Properties

Label 8034.2.a.o.1.4
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 1.4
Root \(-1.86678\)
Character \(\chi\) = 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.72171 q^{5}\) \(+1.00000 q^{6}\) \(+2.39003 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.72171 q^{5}\) \(+1.00000 q^{6}\) \(+2.39003 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-1.72171 q^{10}\) \(-4.25377 q^{11}\) \(-1.00000 q^{12}\) \(+1.00000 q^{13}\) \(-2.39003 q^{14}\) \(-1.72171 q^{15}\) \(+1.00000 q^{16}\) \(+6.64067 q^{17}\) \(-1.00000 q^{18}\) \(+1.39003 q^{19}\) \(+1.72171 q^{20}\) \(-2.39003 q^{21}\) \(+4.25377 q^{22}\) \(+0.660198 q^{23}\) \(+1.00000 q^{24}\) \(-2.03571 q^{25}\) \(-1.00000 q^{26}\) \(-1.00000 q^{27}\) \(+2.39003 q^{28}\) \(-7.21542 q^{29}\) \(+1.72171 q^{30}\) \(-7.06840 q^{31}\) \(-1.00000 q^{32}\) \(+4.25377 q^{33}\) \(-6.64067 q^{34}\) \(+4.11494 q^{35}\) \(+1.00000 q^{36}\) \(+0.542704 q^{37}\) \(-1.39003 q^{38}\) \(-1.00000 q^{39}\) \(-1.72171 q^{40}\) \(+6.29089 q^{41}\) \(+2.39003 q^{42}\) \(-12.5305 q^{43}\) \(-4.25377 q^{44}\) \(+1.72171 q^{45}\) \(-0.660198 q^{46}\) \(-5.06122 q^{47}\) \(-1.00000 q^{48}\) \(-1.28777 q^{49}\) \(+2.03571 q^{50}\) \(-6.64067 q^{51}\) \(+1.00000 q^{52}\) \(+3.16708 q^{53}\) \(+1.00000 q^{54}\) \(-7.32377 q^{55}\) \(-2.39003 q^{56}\) \(-1.39003 q^{57}\) \(+7.21542 q^{58}\) \(+0.644743 q^{59}\) \(-1.72171 q^{60}\) \(+7.01661 q^{61}\) \(+7.06840 q^{62}\) \(+2.39003 q^{63}\) \(+1.00000 q^{64}\) \(+1.72171 q^{65}\) \(-4.25377 q^{66}\) \(-8.17546 q^{67}\) \(+6.64067 q^{68}\) \(-0.660198 q^{69}\) \(-4.11494 q^{70}\) \(+1.21505 q^{71}\) \(-1.00000 q^{72}\) \(-1.21748 q^{73}\) \(-0.542704 q^{74}\) \(+2.03571 q^{75}\) \(+1.39003 q^{76}\) \(-10.1666 q^{77}\) \(+1.00000 q^{78}\) \(-5.16356 q^{79}\) \(+1.72171 q^{80}\) \(+1.00000 q^{81}\) \(-6.29089 q^{82}\) \(-3.97674 q^{83}\) \(-2.39003 q^{84}\) \(+11.4333 q^{85}\) \(+12.5305 q^{86}\) \(+7.21542 q^{87}\) \(+4.25377 q^{88}\) \(-12.3981 q^{89}\) \(-1.72171 q^{90}\) \(+2.39003 q^{91}\) \(+0.660198 q^{92}\) \(+7.06840 q^{93}\) \(+5.06122 q^{94}\) \(+2.39323 q^{95}\) \(+1.00000 q^{96}\) \(-18.4985 q^{97}\) \(+1.28777 q^{98}\) \(-4.25377 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 7q^{36} \) \(\mathstrut +\mathstrut 17q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 7q^{72} \) \(\mathstrut +\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 22q^{86} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 9q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.72171 0.769972 0.384986 0.922922i \(-0.374206\pi\)
0.384986 + 0.922922i \(0.374206\pi\)
