Properties

Label 8001.2.a.o.1.12
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-1.82297\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.82297 q^{2}\) \(+1.32323 q^{4}\) \(-0.630622 q^{5}\) \(+1.00000 q^{7}\) \(-1.23374 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.82297 q^{2}\) \(+1.32323 q^{4}\) \(-0.630622 q^{5}\) \(+1.00000 q^{7}\) \(-1.23374 q^{8}\) \(-1.14961 q^{10}\) \(+2.60824 q^{11}\) \(-4.34638 q^{13}\) \(+1.82297 q^{14}\) \(-4.89553 q^{16}\) \(+1.67481 q^{17}\) \(+7.62672 q^{19}\) \(-0.834455 q^{20}\) \(+4.75474 q^{22}\) \(-4.50538 q^{23}\) \(-4.60232 q^{25}\) \(-7.92333 q^{26}\) \(+1.32323 q^{28}\) \(+1.00235 q^{29}\) \(-6.18227 q^{31}\) \(-6.45692 q^{32}\) \(+3.05313 q^{34}\) \(-0.630622 q^{35}\) \(-0.667280 q^{37}\) \(+13.9033 q^{38}\) \(+0.778025 q^{40}\) \(-8.44630 q^{41}\) \(+0.767479 q^{43}\) \(+3.45128 q^{44}\) \(-8.21318 q^{46}\) \(-1.27605 q^{47}\) \(+1.00000 q^{49}\) \(-8.38989 q^{50}\) \(-5.75124 q^{52}\) \(-9.23546 q^{53}\) \(-1.64481 q^{55}\) \(-1.23374 q^{56}\) \(+1.82725 q^{58}\) \(-3.99665 q^{59}\) \(-6.45858 q^{61}\) \(-11.2701 q^{62}\) \(-1.97973 q^{64}\) \(+2.74093 q^{65}\) \(+5.31265 q^{67}\) \(+2.21615 q^{68}\) \(-1.14961 q^{70}\) \(+9.52764 q^{71}\) \(+4.29370 q^{73}\) \(-1.21643 q^{74}\) \(+10.0919 q^{76}\) \(+2.60824 q^{77}\) \(-2.53600 q^{79}\) \(+3.08723 q^{80}\) \(-15.3974 q^{82}\) \(+4.96788 q^{83}\) \(-1.05617 q^{85}\) \(+1.39909 q^{86}\) \(-3.21789 q^{88}\) \(+0.366460 q^{89}\) \(-4.34638 q^{91}\) \(-5.96163 q^{92}\) \(-2.32620 q^{94}\) \(-4.80958 q^{95}\) \(-10.1853 q^{97}\) \(+1.82297 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.82297 1.28904 0.644518 0.764589i \(-0.277058\pi\)
0.644518 + 0.764589i \(0.277058\pi\)
\(3\) 0 0
\(4\) 1.32323 0.661613
\(5\) −0.630622 −0.282023 −0.141011 0.990008i \(-0.545035\pi\)
−0.141011 + 0.990008i \(0.545035\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.23374 −0.436193
\(9\) 0 0
\(10\) −1.14961 −0.363537
\(11\) 2.60824 0.786413 0.393206 0.919450i \(-0.371366\pi\)
0.393206 + 0.919450i \(0.371366\pi\)
\(12\) 0 0
\(13\) −4.34638 −1.20547 −0.602735 0.797942i \(-0.705922\pi\)
−0.602735 + 0.797942i \(0.705922\pi\)
\(14\) 1.82297 0.487210
\(15\) 0 0
\(16\) −4.89553 −1.22388
\(17\) 1.67481 0.406201 0.203100 0.979158i \(-0.434898\pi\)
0.203100 + 0.979158i \(0.434898\pi\)
\(18\) 0 0
\(19\) 7.62672 1.74969 0.874845 0.484403i \(-0.160963\pi\)
0.874845 + 0.484403i \(0.160963\pi\)
\(20\) −0.834455 −0.186590
\(21\) 0 0
\(22\) 4.75474 1.01371
\(23\) −4.50538 −0.939437 −0.469718 0.882816i \(-0.655645\pi\)
−0.469718 + 0.882816i \(0.655645\pi\)
\(24\) 0 0
\(25\) −4.60232 −0.920463
\(26\) −7.92333 −1.55389
\(27\) 0 0
\(28\) 1.32323 0.250066
\(29\) 1.00235 0.186131 0.0930655 0.995660i \(-0.470333\pi\)
0.0930655 + 0.995660i \(0.470333\pi\)
\(30\) 0 0
\(31\) −6.18227 −1.11037 −0.555184 0.831727i \(-0.687352\pi\)
−0.555184 + 0.831727i \(0.687352\pi\)
\(32\) −6.45692 −1.14143
\(33\) 0 0
\(34\) 3.05313 0.523607
\(35\) −0.630622 −0.106595
\(36\) 0 0
\(37\) −0.667280 −0.109700 −0.0548501 0.998495i \(-0.517468\pi\)
−0.0548501 + 0.998495i \(0.517468\pi\)
\(38\) 13.9033 2.25541
\(39\) 0 0
\(40\) 0.778025 0.123017
\(41\) −8.44630 −1.31909 −0.659545 0.751665i \(-0.729251\pi\)
−0.659545 + 0.751665i \(0.729251\pi\)
\(42\) 0 0
\(43\) 0.767479 0.117039 0.0585197 0.998286i \(-0.481362\pi\)
0.0585197 + 0.998286i \(0.481362\pi\)
\(44\) 3.45128 0.520301
\(45\) 0 0
\(46\) −8.21318 −1.21097
\(47\) −1.27605 −0.186131 −0.0930656 0.995660i \(-0.529667\pi\)
−0.0930656 + 0.995660i \(0.529667\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −8.38989 −1.18651
\(51\) 0 0
\(52\) −5.75124 −0.797554
\(53\) −9.23546 −1.26859 −0.634294 0.773092i \(-0.718709\pi\)
−0.634294 + 0.773092i \(0.718709\pi\)
\(54\) 0 0
\(55\) −1.64481 −0.221786
\(56\) −1.23374 −0.164866
\(57\) 0 0
\(58\) 1.82725 0.239929
\(59\) −3.99665 −0.520320 −0.260160 0.965566i \(-0.583775\pi\)
−0.260160 + 0.965566i \(0.583775\pi\)
\(60\) 0 0
\(61\) −6.45858 −0.826937 −0.413468 0.910518i \(-0.635683\pi\)
−0.413468 + 0.910518i \(0.635683\pi\)
\(62\) −11.2701 −1.43130
\(63\) 0 0
\(64\) −1.97973 −0.247467
\(65\) 2.74093 0.339970
\(66\) 0 0
\(67\) 5.31265 0.649043 0.324522 0.945878i \(-0.394797\pi\)
0.324522 + 0.945878i \(0.394797\pi\)
\(68\) 2.21615 0.268748
\(69\) 0 0
\(70\) −1.14961 −0.137404
\(71\) 9.52764 1.13072 0.565362 0.824843i \(-0.308737\pi\)
0.565362 + 0.824843i \(0.308737\pi\)
