Properties

Label 8034.2.a.o.1.5
Level 8034
Weight 2
Character 8034.1
Self dual Yes
Analytic conductor 64.152
Analytic rank 1
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(2.51101\)
Character \(\chi\) = 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.77686 q^{5}\) \(+1.00000 q^{6}\) \(-3.99413 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.77686 q^{5}\) \(+1.00000 q^{6}\) \(-3.99413 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-1.77686 q^{10}\) \(-0.580058 q^{11}\) \(-1.00000 q^{12}\) \(+1.00000 q^{13}\) \(+3.99413 q^{14}\) \(-1.77686 q^{15}\) \(+1.00000 q^{16}\) \(+6.41168 q^{17}\) \(-1.00000 q^{18}\) \(-4.99413 q^{19}\) \(+1.77686 q^{20}\) \(+3.99413 q^{21}\) \(+0.580058 q^{22}\) \(-6.59303 q^{23}\) \(+1.00000 q^{24}\) \(-1.84277 q^{25}\) \(-1.00000 q^{26}\) \(-1.00000 q^{27}\) \(-3.99413 q^{28}\) \(+1.31057 q^{29}\) \(+1.77686 q^{30}\) \(+6.05760 q^{31}\) \(-1.00000 q^{32}\) \(+0.580058 q^{33}\) \(-6.41168 q^{34}\) \(-7.09702 q^{35}\) \(+1.00000 q^{36}\) \(+6.39448 q^{37}\) \(+4.99413 q^{38}\) \(-1.00000 q^{39}\) \(-1.77686 q^{40}\) \(+6.04948 q^{41}\) \(-3.99413 q^{42}\) \(+11.3839 q^{43}\) \(-0.580058 q^{44}\) \(+1.77686 q^{45}\) \(+6.59303 q^{46}\) \(-6.62715 q^{47}\) \(-1.00000 q^{48}\) \(+8.95309 q^{49}\) \(+1.84277 q^{50}\) \(-6.41168 q^{51}\) \(+1.00000 q^{52}\) \(-13.1198 q^{53}\) \(+1.00000 q^{54}\) \(-1.03068 q^{55}\) \(+3.99413 q^{56}\) \(+4.99413 q^{57}\) \(-1.31057 q^{58}\) \(-10.2716 q^{59}\) \(-1.77686 q^{60}\) \(-12.6576 q^{61}\) \(-6.05760 q^{62}\) \(-3.99413 q^{63}\) \(+1.00000 q^{64}\) \(+1.77686 q^{65}\) \(-0.580058 q^{66}\) \(-2.66759 q^{67}\) \(+6.41168 q^{68}\) \(+6.59303 q^{69}\) \(+7.09702 q^{70}\) \(+3.84167 q^{71}\) \(-1.00000 q^{72}\) \(+12.1465 q^{73}\) \(-6.39448 q^{74}\) \(+1.84277 q^{75}\) \(-4.99413 q^{76}\) \(+2.31683 q^{77}\) \(+1.00000 q^{78}\) \(+2.69447 q^{79}\) \(+1.77686 q^{80}\) \(+1.00000 q^{81}\) \(-6.04948 q^{82}\) \(+7.90079 q^{83}\) \(+3.99413 q^{84}\) \(+11.3927 q^{85}\) \(-11.3839 q^{86}\) \(-1.31057 q^{87}\) \(+0.580058 q^{88}\) \(-3.95413 q^{89}\) \(-1.77686 q^{90}\) \(-3.99413 q^{91}\) \(-6.59303 q^{92}\) \(-6.05760 q^{93}\) \(+6.62715 q^{94}\) \(-8.87388 q^{95}\) \(+1.00000 q^{96}\) \(+8.16221 q^{97}\) \(-8.95309 q^{98}\) \(-0.580058 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 7q^{36} \) \(\mathstrut +\mathstrut 17q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 7q^{72} \) \(\mathstrut +\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 22q^{86} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 9q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 1.77686 0.794636 0.397318 0.917681i \(-0.369941\pi\)
0.397318 + 0.917681i \(0.369941\pi\)
\(6\) 1.00000 0.408248
\(7\) −3.99413 −1.50964 −0.754820 0.655932i \(-0.772276\pi\)
−0.754820 + 0.655932i \(0.772276\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.77686 −0.561893
\(11\) −0.580058 −0.174894 −0.0874470 0.996169i \(-0.527871\pi\)
−0.0874470 + 0.996169i \(0.527871\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 3.99413 1.06748
\(15\) −1.77686 −0.458783
\(16\) 1.00000 0.250000
\(17\) 6.41168 1.55506 0.777531 0.628845i \(-0.216472\pi\)
0.777531 + 0.628845i \(0.216472\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.99413 −1.14573 −0.572866 0.819649i \(-0.694169\pi\)
−0.572866 + 0.819649i \(0.694169\pi\)
\(20\) 1.77686 0.397318
\(21\) 3.99413 0.871591
\(22\) 0.580058 0.123669
\(23\) −6.59303 −1.37474 −0.687371 0.726306i \(-0.741235\pi\)
−0.687371 + 0.726306i \(0.741235\pi\)
\(24\) 1.00000 0.204124
\(25\) −1.84277 −0.368553
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −3.99413 −0.754820
\(29\) 1.31057 0.243367 0.121684 0.992569i \(-0.461171\pi\)
0.121684 + 0.992569i \(0.461171\pi\)
\(30\) 1.77686 0.324409
\(31\) 6.05760 1.08798 0.543988 0.839093i \(-0.316914\pi\)
0.543988 + 0.839093i \(0.316914\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.580058 0.100975
\(34\) −6.41168 −1.09959
\(35\) −7.09702 −1.19961
\(36\) 1.00000 0.166667
\(37\) 6.39448 1.05125 0.525623 0.850718i \(-0.323832\pi\)
0.525623 + 0.850718i \(0.323832\pi\)
\(38\) 4.99413 0.810155
\(39\) −1.00000 −0.160128
\(40\) −1.77686 −0.280946
\(41\) 6.04948 0.944770 0.472385 0.881392i \(-0.343393\pi\)
0.472385 + 0.881392i \(0.343393\pi\)
\(42\) −3.99413 −0.616308
\(43\) 11.3839 1.73604 0.868018 0.496533i \(-0.165394\pi\)
0.868018 + 0.496533i \(0.165394\pi\)
\(44\) −0.580058 −0.0874470
\(45\) 1.77686 0.264879
\(46\) 6.59303 0.972090
\(47\) −6.62715 −0.966669 −0.483334 0.875436i \(-0.660574\pi\)
−0.483334 + 0.875436i \(0.660574\pi\)
\(48\) −1.00000 −0.144338
\(49\) 8.95309 1.27901
\(50\) 1.84277 0.260606
\(51\) −6.41168 −0.897815
\(52\) 1.00000 0.138675
\(53\) −13.1198 −1.80214 −0.901070 0.433673i \(-0.857217\pi\)
−0.901070 + 0.433673i \(0.857217\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.03068 −0.138977
\(56\) 3.99413 0.533738
\(57\) 4.99413 0.661489
\(58\) −1.31057 −0.172087
\(59\) −10.2716 −1.33725 −0.668626 0.743599i \(-0.733117\pi\)
−0.668626 + 0.743599i \(0.733117\pi\)
\(60\) −1.77686 −0.229392
\(61\) −12.6576 −1.62064 −0.810318 0.585990i \(-0.800706\pi\)
