776\pi\)
\(182\) −4.04049 −0.299501
\(183\) −14.0950 −1.04193
\(184\) 3.34034 0.246253
\(185\) 5.31129 0.390493
\(186\) −12.0494 −0.883505
\(187\) −11.4761 −0.839218
\(188\) −5.09558 −0.371633
\(189\) 0.610733 0.0444243
\(190\) −13.0019 −0.943257
\(191\) 17.5942 1.27307 0.636535 0.771248i \(-0.280367\pi\)
0.636535 + 0.771248i \(0.280367\pi\)
\(192\) 2.39691 0.172982
\(193\) 22.9721 1.65357 0.826784 0.562519i \(-0.190168\pi\)
0.826784 + 0.562519i \(0.190168\pi\)
\(194\) −1.99156 −0.142986
\(195\) −17.3602 −1.24319
\(196\) 1.00000 0.0714286
\(197\) 17.8072 1.26871 0.634355 0.773042i \(-0.281266\pi\)
0.634355 + 0.773042i \(0.281266\pi\)
\(198\) −11.0521 −0.785438
\(199\) 24.2918 1.72200 0.860998 0.508608i \(-0.169840\pi\)
0.860998 + 0.508608i \(0.169840\pi\)
\(200\) 1.78681 0.126347
\(201\) −16.8524 −1.18868
\(202\) −12.6691 −0.891395
\(203\) −9.46764 −0.664498
\(204\) −6.83247 −0.478368
\(205\) −0.0980174 −0.00684583
\(206\) −2.70526 −0.188485
\(207\) −9.16990 −0.637352
\(208\) −4.04049 −0.280157
\(209\) 29.2018 2.01993
\(210\) 4.29656 0.296491
\(211\) −3.92205 −0.270005 −0.135002 0.990845i \(-0.543104\pi\)
−0.135002 + 0.990845i \(0.543104\pi\)
\(212\) 6.76559 0.464663
\(213\) 26.9760 1.84836
\(214\) 4.64585 0.317584
\(215\) 4.71189 0.321348
\(216\) 0.610733 0.0415551
\(217\) −5.02705 −0.341258
\(218\) 4.88199 0.330650
\(219\) 39.8336 2.69171
\(220\) 7.21670 0.486550
\(221\) 11.5175 0.774752
\(222\) −7.10206 −0.476659
\(223\) −18.5350 −1.24120 −0.620599 0.784128i \(-0.713110\pi\)
−0.620599 + 0.784128i \(0.713110\pi\)
\(224\) 1.00000 0.0668153
\(225\) −4.90516 −0.327011
\(226\) −5.58515 −0.371518
\(227\) −26.9049 −1.78574 −0.892870 0.450315i \(-0.851312\pi\)
−0.892870 + 0.450315i \(0.851312\pi\)
\(228\) 17.3857 1.15139
\(229\) 15.4154 1.01868 0.509341 0.860565i \(-0.329889\pi\)
0.509341 + 0.860565i \(0.329889\pi\)
\(230\) 5.98768 0.394816
\(231\) −9.64991 −0.634917
\(232\) −9.46764 −0.621581
\(233\) −7.71687 −0.505549 −0.252775 0.967525i \(-0.581343\pi\)
−0.252775 + 0.967525i \(0.581343\pi\)
\(234\) 11.0920 0.725103
\(235\) −9.13401 −0.595837
\(236\) 2.56502 0.166969
\(237\) 24.9955 1.62363
\(238\) −2.85052 −0.184772
\(239\) 0.791586 0.0512034 0.0256017 0.999672i \(-0.491850\pi\)
0.0256017 + 0.999672i \(0.491850\pi\)
\(240\) 4.29656 0.277342
\(241\) −17.5279 −1.12907 −0.564537 0.825408i \(-0.690945\pi\)
−0.564537 + 0.825408i \(0.690945\pi\)
\(242\) −5.20844 −0.334811
\(243\) −21.4166 −1.37388
\(244\) −5.88046 −0.376458
\(245\) 1.79254 0.114521
\(246\) 0.131065 0.00835642
\(247\) −29.3071 −1.86476
\(248\) −5.02705 −0.319218
\(249\) 7.71094 0.488661
\(250\) 12.1656 0.769421
\(251\) 19.7734 1.24809 0.624044 0.781389i \(-0.285488\pi\)
0.624044 + 0.781389i \(0.285488\pi\)
\(252\) −2.74520 −0.172931
\(253\) −13.4481 −0.845475
\(254\) 1.97600 0.123985
\(255\) −12.2474 −0.766965
\(256\) 1.00000 0.0625000
\(257\) 15.2211 0.949469 0.474735 0.880129i \(-0.342544\pi\)
0.474735 + 0.880129i \(0.342544\pi\)
\(258\) −6.30056 −0.392256
\(259\) −2.96300 −0.184112
\(260\) −7.24272 −0.449175
\(261\) 25.9906 1.60878
\(262\) 2.73266 0.168824
\(263\) −17.5612 −1.08287 −0.541434 0.840744i \(-0.682118\pi\)
−0.541434 + 0.840744i \(0.682118\pi\)
\(264\) −9.64991 −0.593911
\(265\) 12.1276 0.744991
\(266\) 7.25335 0.444731
\(267\) −9.51327 −0.582203
\(268\) −7.03088 −0.429479
\(269\) 1.81371 0.110584 0.0552918 0.998470i \(-0.482391\pi\)
0.0552918 + 0.998470i \(0.482391\pi\)
\(270\) 1.09476 0.0666250
\(271\) −6.31173 −0.383410 −0.191705 0.981453i \(-0.561402\pi\)
−0.191705 + 0.981453i \(0.561402\pi\)
\(272\) −2.85052 −0.172838
\(273\) 9.68471 0.586145
\(274\) −2.45556 −0.148346
\(275\) −7.19366 −0.433794
\(276\) −8.00651 −0.481935
\(277\) −15.6035 −0.937526 −0.468763 0.883324i \(-0.655300\pi\)
−0.468763 + 0.883324i \(0.655300\pi\)
\(278\) 15.9287 0.955338
\(279\) 13.8003 0.826200