\(6\) 1.00000 0.408248
\(7\) 2.39003 0.903346 0.451673 0.892184i \(-0.350827\pi\)
0.451673 + 0.892184i \(0.350827\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.72171 −0.544453
\(11\) −4.25377 −1.28256 −0.641281 0.767306i \(-0.721597\pi\)
−0.641281 + 0.767306i \(0.721597\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) −2.39003 −0.638762
\(15\) −1.72171 −0.444544
\(16\) 1.00000 0.250000
\(17\) 6.64067 1.61060 0.805299 0.592869i \(-0.202005\pi\)
0.805299 + 0.592869i \(0.202005\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.39003 0.318894 0.159447 0.987206i \(-0.449029\pi\)
0.159447 + 0.987206i \(0.449029\pi\)
\(20\) 1.72171 0.384986
\(21\) −2.39003 −0.521547
\(22\) 4.25377 0.906908
\(23\) 0.660198 0.137661 0.0688304 0.997628i \(-0.478073\pi\)
0.0688304 + 0.997628i \(0.478073\pi\)
\(24\) 1.00000 0.204124
\(25\) −2.03571 −0.407143
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) 2.39003 0.451673
\(29\) −7.21542 −1.33987 −0.669935 0.742420i \(-0.733678\pi\)
−0.669935 + 0.742420i \(0.733678\pi\)
\(30\) 1.72171 0.314340
\(31\) −7.06840 −1.26952 −0.634761 0.772708i \(-0.718902\pi\)
−0.634761 + 0.772708i \(0.718902\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.25377 0.740487
\(34\) −6.64067 −1.13887
\(35\) 4.11494 0.695551
\(36\) 1.00000 0.166667
\(37\) 0.542704 0.0892199 0.0446100 0.999004i \(-0.485795\pi\)
0.0446100 + 0.999004i \(0.485795\pi\)
\(38\) −1.39003 −0.225492
\(39\) −1.00000 −0.160128
\(40\) −1.72171 −0.272226
\(41\) 6.29089 0.982472 0.491236 0.871027i \(-0.336545\pi\)
0.491236 + 0.871027i \(0.336545\pi\)
\(42\) 2.39003 0.368789
\(43\) −12.5305 −1.91088 −0.955441 0.295182i \(-0.904620\pi\)
−0.955441 + 0.295182i \(0.904620\pi\)
\(44\) −4.25377 −0.641281
\(45\) 1.72171 0.256657
\(46\) −0.660198 −0.0973408
\(47\) −5.06122 −0.738254 −0.369127 0.929379i \(-0.620343\pi\)
−0.369127 + 0.929379i \(0.620343\pi\)
\(48\) −1.00000 −0.144338
\(49\) −1.28777 −0.183967
\(50\) 2.03571 0.287893
\(51\) −6.64067 −0.929879
\(52\) 1.00000 0.138675
\(53\) 3.16708 0.435032 0.217516 0.976057i \(-0.430205\pi\)
0.217516 + 0.976057i \(0.430205\pi\)
\(54\) 1.00000 0.136083
\(55\) −7.32377 −0.987536
\(56\) −2.39003 −0.319381
\(57\) −1.39003 −0.184114
\(58\) 7.21542 0.947431
\(59\) 0.644743 0.0839384 0.0419692 0.999119i \(-0.486637\pi\)
0.0419692 + 0.999119i \(0.486637\pi\)
\(60\) −1.72171 −0.222272
\(61\) 7.01661 0.898384 0.449192 0.893435i \(-0.351712\pi\)
0.449192 + 0.893435i \(0.351712\pi\)
\(62\) 7.06840 0.897688
\(63\) 2.39003 0.301115
\(64\) 1.00000 0.125000
\(65\) 1.72171 0.213552
\(66\) −4.25377 −0.523603