−0.810318 + 0.585990i \(0.800706\pi\)
\(62\) −6.05760 −0.769316
\(63\) −3.99413 −0.503213
\(64\) 1.00000 0.125000
\(65\) 1.77686 0.220392
\(66\) −0.580058 −0.0714002
\(67\) −2.66759 −0.325898 −0.162949 0.986634i \(-0.552101\pi\)
−0.162949 + 0.986634i \(0.552101\pi\)
\(68\) 6.41168 0.777531
\(69\) 6.59303 0.793708
\(70\) 7.09702 0.848256
\(71\) 3.84167 0.455923 0.227961 0.973670i \(-0.426794\pi\)
0.227961 + 0.973670i \(0.426794\pi\)
\(72\) −1.00000 −0.117851
\(73\) 12.1465 1.42164 0.710818 0.703376i \(-0.248325\pi\)
0.710818 + 0.703376i \(0.248325\pi\)
\(74\) −6.39448 −0.743343
\(75\) 1.84277 0.212784
\(76\) −4.99413 −0.572866
\(77\) 2.31683 0.264027
\(78\) 1.00000 0.113228
\(79\) 2.69447 0.303152 0.151576 0.988446i \(-0.451565\pi\)
0.151576 + 0.988446i \(0.451565\pi\)
\(80\) 1.77686 0.198659
\(81\) 1.00000 0.111111
\(82\) −6.04948 −0.668054
\(83\) 7.90079 0.867225 0.433612 0.901099i \(-0.357239\pi\)
0.433612 + 0.901099i \(0.357239\pi\)
\(84\) 3.99413 0.435796
\(85\) 11.3927 1.23571
\(86\) −11.3839 −1.22756
\(87\) −1.31057 −0.140508
\(88\) 0.580058 0.0618344
\(89\) −3.95413 −0.419137 −0.209569 0.977794i \(-0.567206\pi\)
−0.209569 + 0.977794i \(0.567206\pi\)
\(90\) −1.77686 −0.187298
\(91\) −3.99413 −0.418699
\(92\) −6.59303 −0.687371
\(93\) −6.05760 −0.628144
\(94\) 6.62715 0.683538
\(95\) −8.87388 −0.910441
\(96\) 1.00000 0.102062
\(97\) 8.16221 0.828746 0.414373 0.910107i \(-0.364001\pi\)
0.414373 + 0.910107i \(0.364001\pi\)
\(98\) −8.95309 −0.904399
\(99\) −0.580058 −0.0582980
\(100\) −1.84277 −0.184277
\(101\) 12.4955 1.24334 0.621672 0.783278i \(-0.286454\pi\)
0.621672 + 0.783278i \(0.286454\pi\)
\(102\) 6.41168 0.634851
\(103\) 1.00000 0.0985329
\(104\) −1.00000 −0.0980581
\(105\) 7.09702 0.692598
\(106\) 13.1198 1.27431
\(107\) 14.8246 1.43315 0.716573 0.697512i \(-0.245710\pi\)
0.716573 + 0.697512i \(0.245710\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 0.449928 0.0430953 0.0215476 0.999768i \(-0.493141\pi\)
0.0215476 + 0.999768i \(0.493141\pi\)
\(110\) 1.03068 0.0982717
\(111\) −6.39448 −0.606937
\(112\) −3.99413 −0.377410
\(113\) 8.60200 0.809208 0.404604 0.914492i \(-0.367409\pi\)
0.404604 + 0.914492i \(0.367409\pi\)
\(114\) −4.99413 −0.467743
\(115\) −11.7149 −1.09242
\(116\) 1.31057 0.121684
\(117\) 1.00000 0.0924500
\(118\) 10.2716 0.945580
\(119\) −25.6091 −2.34758
\(120\) 1.77686 0.162204
\(121\) −10.6635 −0.969412
\(122\) 12.6576 1.14596
\(123\) −6.04948 −0.545463
\(124\) 6.05760 0.543988
\(125\) −12.1586 −1.08750
\(126\) 3.99413 0.355826
\(127\) −17.6101 −1.56265 −0.781323 0.624126i \(-0.785455\pi\)
−0.781323 + 0.624126i \(0.785455\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −11.3839 −1.00230
\(130\) −1.77686 −0.155841
\(131\) −6.23844 −0.545055 −0.272527 0.962148i \(-0.587860\pi\)
−0.272527 + 0.962148i \(0.587860\pi\)
\(132\) 0.580058 0.0504876
\(133\) 19.9472 1.72964
\(134\) 2.66759 0.230445
\(135\) −1.77686 −0.152928
\(136\) −6.41168 −0.549797
\(137\) −16.0387 −1.37028 −0.685140 0.728412i \(-0.740259\pi\)
−0.685140 + 0.728412i \(0.740259\pi\)
\(138\) −6.59303 −0.561236
\(139\) 5.44497 0.461836 0.230918 0.972973i \(-0.425827\pi\)
0.230918 + 0.972973i \(0.425827\pi\)
\(140\) −7.09702 −0.599807
\(141\) 6.62715 0.558106
\(142\) −3.84167 −0.322386
\(143\) −0.580058 −0.0485069
\(144\) 1.00000 0.0833333
\(145\) 2.32870 0.193388
\(146\) −12.1465 −1.00525
\(147\) −8.95309 −0.738438
\(148\) 6.39448 0.525623
\(149\) 7.66917 0.628283 0.314142 0.949376i \(-0.398283\pi\)
0.314142 + 0.949376i \(0.398283\pi\)
\(150\) −1.84277 −0.150461
\(151\) −24.0732 −1.95905 −0.979524 0.201329i \(-0.935474\pi\)
−0.979524 + 0.201329i \(0.935474\pi\)
\(152\) 4.99413 0.405078
\(153\) 6.41168 0.518354
\(154\) −2.31683 −0.186695
\(155\) 10.7635 0.864546
\(156\) −1.00000 −0.0800641
\(157\) −19.4944 −1.55582 −0.777909 0.628377i \(-0.783720\pi\)
−0.777909 + 0.628377i \(0.783720\pi\)
\(158\) −2.69447 −0.214361
\(159\) 13.1198 1.04047
\(160\) −1.77686 −0.140473
\(161\) 26.3334 2.07537
\(162\) −1.00000 −0.0785674
\(163\) 23.1065 1.80984 0.904920 0.425581i \(-0.139930\pi\)
0.904920 + 0.425581i \(0.139930\pi\)
\(164\) 6.04948 0.472385
\(165\) 1.03068 0.0802385
\(166\) −7.90079 −0.613221
\(167\) 9.42071 0.728996 0.364498 0.931204i \(-0.381241\pi\)
0.364498 + 0.931204i \(0.381241\pi\)
\(168\) −3.99413 −0.308154
\(169\) 1.00000 0.0769231
\(170\) −11.3927 −0.873778
\(171\) −4.99413 −0.381911
\(172\) 11.3839 0.868018
\(173\) −22.0526 −1.67663 −0.838315 0.545186i \(-0.816459\pi\)
−0.838315 + 0.545186i \(0.816459\pi\)
\(174\) 1.31057 0.0993542
\(175\) 7.36025 0.556383
\(176\) −0.580058 −0.0437235
\(177\) 10.2716 0.772063
\(178\) 3.95413 0.296375
\(179\) 4.54176 0.339467 0.169734 0.985490i \(-0.445709\pi\)
0.169734 + 0.985490i \(0.445709\pi\)
\(180\) 1.77686 0.132439
\(181\) 15.0371 1.11770 0.558851 0.829268i \(-0.311242\pi\)
0.558851 + 0.829268i \(0.311242\pi\)
\(182\) 3.99413 0.296065
\(183\) 12.6576 0.935675
\(184\) 6.59303 0.486045
\(185\) 11.3621 0.835358
\(186\) 6.05760 0.444165
\(187\) −3.71915 −0.271971
\(188\) −6.62715 −0.483334
\(189\) 3.99413 0.290530
\(190\) 8.87388 0.643779