\(72\) 0 0
\(73\) 4.29370 0.502539 0.251270 0.967917i \(-0.419152\pi\)
0.251270 + 0.967917i \(0.419152\pi\)
\(74\) −1.21643 −0.141407
\(75\) 0 0
\(76\) 10.0919 1.15762
\(77\) 2.60824 0.297236
\(78\) 0 0
\(79\) −2.53600 −0.285322 −0.142661 0.989772i \(-0.545566\pi\)
−0.142661 + 0.989772i \(0.545566\pi\)
\(80\) 3.08723 0.345163
\(81\) 0 0
\(82\) −15.3974 −1.70035
\(83\) 4.96788 0.545296 0.272648 0.962114i \(-0.412101\pi\)
0.272648 + 0.962114i \(0.412101\pi\)
\(84\) 0 0
\(85\) −1.05617 −0.114558
\(86\) 1.39909 0.150868
\(87\) 0 0
\(88\) −3.21789 −0.343028
\(89\) 0.366460 0.0388447 0.0194223 0.999811i \(-0.493817\pi\)
0.0194223 + 0.999811i \(0.493817\pi\)
\(90\) 0 0
\(91\) −4.34638 −0.455625
\(92\) −5.96163 −0.621543
\(93\) 0 0
\(94\) −2.32620 −0.239930
\(95\) −4.80958 −0.493452
\(96\) 0 0
\(97\) −10.1853 −1.03416 −0.517081 0.855936i \(-0.672982\pi\)
−0.517081 + 0.855936i \(0.672982\pi\)
\(98\) 1.82297 0.184148
\(99\) 0 0
\(100\) −6.08990 −0.608990
\(101\) 5.28628 0.526005 0.263002 0.964795i \(-0.415287\pi\)
0.263002 + 0.964795i \(0.415287\pi\)
\(102\) 0 0
\(103\) 7.16287 0.705779 0.352890 0.935665i \(-0.385199\pi\)
0.352890 + 0.935665i \(0.385199\pi\)
\(104\) 5.36231 0.525818
\(105\) 0 0
\(106\) −16.8360 −1.63526
\(107\) 6.68923 0.646672 0.323336 0.946284i \(-0.395196\pi\)
0.323336 + 0.946284i \(0.395196\pi\)
\(108\) 0 0
\(109\) −3.17404 −0.304018 −0.152009 0.988379i \(-0.548574\pi\)
−0.152009 + 0.988379i \(0.548574\pi\)
\(110\) −2.99845 −0.285891
\(111\) 0 0
\(112\) −4.89553 −0.462584
\(113\) −2.64523 −0.248843 −0.124421 0.992229i \(-0.539707\pi\)
−0.124421 + 0.992229i \(0.539707\pi\)
\(114\) 0 0
\(115\) 2.84119 0.264943
\(116\) 1.32633 0.123147
\(117\) 0 0
\(118\) −7.28578 −0.670710
\(119\) 1.67481 0.153529
\(120\) 0 0
\(121\) −4.19710 −0.381555
\(122\) −11.7738 −1.06595
\(123\) 0 0
\(124\) −8.18053 −0.734634
\(125\) 6.05543 0.541615
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 9.30485 0.822440
\(129\) 0 0
\(130\) 4.99663 0.438233
\(131\) −20.6980 −1.80840 −0.904198 0.427114i \(-0.859530\pi\)
−0.904198 + 0.427114i \(0.859530\pi\)
\(132\) 0 0
\(133\) 7.62672 0.661321
\(134\) 9.68481 0.836640
\(135\) 0 0
\(136\) −2.06628 −0.177182
\(137\) −13.2703 −1.13376 −0.566878 0.823802i \(-0.691849\pi\)
−0.566878 + 0.823802i \(0.691849\pi\)
\(138\) 0 0
\(139\) −11.5563 −0.980193 −0.490096 0.871668i \(-0.663038\pi\)
−0.490096 + 0.871668i \(0.663038\pi\)
\(140\) −0.834455 −0.0705243
\(141\) 0 0
\(142\) 17.3686 1.45754
\(143\) −11.3364 −0.947997
\(144\) 0 0
\(145\) −0.632102 −0.0524932
\(146\) 7.82729 0.647791
\(147\) 0 0
\(148\) −0.882962 −0.0725790
\(149\) −19.7584 −1.61867 −0.809334 0.587349i \(-0.800172\pi\)
−0.809334 + 0.587349i \(0.800172\pi\)
\(150\) 0 0
\(151\) 6.99658 0.569373 0.284687 0.958621i \(-0.408110\pi\)
0.284687 + 0.958621i \(0.408110\pi\)
\(152\) −9.40940 −0.763203
\(153\) 0 0
\(154\) 4.75474 0.383148
\(155\) 3.89868 0.313149
\(156\) 0 0
\(157\) 8.51770 0.679787 0.339893 0.940464i \(-0.389609\pi\)
0.339893 + 0.940464i \(0.389609\pi\)
\(158\) −4.62305 −0.367790
\(159\) 0 0
\(160\) 4.07188 0.321910
\(161\) −4.50538 −0.355074
\(162\) 0 0
\(163\) −8.81012 −0.690062 −0.345031 0.938591i \(-0.612132\pi\)
−0.345031 + 0.938591i \(0.612132\pi\)
\(164\) −11.1764 −0.872727
\(165\) 0 0
\(166\) 9.05631 0.702906
\(167\) −9.41023 −0.728186 −0.364093 0.931363i \(-0.618621\pi\)
−0.364093 + 0.931363i \(0.618621\pi\)
\(168\) 0 0
\(169\) 5.89104 0.453157
\(170\) −1.92537 −0.147669
\(171\) 0 0
\(172\) 1.01555 0.0774348
\(173\) −25.9259 −1.97111 −0.985554 0.169360i \(-0.945830\pi\)
−0.985554 + 0.169360i \(0.945830\pi\)
\(174\) 0 0
\(175\) −4.60232 −0.347902
\(176\) −12.7687 −0.962476
\(177\) 0 0
\(178\) 0.668046 0.0500721
\(179\) −20.8930 −1.56162 −0.780809 0.624770i \(-0.785193\pi\)
−0.780809 + 0.624770i \(0.785193\pi\)
\(180\) 0 0
\(181\) −17.6229 −1.30990 −0.654950 0.755672i \(-0.727310\pi\)
−0.654950 + 0.755672i \(0.727310\pi\)
\(182\) −7.92333 −0.587316
\(183\) 0 0
\(184\) 5.55847 0.409776
\(185\) 0.420802 0.0309380
\(186\) 0 0
\(187\) 4.36830 0.319442
\(188\) −1.68850 −0.123147
\(189\) 0 0
\(190\) −8.76773 −0.636078
\(191\) −4.36797 −0.316055 −0.158028 0.987435i \(-0.550514\pi\)
−0.158028 + 0.987435i \(0.550514\pi\)
\(192\) 0 0
\(193\) −8.07471 −0.581230 −0.290615 0.956840i \(-0.593860\pi\)
−0.290615 + 0.956840i \(0.593860\pi\)
\(194\) −18.5676 −1.33307
\(195\) 0 0
\(196\) 1.32323 0.0945161