\(280\) 1.79254 0.107125
\(281\) −19.2854 −1.15047 −0.575234 0.817989i \(-0.695089\pi\)
−0.575234 + 0.817989i \(0.695089\pi\)
\(282\) 12.2137 0.727313
\(283\) 7.79751 0.463514 0.231757 0.972774i \(-0.425553\pi\)
0.231757 + 0.972774i \(0.425553\pi\)
\(284\) 11.2544 0.667829
\(285\) 31.1644 1.84602
\(286\) 16.2669 0.961881
\(287\) 0.0546808 0.00322771
\(288\) −2.74520 −0.161762
\(289\) −8.87451 −0.522030
\(290\) −16.9711 −0.996577
\(291\) 4.77361 0.279834
\(292\) 16.6187 0.972536
\(293\) −2.77445 −0.162085 −0.0810425 0.996711i \(-0.525825\pi\)
−0.0810425 + 0.996711i \(0.525825\pi\)
\(294\) −2.39691 −0.139791
\(295\) 4.59789 0.267700
\(296\) −2.96300 −0.172221
\(297\) −2.45879 −0.142674
\(298\) 20.2934 1.17557
\(299\) 13.4966 0.780528
\(300\) −4.28284 −0.247270
\(301\) −2.62861 −0.151511
\(302\) −4.16224 −0.239510
\(303\) 30.3668 1.74452
\(304\) 7.25335 0.416008
\(305\) −10.5409 −0.603572
\(306\) 7.82526 0.447340
\(307\) −6.03359 −0.344355 −0.172177 0.985066i \(-0.555080\pi\)
−0.172177 + 0.985066i \(0.555080\pi\)
\(308\) −4.02597 −0.229401
\(309\) 6.48429 0.368878
\(310\) −9.01117 −0.511800
\(311\) −14.3379 −0.813025 −0.406513 0.913645i \(-0.633255\pi\)
−0.406513 + 0.913645i \(0.633255\pi\)
\(312\) 9.68471 0.548289
\(313\) −0.336510 −0.0190207 −0.00951034 0.999955i \(-0.503027\pi\)
−0.00951034 + 0.999955i \(0.503027\pi\)
\(314\) −21.6335 −1.22085
\(315\) −4.92087 −0.277260
\(316\) 10.4282 0.586631
\(317\) −22.7900 −1.28001 −0.640007 0.768369i \(-0.721069\pi\)
−0.640007 + 0.768369i \(0.721069\pi\)
\(318\) −16.2165 −0.909379
\(319\) 38.1165 2.13411
\(320\) 1.79254 0.100206
\(321\) −11.1357 −0.621534
\(322\) −3.34034 −0.186150
\(323\) −20.6759 −1.15044
\(324\) −9.69948 −0.538860
\(325\) 7.21960 0.400471
\(326\) 5.77547 0.319874
\(327\) −11.7017 −0.647107
\(328\) 0.0546808 0.00301924
\(329\) 5.09558 0.280928
\(330\) −17.2978 −0.952213
\(331\) 10.4111 0.572246 0.286123 0.958193i \(-0.407633\pi\)
0.286123 + 0.958193i \(0.407633\pi\)
\(332\) 3.21703 0.176557
\(333\) 8.13403 0.445742
\(334\) 12.7031 0.695083
\(335\) −12.6031 −0.688581
\(336\) −2.39691 −0.130762
\(337\) −31.5270 −1.71738 −0.858692 0.512492i \(-0.828723\pi\)
−0.858692 + 0.512492i \(0.828723\pi\)
\(338\) −3.32555 −0.180886
\(339\) 13.3871 0.727089
\(340\) −5.10967 −0.277111
\(341\) 20.2388 1.09599
\(342\) −19.9119 −1.07671
\(343\) −1.00000 −0.0539949
\(344\) −2.62861 −0.141725
\(345\) −14.3520 −0.772683
\(346\) −6.98665 −0.375605
\(347\) 0.164008 0.00880439 0.00440220 0.999990i \(-0.498599\pi\)
0.00440220 + 0.999990i \(0.498599\pi\)
\(348\) 22.6931 1.21648
\(349\) 28.8205 1.54273 0.771363 0.636396i \(-0.219575\pi\)
0.771363 + 0.636396i \(0.219575\pi\)
\(350\) −1.78681 −0.0955092
\(351\) 2.46766 0.131714
\(352\) −4.02597 −0.214585
\(353\) 14.2253 0.757138 0.378569 0.925573i \(-0.376416\pi\)
0.378569 + 0.925573i \(0.376416\pi\)
\(354\) −6.14814 −0.326770
\(355\) 20.1740 1.07073
\(356\) −3.96897 −0.210355
\(357\) 6.83247 0.361612
\(358\) −0.807690 −0.0426877
\(359\) −10.6946 −0.564440 −0.282220 0.959350i \(-0.591071\pi\)
−0.282220 + 0.959350i \(0.591071\pi\)
\(360\) −4.92087 −0.259353
\(361\) 33.6111 1.76900
\(362\) −23.9060 −1.25647
\(363\) 12.4842 0.655250
\(364\) 4.04049 0.211779
\(365\) 29.7896 1.55926
\(366\) 14.0950 0.736755
\(367\) −7.70210 −0.402047 −0.201023 0.979586i \(-0.564427\pi\)
−0.201023 + 0.979586i \(0.564427\pi\)
\(368\) −3.34034 −0.174127
\(369\) −0.150110 −0.00781440
\(370\) −5.31129 −0.276121
\(371\) −6.76559 −0.351252
\(372\) 12.0494 0.624733
\(373\) 12.5959 0.652193 0.326096 0.945337i \(-0.394267\pi\)
0.326096 + 0.945337i \(0.394267\pi\)
\(374\) 11.4761 0.593417
\(375\) −29.1599 −1.50581
\(376\) 5.09558 0.262784
\(377\) −38.2539 −1.97018
\(378\) −0.610733 −0.0314127
\(379\) −13.6261 −0.699928 −0.349964 0.936763i \(-0.613806\pi\)
−0.349964 + 0.936763i \(0.613806\pi\)
\(380\) 13.0019 0.666983