\(67\) −8.17546 −0.998792 −0.499396 0.866374i \(-0.666445\pi\)
−0.499396 + 0.866374i \(0.666445\pi\)
\(68\) 6.64067 0.805299
\(69\) −0.660198 −0.0794784
\(70\) −4.11494 −0.491829
\(71\) 1.21505 0.144200 0.0720998 0.997397i \(-0.477030\pi\)
0.0720998 + 0.997397i \(0.477030\pi\)
\(72\) −1.00000 −0.117851
\(73\) −1.21748 −0.142495 −0.0712475 0.997459i \(-0.522698\pi\)
−0.0712475 + 0.997459i \(0.522698\pi\)
\(74\) −0.542704 −0.0630880
\(75\) 2.03571 0.235064
\(76\) 1.39003 0.159447
\(77\) −10.1666 −1.15860
\(78\) 1.00000 0.113228
\(79\) −5.16356 −0.580946 −0.290473 0.956883i \(-0.593813\pi\)
−0.290473 + 0.956883i \(0.593813\pi\)
\(80\) 1.72171 0.192493
\(81\) 1.00000 0.111111
\(82\) −6.29089 −0.694713
\(83\) −3.97674 −0.436504 −0.218252 0.975892i \(-0.570035\pi\)
−0.218252 + 0.975892i \(0.570035\pi\)
\(84\) −2.39003 −0.260773
\(85\) 11.4333 1.24012
\(86\) 12.5305 1.35120
\(87\) 7.21542 0.773574
\(88\) 4.25377 0.453454
\(89\) −12.3981 −1.31420 −0.657099 0.753804i \(-0.728217\pi\)
−0.657099 + 0.753804i \(0.728217\pi\)
\(90\) −1.72171 −0.181484
\(91\) 2.39003 0.250543
\(92\) 0.660198 0.0688304
\(93\) 7.06840 0.732959
\(94\) 5.06122 0.522025
\(95\) 2.39323 0.245540
\(96\) 1.00000 0.102062
\(97\) −18.4985 −1.87824 −0.939120 0.343589i \(-0.888357\pi\)
−0.939120 + 0.343589i \(0.888357\pi\)
\(98\) 1.28777 0.130084
\(99\) −4.25377 −0.427520
\(100\) −2.03571 −0.203571
\(101\) 18.3579 1.82668 0.913338 0.407201i \(-0.133495\pi\)
0.913338 + 0.407201i \(0.133495\pi\)
\(102\) 6.64067 0.657524
\(103\) 1.00000 0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −4.11494 −0.401577
\(106\) −3.16708 −0.307614
\(107\) −14.1501 −1.36794 −0.683971 0.729509i \(-0.739749\pi\)
−0.683971 + 0.729509i \(0.739749\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 1.16806 0.111880 0.0559400 0.998434i \(-0.482184\pi\)
0.0559400 + 0.998434i \(0.482184\pi\)
\(110\) 7.32377 0.698294
\(111\) −0.542704 −0.0515112
\(112\) 2.39003 0.225836
\(113\) −6.56362 −0.617453 −0.308726 0.951151i \(-0.599903\pi\)
−0.308726 + 0.951151i \(0.599903\pi\)
\(114\) 1.39003 0.130188
\(115\) 1.13667 0.105995
\(116\) −7.21542 −0.669935
\(117\) 1.00000 0.0924500
\(118\) −0.644743 −0.0593534
\(119\) 15.8714 1.45493
\(120\) 1.72171 0.157170
\(121\) 7.09460 0.644963
\(122\) −7.01661 −0.635254
\(123\) −6.29089 −0.567230
\(124\) −7.06840 −0.634761
\(125\) −12.1135 −1.08346
\(126\) −2.39003 −0.212921
\(127\) −18.3701 −1.63008 −0.815042 0.579402i \(-0.803286\pi\)
−0.815042 + 0.579402i \(0.803286\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 12.5305 1.10325
\(130\) −1.72171 −0.151004
\(131\) 19.5981 1.71230 0.856149 0.516730i \(-0.172851\pi\)