\(197\) −19.0457 −1.35695 −0.678474 0.734625i \(-0.737358\pi\)
−0.678474 + 0.734625i \(0.737358\pi\)
\(198\) 0 0
\(199\) 24.0658 1.70598 0.852990 0.521927i \(-0.174787\pi\)
0.852990 + 0.521927i \(0.174787\pi\)
\(200\) 5.67807 0.401500
\(201\) 0 0
\(202\) 9.63674 0.678039
\(203\) 1.00235 0.0703509
\(204\) 0 0
\(205\) 5.32642 0.372014
\(206\) 13.0577 0.909774
\(207\) 0 0
\(208\) 21.2778 1.47535
\(209\) 19.8923 1.37598
\(210\) 0 0
\(211\) −11.4713 −0.789720 −0.394860 0.918741i \(-0.629207\pi\)
−0.394860 + 0.918741i \(0.629207\pi\)
\(212\) −12.2206 −0.839314
\(213\) 0 0
\(214\) 12.1943 0.833583
\(215\) −0.483989 −0.0330078
\(216\) 0 0
\(217\) −6.18227 −0.419680
\(218\) −5.78618 −0.391889
\(219\) 0 0
\(220\) −2.17646 −0.146737
\(221\) −7.27936 −0.489663
\(222\) 0 0
\(223\) 29.3326 1.96426 0.982129 0.188211i \(-0.0602687\pi\)
0.982129 + 0.188211i \(0.0602687\pi\)
\(224\) −6.45692 −0.431421
\(225\) 0 0
\(226\) −4.82219 −0.320767
\(227\) 16.9327 1.12386 0.561930 0.827185i \(-0.310059\pi\)
0.561930 + 0.827185i \(0.310059\pi\)
\(228\) 0 0
\(229\) 29.4027 1.94298 0.971492 0.237070i \(-0.0761872\pi\)
0.971492 + 0.237070i \(0.0761872\pi\)
\(230\) 5.17942 0.341521
\(231\) 0 0
\(232\) −1.23664 −0.0811891
\(233\) −3.31695 −0.217301 −0.108650 0.994080i \(-0.534653\pi\)
−0.108650 + 0.994080i \(0.534653\pi\)
\(234\) 0 0
\(235\) 0.804706 0.0524932
\(236\) −5.28847 −0.344250
\(237\) 0 0
\(238\) 3.05313 0.197905
\(239\) 1.52032 0.0983415 0.0491707 0.998790i \(-0.484342\pi\)
0.0491707 + 0.998790i \(0.484342\pi\)
\(240\) 0 0
\(241\) −9.95634 −0.641344 −0.320672 0.947190i \(-0.603909\pi\)
−0.320672 + 0.947190i \(0.603909\pi\)
\(242\) −7.65120 −0.491837
\(243\) 0 0
\(244\) −8.54616 −0.547112
\(245\) −0.630622 −0.0402890
\(246\) 0 0
\(247\) −33.1486 −2.10920
\(248\) 7.62732 0.484335
\(249\) 0 0
\(250\) 11.0389 0.698160
\(251\) 9.73220 0.614291 0.307146 0.951663i \(-0.400626\pi\)
0.307146 + 0.951663i \(0.400626\pi\)
\(252\) 0 0
\(253\) −11.7511 −0.738785
\(254\) −1.82297 −0.114383
\(255\) 0 0
\(256\) 20.9219 1.30762
\(257\) −27.0819 −1.68932 −0.844661 0.535302i \(-0.820198\pi\)
−0.844661 + 0.535302i \(0.820198\pi\)
\(258\) 0 0
\(259\) −0.667280 −0.0414628
\(260\) 3.62686 0.224928
\(261\) 0 0
\(262\) −37.7319 −2.33109
\(263\) −4.38851 −0.270607 −0.135304 0.990804i \(-0.543201\pi\)
−0.135304 + 0.990804i \(0.543201\pi\)
\(264\) 0 0
\(265\) 5.82409 0.357771
\(266\) 13.9033 0.852466
\(267\) 0 0
\(268\) 7.02983 0.429415
\(269\) −15.3450 −0.935604 −0.467802 0.883833i \(-0.654954\pi\)
−0.467802 + 0.883833i \(0.654954\pi\)
\(270\) 0 0
\(271\) −4.68264 −0.284450 −0.142225 0.989834i \(-0.545426\pi\)
−0.142225 + 0.989834i \(0.545426\pi\)
\(272\) −8.19907 −0.497142
\(273\) 0 0
\(274\) −24.1913 −1.46145
\(275\) −12.0039 −0.723864
\(276\) 0 0
\(277\) −16.7745 −1.00788 −0.503942 0.863738i \(-0.668117\pi\)
−0.503942 + 0.863738i \(0.668117\pi\)
\(278\) −21.0668 −1.26350
\(279\) 0 0
\(280\) 0.778025 0.0464959
\(281\) −25.1133 −1.49813 −0.749066 0.662495i \(-0.769498\pi\)
−0.749066 + 0.662495i \(0.769498\pi\)
\(282\) 0 0
\(283\) 14.7143 0.874674 0.437337 0.899298i \(-0.355922\pi\)
0.437337 + 0.899298i \(0.355922\pi\)
\(284\) 12.6072 0.748101
\(285\) 0 0
\(286\) −20.6659 −1.22200
\(287\) −8.44630 −0.498569
\(288\) 0 0
\(289\) −14.1950 −0.835001
\(290\) −1.15230 −0.0676656
\(291\) 0 0
\(292\) 5.68153 0.332486
\(293\) −0.0711543 −0.00415688 −0.00207844 0.999998i \(-0.500662\pi\)
−0.00207844 + 0.999998i \(0.500662\pi\)
\(294\) 0 0
\(295\) 2.52038 0.146742
\(296\) 0.823251 0.0478505
\(297\) 0 0
\(298\) −36.0189 −2.08652
\(299\) 19.5821 1.13246
\(300\) 0 0
\(301\) 0.767479 0.0442367
\(302\) 12.7546 0.733942
\(303\) 0 0
\(304\) −37.3368 −2.14141
\(305\) 4.07293 0.233215
\(306\) 0 0
\(307\) 13.3153 0.759942 0.379971 0.924998i \(-0.375934\pi\)
0.379971 + 0.924998i \(0.375934\pi\)
\(308\) 3.45128 0.196655
\(309\) 0 0
\(310\) 7.10718 0.403661
\(311\) 1.35589 0.0768855 0.0384427 0.999261i \(-0.487760\pi\)
0.0384427 + 0.999261i \(0.487760\pi\)
\(312\) 0 0
\(313\) 14.3146 0.809108 0.404554 0.914514i \(-0.367427\pi\)
0.404554 + 0.914514i \(0.367427\pi\)
\(314\) 15.5275 0.876269
\(315\) 0 0
\(316\) −3.35569 −0.188773
\(317\) −2.01097 −0.112948 −0.0564738 0.998404i \(-0.517986\pi\)
−0.0564738 + 0.998404i \(0.517986\pi\)
\(318\) 0 0
\(319\) 2.61435 0.146376
\(320\) 1.24846 0.0697912
\(321\) 0 0
\(322\) −8.21318 −0.457703
\(323\) 12.7733 0.710725
\(324\) 0 0
\(325\) 20.0034 1.10959
\(326\) −16.0606 −0.889514