\(381\) −4.73630 −0.242648
\(382\) −17.5942 −0.900196
\(383\) 17.1341 0.875512 0.437756 0.899094i \(-0.355773\pi\)
0.437756 + 0.899094i \(0.355773\pi\)
\(384\) −2.39691 −0.122317
\(385\) −7.21670 −0.367797
\(386\) −22.9721 −1.16925
\(387\) 7.21607 0.366814
\(388\) 1.99156 0.101106
\(389\) −22.1410 −1.12259 −0.561296 0.827615i \(-0.689697\pi\)
−0.561296 + 0.827615i \(0.689697\pi\)
\(390\) 17.3602 0.879067
\(391\) 9.52172 0.481534
\(392\) −1.00000 −0.0505076
\(393\) −6.54994 −0.330401
\(394\) −17.8072 −0.897114
\(395\) 18.6929 0.940542
\(396\) 11.0521 0.555389
\(397\) 1.39916 0.0702219 0.0351109 0.999383i \(-0.488822\pi\)
0.0351109 + 0.999383i \(0.488822\pi\)
\(398\) −24.2918 −1.21764
\(399\) −17.3857 −0.870372
\(400\) −1.78681 −0.0893406
\(401\) −33.6838 −1.68209 −0.841044 0.540967i \(-0.818058\pi\)
−0.841044 + 0.540967i \(0.818058\pi\)
\(402\) 16.8524 0.840522
\(403\) −20.3117 −1.01180
\(404\) 12.6691 0.630311
\(405\) −17.3867 −0.863950
\(406\) 9.46764 0.469871
\(407\) 11.9290 0.591296
\(408\) 6.83247 0.338257
\(409\) −7.24776 −0.358379 −0.179189 0.983815i \(-0.557347\pi\)
−0.179189 + 0.983815i \(0.557347\pi\)
\(410\) 0.0980174 0.00484073
\(411\) 5.88578 0.290324
\(412\) 2.70526 0.133279
\(413\) −2.56502 −0.126216
\(414\) 9.16990 0.450676
\(415\) 5.76664 0.283073
\(416\) 4.04049 0.198101
\(417\) −38.1797 −1.86967
\(418\) −29.2018 −1.42831
\(419\) 7.13131 0.348387 0.174194 0.984711i \(-0.444268\pi\)
0.174194 + 0.984711i \(0.444268\pi\)
\(420\) −4.29656 −0.209651
\(421\) −11.7180 −0.571102 −0.285551 0.958363i \(-0.592177\pi\)
−0.285551 + 0.958363i \(0.592177\pi\)
\(422\) 3.92205 0.190922
\(423\) −13.9884 −0.680139
\(424\) −6.76559 −0.328566
\(425\) 5.09335 0.247064
\(426\) −26.9760 −1.30699
\(427\) 5.88046 0.284575
\(428\) −4.64585 −0.224565
\(429\) −38.9903 −1.88247
\(430\) −4.71189 −0.227227
\(431\) 1.00000 0.0481683
\(432\) −0.610733 −0.0293839
\(433\) −24.0001 −1.15337 −0.576685 0.816967i \(-0.695654\pi\)
−0.576685 + 0.816967i \(0.695654\pi\)
\(434\) 5.02705 0.241306
\(435\) 40.6783 1.95037
\(436\) −4.88199 −0.233805
\(437\) −24.2286 −1.15901
\(438\) −39.8336 −1.90332
\(439\) −33.7019 −1.60851 −0.804253 0.594287i \(-0.797434\pi\)
−0.804253 + 0.594287i \(0.797434\pi\)
\(440\) −7.21670 −0.344043
\(441\) 2.74520 0.130724
\(442\) −11.5175 −0.547832
\(443\) −2.79816 −0.132945 −0.0664723 0.997788i \(-0.521174\pi\)
−0.0664723 + 0.997788i \(0.521174\pi\)
\(444\) 7.10206 0.337049
\(445\) −7.11451 −0.337260
\(446\) 18.5350 0.877659
\(447\) −48.6416 −2.30067
\(448\) −1.00000 −0.0472456
\(449\) −0.954714 −0.0450557 −0.0225279 0.999746i \(-0.507171\pi\)
−0.0225279 + 0.999746i \(0.507171\pi\)
\(450\) 4.90516 0.231231
\(451\) −0.220143 −0.0103661
\(452\) 5.58515 0.262703
\(453\) 9.97654 0.468739
\(454\) 26.9049 1.26271
\(455\) 7.24272 0.339544
\(456\) −17.3857 −0.814158
\(457\) −23.9113 −1.11853 −0.559263 0.828990i \(-0.688916\pi\)
−0.559263 + 0.828990i \(0.688916\pi\)
\(458\) −15.4154 −0.720316
\(459\) 1.74091 0.0812587
\(460\) −5.98768 −0.279177
\(461\) 22.8075 1.06225 0.531126 0.847293i \(-0.321769\pi\)
0.531126 + 0.847293i \(0.321769\pi\)
\(462\) 9.64991 0.448954
\(463\) −27.0052 −1.25504 −0.627519 0.778601i \(-0.715930\pi\)
−0.627519 + 0.778601i \(0.715930\pi\)
\(464\) 9.46764 0.439524
\(465\) 21.5990 1.00163
\(466\) 7.71687 0.357477
\(467\) 23.8836 1.10520 0.552601 0.833446i \(-0.313635\pi\)
0.552601 + 0.833446i \(0.313635\pi\)
\(468\) −11.0920 −0.512726
\(469\) 7.03088 0.324656
\(470\) 9.13401 0.421321
\(471\) 51.8538 2.38930
\(472\) −2.56502 −0.118065
\(473\) 10.5827 0.486594
\(474\) −24.9955 −1.14808
\(475\) −12.9604 −0.594663
\(476\) 2.85052 0.130654
\(477\) 18.5729 0.850395
\(478\) −0.791586 −0.0362063
\(479\) −27.9871 −1.27876 −0.639382 0.768889i \(-0.720810\pi\)
−0.639382 + 0.768889i \(0.720810\pi\)
\(480\) −4.29656 −0.196110
\(481\) −11.9720 −0.545875