0.856149 + 0.516730i \(0.172851\pi\)
\(132\) 4.25377 0.370244
\(133\) 3.32221 0.288072
\(134\) 8.17546 0.706253
\(135\) −1.72171 −0.148181
\(136\) −6.64067 −0.569433
\(137\) 9.23862 0.789308 0.394654 0.918830i \(-0.370864\pi\)
0.394654 + 0.918830i \(0.370864\pi\)
\(138\) 0.660198 0.0561997
\(139\) −16.8128 −1.42604 −0.713020 0.701144i \(-0.752673\pi\)
−0.713020 + 0.701144i \(0.752673\pi\)
\(140\) 4.11494 0.347776
\(141\) 5.06122 0.426231
\(142\) −1.21505 −0.101965
\(143\) −4.25377 −0.355718
\(144\) 1.00000 0.0833333
\(145\) −12.4229 −1.03166
\(146\) 1.21748 0.100759
\(147\) 1.28777 0.106213
\(148\) 0.542704 0.0446100
\(149\) 3.72254 0.304962 0.152481 0.988306i \(-0.451274\pi\)
0.152481 + 0.988306i \(0.451274\pi\)
\(150\) −2.03571 −0.166215
\(151\) −15.0853 −1.22762 −0.613812 0.789452i \(-0.710365\pi\)
−0.613812 + 0.789452i \(0.710365\pi\)
\(152\) −1.39003 −0.112746
\(153\) 6.64067 0.536866
\(154\) 10.1666 0.819251
\(155\) −12.1697 −0.977497
\(156\) −1.00000 −0.0800641
\(157\) −22.4610 −1.79258 −0.896292 0.443464i \(-0.853749\pi\)
−0.896292 + 0.443464i \(0.853749\pi\)
\(158\) 5.16356 0.410791
\(159\) −3.16708 −0.251166
\(160\) −1.72171 −0.136113
\(161\) 1.57789 0.124355
\(162\) −1.00000 −0.0785674
\(163\) 15.9747 1.25123 0.625616 0.780131i \(-0.284848\pi\)
0.625616 + 0.780131i \(0.284848\pi\)
\(164\) 6.29089 0.491236
\(165\) 7.32377 0.570154
\(166\) 3.97674 0.308655
\(167\) 12.6294 0.977291 0.488645 0.872482i \(-0.337491\pi\)
0.488645 + 0.872482i \(0.337491\pi\)
\(168\) 2.39003 0.184395
\(169\) 1.00000 0.0769231
\(170\) −11.4333 −0.876894
\(171\) 1.39003 0.106298
\(172\) −12.5305 −0.955441
\(173\) −0.502612 −0.0382129 −0.0191064 0.999817i \(-0.506082\pi\)
−0.0191064 + 0.999817i \(0.506082\pi\)
\(174\) −7.21542 −0.546999
\(175\) −4.86541 −0.367791
\(176\) −4.25377 −0.320640
\(177\) −0.644743 −0.0484619
\(178\) 12.3981 0.929278
\(179\) 2.79727 0.209078 0.104539 0.994521i \(-0.466663\pi\)
0.104539 + 0.994521i \(0.466663\pi\)
\(180\) 1.72171 0.128329
\(181\) −21.0300 −1.56315 −0.781574 0.623813i \(-0.785583\pi\)
−0.781574 + 0.623813i \(0.785583\pi\)
\(182\) −2.39003 −0.177161
\(183\) −7.01661 −0.518682
\(184\) −0.660198 −0.0486704
\(185\) 0.934379 0.0686969
\(186\) −7.06840 −0.518281
\(187\) −28.2479 −2.06569
\(188\) −5.06122 −0.369127
\(189\) −2.39003 −0.173849
\(190\) −2.39323 −0.173623
\(191\) −14.3576 −1.03888 −0.519441 0.854506i \(-0.673860\pi\)
−0.519441 + 0.854506i \(0.673860\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 8.89416 0.640216 0.320108 0.947381i \(-0.396281\pi\)
0.320108 + 0.947381i \(0.396281\pi\)
\(194\) 18.4985 1.32812