\(327\) 0 0
\(328\) 10.4205 0.575378
\(329\) −1.27605 −0.0703510
\(330\) 0 0
\(331\) −1.88305 −0.103502 −0.0517508 0.998660i \(-0.516480\pi\)
−0.0517508 + 0.998660i \(0.516480\pi\)
\(332\) 6.57363 0.360775
\(333\) 0 0
\(334\) −17.1546 −0.938657
\(335\) −3.35028 −0.183045
\(336\) 0 0
\(337\) 1.13790 0.0619855 0.0309928 0.999520i \(-0.490133\pi\)
0.0309928 + 0.999520i \(0.490133\pi\)
\(338\) 10.7392 0.584136
\(339\) 0 0
\(340\) −1.39755 −0.0757930
\(341\) −16.1248 −0.873208
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −0.946870 −0.0510518
\(345\) 0 0
\(346\) −47.2621 −2.54083
\(347\) −10.1578 −0.545299 −0.272649 0.962113i \(-0.587900\pi\)
−0.272649 + 0.962113i \(0.587900\pi\)
\(348\) 0 0
\(349\) 1.60321 0.0858179 0.0429089 0.999079i \(-0.486337\pi\)
0.0429089 + 0.999079i \(0.486337\pi\)
\(350\) −8.38989 −0.448458
\(351\) 0 0
\(352\) −16.8412 −0.897638
\(353\) 2.04982 0.109101 0.0545505 0.998511i \(-0.482627\pi\)
0.0545505 + 0.998511i \(0.482627\pi\)
\(354\) 0 0
\(355\) −6.00835 −0.318890
\(356\) 0.484909 0.0257001
\(357\) 0 0
\(358\) −38.0874 −2.01298
\(359\) 7.82477 0.412976 0.206488 0.978449i \(-0.433797\pi\)
0.206488 + 0.978449i \(0.433797\pi\)
\(360\) 0 0
\(361\) 39.1669 2.06141
\(362\) −32.1261 −1.68851
\(363\) 0 0
\(364\) −5.75124 −0.301447
\(365\) −2.70770 −0.141728
\(366\) 0 0
\(367\) 19.6337 1.02487 0.512435 0.858726i \(-0.328744\pi\)
0.512435 + 0.858726i \(0.328744\pi\)
\(368\) 22.0562 1.14976
\(369\) 0 0
\(370\) 0.767110 0.0398801
\(371\) −9.23546 −0.479481
\(372\) 0 0
\(373\) 12.5065 0.647561 0.323780 0.946132i \(-0.395046\pi\)
0.323780 + 0.946132i \(0.395046\pi\)
\(374\) 7.96328 0.411772
\(375\) 0 0
\(376\) 1.57432 0.0811892
\(377\) −4.35658 −0.224375
\(378\) 0 0
\(379\) 34.4032 1.76717 0.883587 0.468266i \(-0.155121\pi\)
0.883587 + 0.468266i \(0.155121\pi\)
\(380\) −6.36416 −0.326474
\(381\) 0 0
\(382\) −7.96269 −0.407407
\(383\) 11.1574 0.570115 0.285057 0.958510i \(-0.407987\pi\)
0.285057 + 0.958510i \(0.407987\pi\)
\(384\) 0 0
\(385\) −1.64481 −0.0838274
\(386\) −14.7200 −0.749226
\(387\) 0 0
\(388\) −13.4775 −0.684215
\(389\) −5.94990 −0.301672 −0.150836 0.988559i \(-0.548197\pi\)
−0.150836 + 0.988559i \(0.548197\pi\)
\(390\) 0 0
\(391\) −7.54565 −0.381600
\(392\) −1.23374 −0.0623133
\(393\) 0 0
\(394\) −34.7197 −1.74915
\(395\) 1.59926 0.0804673
\(396\) 0 0
\(397\) 6.47617 0.325029 0.162515 0.986706i \(-0.448039\pi\)
0.162515 + 0.986706i \(0.448039\pi\)
\(398\) 43.8713 2.19907
\(399\) 0 0
\(400\) 22.5308 1.12654
\(401\) 3.27212 0.163402 0.0817010 0.996657i \(-0.473965\pi\)
0.0817010 + 0.996657i \(0.473965\pi\)
\(402\) 0 0
\(403\) 26.8705 1.33852
\(404\) 6.99494 0.348011
\(405\) 0 0
\(406\) 1.82725 0.0906848
\(407\) −1.74042 −0.0862696
\(408\) 0 0
\(409\) 12.9834 0.641990 0.320995 0.947081i \(-0.395983\pi\)
0.320995 + 0.947081i \(0.395983\pi\)
\(410\) 9.70992 0.479539
\(411\) 0 0
\(412\) 9.47810 0.466952
\(413\) −3.99665 −0.196662
\(414\) 0 0
\(415\) −3.13286 −0.153786
\(416\) 28.0642 1.37596
\(417\) 0 0
\(418\) 36.2631 1.77369
\(419\) −0.228730 −0.0111742 −0.00558710 0.999984i \(-0.501778\pi\)
−0.00558710 + 0.999984i \(0.501778\pi\)
\(420\) 0 0
\(421\) 13.6768 0.666566 0.333283 0.942827i \(-0.391843\pi\)
0.333283 + 0.942827i \(0.391843\pi\)
\(422\) −20.9119 −1.01798
\(423\) 0 0
\(424\) 11.3942 0.553350
\(425\) −7.70800 −0.373893
\(426\) 0 0
\(427\) −6.45858 −0.312553
\(428\) 8.85135 0.427846
\(429\) 0 0
\(430\) −0.882299 −0.0425482
\(431\) 16.7015 0.804482 0.402241 0.915534i \(-0.368231\pi\)
0.402241 + 0.915534i \(0.368231\pi\)
\(432\) 0 0
\(433\) 31.0013 1.48983 0.744913 0.667161i \(-0.232491\pi\)
0.744913 + 0.667161i \(0.232491\pi\)
\(434\) −11.2701 −0.540982
\(435\) 0 0
\(436\) −4.19996 −0.201142
\(437\) −34.3613 −1.64372
\(438\) 0 0
\(439\) −31.0227 −1.48063 −0.740317 0.672258i \(-0.765325\pi\)
−0.740317 + 0.672258i \(0.765325\pi\)
\(440\) 2.02927 0.0967418
\(441\) 0 0
\(442\) −13.2701 −0.631193
\(443\) −17.4735 −0.830191 −0.415096 0.909778i \(-0.636252\pi\)
−0.415096 + 0.909778i \(0.636252\pi\)
\(444\) 0 0
\(445\) −0.231098 −0.0109551
\(446\) 53.4725 2.53200
\(447\) 0 0
\(448\) −1.97973 −0.0935336
\(449\) 37.0459 1.74831 0.874153 0.485651i \(-0.161417\pi\)
0.874153 + 0.485651i \(0.161417\pi\)
\(450\) 0 0
\(451\) −22.0299 −1.03735
\(452\) −3.50024 −0.164637
\(453\) 0 0
\(454\) 30.8677 1.44870
\(455\) 2.74093 0.128497
\(456\) 0 0
\(457\) 29.9331 1.40021 0.700106 0.714039i \(-0.253136\pi\)