\(482\) 17.5279 0.798376
\(483\) 8.00651 0.364309
\(484\) 5.20844 0.236747
\(485\) 3.56995 0.162103
\(486\) 21.4166 0.971478
\(487\) −7.74676 −0.351039 −0.175520 0.984476i \(-0.556161\pi\)
−0.175520 + 0.984476i \(0.556161\pi\)
\(488\) 5.88046 0.266196
\(489\) −13.8433 −0.626016
\(490\) −1.79254 −0.0809785
\(491\) −6.51264 −0.293911 −0.146956 0.989143i \(-0.546947\pi\)
−0.146956 + 0.989143i \(0.546947\pi\)
\(492\) −0.131065 −0.00590888
\(493\) −26.9878 −1.21547
\(494\) 29.3071 1.31859
\(495\) 19.8113 0.890451
\(496\) 5.02705 0.225721
\(497\) −11.2544 −0.504831
\(498\) −7.71094 −0.345535
\(499\) 28.7625 1.28759 0.643794 0.765199i \(-0.277359\pi\)
0.643794 + 0.765199i \(0.277359\pi\)
\(500\) −12.1656 −0.544063
\(501\) −30.4483 −1.36033
\(502\) −19.7734 −0.882532
\(503\) 29.1864 1.30136 0.650678 0.759354i \(-0.274485\pi\)
0.650678 + 0.759354i \(0.274485\pi\)
\(504\) 2.74520 0.122281
\(505\) 22.7098 1.01057
\(506\) 13.4481 0.597841
\(507\) 7.97105 0.354007
\(508\) −1.97600 −0.0876708
\(509\) −3.23493 −0.143386 −0.0716928 0.997427i \(-0.522840\pi\)
−0.0716928 + 0.997427i \(0.522840\pi\)
\(510\) 12.2474 0.542326
\(511\) −16.6187 −0.735168
\(512\) −1.00000 −0.0441942
\(513\) −4.42986 −0.195583
\(514\) −15.2211 −0.671376
\(515\) 4.84928 0.213685
\(516\) 6.30056 0.277367
\(517\) −20.5147 −0.902234
\(518\) 2.96300 0.130187
\(519\) 16.7464 0.735086
\(520\) 7.24272 0.317614
\(521\) 33.8468 1.48285 0.741427 0.671034i \(-0.234149\pi\)
0.741427 + 0.671034i \(0.234149\pi\)
\(522\) −25.9906 −1.13758
\(523\) −15.9769 −0.698622 −0.349311 0.937007i \(-0.613584\pi\)
−0.349311 + 0.937007i \(0.613584\pi\)
\(524\) −2.73266 −0.119377
\(525\) 4.28284 0.186918
\(526\) 17.5612 0.765703
\(527\) −14.3297 −0.624213
\(528\) 9.64991 0.419958
\(529\) −11.8421 −0.514876
\(530\) −12.1276 −0.526788
\(531\) 7.04150 0.305575
\(532\) −7.25335 −0.314473
\(533\) 0.220937 0.00956985
\(534\) 9.51327 0.411680
\(535\) −8.32785 −0.360044
\(536\) 7.03088 0.303688
\(537\) 1.93596 0.0835430
\(538\) −1.81371 −0.0781944
\(539\) 4.02597 0.173411
\(540\) −1.09476 −0.0471110
\(541\) −19.7792 −0.850374 −0.425187 0.905105i \(-0.639792\pi\)
−0.425187 + 0.905105i \(0.639792\pi\)
\(542\) 6.31173 0.271112
\(543\) 57.3006 2.45901
\(544\) 2.85052 0.122215
\(545\) −8.75115 −0.374858
\(546\) −9.68471 −0.414467
\(547\) −18.8530 −0.806094 −0.403047 0.915179i \(-0.632049\pi\)
−0.403047 + 0.915179i \(0.632049\pi\)
\(548\) 2.45556 0.104897
\(549\) −16.1430 −0.688968
\(550\) 7.19366 0.306739
\(551\) 68.6721 2.92553
\(552\) 8.00651 0.340779
\(553\) −10.4282 −0.443451
\(554\) 15.6035 0.662931
\(555\) 12.7307 0.540388
\(556\) −15.9287 −0.675526
\(557\) −15.7717 −0.668268 −0.334134 0.942526i \(-0.608444\pi\)
−0.334134 + 0.942526i \(0.608444\pi\)
\(558\) −13.8003 −0.584211
\(559\) −10.6209 −0.449216
\(560\) −1.79254 −0.0757485
\(561\) −27.5073 −1.16136
\(562\) 19.2854 0.813504
\(563\) −16.8831 −0.711538 −0.355769 0.934574i \(-0.615781\pi\)
−0.355769 + 0.934574i \(0.615781\pi\)
\(564\) −12.2137 −0.514288
\(565\) 10.0116 0.421190
\(566\) −7.79751 −0.327754
\(567\) 9.69948 0.407340
\(568\) −11.2544 −0.472226
\(569\) −24.2764 −1.01772 −0.508859 0.860850i \(-0.669933\pi\)
−0.508859 + 0.860850i \(0.669933\pi\)
\(570\) −31.1644 −1.30533
\(571\) 7.62414 0.319060 0.159530 0.987193i \(-0.449002\pi\)
0.159530 + 0.987193i \(0.449002\pi\)
\(572\) −16.2669 −0.680153
\(573\) 42.1717 1.76175
\(574\) −0.0546808 −0.00228233
\(575\) 5.96856 0.248906
\(576\) 2.74520 0.114383
\(577\) 39.7578 1.65514 0.827570 0.561362i \(-0.189723\pi\)
0.827570 + 0.561362i \(0.189723\pi\)
\(578\) 8.87451 0.369131
\(579\) 55.0622 2.28831
\(580\) 16.9711 0.704687
\(581\) −3.21703 −0.133465
\(582\) −4.77361 −0.197873
\(583\) 27.2381 1.12809
\(584\) −16.6187 −0.687687
\(585\) −19.8827 −0.822050
\(586\) 2.77445 0.114611
\(587\) 18.2754 0.754305 0.377152 0.926151i \(-0.376903\pi\)