\(195\) −1.72171 −0.123294
\(196\) −1.28777 −0.0919833
\(197\) 18.5418 1.32105 0.660525 0.750804i \(-0.270334\pi\)
0.660525 + 0.750804i \(0.270334\pi\)
\(198\) 4.25377 0.302303
\(199\) 8.13646 0.576779 0.288389 0.957513i \(-0.406880\pi\)
0.288389 + 0.957513i \(0.406880\pi\)
\(200\) 2.03571 0.143947
\(201\) 8.17546 0.576653
\(202\) −18.3579 −1.29166
\(203\) −17.2451 −1.21037
\(204\) −6.64067 −0.464940
\(205\) 10.8311 0.756476
\(206\) −1.00000 −0.0696733
\(207\) 0.660198 0.0458869
\(208\) 1.00000 0.0693375
\(209\) −5.91287 −0.409001
\(210\) 4.11494 0.283958
\(211\) 15.3277 1.05520 0.527602 0.849491i \(-0.323091\pi\)
0.527602 + 0.849491i \(0.323091\pi\)
\(212\) 3.16708 0.217516
\(213\) −1.21505 −0.0832537
\(214\) 14.1501 0.967281
\(215\) −21.5739 −1.47133
\(216\) 1.00000 0.0680414
\(217\) −16.8937 −1.14682
\(218\) −1.16806 −0.0791112
\(219\) 1.21748 0.0822696
\(220\) −7.32377 −0.493768
\(221\) 6.64067 0.446700
\(222\) 0.542704 0.0364239
\(223\) 15.4713 1.03604 0.518018 0.855370i \(-0.326670\pi\)
0.518018 + 0.855370i \(0.326670\pi\)
\(224\) −2.39003 −0.159690
\(225\) −2.03571 −0.135714
\(226\) 6.56362 0.436605
\(227\) 12.8564 0.853312 0.426656 0.904414i \(-0.359692\pi\)
0.426656 + 0.904414i \(0.359692\pi\)
\(228\) −1.39003 −0.0920569
\(229\) 18.6495 1.23239 0.616196 0.787593i \(-0.288673\pi\)
0.616196 + 0.787593i \(0.288673\pi\)
\(230\) −1.13667 −0.0749497
\(231\) 10.1666 0.668916
\(232\) 7.21542 0.473715
\(233\) −24.7604 −1.62210 −0.811052 0.584974i \(-0.801105\pi\)
−0.811052 + 0.584974i \(0.801105\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −8.71395 −0.568435
\(236\) 0.644743 0.0419692
\(237\) 5.16356 0.335409
\(238\) −15.8714 −1.02879
\(239\) 6.41094 0.414689 0.207345 0.978268i \(-0.433518\pi\)
0.207345 + 0.978268i \(0.433518\pi\)
\(240\) −1.72171 −0.111136
\(241\) −9.82599 −0.632948 −0.316474 0.948601i \(-0.602499\pi\)
−0.316474 + 0.948601i \(0.602499\pi\)
\(242\) −7.09460 −0.456058
\(243\) −1.00000 −0.0641500
\(244\) 7.01661 0.449192
\(245\) −2.21716 −0.141649
\(246\) 6.29089 0.401093
\(247\) 1.39003 0.0884454
\(248\) 7.06840 0.448844
\(249\) 3.97674 0.252016
\(250\) 12.1135 0.766123
\(251\) 0.529566 0.0334259 0.0167130 0.999860i \(-0.494680\pi\)
0.0167130 + 0.999860i \(0.494680\pi\)
\(252\) 2.39003 0.150558
\(253\) −2.80833 −0.176558
\(254\) 18.3701 1.15264
\(255\) −11.4333 −0.715981
\(256\) 1.00000 0.0625000
\(257\) −16.9954 −1.06014 −0.530071 0.847953i \(-0.677835\pi\)
−0.530071 + 0.847953i \(0.677835\pi\)
\(258\) −12.5305 −0.780114
\(259\) 1.29708 0.0805965
\(260\) 1.72171 0.106776
\(261\) −7.21542 −0.446623
\(262\) −19.5981 −1.21078