0.700106 + 0.714039i \(0.253136\pi\)
\(458\) 53.6003 2.50458
\(459\) 0 0
\(460\) 3.75954 0.175289
\(461\) −0.774046 −0.0360509 −0.0180255 0.999838i \(-0.505738\pi\)
−0.0180255 + 0.999838i \(0.505738\pi\)
\(462\) 0 0
\(463\) −18.6451 −0.866509 −0.433255 0.901272i \(-0.642635\pi\)
−0.433255 + 0.901272i \(0.642635\pi\)
\(464\) −4.90701 −0.227802
\(465\) 0 0
\(466\) −6.04670 −0.280108
\(467\) 24.7279 1.14427 0.572136 0.820158i \(-0.306115\pi\)
0.572136 + 0.820158i \(0.306115\pi\)
\(468\) 0 0
\(469\) 5.31265 0.245315
\(470\) 1.46696 0.0676657
\(471\) 0 0
\(472\) 4.93083 0.226960
\(473\) 2.00177 0.0920413
\(474\) 0 0
\(475\) −35.1006 −1.61052
\(476\) 2.21615 0.101577
\(477\) 0 0
\(478\) 2.77150 0.126766
\(479\) 35.4021 1.61756 0.808782 0.588109i \(-0.200127\pi\)
0.808782 + 0.588109i \(0.200127\pi\)
\(480\) 0 0
\(481\) 2.90025 0.132240
\(482\) −18.1501 −0.826716
\(483\) 0 0
\(484\) −5.55371 −0.252441
\(485\) 6.42309 0.291658
\(486\) 0 0
\(487\) −15.3543 −0.695768 −0.347884 0.937538i \(-0.613100\pi\)
−0.347884 + 0.937538i \(0.613100\pi\)
\(488\) 7.96822 0.360704
\(489\) 0 0
\(490\) −1.14961 −0.0519339
\(491\) 0.585211 0.0264102 0.0132051 0.999913i \(-0.495797\pi\)
0.0132051 + 0.999913i \(0.495797\pi\)
\(492\) 0 0
\(493\) 1.67874 0.0756065
\(494\) −60.4290 −2.71883
\(495\) 0 0
\(496\) 30.2655 1.35896
\(497\) 9.52764 0.427373
\(498\) 0 0
\(499\) −20.9905 −0.939662 −0.469831 0.882756i \(-0.655685\pi\)
−0.469831 + 0.882756i \(0.655685\pi\)
\(500\) 8.01270 0.358339
\(501\) 0 0
\(502\) 17.7415 0.791843
\(503\) 5.24106 0.233687 0.116844 0.993150i \(-0.462722\pi\)
0.116844 + 0.993150i \(0.462722\pi\)
\(504\) 0 0
\(505\) −3.33365 −0.148345
\(506\) −21.4219 −0.952321
\(507\) 0 0
\(508\) −1.32323 −0.0587086
\(509\) −10.4086 −0.461353 −0.230677 0.973030i \(-0.574094\pi\)
−0.230677 + 0.973030i \(0.574094\pi\)
\(510\) 0 0
\(511\) 4.29370 0.189942
\(512\) 19.5304 0.863130
\(513\) 0 0
\(514\) −49.3695 −2.17760
\(515\) −4.51707 −0.199046
\(516\) 0 0
\(517\) −3.32824 −0.146376
\(518\) −1.21643 −0.0534470
\(519\) 0 0
\(520\) −3.38159 −0.148293
\(521\) −6.18793 −0.271098 −0.135549 0.990771i \(-0.543280\pi\)
−0.135549 + 0.990771i \(0.543280\pi\)
\(522\) 0 0
\(523\) 40.4704 1.76965 0.884823 0.465927i \(-0.154279\pi\)
0.884823 + 0.465927i \(0.154279\pi\)
\(524\) −27.3882 −1.19646
\(525\) 0 0
\(526\) −8.00014 −0.348823
\(527\) −10.3541 −0.451033
\(528\) 0 0
\(529\) −2.70154 −0.117458
\(530\) 10.6171 0.461180
\(531\) 0 0
\(532\) 10.0919 0.437538
\(533\) 36.7108 1.59012
\(534\) 0 0
\(535\) −4.21838 −0.182376
\(536\) −6.55443 −0.283108
\(537\) 0 0
\(538\) −27.9736 −1.20603
\(539\) 2.60824 0.112345
\(540\) 0 0
\(541\) 21.7350 0.934461 0.467231 0.884135i \(-0.345252\pi\)
0.467231 + 0.884135i \(0.345252\pi\)
\(542\) −8.53631 −0.366666
\(543\) 0 0
\(544\) −10.8141 −0.463651
\(545\) 2.00162 0.0857399
\(546\) 0 0
\(547\) −11.4270 −0.488582 −0.244291 0.969702i \(-0.578555\pi\)
−0.244291 + 0.969702i \(0.578555\pi\)
\(548\) −17.5596 −0.750107
\(549\) 0 0
\(550\) −21.8828 −0.933087
\(551\) 7.64461 0.325671
\(552\) 0 0
\(553\) −2.53600 −0.107842
\(554\) −30.5795 −1.29920
\(555\) 0 0
\(556\) −15.2916 −0.648508
\(557\) −32.5753 −1.38026 −0.690129 0.723686i \(-0.742446\pi\)
−0.690129 + 0.723686i \(0.742446\pi\)
\(558\) 0 0
\(559\) −3.33576 −0.141087
\(560\) 3.08723 0.130459
\(561\) 0 0
\(562\) −45.7808 −1.93115
\(563\) 23.5920 0.994282 0.497141 0.867670i \(-0.334383\pi\)
0.497141 + 0.867670i \(0.334383\pi\)
\(564\) 0 0
\(565\) 1.66814 0.0701793
\(566\) 26.8237 1.12749
\(567\) 0 0
\(568\) −11.7546 −0.493214
\(569\) −23.4064 −0.981248 −0.490624 0.871371i \(-0.663231\pi\)
−0.490624 + 0.871371i \(0.663231\pi\)
\(570\) 0 0
\(571\) −33.5499 −1.40402 −0.702010 0.712167i \(-0.747714\pi\)
−0.702010 + 0.712167i \(0.747714\pi\)
\(572\) −15.0006 −0.627207
\(573\) 0 0
\(574\) −15.3974 −0.642673
\(575\) 20.7352 0.864717
\(576\) 0 0
\(577\) −20.4275 −0.850406 −0.425203 0.905098i \(-0.639797\pi\)
−0.425203 + 0.905098i \(0.639797\pi\)
\(578\) −25.8771 −1.07635
\(579\) 0 0
\(580\) −0.836413 −0.0347301
\(581\) 4.96788 0.206103
\(582\) 0 0
\(583\) −24.0883 −0.997634
\(584\) −5.29731 −0.219204
\(585\) 0 0
\(586\) −0.129712 −0.00535836
\(587\) 22.6860 0.936350 0.468175 0.883636i \(-0.344912\pi\)
0.468175 + 0.883636i \(0.344912\pi\)
\(588\) 0 0
\(589\) −47.1504 −1.94280
\(590\) 4.59457 0.189156
\(591\) 0 0
\(592\) 3.26669 0.134260
\(593\) 3.77769 0.155131 0.0775656 0.996987i \(-0.475285\pi\)