0.377152 + 0.926151i \(0.376903\pi\)
\(588\) 2.39691 0.0988471
\(589\) 36.4629 1.50243
\(590\) −4.59789 −0.189292
\(591\) 42.6823 1.75572
\(592\) 2.96300 0.121779
\(593\) −47.3309 −1.94365 −0.971824 0.235706i \(-0.924260\pi\)
−0.971824 + 0.235706i \(0.924260\pi\)
\(594\) 2.45879 0.100886
\(595\) 5.10967 0.209476
\(596\) −20.2934 −0.831251
\(597\) 58.2253 2.38300
\(598\) −13.4966 −0.551917
\(599\) 39.1245 1.59858 0.799292 0.600942i \(-0.205208\pi\)
0.799292 + 0.600942i \(0.205208\pi\)
\(600\) 4.28284 0.174846
\(601\) −40.8160 −1.66492 −0.832461 0.554084i \(-0.813069\pi\)
−0.832461 + 0.554084i \(0.813069\pi\)
\(602\) 2.62861 0.107134
\(603\) −19.3012 −0.786004
\(604\) 4.16224 0.169359
\(605\) 9.33633 0.379576
\(606\) −30.3668 −1.23357
\(607\) −8.15634 −0.331056 −0.165528 0.986205i \(-0.552933\pi\)
−0.165528 + 0.986205i \(0.552933\pi\)
\(608\) −7.25335 −0.294162
\(609\) −22.6931 −0.919572
\(610\) 10.5409 0.426790
\(611\) 20.5886 0.832927
\(612\) −7.82526 −0.316317
\(613\) 32.6147 1.31730 0.658648 0.752451i \(-0.271129\pi\)
0.658648 + 0.752451i \(0.271129\pi\)
\(614\) 6.03359 0.243496
\(615\) −0.234939 −0.00947367
\(616\) 4.02597 0.162211
\(617\) −14.3600 −0.578111 −0.289056 0.957312i \(-0.593341\pi\)
−0.289056 + 0.957312i \(0.593341\pi\)
\(618\) −6.48429 −0.260836
\(619\) −48.3287 −1.94249 −0.971247 0.238074i \(-0.923484\pi\)
−0.971247 + 0.238074i \(0.923484\pi\)
\(620\) 9.01117 0.361897
\(621\) 2.04005 0.0818646
\(622\) 14.3379 0.574896
\(623\) 3.96897 0.159013
\(624\) −9.68471 −0.387699
\(625\) −12.8732 −0.514929
\(626\) 0.336510 0.0134497
\(627\) 69.9942 2.79530
\(628\) 21.6335 0.863273
\(629\) −8.44610 −0.336768
\(630\) 4.92087 0.196052
\(631\) 10.4290 0.415174 0.207587 0.978217i \(-0.433439\pi\)
0.207587 + 0.978217i \(0.433439\pi\)
\(632\) −10.4282 −0.414811
\(633\) −9.40081 −0.373649
\(634\) 22.7900 0.905107
\(635\) −3.54205 −0.140562
\(636\) 16.2165 0.643028
\(637\) −4.04049 −0.160090
\(638\) −38.1165 −1.50905
\(639\) 30.8957 1.22222
\(640\) −1.79254 −0.0708562
\(641\) 31.5825 1.24743 0.623717 0.781650i \(-0.285622\pi\)
0.623717 + 0.781650i \(0.285622\pi\)
\(642\) 11.1357 0.439491
\(643\) −11.3562 −0.447843 −0.223922 0.974607i \(-0.571886\pi\)
−0.223922 + 0.974607i \(0.571886\pi\)
\(644\) 3.34034 0.131628
\(645\) 11.2940 0.444700
\(646\) 20.6759 0.813481
\(647\) 21.6900 0.852723 0.426362 0.904553i \(-0.359795\pi\)
0.426362 + 0.904553i \(0.359795\pi\)
\(648\) 9.69948 0.381031
\(649\) 10.3267 0.405359
\(650\) −7.21960 −0.283176
\(651\) −12.0494 −0.472253
\(652\) −5.77547 −0.226185
\(653\) 26.9783 1.05574 0.527871 0.849325i \(-0.322991\pi\)
0.527871 + 0.849325i \(0.322991\pi\)
\(654\) 11.7017 0.457574
\(655\) −4.89838 −0.191396
\(656\) −0.0546808 −0.00213493
\(657\) 45.6217 1.77987
\(658\) −5.09558 −0.198646
\(659\) 28.3453 1.10417 0.552087 0.833786i \(-0.313831\pi\)
0.552087 + 0.833786i \(0.313831\pi\)
\(660\) 17.2978 0.673317
\(661\) 0.826372 0.0321422 0.0160711 0.999871i \(-0.494884\pi\)
0.0160711 + 0.999871i \(0.494884\pi\)
\(662\) −10.4111 −0.404639
\(663\) 27.6065 1.07215
\(664\) −3.21703 −0.124845
\(665\) −13.0019 −0.504192
\(666\) −8.13403 −0.315187
\(667\) −31.6251 −1.22453
\(668\) −12.7031 −0.491498
\(669\) −44.4269 −1.71764
\(670\) 12.6031 0.486900
\(671\) −23.6746 −0.913946
\(672\) 2.39691 0.0924630
\(673\) −26.4531 −1.01969 −0.509846 0.860265i \(-0.670298\pi\)
−0.509846 + 0.860265i \(0.670298\pi\)
\(674\) 31.5270 1.21437
\(675\) 1.09127 0.0420028
\(676\) 3.32555 0.127906
\(677\) 2.84985 0.109529 0.0547644 0.998499i \(-0.482559\pi\)
0.0547644 + 0.998499i \(0.482559\pi\)
\(678\) −13.3871 −0.514129
\(679\) −1.99156 −0.0764292
\(680\) 5.10967 0.195947
\(681\) −64.4887 −2.47121
\(682\) −20.2388 −0.774982
\(683\) 30.6848 1.17412 0.587061 0.809543i \(-0.300285\pi\)
0.587061 + 0.809543i \(0.300285\pi\)
\(684\) 19.9119 0.761351
\(685\) 4.40169 0.168180