\(191\) −14.4869 −1.04823 −0.524117 0.851646i \(-0.675605\pi\)
−0.524117 + 0.851646i \(0.675605\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 4.70533 0.338697 0.169348 0.985556i \(-0.445834\pi\)
0.169348 + 0.985556i \(0.445834\pi\)
\(194\) −8.16221 −0.586012
\(195\) −1.77686 −0.127244
\(196\) 8.95309 0.639506
\(197\) 18.9174 1.34781 0.673904 0.738819i \(-0.264616\pi\)
0.673904 + 0.738819i \(0.264616\pi\)
\(198\) 0.580058 0.0412229
\(199\) −17.0528 −1.20884 −0.604421 0.796665i \(-0.706595\pi\)
−0.604421 + 0.796665i \(0.706595\pi\)
\(200\) 1.84277 0.130303
\(201\) 2.66759 0.188157
\(202\) −12.4955 −0.879177
\(203\) −5.23460 −0.367397
\(204\) −6.41168 −0.448908
\(205\) 10.7491 0.750749
\(206\) −1.00000 −0.0696733
\(207\) −6.59303 −0.458248
\(208\) 1.00000 0.0693375
\(209\) 2.89689 0.200382
\(210\) −7.09702 −0.489741
\(211\) −7.46310 −0.513781 −0.256891 0.966440i \(-0.582698\pi\)
−0.256891 + 0.966440i \(0.582698\pi\)
\(212\) −13.1198 −0.901070
\(213\) −3.84167 −0.263227
\(214\) −14.8246 −1.01339
\(215\) 20.2277 1.37952
\(216\) 1.00000 0.0680414
\(217\) −24.1948 −1.64245
\(218\) −0.449928 −0.0304730
\(219\) −12.1465 −0.820782
\(220\) −1.03068 −0.0694886
\(221\) 6.41168 0.431296
\(222\) 6.39448 0.429169
\(223\) −14.0884 −0.943428 −0.471714 0.881752i \(-0.656365\pi\)
−0.471714 + 0.881752i \(0.656365\pi\)
\(224\) 3.99413 0.266869
\(225\) −1.84277 −0.122851
\(226\) −8.60200 −0.572197
\(227\) 11.7368 0.779000 0.389500 0.921026i \(-0.372648\pi\)
0.389500 + 0.921026i \(0.372648\pi\)
\(228\) 4.99413 0.330744
\(229\) −22.2214 −1.46843 −0.734215 0.678917i \(-0.762450\pi\)
−0.734215 + 0.678917i \(0.762450\pi\)
\(230\) 11.7149 0.772458
\(231\) −2.31683 −0.152436
\(232\) −1.31057 −0.0860433
\(233\) −2.45597 −0.160896 −0.0804480 0.996759i \(-0.525635\pi\)
−0.0804480 + 0.996759i \(0.525635\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −11.7755 −0.768150
\(236\) −10.2716 −0.668626
\(237\) −2.69447 −0.175025
\(238\) 25.6091 1.65999
\(239\) 0.439459 0.0284262 0.0142131 0.999899i \(-0.495476\pi\)
0.0142131 + 0.999899i \(0.495476\pi\)
\(240\) −1.77686 −0.114696
\(241\) −25.8545 −1.66543 −0.832717 0.553699i \(-0.813216\pi\)
−0.832717 + 0.553699i \(0.813216\pi\)
\(242\) 10.6635 0.685478
\(243\) −1.00000 −0.0641500
\(244\) −12.6576 −0.810318
\(245\) 15.9084 1.01635
\(246\) 6.04948 0.385701
\(247\) −4.99413 −0.317769
\(248\) −6.05760 −0.384658
\(249\) −7.90079 −0.500692
\(250\) 12.1586 0.768980
\(251\) −22.2828 −1.40648 −0.703240 0.710952i \(-0.748264\pi\)
−0.703240 + 0.710952i \(0.748264\pi\)
\(252\) −3.99413 −0.251607
\(253\) 3.82434 0.240434
\(254\) 17.6101 1.10496
\(255\) −11.3927 −0.713436
\(256\) 1.00000 0.0625000
\(257\) 21.2192 1.32362 0.661809 0.749672i \(-0.269789\pi\)
0.661809 + 0.749672i \(0.269789\pi\)
\(258\) 11.3839 0.708733
\(259\) −25.5404 −1.58700
\(260\) 1.77686 0.110196
\(261\) 1.31057 0.0811224
\(262\) 6.23844 0.385412
\(263\) −30.7091 −1.89360 −0.946802 0.321816i \(-0.895707\pi\)
−0.946802 + 0.321816i \(0.895707\pi\)
\(264\) −0.580058 −0.0357001
\(265\) −23.3120 −1.43205
\(266\) −19.9472 −1.22304
\(267\) 3.95413 0.241989
\(268\) −2.66759 −0.162949
\(269\) −5.25791 −0.320580 −0.160290 0.987070i \(-0.551243\pi\)
−0.160290 + 0.987070i \(0.551243\pi\)
\(270\) 1.77686 0.108136
\(271\) 8.79084 0.534006 0.267003 0.963696i \(-0.413967\pi\)
0.267003 + 0.963696i \(0.413967\pi\)
\(272\) 6.41168 0.388765
\(273\) 3.99413 0.241736
\(274\) 16.0387 0.968934
\(275\) 1.06891 0.0644578
\(276\) 6.59303 0.396854
\(277\) −22.0601 −1.32547 −0.662733 0.748856i \(-0.730604\pi\)
−0.662733 + 0.748856i \(0.730604\pi\)
\(278\) −5.44497 −0.326567
\(279\) 6.05760 0.362659
\(280\) 7.09702 0.424128
\(281\) −2.69154 −0.160564 −0.0802820 0.996772i \(-0.525582\pi\)
−0.0802820 + 0.996772i \(0.525582\pi\)
\(282\) −6.62715 −0.394641
\(283\) 1.11537 0.0663018 0.0331509 0.999450i \(-0.489446\pi\)
0.0331509 + 0.999450i \(0.489446\pi\)
\(284\) 3.84167 0.227961
\(285\) 8.87388 0.525643
\(286\) 0.580058 0.0342995
\(287\) −24.1624 −1.42626
\(288\) −1.00000 −0.0589256
\(289\) 24.1097 1.41822
\(290\) −2.32870 −0.136746
\(291\) −8.16221 −0.478477
\(292\) 12.1465 0.710818
\(293\) 23.8587 1.39384 0.696919 0.717149i \(-0.254553\pi\)
0.696919 + 0.717149i \(0.254553\pi\)
\(294\) 8.95309 0.522155
\(295\) −18.2513 −1.06263
\(296\) −6.39448 −0.371672
\(297\) 0.580058 0.0336584
\(298\) −7.66917 −0.444263
\(299\) −6.59303 −0.381285
\(300\) 1.84277 0.106392
\(301\) −45.4690 −2.62079
\(302\) 24.0732 1.38526
\(303\) −12.4955 −0.717845
\(304\) −4.99413 −0.286433
\(305\) −22.4907 −1.28782
\(306\) −6.41168 −0.366531
\(307\) 18.1999 1.03873 0.519363 0.854554i \(-0.326169\pi\)
0.519363 + 0.854554i \(0.326169\pi\)
\(308\) 2.31683 0.132014
\(309\) −1.00000 −0.0568880
\(310\) −10.7635 −0.611326
\(311\) 16.7588 0.950305 0.475153 0.879903i \(-0.342393\pi\)
0.475153 + 0.879903i \(0.342393\pi\)
\(312\) 1.00000 0.0566139
\(313\) 15.1054 0.853809 0.426904 0.904297i \(-0.359604\pi\)
0.426904 + 0.904297i \(0.359604\pi\)
\(314\) 19.4944 1.10013
\(315\) −7.09702 −0.399872
\(316\) 2.69447 0.151576
\(317\) 26.7194 1.50071 0.750355 0.661035i \(-0.229882\pi\)
0.750355 + 0.661035i \(0.229882\pi\)