0.0775656 + 0.996987i \(0.475285\pi\)
\(594\) 0 0
\(595\) −1.05617 −0.0432988
\(596\) −26.1447 −1.07093
\(597\) 0 0
\(598\) 35.6976 1.45978
\(599\) 23.7126 0.968869 0.484435 0.874827i \(-0.339025\pi\)
0.484435 + 0.874827i \(0.339025\pi\)
\(600\) 0 0
\(601\) 27.5139 1.12231 0.561157 0.827709i \(-0.310356\pi\)
0.561157 + 0.827709i \(0.310356\pi\)
\(602\) 1.39909 0.0570227
\(603\) 0 0
\(604\) 9.25804 0.376704
\(605\) 2.64679 0.107607
\(606\) 0 0
\(607\) 48.7476 1.97860 0.989301 0.145887i \(-0.0466035\pi\)
0.989301 + 0.145887i \(0.0466035\pi\)
\(608\) −49.2451 −1.99715
\(609\) 0 0
\(610\) 7.42483 0.300622
\(611\) 5.54621 0.224375
\(612\) 0 0
\(613\) −20.2080 −0.816193 −0.408096 0.912939i \(-0.633807\pi\)
−0.408096 + 0.912939i \(0.633807\pi\)
\(614\) 24.2733 0.979593
\(615\) 0 0
\(616\) −3.21789 −0.129652
\(617\) −4.52887 −0.182326 −0.0911628 0.995836i \(-0.529058\pi\)
−0.0911628 + 0.995836i \(0.529058\pi\)
\(618\) 0 0
\(619\) −3.54068 −0.142312 −0.0711560 0.997465i \(-0.522669\pi\)
−0.0711560 + 0.997465i \(0.522669\pi\)
\(620\) 5.15883 0.207184
\(621\) 0 0
\(622\) 2.47175 0.0991081
\(623\) 0.366460 0.0146819
\(624\) 0 0
\(625\) 19.1929 0.767715
\(626\) 26.0951 1.04297
\(627\) 0 0
\(628\) 11.2708 0.449756
\(629\) −1.11757 −0.0445603
\(630\) 0 0
\(631\) 3.26907 0.130140 0.0650698 0.997881i \(-0.479273\pi\)
0.0650698 + 0.997881i \(0.479273\pi\)
\(632\) 3.12876 0.124455
\(633\) 0 0
\(634\) −3.66595 −0.145593
\(635\) 0.630622 0.0250255
\(636\) 0 0
\(637\) −4.34638 −0.172210
\(638\) 4.76589 0.188684
\(639\) 0 0
\(640\) −5.86784 −0.231947
\(641\) −24.7808 −0.978781 −0.489390 0.872065i \(-0.662781\pi\)
−0.489390 + 0.872065i \(0.662781\pi\)
\(642\) 0 0
\(643\) 4.30104 0.169616 0.0848082 0.996397i \(-0.472972\pi\)
0.0848082 + 0.996397i \(0.472972\pi\)
\(644\) −5.96163 −0.234921
\(645\) 0 0
\(646\) 23.2854 0.916150
\(647\) −36.0020 −1.41538 −0.707692 0.706522i \(-0.750263\pi\)
−0.707692 + 0.706522i \(0.750263\pi\)
\(648\) 0 0
\(649\) −10.4242 −0.409186
\(650\) 36.4657 1.43030
\(651\) 0 0
\(652\) −11.6578 −0.456554
\(653\) −33.7337 −1.32010 −0.660051 0.751221i \(-0.729465\pi\)
−0.660051 + 0.751221i \(0.729465\pi\)
\(654\) 0 0
\(655\) 13.0526 0.510009
\(656\) 41.3491 1.61441
\(657\) 0 0
\(658\) −2.32620 −0.0906849
\(659\) 35.5995 1.38676 0.693380 0.720572i \(-0.256121\pi\)
0.693380 + 0.720572i \(0.256121\pi\)
\(660\) 0 0
\(661\) −7.65803 −0.297863 −0.148931 0.988848i \(-0.547583\pi\)
−0.148931 + 0.988848i \(0.547583\pi\)
\(662\) −3.43274 −0.133417
\(663\) 0 0
\(664\) −6.12908 −0.237855
\(665\) −4.80958 −0.186508
\(666\) 0 0
\(667\) −4.51595 −0.174858
\(668\) −12.4519 −0.481777
\(669\) 0 0
\(670\) −6.10746 −0.235952
\(671\) −16.8455 −0.650314
\(672\) 0 0
\(673\) −5.29132 −0.203965 −0.101983 0.994786i \(-0.532519\pi\)
−0.101983 + 0.994786i \(0.532519\pi\)
\(674\) 2.07437 0.0799016
\(675\) 0 0
\(676\) 7.79518 0.299814
\(677\) −45.8433 −1.76190 −0.880951 0.473208i \(-0.843096\pi\)
−0.880951 + 0.473208i \(0.843096\pi\)
\(678\) 0 0
\(679\) −10.1853 −0.390877
\(680\) 1.30304 0.0499694
\(681\) 0 0
\(682\) −29.3951 −1.12560
\(683\) 38.6903 1.48044 0.740222 0.672362i \(-0.234720\pi\)
0.740222 + 0.672362i \(0.234720\pi\)
\(684\) 0 0
\(685\) 8.36853 0.319745
\(686\) 1.82297 0.0696014
\(687\) 0 0
\(688\) −3.75721 −0.143242
\(689\) 40.1409 1.52924
\(690\) 0 0
\(691\) 31.5628 1.20071 0.600353 0.799735i \(-0.295027\pi\)
0.600353 + 0.799735i \(0.295027\pi\)
\(692\) −34.3058 −1.30411
\(693\) 0 0
\(694\) −18.5174 −0.702910
\(695\) 7.28766 0.276437
\(696\) 0 0
\(697\) −14.1459 −0.535816
\(698\) 2.92261 0.110622
\(699\) 0 0
\(700\) −6.08990 −0.230177
\(701\) −7.21972 −0.272685 −0.136342 0.990662i \(-0.543535\pi\)
−0.136342 + 0.990662i \(0.543535\pi\)
\(702\) 0 0
\(703\) −5.08916 −0.191941
\(704\) −5.16361 −0.194611
\(705\) 0 0
\(706\) 3.73676 0.140635
\(707\) 5.28628 0.198811
\(708\) 0 0
\(709\) −20.6634 −0.776030 −0.388015 0.921653i \(-0.626839\pi\)
−0.388015 + 0.921653i \(0.626839\pi\)
\(710\) −10.9530 −0.411060
\(711\) 0 0
\(712\) −0.452116 −0.0169438
\(713\) 27.8535 1.04312
\(714\) 0 0
\(715\) 7.14898 0.267357
\(716\) −27.6462 −1.03319
\(717\) 0 0
\(718\) 14.2643 0.532340
\(719\) 8.94913 0.333746 0.166873 0.985978i \(-0.446633\pi\)
0.166873 + 0.985978i \(0.446633\pi\)
\(720\) 0 0
\(721\) 7.16287 0.266759
\(722\) 71.4001 2.65724
\(723\) 0 0
\(724\) −23.3191 −0.866647
\(725\) −4.61311 −0.171327
\(726\) 0 0