\(686\) 1.00000 0.0381802
\(687\) 36.9495 1.40971
\(688\) 2.62861 0.100215
\(689\) −27.3363 −1.04143
\(690\) 14.3520 0.546370
\(691\) −8.08139 −0.307431 −0.153715 0.988115i \(-0.549124\pi\)
−0.153715 + 0.988115i \(0.549124\pi\)
\(692\) 6.98665 0.265593
\(693\) −11.0521 −0.419834
\(694\) −0.164008 −0.00622564
\(695\) −28.5527 −1.08307
\(696\) −22.6931 −0.860181
\(697\) 0.155869 0.00590396
\(698\) −28.8205 −1.09087
\(699\) −18.4967 −0.699609
\(700\) 1.78681 0.0675352
\(701\) 33.0856 1.24963 0.624813 0.780775i \(-0.285175\pi\)
0.624813 + 0.780775i \(0.285175\pi\)
\(702\) −2.46766 −0.0931358
\(703\) 21.4917 0.810574
\(704\) 4.02597 0.151735
\(705\) −21.8934 −0.824555
\(706\) −14.2253 −0.535377
\(707\) −12.6691 −0.476471
\(708\) 6.14814 0.231061
\(709\) 18.7668 0.704801 0.352401 0.935849i \(-0.385365\pi\)
0.352401 + 0.935849i \(0.385365\pi\)
\(710\) −20.1740 −0.757117
\(711\) 28.6275 1.07361
\(712\) 3.96897 0.148743
\(713\) −16.7920 −0.628867
\(714\) −6.83247 −0.255699
\(715\) −29.1590 −1.09048
\(716\) 0.807690 0.0301848
\(717\) 1.89736 0.0708583
\(718\) 10.6946 0.399120
\(719\) −19.2369 −0.717417 −0.358708 0.933450i \(-0.616783\pi\)
−0.358708 + 0.933450i \(0.616783\pi\)
\(720\) 4.92087 0.183390
\(721\) −2.70526 −0.100749
\(722\) −33.6111 −1.25088
\(723\) −42.0130 −1.56248
\(724\) 23.9060 0.888459
\(725\) −16.9169 −0.628278
\(726\) −12.4842 −0.463332
\(727\) −12.4546 −0.461915 −0.230958 0.972964i \(-0.574186\pi\)
−0.230958 + 0.972964i \(0.574186\pi\)
\(728\) −4.04049 −0.149750
\(729\) −22.2354 −0.823533
\(730\) −29.7896 −1.10256
\(731\) −7.49293 −0.277136
\(732\) −14.0950 −0.520964
\(733\) 30.6175 1.13088 0.565442 0.824788i \(-0.308706\pi\)
0.565442 + 0.824788i \(0.308706\pi\)
\(734\) 7.70210 0.284290
\(735\) 4.29656 0.158481
\(736\) 3.34034 0.123126
\(737\) −28.3061 −1.04267
\(738\) 0.150110 0.00552562
\(739\) −11.7588 −0.432554 −0.216277 0.976332i \(-0.569391\pi\)
−0.216277 + 0.976332i \(0.569391\pi\)
\(740\) 5.31129 0.195247
\(741\) −70.2466 −2.58057
\(742\) 6.76559 0.248373
\(743\) 42.2389 1.54960 0.774798 0.632209i \(-0.217852\pi\)
0.774798 + 0.632209i \(0.217852\pi\)
\(744\) −12.0494 −0.441753
\(745\) −36.3767 −1.33274
\(746\) −12.5959 −0.461170
\(747\) 8.83138 0.323123
\(748\) −11.4761 −0.419609
\(749\) 4.64585 0.169756
\(750\) 29.1599 1.06477
\(751\) 25.6772 0.936974 0.468487 0.883470i \(-0.344799\pi\)
0.468487 + 0.883470i \(0.344799\pi\)
\(752\) −5.09558 −0.185817
\(753\) 47.3953 1.72718
\(754\) 38.2539 1.39313
\(755\) 7.46097 0.271533
\(756\) 0.610733 0.0222121
\(757\) −15.9337 −0.579119 −0.289560 0.957160i \(-0.593509\pi\)
−0.289560 + 0.957160i \(0.593509\pi\)
\(758\) 13.6261 0.494924
\(759\) −32.2340 −1.17002
\(760\) −13.0019 −0.471628
\(761\) −41.4978 −1.50429 −0.752147 0.658996i \(-0.770982\pi\)
−0.752147 + 0.658996i \(0.770982\pi\)
\(762\) 4.73630 0.171578
\(763\) 4.88199 0.176740
\(764\) 17.5942 0.636535
\(765\) −14.0271 −0.507150
\(766\) −17.1341 −0.619081
\(767\) −10.3639 −0.374220
\(768\) 2.39691 0.0864912
\(769\) 32.8373 1.18414 0.592072 0.805885i \(-0.298310\pi\)
0.592072 + 0.805885i \(0.298310\pi\)
\(770\) 7.21670 0.260072
\(771\) 36.4838 1.31393
\(772\) 22.9721 0.826784
\(773\) 15.5450 0.559114 0.279557 0.960129i \(-0.409812\pi\)
0.279557 + 0.960129i \(0.409812\pi\)
\(774\) −7.21607 −0.259376
\(775\) −8.98239 −0.322657
\(776\) −1.99156 −0.0714930
\(777\) −7.10206 −0.254785
\(778\) 22.1410 0.793793
\(779\) −0.396619 −0.0142104
\(780\) −17.3602 −0.621595
\(781\) 45.3101 1.62132
\(782\) −9.52172 −0.340496
\(783\) −5.78220 −0.206639
\(784\) 1.00000 0.0357143
\(785\) 38.7789 1.38408
\(786\) 6.54994 0.233629
\(787\) −32.2109 −1.14819 −0.574097 0.818787i \(-0.694647\pi\)
−0.574097 + 0.818787i \(0.694647\pi\)
\(788\) 17.8072 0.634355
\(789\) −42.0926 −1.49854
\(790\) −18.6929 −0.665064
\(791\) −5.58515 −0.198585
\(792\) −11.0521 −0.392719
\(793\) 23.7599 0.843739