\(318\) −13.1198 −0.735721
\(319\) −0.760208 −0.0425635
\(320\) 1.77686 0.0993295
\(321\) −14.8246 −0.827427
\(322\) −26.3334 −1.46751
\(323\) −32.0208 −1.78168
\(324\) 1.00000 0.0555556
\(325\) −1.84277 −0.102218
\(326\) −23.1065 −1.27975
\(327\) −0.449928 −0.0248811
\(328\) −6.04948 −0.334027
\(329\) 26.4697 1.45932
\(330\) −1.03068 −0.0567372
\(331\) −30.1515 −1.65728 −0.828638 0.559784i \(-0.810884\pi\)
−0.828638 + 0.559784i \(0.810884\pi\)
\(332\) 7.90079 0.433612
\(333\) 6.39448 0.350415
\(334\) −9.42071 −0.515478
\(335\) −4.73994 −0.258971
\(336\) 3.99413 0.217898
\(337\) −2.90829 −0.158425 −0.0792123 0.996858i \(-0.525241\pi\)
−0.0792123 + 0.996858i \(0.525241\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −8.60200 −0.467197
\(340\) 11.3927 0.617854
\(341\) −3.51376 −0.190281
\(342\) 4.99413 0.270052
\(343\) −7.80090 −0.421209
\(344\) −11.3839 −0.613781
\(345\) 11.7149 0.630709
\(346\) 22.0526 1.18556
\(347\) −26.1265 −1.40255 −0.701273 0.712893i \(-0.747385\pi\)
−0.701273 + 0.712893i \(0.747385\pi\)
\(348\) −1.31057 −0.0702541
\(349\) −19.4604 −1.04169 −0.520846 0.853651i \(-0.674383\pi\)
−0.520846 + 0.853651i \(0.674383\pi\)
\(350\) −7.36025 −0.393422
\(351\) −1.00000 −0.0533761
\(352\) 0.580058 0.0309172
\(353\) 14.8833 0.792158 0.396079 0.918216i \(-0.370371\pi\)
0.396079 + 0.918216i \(0.370371\pi\)
\(354\) −10.2716 −0.545931
\(355\) 6.82612 0.362293
\(356\) −3.95413 −0.209569
\(357\) 25.6091 1.35538
\(358\) −4.54176 −0.240040
\(359\) −6.94723 −0.366661 −0.183330 0.983051i \(-0.558688\pi\)
−0.183330 + 0.983051i \(0.558688\pi\)
\(360\) −1.77686 −0.0936488
\(361\) 5.94135 0.312703
\(362\) −15.0371 −0.790335
\(363\) 10.6635 0.559690
\(364\) −3.99413 −0.209349
\(365\) 21.5826 1.12968
\(366\) −12.6576 −0.661622
\(367\) −16.9537 −0.884978 −0.442489 0.896774i \(-0.645904\pi\)
−0.442489 + 0.896774i \(0.645904\pi\)
\(368\) −6.59303 −0.343686
\(369\) 6.04948 0.314923
\(370\) −11.3621 −0.590687
\(371\) 52.4021 2.72058
\(372\) −6.05760 −0.314072
\(373\) −13.4320 −0.695484 −0.347742 0.937590i \(-0.613051\pi\)
−0.347742 + 0.937590i \(0.613051\pi\)
\(374\) 3.71915 0.192313
\(375\) 12.1586 0.627870
\(376\) 6.62715 0.341769
\(377\) 1.31057 0.0674979
\(378\) −3.99413 −0.205436
\(379\) 22.2036 1.14052 0.570260 0.821464i \(-0.306842\pi\)
0.570260 + 0.821464i \(0.306842\pi\)
\(380\) −8.87388 −0.455220
\(381\) 17.6101 0.902195
\(382\) 14.4869 0.741214
\(383\) 32.3119 1.65106 0.825530 0.564358i \(-0.190876\pi\)
0.825530 + 0.564358i \(0.190876\pi\)
\(384\) 1.00000 0.0510310
\(385\) 4.11668 0.209805
\(386\) −4.70533 −0.239495
\(387\) 11.3839 0.578678
\(388\) 8.16221 0.414373
\(389\) 6.20757 0.314736 0.157368 0.987540i \(-0.449699\pi\)
0.157368 + 0.987540i \(0.449699\pi\)
\(390\) 1.77686 0.0899748
\(391\) −42.2724 −2.13781
\(392\) −8.95309 −0.452199
\(393\) 6.23844 0.314687
\(394\) −18.9174 −0.953044
\(395\) 4.78770 0.240895
\(396\) −0.580058 −0.0291490
\(397\) −31.7721 −1.59460 −0.797298 0.603586i \(-0.793738\pi\)
−0.797298 + 0.603586i \(0.793738\pi\)
\(398\) 17.0528 0.854780
\(399\) −19.9472 −0.998610
\(400\) −1.84277 −0.0921383
\(401\) −1.07631 −0.0537483 −0.0268742 0.999639i \(-0.508555\pi\)
−0.0268742 + 0.999639i \(0.508555\pi\)
\(402\) −2.66759 −0.133047
\(403\) 6.05760 0.301750
\(404\) 12.4955 0.621672
\(405\) 1.77686 0.0882929
\(406\) 5.23460 0.259789
\(407\) −3.70917 −0.183857
\(408\) 6.41168 0.317426
\(409\) −9.73909 −0.481567 −0.240783 0.970579i \(-0.577404\pi\)
−0.240783 + 0.970579i \(0.577404\pi\)
\(410\) −10.7491 −0.530860
\(411\) 16.0387 0.791131
\(412\) 1.00000 0.0492665
\(413\) 41.0262 2.01877
\(414\) 6.59303 0.324030
\(415\) 14.0386 0.689128
\(416\) −1.00000 −0.0490290
\(417\) −5.44497 −0.266641
\(418\) −2.89689 −0.141691
\(419\) 15.8585 0.774740 0.387370 0.921924i \(-0.373384\pi\)
0.387370 + 0.921924i \(0.373384\pi\)
\(420\) 7.09702 0.346299
\(421\) 7.52106 0.366554 0.183277 0.983061i \(-0.441329\pi\)
0.183277 + 0.983061i \(0.441329\pi\)
\(422\) 7.46310 0.363298
\(423\) −6.62715 −0.322223
\(424\) 13.1198 0.637153
\(425\) −11.8152 −0.573123
\(426\) 3.84167 0.186130
\(427\) 50.5560 2.44658
\(428\) 14.8246 0.716573
\(429\) 0.580058 0.0280055
\(430\) −20.2277 −0.975466
\(431\) −2.73677 −0.131826 −0.0659129 0.997825i \(-0.520996\pi\)
−0.0659129 + 0.997825i \(0.520996\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −12.6570 −0.608259 −0.304129 0.952631i \(-0.598365\pi\)
−0.304129 + 0.952631i \(0.598365\pi\)
\(434\) 24.1948 1.16139
\(435\) −2.32870 −0.111653
\(436\) 0.449928 0.0215476
\(437\) 32.9265 1.57509
\(438\) 12.1465 0.580380
\(439\) 26.3495 1.25759 0.628795 0.777571i \(-0.283548\pi\)
0.628795 + 0.777571i \(0.283548\pi\)
\(440\) 1.03068 0.0491358
\(441\) 8.95309 0.426338
\(442\) −6.41168 −0.304973
\(443\) −1.36156 −0.0646897 −0.0323448 0.999477i \(-0.510297\pi\)
−0.0323448 + 0.999477i \(0.510297\pi\)
\(444\) −6.39448 −0.303469
\(445\) −7.02594 −0.333062
\(446\) 14.0884 0.667104
\(447\) −7.66917 −0.362740
\(448\) −3.99413 −0.188705
\(449\) −8.70559 −0.410842 −0.205421 0.978674i \(-0.565856\pi\)
−0.205421 + 0.978674i \(0.565856\pi\)
\(450\) 1.84277 0.0868688
\(451\) −3.50905 −0.165235