\(727\) −34.3031 −1.27223 −0.636117 0.771593i \(-0.719460\pi\)
−0.636117 + 0.771593i \(0.719460\pi\)
\(728\) 5.36231 0.198740
\(729\) 0 0
\(730\) −4.93606 −0.182692
\(731\) 1.28538 0.0475415
\(732\) 0 0
\(733\) 23.7264 0.876354 0.438177 0.898889i \(-0.355624\pi\)
0.438177 + 0.898889i \(0.355624\pi\)
\(734\) 35.7916 1.32109
\(735\) 0 0
\(736\) 29.0909 1.07230
\(737\) 13.8566 0.510416
\(738\) 0 0
\(739\) 19.8370 0.729715 0.364858 0.931063i \(-0.381118\pi\)
0.364858 + 0.931063i \(0.381118\pi\)
\(740\) 0.556815 0.0204689
\(741\) 0 0
\(742\) −16.8360 −0.618069
\(743\) −16.6001 −0.608999 −0.304500 0.952512i \(-0.598489\pi\)
−0.304500 + 0.952512i \(0.598489\pi\)
\(744\) 0 0
\(745\) 12.4601 0.456501
\(746\) 22.7990 0.834729
\(747\) 0 0
\(748\) 5.78024 0.211347
\(749\) 6.68923 0.244419
\(750\) 0 0
\(751\) −34.3894 −1.25489 −0.627444 0.778662i \(-0.715899\pi\)
−0.627444 + 0.778662i \(0.715899\pi\)
\(752\) 6.24694 0.227802
\(753\) 0 0
\(754\) −7.94192 −0.289228
\(755\) −4.41220 −0.160576
\(756\) 0 0
\(757\) 44.4907 1.61704 0.808522 0.588466i \(-0.200268\pi\)
0.808522 + 0.588466i \(0.200268\pi\)
\(758\) 62.7161 2.27795
\(759\) 0 0
\(760\) 5.93378 0.215241
\(761\) 23.9855 0.869474 0.434737 0.900557i \(-0.356841\pi\)
0.434737 + 0.900557i \(0.356841\pi\)
\(762\) 0 0
\(763\) −3.17404 −0.114908
\(764\) −5.77981 −0.209106
\(765\) 0 0
\(766\) 20.3396 0.734898
\(767\) 17.3710 0.627229
\(768\) 0 0
\(769\) −31.5927 −1.13926 −0.569632 0.821900i \(-0.692914\pi\)
−0.569632 + 0.821900i \(0.692914\pi\)
\(770\) −2.99845 −0.108056
\(771\) 0 0
\(772\) −10.6847 −0.384549
\(773\) −28.0666 −1.00949 −0.504743 0.863270i \(-0.668413\pi\)
−0.504743 + 0.863270i \(0.668413\pi\)
\(774\) 0 0
\(775\) 28.4528 1.02205
\(776\) 12.5661 0.451095
\(777\) 0 0
\(778\) −10.8465 −0.388866
\(779\) −64.4176 −2.30800
\(780\) 0 0
\(781\) 24.8504 0.889216
\(782\) −13.7555 −0.491896
\(783\) 0 0
\(784\) −4.89553 −0.174840
\(785\) −5.37145 −0.191715
\(786\) 0 0
\(787\) 7.58794 0.270481 0.135240 0.990813i \(-0.456819\pi\)
0.135240 + 0.990813i \(0.456819\pi\)
\(788\) −25.2017 −0.897773
\(789\) 0 0
\(790\) 2.91540 0.103725
\(791\) −2.64523 −0.0940537
\(792\) 0 0
\(793\) 28.0715 0.996847
\(794\) 11.8059 0.418975
\(795\) 0 0
\(796\) 31.8445 1.12870
\(797\) −23.3421 −0.826819 −0.413409 0.910545i \(-0.635662\pi\)
−0.413409 + 0.910545i \(0.635662\pi\)
\(798\) 0 0
\(799\) −2.13714 −0.0756066
\(800\) 29.7168 1.05065
\(801\) 0 0
\(802\) 5.96499 0.210631
\(803\) 11.1990 0.395203
\(804\) 0 0
\(805\) 2.84119 0.100139
\(806\) 48.9842 1.72539
\(807\) 0 0
\(808\) −6.52190 −0.229440
\(809\) 6.17157 0.216981 0.108490 0.994098i \(-0.465398\pi\)
0.108490 + 0.994098i \(0.465398\pi\)
\(810\) 0 0
\(811\) −3.28794 −0.115455 −0.0577276 0.998332i \(-0.518385\pi\)
−0.0577276 + 0.998332i \(0.518385\pi\)
\(812\) 1.32633 0.0465450
\(813\) 0 0
\(814\) −3.17274 −0.111205
\(815\) 5.55586 0.194613
\(816\) 0 0
\(817\) 5.85335 0.204783
\(818\) 23.6685 0.827548
\(819\) 0 0
\(820\) 7.04806 0.246129
\(821\) −11.6698 −0.407278 −0.203639 0.979046i \(-0.565277\pi\)
−0.203639 + 0.979046i \(0.565277\pi\)
\(822\) 0 0
\(823\) −20.2596 −0.706206 −0.353103 0.935584i \(-0.614873\pi\)
−0.353103 + 0.935584i \(0.614873\pi\)
\(824\) −8.83713 −0.307856
\(825\) 0 0
\(826\) −7.28578 −0.253505
\(827\) −18.1291 −0.630412 −0.315206 0.949023i \(-0.602074\pi\)
−0.315206 + 0.949023i \(0.602074\pi\)
\(828\) 0 0
\(829\) 28.8821 1.00312 0.501559 0.865123i \(-0.332760\pi\)
0.501559 + 0.865123i \(0.332760\pi\)
\(830\) −5.71111 −0.198236
\(831\) 0 0
\(832\) 8.60467 0.298313
\(833\) 1.67481 0.0580287
\(834\) 0 0
\(835\) 5.93430 0.205365
\(836\) 26.3220 0.910365
\(837\) 0 0
\(838\) −0.416968 −0.0144039
\(839\) −15.1979 −0.524689 −0.262344 0.964974i \(-0.584496\pi\)
−0.262344 + 0.964974i \(0.584496\pi\)
\(840\) 0 0
\(841\) −27.9953 −0.965355
\(842\) 24.9324 0.859228
\(843\) 0 0
\(844\) −15.1792 −0.522489
\(845\) −3.71502 −0.127801
\(846\) 0 0
\(847\) −4.19710 −0.144214
\(848\) 45.2124 1.55260
\(849\) 0 0
\(850\) −14.0515 −0.481961
\(851\) 3.00635 0.103056
\(852\) 0 0
\(853\) −1.96381 −0.0672397 −0.0336199 0.999435i \(-0.510704\pi\)
−0.0336199 + 0.999435i \(0.510704\pi\)
\(854\) −11.7738 −0.402892
\(855\) 0 0
\(856\) −8.25277 −0.282074
\(857\) 26.9219 0.919634 0.459817 0.888014i \(-0.347915\pi\)
0.459817 + 0.888014i \(0.347915\pi\)
\(858\) 0 0
\(859\) 19.4044 0.662070 0.331035 0.943618i \(-0.392602\pi\)
0.331035 + 0.943618i \(0.392602\pi\)
\(860\) −0.640427 −0.0218384