\(794\) −1.39916 −0.0496544
\(795\) 29.0688 1.03096
\(796\) 24.2918 0.860998
\(797\) 36.8160 1.30409 0.652045 0.758180i \(-0.273911\pi\)
0.652045 + 0.758180i \(0.273911\pi\)
\(798\) 17.3857 0.615446
\(799\) 14.5251 0.513860
\(800\) 1.78681 0.0631734
\(801\) −10.8956 −0.384977
\(802\) 33.6838 1.18942
\(803\) 66.9064 2.36108
\(804\) −16.8524 −0.594339
\(805\) 5.98768 0.211038
\(806\) 20.3117 0.715450
\(807\) 4.34730 0.153032
\(808\) −12.6691 −0.445697
\(809\) 30.5157 1.07287 0.536437 0.843940i \(-0.319770\pi\)
0.536437 + 0.843940i \(0.319770\pi\)
\(810\) 17.3867 0.610905
\(811\) −39.8553 −1.39951 −0.699755 0.714383i \(-0.746708\pi\)
−0.699755 + 0.714383i \(0.746708\pi\)
\(812\) −9.46764 −0.332249
\(813\) −15.1287 −0.530586
\(814\) −11.9290 −0.418110
\(815\) −10.3527 −0.362641
\(816\) −6.83247 −0.239184
\(817\) 19.0663 0.667044
\(818\) 7.24776 0.253412
\(819\) 11.0920 0.387584
\(820\) −0.0980174 −0.00342291
\(821\) 22.7042 0.792383 0.396192 0.918168i \(-0.370332\pi\)
0.396192 + 0.918168i \(0.370332\pi\)
\(822\) −5.88578 −0.205290
\(823\) −48.3530 −1.68548 −0.842739 0.538322i \(-0.819058\pi\)
−0.842739 + 0.538322i \(0.819058\pi\)
\(824\) −2.70526 −0.0942423
\(825\) −17.2426 −0.600310
\(826\) 2.56502 0.0892485
\(827\) 27.4595 0.954859 0.477430 0.878670i \(-0.341569\pi\)
0.477430 + 0.878670i \(0.341569\pi\)
\(828\) −9.16990 −0.318676
\(829\) −36.2206 −1.25799 −0.628996 0.777408i \(-0.716534\pi\)
−0.628996 + 0.777408i \(0.716534\pi\)
\(830\) −5.76664 −0.200163
\(831\) −37.4004 −1.29740
\(832\) −4.04049 −0.140079
\(833\) −2.85052 −0.0987648
\(834\) 38.1797 1.32205
\(835\) −22.7708 −0.788016
\(836\) 29.2018 1.00996
\(837\) −3.07018 −0.106121
\(838\) −7.13131 −0.246347
\(839\) −0.273845 −0.00945418 −0.00472709 0.999989i \(-0.501505\pi\)
−0.00472709 + 0.999989i \(0.501505\pi\)
\(840\) 4.29656 0.148245
\(841\) 60.6363 2.09091
\(842\) 11.7180 0.403830
\(843\) −46.2254 −1.59209
\(844\) −3.92205 −0.135002
\(845\) 5.96116 0.205070
\(846\) 13.9884 0.480931
\(847\) −5.20844 −0.178964
\(848\) 6.76559 0.232331
\(849\) 18.6900 0.641438
\(850\) −5.09335 −0.174701
\(851\) −9.89742 −0.339279
\(852\) 26.9760 0.924181
\(853\) −25.0008 −0.856011 −0.428006 0.903776i \(-0.640784\pi\)
−0.428006 + 0.903776i \(0.640784\pi\)
\(854\) −5.88046 −0.201225
\(855\) 35.6928 1.22067
\(856\) 4.64585 0.158792
\(857\) −26.3456 −0.899949 −0.449974 0.893041i \(-0.648567\pi\)
−0.449974 + 0.893041i \(0.648567\pi\)
\(858\) 38.9903 1.33111
\(859\) 49.4564 1.68743 0.843716 0.536791i \(-0.180363\pi\)
0.843716 + 0.536791i \(0.180363\pi\)
\(860\) 4.71189 0.160674
\(861\) 0.131065 0.00446669
\(862\) −1.00000 −0.0340601
\(863\) 10.2936 0.350399 0.175200 0.984533i \(-0.443943\pi\)
0.175200 + 0.984533i \(0.443943\pi\)
\(864\) 0.610733 0.0207776
\(865\) 12.5238 0.425823
\(866\) 24.0001 0.815556
\(867\) −21.2714 −0.722416
\(868\) −5.02705 −0.170629
\(869\) 41.9836 1.42420
\(870\) −40.6783 −1.37912
\(871\) 28.4082 0.962574
\(872\) 4.88199 0.165325
\(873\) 5.46724 0.185038
\(874\) 24.2286 0.819546
\(875\) 12.1656 0.411273
\(876\) 39.8336 1.34585
\(877\) 6.71712 0.226821 0.113411 0.993548i \(-0.463822\pi\)
0.113411 + 0.993548i \(0.463822\pi\)
\(878\) 33.7019 1.13739
\(879\) −6.65012 −0.224303
\(880\) 7.21670 0.243275
\(881\) 2.53128 0.0852810 0.0426405 0.999090i \(-0.486423\pi\)
0.0426405 + 0.999090i \(0.486423\pi\)
\(882\) −2.74520 −0.0924357
\(883\) −29.3405 −0.987385 −0.493693 0.869637i \(-0.664353\pi\)
−0.493693 + 0.869637i \(0.664353\pi\)
\(884\) 11.5175 0.387376
\(885\) 11.0208 0.370459
\(886\) 2.79816 0.0940061
\(887\) −0.635076 −0.0213238 −0.0106619 0.999943i \(-0.503394\pi\)
−0.0106619 + 0.999943i \(0.503394\pi\)
\(888\) −7.10206 −0.238329
\(889\) 1.97600 0.0662729
\(890\) 7.11451 0.238479
\(891\) −39.0498 −1.30822
\(892\) −18.5350 −0.620599
\(893\) −36.9600 −1.23682
\(894\) 48.6416 1.62682