\(452\) 8.60200 0.404604
\(453\) 24.0732 1.13106
\(454\) −11.7368 −0.550836
\(455\) −7.09702 −0.332713
\(456\) −4.99413 −0.233872
\(457\) 35.5594 1.66340 0.831700 0.555225i \(-0.187368\pi\)
0.831700 + 0.555225i \(0.187368\pi\)
\(458\) 22.2214 1.03834
\(459\) −6.41168 −0.299272
\(460\) −11.7149 −0.546210
\(461\) −28.8532 −1.34383 −0.671913 0.740630i \(-0.734527\pi\)
−0.671913 + 0.740630i \(0.734527\pi\)
\(462\) 2.31683 0.107789
\(463\) 28.1865 1.30994 0.654970 0.755655i \(-0.272681\pi\)
0.654970 + 0.755655i \(0.272681\pi\)
\(464\) 1.31057 0.0608418
\(465\) −10.7635 −0.499146
\(466\) 2.45597 0.113771
\(467\) −24.3804 −1.12819 −0.564095 0.825710i \(-0.690775\pi\)
−0.564095 + 0.825710i \(0.690775\pi\)
\(468\) 1.00000 0.0462250
\(469\) 10.6547 0.491989
\(470\) 11.7755 0.543164
\(471\) 19.4944 0.898252
\(472\) 10.2716 0.472790
\(473\) −6.60335 −0.303622
\(474\) 2.69447 0.123761
\(475\) 9.20301 0.422263
\(476\) −25.6091 −1.17379
\(477\) −13.1198 −0.600713
\(478\) −0.439459 −0.0201004
\(479\) 3.35175 0.153145 0.0765727 0.997064i \(-0.475602\pi\)
0.0765727 + 0.997064i \(0.475602\pi\)
\(480\) 1.77686 0.0811022
\(481\) 6.39448 0.291563
\(482\) 25.8545 1.17764
\(483\) −26.3334 −1.19821
\(484\) −10.6635 −0.484706
\(485\) 14.5031 0.658552
\(486\) 1.00000 0.0453609
\(487\) −27.2724 −1.23583 −0.617915 0.786245i \(-0.712022\pi\)
−0.617915 + 0.786245i \(0.712022\pi\)
\(488\) 12.6576 0.572981
\(489\) −23.1065 −1.04491
\(490\) −15.9084 −0.718668
\(491\) −8.42210 −0.380084 −0.190042 0.981776i \(-0.560862\pi\)
−0.190042 + 0.981776i \(0.560862\pi\)
\(492\) −6.04948 −0.272732
\(493\) 8.40297 0.378451
\(494\) 4.99413 0.224697
\(495\) −1.03068 −0.0463257
\(496\) 6.05760 0.271994
\(497\) −15.3441 −0.688279
\(498\) 7.90079 0.354043
\(499\) −9.31527 −0.417009 −0.208504 0.978021i \(-0.566860\pi\)
−0.208504 + 0.978021i \(0.566860\pi\)
\(500\) −12.1586 −0.543751
\(501\) −9.42071 −0.420886
\(502\) 22.2828 0.994532
\(503\) −24.8290 −1.10707 −0.553534 0.832826i \(-0.686721\pi\)
−0.553534 + 0.832826i \(0.686721\pi\)
\(504\) 3.99413 0.177913
\(505\) 22.2027 0.988006
\(506\) −3.82434 −0.170013
\(507\) −1.00000 −0.0444116
\(508\) −17.6101 −0.781323
\(509\) −25.2050 −1.11719 −0.558595 0.829440i \(-0.688660\pi\)
−0.558595 + 0.829440i \(0.688660\pi\)
\(510\) 11.3927 0.504476
\(511\) −48.5146 −2.14616
\(512\) −1.00000 −0.0441942
\(513\) 4.99413 0.220496
\(514\) −21.2192 −0.935939
\(515\) 1.77686 0.0782978
\(516\) −11.3839 −0.501150
\(517\) 3.84413 0.169065
\(518\) 25.5404 1.12218
\(519\) 22.0526 0.968003
\(520\) −1.77686 −0.0779205
\(521\) −31.4155 −1.37634 −0.688169 0.725551i \(-0.741585\pi\)
−0.688169 + 0.725551i \(0.741585\pi\)
\(522\) −1.31057 −0.0573622
\(523\) −23.4078 −1.02355 −0.511775 0.859119i \(-0.671012\pi\)
−0.511775 + 0.859119i \(0.671012\pi\)
\(524\) −6.23844 −0.272527
\(525\) −7.36025 −0.321228
\(526\) 30.7091 1.33898
\(527\) 38.8394 1.69187
\(528\) 0.580058 0.0252438
\(529\) 20.4681 0.889917
\(530\) 23.3120 1.01261
\(531\) −10.2716 −0.445751
\(532\) 19.9472 0.864822
\(533\) 6.04948 0.262032
\(534\) −3.95413 −0.171112
\(535\) 26.3412 1.13883
\(536\) 2.66759 0.115222
\(537\) −4.54176 −0.195992
\(538\) 5.25791 0.226684
\(539\) −5.19331 −0.223692
\(540\) −1.77686 −0.0764639
\(541\) −19.2659 −0.828307 −0.414153 0.910207i \(-0.635922\pi\)
−0.414153 + 0.910207i \(0.635922\pi\)
\(542\) −8.79084 −0.377599
\(543\) −15.0371 −0.645306
\(544\) −6.41168 −0.274899
\(545\) 0.799460 0.0342451
\(546\) −3.99413 −0.170933
\(547\) −18.6484 −0.797350 −0.398675 0.917092i \(-0.630530\pi\)
−0.398675 + 0.917092i \(0.630530\pi\)
\(548\) −16.0387 −0.685140
\(549\) −12.6576 −0.540212
\(550\) −1.06891 −0.0455785
\(551\) −6.54517 −0.278834
\(552\) −6.59303 −0.280618
\(553\) −10.7621 −0.457650
\(554\) 22.0601 0.937246
\(555\) −11.3621 −0.482294
\(556\) 5.44497 0.230918
\(557\) −28.1898 −1.19444 −0.597219 0.802078i \(-0.703728\pi\)
−0.597219 + 0.802078i \(0.703728\pi\)
\(558\) −6.05760 −0.256439
\(559\) 11.3839 0.481490
\(560\) −7.09702 −0.299904
\(561\) 3.71915 0.157023
\(562\) 2.69154 0.113536
\(563\) −20.6201 −0.869036 −0.434518 0.900663i \(-0.643081\pi\)
−0.434518 + 0.900663i \(0.643081\pi\)
\(564\) 6.62715 0.279053
\(565\) 15.2846 0.643026
\(566\) −1.11537 −0.0468825
\(567\) −3.99413 −0.167738
\(568\) −3.84167 −0.161193
\(569\) −20.5789 −0.862711 −0.431356 0.902182i \(-0.641965\pi\)
−0.431356 + 0.902182i \(0.641965\pi\)
\(570\) −8.87388 −0.371686
\(571\) −12.2975 −0.514634 −0.257317 0.966327i \(-0.582839\pi\)
−0.257317 + 0.966327i \(0.582839\pi\)
\(572\) −0.580058 −0.0242534
\(573\) 14.4869 0.605199
\(574\) 24.1624 1.00852
\(575\) 12.1494 0.506666
\(576\) 1.00000 0.0416667
\(577\) −35.7752 −1.48934 −0.744670 0.667433i \(-0.767393\pi\)
−0.744670 + 0.667433i \(0.767393\pi\)
\(578\) −24.1097 −1.00283
\(579\) −4.70533 −0.195547
\(580\) 2.32870 0.0966942
\(581\) −31.5568 −1.30920
\(582\) 8.16221 0.338334
\(583\) 7.61023 0.315184
\(584\) −12.1465 −0.502624
\(585\) 1.77686 0.0734642
\(586\) −23.8587 −0.985593
\(587\) 11.6995 0.482891 0.241445 0.970414i \(-0.422379\pi\)
0.241445 + 0.970414i \(0.422379\pi\)
\(588\) −8.95309 −0.369219
\(589\) −30.2524 −1.24653
\(590\) 18.2513 0.751392