\(861\) 0 0
\(862\) 30.4463 1.03701
\(863\) 11.8491 0.403347 0.201673 0.979453i \(-0.435362\pi\)
0.201673 + 0.979453i \(0.435362\pi\)
\(864\) 0 0
\(865\) 16.3494 0.555898
\(866\) 56.5144 1.92044
\(867\) 0 0
\(868\) −8.18053 −0.277665
\(869\) −6.61448 −0.224381
\(870\) 0 0
\(871\) −23.0908 −0.782402
\(872\) 3.91594 0.132610
\(873\) 0 0
\(874\) −62.6396 −2.11882
\(875\) 6.05543 0.204711
\(876\) 0 0
\(877\) 12.8788 0.434885 0.217442 0.976073i \(-0.430229\pi\)
0.217442 + 0.976073i \(0.430229\pi\)
\(878\) −56.5536 −1.90859
\(879\) 0 0
\(880\) 8.05222 0.271440
\(881\) −41.4610 −1.39686 −0.698428 0.715680i \(-0.746117\pi\)
−0.698428 + 0.715680i \(0.746117\pi\)
\(882\) 0 0
\(883\) 55.6753 1.87362 0.936812 0.349833i \(-0.113762\pi\)
0.936812 + 0.349833i \(0.113762\pi\)
\(884\) −9.63223 −0.323967
\(885\) 0 0
\(886\) −31.8537 −1.07015
\(887\) 14.9769 0.502875 0.251437 0.967874i \(-0.419097\pi\)
0.251437 + 0.967874i \(0.419097\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) −0.421284 −0.0141215
\(891\) 0 0
\(892\) 38.8137 1.29958
\(893\) −9.73208 −0.325672
\(894\) 0 0
\(895\) 13.1756 0.440412
\(896\) 9.30485 0.310853
\(897\) 0 0
\(898\) 67.5337 2.25363
\(899\) −6.19677 −0.206674
\(900\) 0 0
\(901\) −15.4676 −0.515302
\(902\) −40.1600 −1.33718
\(903\) 0 0
\(904\) 3.26354 0.108544
\(905\) 11.1134 0.369422
\(906\) 0 0
\(907\) −8.74858 −0.290492 −0.145246 0.989396i \(-0.546397\pi\)
−0.145246 + 0.989396i \(0.546397\pi\)
\(908\) 22.4057 0.743560
\(909\) 0 0
\(910\) 4.99663 0.165637
\(911\) 44.8105 1.48464 0.742319 0.670047i \(-0.233726\pi\)
0.742319 + 0.670047i \(0.233726\pi\)
\(912\) 0 0
\(913\) 12.9574 0.428828
\(914\) 54.5672 1.80492
\(915\) 0 0
\(916\) 38.9064 1.28550
\(917\) −20.6980 −0.683509
\(918\) 0 0
\(919\) −47.4135 −1.56403 −0.782013 0.623262i \(-0.785807\pi\)
−0.782013 + 0.623262i \(0.785807\pi\)
\(920\) −3.50530 −0.115566
\(921\) 0 0
\(922\) −1.41106 −0.0464709
\(923\) −41.4108 −1.36305
\(924\) 0 0
\(925\) 3.07103 0.100975
\(926\) −33.9894 −1.11696
\(927\) 0 0
\(928\) −6.47207 −0.212456
\(929\) 46.1776 1.51504 0.757519 0.652814i \(-0.226412\pi\)
0.757519 + 0.652814i \(0.226412\pi\)
\(930\) 0 0
\(931\) 7.62672 0.249956
\(932\) −4.38907 −0.143769
\(933\) 0 0
\(934\) 45.0783 1.47501
\(935\) −2.75475 −0.0900898
\(936\) 0 0
\(937\) 27.9526 0.913170 0.456585 0.889680i \(-0.349072\pi\)
0.456585 + 0.889680i \(0.349072\pi\)
\(938\) 9.68481 0.316220
\(939\) 0 0
\(940\) 1.06481 0.0347302
\(941\) −50.7404 −1.65409 −0.827045 0.562136i \(-0.809980\pi\)
−0.827045 + 0.562136i \(0.809980\pi\)
\(942\) 0 0
\(943\) 38.0538 1.23920
\(944\) 19.5657 0.636809
\(945\) 0 0
\(946\) 3.64916 0.118645
\(947\) 27.3407 0.888452 0.444226 0.895915i \(-0.353479\pi\)
0.444226 + 0.895915i \(0.353479\pi\)
\(948\) 0 0
\(949\) −18.6621 −0.605796
\(950\) −63.9873 −2.07602
\(951\) 0 0
\(952\) −2.06628 −0.0669686
\(953\) 13.4298 0.435035 0.217517 0.976056i \(-0.430204\pi\)
0.217517 + 0.976056i \(0.430204\pi\)
\(954\) 0 0
\(955\) 2.75454 0.0891348
\(956\) 2.01173 0.0650639
\(957\) 0 0
\(958\) 64.5370 2.08510
\(959\) −13.2703 −0.428520
\(960\) 0 0
\(961\) 7.22046 0.232918
\(962\) 5.28708 0.170462
\(963\) 0 0
\(964\) −13.1745 −0.424322
\(965\) 5.09209 0.163920
\(966\) 0 0
\(967\) 28.4687 0.915493 0.457747 0.889083i \(-0.348657\pi\)
0.457747 + 0.889083i \(0.348657\pi\)
\(968\) 5.17814 0.166432
\(969\) 0 0
\(970\) 11.7091 0.375957
\(971\) 34.5802 1.10973 0.554866 0.831940i \(-0.312769\pi\)
0.554866 + 0.831940i \(0.312769\pi\)
\(972\) 0 0
\(973\) −11.5563 −0.370478
\(974\) −27.9904 −0.896870
\(975\) 0 0
\(976\) 31.6182 1.01207
\(977\) 27.6629 0.885013 0.442507 0.896765i \(-0.354089\pi\)
0.442507 + 0.896765i \(0.354089\pi\)
\(978\) 0 0
\(979\) 0.955814 0.0305479
\(980\) −0.834455 −0.0266557
\(981\) 0 0
\(982\) 1.06682 0.0340437
\(983\) 37.8392 1.20688 0.603442 0.797407i \(-0.293796\pi\)
0.603442 + 0.797407i \(0.293796\pi\)
\(984\) 0 0
\(985\) 12.0106 0.382690
\(986\) 3.06029 0.0974595
\(987\) 0 0
\(988\) −43.8631 −1.39547
\(989\) −3.45778 −0.109951
\(990\) 0 0
\(991\) 29.1907 0.927272 0.463636 0.886026i \(-0.346544\pi\)
0.463636 + 0.886026i \(0.346544\pi\)
\(992\) 39.9184 1.26741
\(993\) 0 0
\(994\) 17.3686 0.550899
\(995\) −15.1764 −0.481126
\(996\) 0 0
\(997\) 6.89333 0.218314 0.109157 0.994025i \(-0.465185\pi\)
0.109157 + 0.994025i \(0.465185\pi\)
\(998\) −38.2650 −1.21126
\(999\) 0 0
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 \(a_p\))