\(895\) 1.44781 0.0483951
\(896\) 1.00000 0.0334077
\(897\) 32.3502 1.08014
\(898\) 0.954714 0.0318592
\(899\) 47.5943 1.58736
\(900\) −4.90516 −0.163505
\(901\) −19.2855 −0.642493
\(902\) 0.220143 0.00732997
\(903\) −6.30056 −0.209670
\(904\) −5.58515 −0.185759
\(905\) 42.8524 1.42446
\(906\) −9.97654 −0.331448
\(907\) 24.2201 0.804215 0.402107 0.915593i \(-0.368278\pi\)
0.402107 + 0.915593i \(0.368278\pi\)
\(908\) −26.9049 −0.892870
\(909\) 34.7792 1.15355
\(910\) −7.24272 −0.240094
\(911\) −50.3176 −1.66710 −0.833548 0.552447i \(-0.813694\pi\)
−0.833548 + 0.552447i \(0.813694\pi\)
\(912\) 17.3857 0.575697
\(913\) 12.9517 0.428637
\(914\) 23.9113 0.790917
\(915\) −25.2657 −0.835259
\(916\) 15.4154 0.509341
\(917\) 2.73266 0.0902402
\(918\) −1.74091 −0.0574586
\(919\) 38.9447 1.28467 0.642334 0.766425i \(-0.277966\pi\)
0.642334 + 0.766425i \(0.277966\pi\)
\(920\) 5.98768 0.197408
\(921\) −14.4620 −0.476539
\(922\) −22.8075 −0.751125
\(923\) −45.4735 −1.49678
\(924\) −9.64991 −0.317459
\(925\) −5.29433 −0.174076
\(926\) 27.0052 0.887446
\(927\) 7.42649 0.243918
\(928\) −9.46764 −0.310791
\(929\) −5.94887 −0.195176 −0.0975880 0.995227i \(-0.531113\pi\)
−0.0975880 + 0.995227i \(0.531113\pi\)
\(930\) −21.5990 −0.708259
\(931\) 7.25335 0.237719
\(932\) −7.71687 −0.252775
\(933\) −34.3666 −1.12511
\(934\) −23.8836 −0.781496
\(935\) −20.5714 −0.672756
\(936\) 11.0920 0.362552
\(937\) −34.5051 −1.12723 −0.563616 0.826037i \(-0.690590\pi\)
−0.563616 + 0.826037i \(0.690590\pi\)
\(938\) −7.03088 −0.229566
\(939\) −0.806586 −0.0263219
\(940\) −9.13401 −0.297919
\(941\) 13.0129 0.424210 0.212105 0.977247i \(-0.431968\pi\)
0.212105 + 0.977247i \(0.431968\pi\)
\(942\) −51.8538 −1.68949
\(943\) 0.182652 0.00594798
\(944\) 2.56502 0.0834843
\(945\) 1.09476 0.0356126
\(946\) −10.5827 −0.344074
\(947\) 38.1388 1.23935 0.619673 0.784860i \(-0.287265\pi\)
0.619673 + 0.784860i \(0.287265\pi\)
\(948\) 24.9955 0.811815
\(949\) −67.1477 −2.17971
\(950\) 12.9604 0.420490
\(951\) −54.6257 −1.77136
\(952\) −2.85052 −0.0923860
\(953\) −4.79028 −0.155172 −0.0775862 0.996986i \(-0.524721\pi\)
−0.0775862 + 0.996986i \(0.524721\pi\)
\(954\) −18.5729 −0.601320
\(955\) 31.5382 1.02055
\(956\) 0.791586 0.0256017
\(957\) 91.3619 2.95331
\(958\) 27.9871 0.904222
\(959\) −2.45556 −0.0792943
\(960\) 4.29656 0.138671
\(961\) −5.72878 −0.184799
\(962\) 11.9720 0.385992
\(963\) −12.7538 −0.410985
\(964\) −17.5279 −0.564537
\(965\) 41.1783 1.32558
\(966\) −8.00651 −0.257605
\(967\) −29.0804 −0.935163 −0.467582 0.883950i \(-0.654875\pi\)
−0.467582 + 0.883950i \(0.654875\pi\)
\(968\) −5.20844 −0.167406
\(969\) −49.5583 −1.59204
\(970\) −3.56995 −0.114624
\(971\) 19.7138 0.632646 0.316323 0.948652i \(-0.397552\pi\)
0.316323 + 0.948652i \(0.397552\pi\)
\(972\) −21.4166 −0.686938
\(973\) 15.9287 0.510650
\(974\) 7.74676 0.248222
\(975\) 17.3048 0.554196
\(976\) −5.88046 −0.188229
\(977\) −41.6991 −1.33407 −0.667036 0.745026i \(-0.732437\pi\)
−0.667036 + 0.745026i \(0.732437\pi\)
\(978\) 13.8433 0.442660
\(979\) −15.9789 −0.510689
\(980\) 1.79254 0.0572605
\(981\) −13.4021 −0.427895
\(982\) 6.51264 0.207827
\(983\) 49.2891 1.57208 0.786039 0.618176i \(-0.212128\pi\)
0.786039 + 0.618176i \(0.212128\pi\)
\(984\) 0.131065 0.00417821
\(985\) 31.9201 1.01706
\(986\) 26.9878 0.859465
\(987\) 12.2137 0.388765
\(988\) −29.3071 −0.932382
\(989\) −8.78046 −0.279202
\(990\) −19.8113 −0.629644
\(991\) 23.0275 0.731493 0.365747 0.930715i \(-0.380814\pi\)
0.365747 + 0.930715i \(0.380814\pi\)
\(992\) −5.02705 −0.159609
\(993\) 24.9545 0.791909
\(994\) 11.2544 0.356969
\(995\) 43.5439 1.38043
\(996\) 7.71094 0.244330
\(997\) −51.1388 −1.61958 −0.809790 0.586719i \(-0.800419\pi\)
−0.809790 + 0.586719i \(0.800419\pi\)
\(998\) −28.7625 −0.910463
\(999\) −1.80960 −0.0572533
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 \(a_p\))