\(591\) −18.9174 −0.778157
\(592\) 6.39448 0.262811
\(593\) 13.9057 0.571037 0.285519 0.958373i \(-0.407834\pi\)
0.285519 + 0.958373i \(0.407834\pi\)
\(594\) −0.580058 −0.0238001
\(595\) −45.5038 −1.86547
\(596\) 7.66917 0.314142
\(597\) 17.0528 0.697925
\(598\) 6.59303 0.269609
\(599\) −7.48070 −0.305653 −0.152827 0.988253i \(-0.548838\pi\)
−0.152827 + 0.988253i \(0.548838\pi\)
\(600\) −1.84277 −0.0752306
\(601\) −42.2169 −1.72206 −0.861031 0.508552i \(-0.830181\pi\)
−0.861031 + 0.508552i \(0.830181\pi\)
\(602\) 45.4690 1.85318
\(603\) −2.66759 −0.108633
\(604\) −24.0732 −0.979524
\(605\) −18.9476 −0.770330
\(606\) 12.4955 0.507593
\(607\) −10.4445 −0.423930 −0.211965 0.977277i \(-0.567986\pi\)
−0.211965 + 0.977277i \(0.567986\pi\)
\(608\) 4.99413 0.202539
\(609\) 5.23460 0.212117
\(610\) 22.4907 0.910624
\(611\) −6.62715 −0.268106
\(612\) 6.41168 0.259177
\(613\) 13.2739 0.536128 0.268064 0.963401i \(-0.413616\pi\)
0.268064 + 0.963401i \(0.413616\pi\)
\(614\) −18.1999 −0.734490
\(615\) −10.7491 −0.433445
\(616\) −2.31683 −0.0933477
\(617\) −33.9656 −1.36741 −0.683703 0.729761i \(-0.739631\pi\)
−0.683703 + 0.729761i \(0.739631\pi\)
\(618\) 1.00000 0.0402259
\(619\) 32.9674 1.32507 0.662536 0.749030i \(-0.269480\pi\)
0.662536 + 0.749030i \(0.269480\pi\)
\(620\) 10.7635 0.432273
\(621\) 6.59303 0.264569
\(622\) −16.7588 −0.671967
\(623\) 15.7933 0.632746
\(624\) −1.00000 −0.0400320
\(625\) −12.3904 −0.495615
\(626\) −15.1054 −0.603734
\(627\) −2.89689 −0.115690
\(628\) −19.4944 −0.777909
\(629\) 40.9994 1.63475
\(630\) 7.09702 0.282752
\(631\) 15.2257 0.606124 0.303062 0.952971i \(-0.401991\pi\)
0.303062 + 0.952971i \(0.401991\pi\)
\(632\) −2.69447 −0.107180
\(633\) 7.46310 0.296632
\(634\) −26.7194 −1.06116
\(635\) −31.2908 −1.24174
\(636\) 13.1198 0.520233
\(637\) 8.95309 0.354734
\(638\) 0.760208 0.0300969
\(639\) 3.84167 0.151974
\(640\) −1.77686 −0.0702366
\(641\) 13.3374 0.526796 0.263398 0.964687i \(-0.415157\pi\)
0.263398 + 0.964687i \(0.415157\pi\)
\(642\) 14.8246 0.585079
\(643\) −22.2996 −0.879410 −0.439705 0.898142i \(-0.644917\pi\)
−0.439705 + 0.898142i \(0.644917\pi\)
\(644\) 26.3334 1.03768
\(645\) −20.2277 −0.796464
\(646\) 32.0208 1.25984
\(647\) −30.3519 −1.19326 −0.596629 0.802517i \(-0.703493\pi\)
−0.596629 + 0.802517i \(0.703493\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 5.95814 0.233877
\(650\) 1.84277 0.0722792
\(651\) 24.1948 0.948271
\(652\) 23.1065 0.904920
\(653\) 45.5866 1.78394 0.891972 0.452091i \(-0.149322\pi\)
0.891972 + 0.452091i \(0.149322\pi\)
\(654\) 0.449928 0.0175936
\(655\) −11.0848 −0.433120
\(656\) 6.04948 0.236193
\(657\) 12.1465 0.473879
\(658\) −26.4697 −1.03190
\(659\) 13.9845 0.544758 0.272379 0.962190i \(-0.412190\pi\)
0.272379 + 0.962190i \(0.412190\pi\)
\(660\) 1.03068 0.0401193
\(661\) 18.5805 0.722698 0.361349 0.932431i \(-0.382316\pi\)
0.361349 + 0.932431i \(0.382316\pi\)
\(662\) 30.1515 1.17187
\(663\) −6.41168 −0.249009
\(664\) −7.90079 −0.306610
\(665\) 35.4434 1.37444
\(666\) −6.39448 −0.247781
\(667\) −8.64065 −0.334567
\(668\) 9.42071 0.364498
\(669\) 14.0884 0.544688
\(670\) 4.73994 0.183120
\(671\) 7.34213 0.283440
\(672\) −3.99413 −0.154077
\(673\) −15.7021 −0.605272 −0.302636 0.953106i \(-0.597867\pi\)
−0.302636 + 0.953106i \(0.597867\pi\)
\(674\) 2.90829 0.112023
\(675\) 1.84277 0.0709281
\(676\) 1.00000 0.0384615
\(677\) −24.4464 −0.939553 −0.469777 0.882785i \(-0.655666\pi\)
−0.469777 + 0.882785i \(0.655666\pi\)
\(678\) 8.60200 0.330358
\(679\) −32.6009 −1.25111
\(680\) −11.3927 −0.436889
\(681\) −11.7368 −0.449756
\(682\) 3.51376 0.134549
\(683\) 41.5076 1.58824 0.794122 0.607759i \(-0.207931\pi\)
0.794122 + 0.607759i \(0.207931\pi\)
\(684\) −4.99413 −0.190955
\(685\) −28.4986 −1.08887
\(686\) 7.80090 0.297840
\(687\) 22.2214 0.847798
\(688\) 11.3839 0.434009
\(689\) −13.1198 −0.499824
\(690\) −11.7149 −0.445979
\(691\) −9.63399 −0.366494 −0.183247 0.983067i \(-0.558661\pi\)
−0.183247 + 0.983067i \(0.558661\pi\)
\(692\) −22.0526 −0.838315
\(693\) 2.31683 0.0880090
\(694\) 26.1265 0.991750
\(695\) 9.67495 0.366992
\(696\) 1.31057 0.0496771
\(697\) 38.7874 1.46918
\(698\) 19.4604 0.736587
\(699\) 2.45597 0.0928933
\(700\) 7.36025 0.278191
\(701\) 8.61709 0.325463 0.162732 0.986670i \(-0.447970\pi\)
0.162732 + 0.986670i \(0.447970\pi\)
\(702\) 1.00000 0.0377426
\(703\) −31.9349 −1.20445
\(704\) −0.580058 −0.0218618
\(705\) 11.7755 0.443492
\(706\) −14.8833 −0.560141
\(707\) −49.9085 −1.87700
\(708\) 10.2716 0.386032
\(709\) −41.2159 −1.54790 −0.773949 0.633248i \(-0.781721\pi\)
−0.773949 + 0.633248i \(0.781721\pi\)
\(710\) −6.82612 −0.256180
\(711\) 2.69447 0.101051
\(712\) 3.95413 0.148187
\(713\) −39.9380 −1.49569
\(714\) −25.6091 −0.958397
\(715\) −1.03068 −0.0385453
\(716\) 4.54176 0.169734
\(717\) −0.439459 −0.0164119
\(718\) 6.94723 0.259268
\(719\) 12.5409 0.467697 0.233849 0.972273i \(-0.424868\pi\)
0.233849 + 0.972273i \(0.424868\pi\)
\(720\) 1.77686 0.0662197
\(721\) −3.99413 −0.148749
\(722\) −5.94135 −0.221114
\(723\) 25.8545 0.961538
\(724\) 15.0371 0.558851
\(725\) −2.41508 −0.0896938
\(726\) −10.6635 −0.395761
\(727\) −15.0778 −0.559204 −0.279602 0.960116i \(-0.590202\pi\)
−0.279602 + 0.960116i \(0.590202\pi\)
\(728\) 3.99413 0.148032
\(729\) 1.00000 0.0370370
\(730\) −21.5826 −0.798807
\(731\) 72.9902 2.69964
\(732\) 12.6576 0.467837
\(733\) 22.3904 0.827007 0.413504 0.910503i \(-0.364305\pi\)
0.413504 + 0.910503i \(0.364305\pi\)
\(734\) 16.9537 0.625774
\(735\) −15.9084 −0.586790
\(736\) 6.59303 0.243022
\(737\) 1.54736 0.0569977
\(738\) −6.04948 −0.222685
\(739\) −51.4528 −1.89272 −0.946360 0.323113i \(-0.895271\pi\)
−0.946360 + 0.323113i \(0.895271\pi\)
\(740\) 11.3621 0.417679
\(741\) 4.99413 0.183464
\(742\) −52.4021 −1.92374
\(743\) 5.34412 0.196057 0.0980283 0.995184i \(-0.468746\pi\)
0.0980283 + 0.995184i \(0.468746\pi\)
\(744\) 6.05760 0.222082
\(745\) 13.6271 0.499257
\(746\) 13.4320 0.491781
\(747\) 7.90079 0.289075
\(748\) −3.71915 −0.135985
\(749\) −59.2113 −2.16353
\(750\) −12.1586 −0.443971
\(751\) 24.3927 0.890102 0.445051 0.895505i \(-0.353186\pi\)
0.445051 + 0.895505i \(0.353186\pi\)
\(752\) −6.62715 −0.241667
\(753\) 22.2828 0.812032
\(754\) −1.31057 −0.0477282
\(755\) −42.7747 −1.55673
\(756\) 3.99413 0.145265
\(757\) −24.3390 −0.884615 −0.442307 0.896864i \(-0.645840\pi\)
−0.442307 + 0.896864i \(0.645840\pi\)
\(758\) −22.2036 −0.806470
\(759\) −3.82434 −0.138815
\(760\) 8.87388 0.321889
\(761\) −22.6685 −0.821734 −0.410867 0.911695i \(-0.634774\pi\)
−0.410867 + 0.911695i \(0.634774\pi\)
\(762\) −17.6101 −0.637948
\(763\) −1.79707 −0.0650584
\(764\) −14.4869 −0.524117
\(765\) 11.3927 0.411903
\(766\) −32.3119 −1.16748
\(767\) −10.2716 −0.370887
\(768\) −1.00000 −0.0360844
\(769\) −39.2405 −1.41505 −0.707525 0.706688i \(-0.750188\pi\)
−0.707525 + 0.706688i \(0.750188\pi\)
\(770\) −4.11668 −0.148355
\(771\) −21.2192 −0.764191
\(772\) 4.70533 0.169348
\(773\) −36.1583 −1.30052 −0.650262 0.759710i \(-0.725341\pi\)
−0.650262 + 0.759710i \(0.725341\pi\)
\(774\) −11.3839 −0.409187
\(775\) −11.1627 −0.400977
\(776\) −8.16221 −0.293006
\(777\) 25.5404 0.916256
\(778\) −6.20757 −0.222552
\(779\) −30.2119 −1.08245
\(780\) −1.77686 −0.0636218
\(781\) −2.22839 −0.0797382
\(782\) 42.2724 1.51166
\(783\) −1.31057 −0.0468360
\(784\) 8.95309 0.319753
\(785\) −34.6387 −1.23631
\(786\) −6.23844 −0.222518
\(787\) −13.0837 −0.466383 −0.233192 0.972431i \(-0.574917\pi\)
−0.233192 + 0.972431i \(0.574917\pi\)
\(788\) 18.9174 0.673904
\(789\) 30.7091 1.09327
\(790\) −4.78770 −0.170339
\(791\) −34.3575 −1.22161
\(792\) 0.580058 0.0206115
\(793\) −12.6576 −0.449484
\(794\) 31.7721 1.12755
\(795\) 23.3120 0.826792
\(796\) −17.0528 −0.604421
\(797\) −18.0958 −0.640986 −0.320493 0.947251i \(-0.603849\pi\)
−0.320493 + 0.947251i \(0.603849\pi\)
\(798\) 19.9472 0.706124
\(799\) −42.4912 −1.50323
\(800\) 1.84277 0.0651516
\(801\) −3.95413 −0.139712
\(802\) 1.07631 0.0380058
\(803\) −7.04565 −0.248636
\(804\) 2.66759 0.0940787
\(805\) 46.7909 1.64916
\(806\) −6.05760 −0.213370
\(807\) 5.25791 0.185087
\(808\) −12.4955 −0.439589
\(809\) −25.8625 −0.909279 −0.454639 0.890676i \(-0.650232\pi\)
−0.454639 + 0.890676i \(0.650232\pi\)
\(810\) −1.77686 −0.0624325
\(811\) 29.4105 1.03274 0.516372 0.856365i \(-0.327282\pi\)
0.516372 + 0.856365i \(0.327282\pi\)
\(812\) −5.23460 −0.183698
\(813\) −8.79084 −0.308308
\(814\) 3.70917 0.130006
\(815\) 41.0570 1.43816
\(816\) −6.41168 −0.224454
\(817\) −56.8529 −1.98903
\(818\) 9.73909 0.340519
\(819\) −3.99413 −0.139566
\(820\) 10.7491 0.375374
\(821\) −36.3972 −1.27027 −0.635136 0.772401i \(-0.719056\pi\)
−0.635136 + 0.772401i \(0.719056\pi\)
\(822\) −16.0387 −0.559414
\(823\) 0.996537 0.0347371 0.0173686 0.999849i \(-0.494471\pi\)
0.0173686 + 0.999849i \(0.494471\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −1.06891 −0.0372147
\(826\) −41.0262 −1.42749
\(827\) −50.7933 −1.76626 −0.883129 0.469131i \(-0.844567\pi\)
−0.883129 + 0.469131i \(0.844567\pi\)
\(828\) −6.59303 −0.229124
\(829\) −4.46349 −0.155023 −0.0775116 0.996991i \(-0.524697\pi\)
−0.0775116 + 0.996991i \(0.524697\pi\)
\(830\) −14.0386 −0.487287
\(831\) 22.0601 0.765258
\(832\) 1.00000 0.0346688
\(833\) 57.4044 1.98894
\(834\) 5.44497 0.188544
\(835\) 16.7393 0.579287
\(836\) 2.89689 0.100191
\(837\) −6.05760 −0.209381
\(838\) −15.8585 −0.547824
\(839\) −34.3485 −1.18584 −0.592921 0.805261i \(-0.702025\pi\)
−0.592921 + 0.805261i \(0.702025\pi\)
\(840\) −7.09702 −0.244870
\(841\) −27.2824 −0.940772
\(842\) −7.52106 −0.259193
\(843\) 2.69154 0.0927017
\(844\) −7.46310 −0.256891
\(845\) 1.77686 0.0611259
\(846\) 6.62715 0.227846
\(847\) 42.5916 1.46346
\(848\) −13.1198 −0.450535
\(849\) −1.11537 −0.0382794
\(850\) 11.8152 0.405259
\(851\) −42.1590 −1.44519
\(852\) −3.84167 −0.131614
\(853\) −2.70374 −0.0925743 −0.0462872 0.998928i \(-0.514739\pi\)
−0.0462872 + 0.998928i \(0.514739\pi\)
\(854\) −50.5560 −1.72999
\(855\) −8.87388 −0.303480
\(856\) −14.8246 −0.506694
\(857\) −8.73255 −0.298298 −0.149149 0.988815i \(-0.547653\pi\)
−0.149149 + 0.988815i \(0.547653\pi\)
\(858\) −0.580058 −0.0198029
\(859\) −31.1071 −1.06136 −0.530681 0.847572i \(-0.678064\pi\)
−0.530681 + 0.847572i \(0.678064\pi\)
\(860\) 20.2277 0.689758
\(861\) 24.1624 0.823453
\(862\) 2.73677 0.0932149
\(863\) −21.0751 −0.717405 −0.358702 0.933452i \(-0.616781\pi\)
−0.358702 + 0.933452i \(0.616781\pi\)
\(864\) 1.00000 0.0340207
\(865\) −39.1844 −1.33231
\(866\) 12.6570 0.430104
\(867\) −24.1097 −0.818807
\(868\) −24.1948 −0.821227
\(869\) −1.56295 −0.0530194
\(870\) 2.32870 0.0789505
\(871\) −2.66759 −0.0903879
\(872\) −0.449928 −0.0152365
\(873\) 8.16221 0.276249
\(874\) −32.9265 −1.11375
\(875\) 48.5632 1.64174
\(876\) −12.1465 −0.410391
\(877\) 41.3978 1.39790 0.698952 0.715168i \(-0.253650\pi\)
0.698952 + 0.715168i \(0.253650\pi\)
\(878\) −26.3495 −0.889251
\(879\) −23.8587 −0.804733
\(880\) −1.03068 −0.0347443
\(881\) 45.4935 1.53272 0.766358 0.642414i \(-0.222067\pi\)
0.766358 + 0.642414i \(0.222067\pi\)
\(882\) −8.95309 −0.301466
\(883\) −3.89717 −0.131150 −0.0655751 0.997848i \(-0.520888\pi\)
−0.0655751 + 0.997848i \(0.520888\pi\)
\(884\) 6.41168 0.215648
\(885\) 18.2513 0.613509
\(886\) 1.36156 0.0457425
\(887\) 30.0627 1.00941 0.504703 0.863293i \(-0.331602\pi\)
0.504703 + 0.863293i \(0.331602\pi\)
\(888\) 6.39448 0.214585
\(889\) 70.3372 2.35903
\(890\) 7.02594 0.235510
\(891\) −0.580058 −0.0194327
\(892\) −14.0884 −0.471714
\(893\) 33.0968 1.10754
\(894\) 7.66917 0.256496
\(895\) 8.07008 0.269753
\(896\) 3.99413 0.133435
\(897\) 6.59303 0.220135
\(898\) 8.70559 0.290509
\(899\) 7.93892 0.264778
\(900\) −1.84277 −0.0614255
\(901\) −84.1199 −2.80244
\(902\) 3.50905 0.116839
\(903\) 45.4690 1.51311
\(904\) −8.60200 −0.286098
\(905\) 26.7189 0.888167
\(906\) −24.0732 −0.799778
\(907\) −18.6460 −0.619131 −0.309565 0.950878i \(-0.600184\pi\)
−0.309565 + 0.950878i \(0.600184\pi\)
\(908\) 11.7368 0.389500
\(909\) 12.4955 0.414448
\(910\) 7.09702 0.235264
\(911\) 9.08947 0.301148 0.150574 0.988599i \(-0.451888\pi\)
0.150574 + 0.988599i \(0.451888\pi\)
\(912\) 4.99413 0.165372
\(913\) −4.58292 −0.151672
\(914\) −35.5594 −1.17620
\(915\) 22.4907 0.743521
\(916\) −22.2214 −0.734215
\(917\) 24.9171 0.822836
\(918\) 6.41168 0.211617
\(919\) −38.1617 −1.25884 −0.629420 0.777066i \(-0.716707\pi\)
−0.629420 + 0.777066i \(0.716707\pi\)
\(920\) 11.7149 0.386229
\(921\) −18.1999 −0.599708
\(922\) 28.8532 0.950228
\(923\) 3.84167 0.126450
\(924\) −2.31683 −0.0762180
\(925\) −11.7835 −0.387440
\(926\) −28.1865 −0.926267
\(927\) 1.00000 0.0328443
\(928\) −1.31057 −0.0430217
\(929\) 30.0092 0.984569 0.492284 0.870434i \(-0.336162\pi\)
0.492284 + 0.870434i \(0.336162\pi\)
\(930\) 10.7635 0.352949
\(931\) −44.7129 −1.46541
\(932\) −2.45597 −0.0804480
\(933\) −16.7588 −0.548659
\(934\) 24.3804 0.797751
\(935\) −6.60841 −0.216118
\(936\) −1.00000 −0.0326860
\(937\) −8.65798 −0.282844 −0.141422 0.989949i \(-0.545167\pi\)
−0.141422 + 0.989949i \(0.545167\pi\)
\(938\) −10.6547 −0.347889
\(939\) −15.1054 −0.492947
\(940\) −11.7755 −0.384075
\(941\) −47.0434 −1.53357 −0.766786 0.641903i \(-0.778145\pi\)
−0.766786 + 0.641903i \(0.778145\pi\)
\(942\) −19.4944 −0.635160
\(943\) −39.8844 −1.29882
\(944\) −10.2716 −0.334313
\(945\) 7.09702 0.230866
\(946\) 6.60335 0.214693
\(947\) 37.1553 1.20739 0.603693 0.797217i \(-0.293695\pi\)
0.603693 + 0.797217i \(0.293695\pi\)
\(948\) −2.69447 −0.0875124
\(949\) 12.1465 0.394291
\(950\) −9.20301 −0.298585
\(951\) −26.7194 −0.866436
\(952\) 25.6091 0.829996
\(953\) −3.14924 −0.102014 −0.0510070 0.998698i \(-0.516243\pi\)
−0.0510070 + 0.998698i \(0.516243\pi\)
\(954\) 13.1198 0.424769
\(955\) −25.7412 −0.832965
\(956\) 0.439459 0.0142131
\(957\) 0.760208 0.0245740
\(958\) −3.35175 −0.108290
\(959\) 64.0607 2.06863
\(960\) −1.77686 −0.0573479
\(961\) 5.69450 0.183693
\(962\) −6.39448 −0.206166
\(963\) 14.8246 0.477715
\(964\) −25.8545 −0.832717
\(965\) 8.36071 0.269141
\(966\) 26.3334 0.847265
\(967\) 12.7204 0.409059 0.204529 0.978860i \(-0.434434\pi\)
0.204529 + 0.978860i \(0.434434\pi\)
\(968\) 10.6635 0.342739
\(969\) 32.0208 1.02866
\(970\) −14.5031 −0.465667
\(971\) 53.9868 1.73252 0.866259 0.499595i \(-0.166518\pi\)
0.866259 + 0.499595i \(0.166518\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −21.7479 −0.697206
\(974\) 27.2724 0.873864
\(975\) 1.84277 0.0590157
\(976\) −12.6576 −0.405159
\(977\) 41.5695 1.32993 0.664963 0.746877i \(-0.268447\pi\)
0.664963 + 0.746877i \(0.268447\pi\)
\(978\) 23.1065 0.738864
\(979\) 2.29363 0.0733046
\(980\) 15.9084 0.508175
\(981\) 0.449928 0.0143651
\(982\) 8.42210 0.268760
\(983\) −30.8874 −0.985156 −0.492578 0.870268i \(-0.663945\pi\)
−0.492578 + 0.870268i \(0.663945\pi\)
\(984\) 6.04948 0.192850
\(985\) 33.6136 1.07102
\(986\) −8.40297 −0.267605
\(987\) −26.4697 −0.842540
\(988\) −4.99413 −0.158885
\(989\) −75.0547 −2.38660
\(990\) 1.03068 0.0327572
\(991\) 30.8564 0.980185 0.490092 0.871670i \(-0.336963\pi\)
0.490092 + 0.871670i \(0.336963\pi\)
\(992\) −6.05760 −0.192329
\(993\) 30.1515 0.956829
\(994\) 15.3441 0.486687
\(995\) −30.3005 −0.960589
\(996\) −7.90079 −0.250346
\(997\) −18.2690 −0.578584 −0.289292 0.957241i \(-0.593420\pi\)
−0.289292 + 0.957241i \(0.593420\pi\)
\(998\) 9.31527 0.294870
\(999\) −6.39448 −0.202312
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 \(a_p\))