\(263\) −20.0780 −1.23806 −0.619030 0.785367i \(-0.712474\pi\)
−0.619030 + 0.785367i \(0.712474\pi\)
\(264\) −4.25377 −0.261802
\(265\) 5.45280 0.334963
\(266\) −3.32221 −0.203698
\(267\) 12.3981 0.758752
\(268\) −8.17546 −0.499396
\(269\) 9.40162 0.573227 0.286613 0.958046i \(-0.407470\pi\)
0.286613 + 0.958046i \(0.407470\pi\)
\(270\) 1.72171 0.104780
\(271\) −19.3124 −1.17315 −0.586573 0.809896i \(-0.699523\pi\)
−0.586573 + 0.809896i \(0.699523\pi\)
\(272\) 6.64067 0.402650
\(273\) −2.39003 −0.144651
\(274\) −9.23862 −0.558125
\(275\) 8.65947 0.522186
\(276\) −0.660198 −0.0397392
\(277\) 30.6289 1.84031 0.920155 0.391555i \(-0.128063\pi\)
0.920155 + 0.391555i \(0.128063\pi\)
\(278\) 16.8128 1.00836
\(279\) −7.06840 −0.423174
\(280\) −4.11494 −0.245914
\(281\) −18.9263 −1.12905 −0.564524 0.825416i \(-0.690940\pi\)
−0.564524 + 0.825416i \(0.690940\pi\)
\(282\) −5.06122 −0.301391
\(283\) 28.5045 1.69442 0.847208 0.531262i \(-0.178282\pi\)
0.847208 + 0.531262i \(0.178282\pi\)
\(284\) 1.21505 0.0720998
\(285\) −2.39323 −0.141762
\(286\) 4.25377 0.251531
\(287\) 15.0354 0.887512
\(288\) −1.00000 −0.0589256
\(289\) 27.0985 1.59403
\(290\) 12.4229 0.729495
\(291\) 18.4985 1.08440
\(292\) −1.21748 −0.0712475
\(293\) 1.45581 0.0850493 0.0425247 0.999095i \(-0.486460\pi\)
0.0425247 + 0.999095i \(0.486460\pi\)
\(294\) −1.28777 −0.0751040
\(295\) 1.11006 0.0646302
\(296\) −0.542704 −0.0315440
\(297\) 4.25377 0.246829
\(298\) −3.72254 −0.215641
\(299\) 0.660198 0.0381802
\(300\) 2.03571 0.117532
\(301\) −29.9482 −1.72619
\(302\) 15.0853 0.868061
\(303\) −18.3579 −1.05463
\(304\) 1.39003 0.0797236
\(305\) 12.0806 0.691731
\(306\) −6.64067 −0.379622
\(307\) −11.7328 −0.669626 −0.334813 0.942285i \(-0.608673\pi\)
−0.334813 + 0.942285i \(0.608673\pi\)
\(308\) −10.1666 −0.579298
\(309\) −1.00000 −0.0568880
\(310\) 12.1697 0.691195
\(311\) −18.1845 −1.03115 −0.515574 0.856845i \(-0.672421\pi\)
−0.515574 + 0.856845i \(0.672421\pi\)
\(312\) 1.00000 0.0566139
\(313\) −4.10088 −0.231796 −0.115898 0.993261i \(-0.536975\pi\)
−0.115898 + 0.993261i \(0.536975\pi\)
\(314\) 22.4610 1.26755
\(315\) 4.11494 0.231850
\(316\) −5.16356 −0.290473
\(317\) 5.55377 0.311931 0.155965 0.987763i \(-0.450151\pi\)
0.155965 + 0.987763i \(0.450151\pi\)
\(318\) 3.16708 0.177601
\(319\) 30.6928 1.71846
\(320\) 1.72171 0.0962465
\(321\) 14.1501 0.789782
\(322\) −1.57789 −0.0879324
\(323\) 9.23071 0.513611
\(324\) 1.00000 0.0555556
\(325\) −2.03571 −0.112921
\(326\) −15.9747 −0.884755
\(327\) −1.16806 −0.0645940
\(328\) −6.29089 −0.347356
\(329\) −12.0965 −0.666899
\(330\) −7.32377 −0.403160
\(331\) 20.6613 1.13565 0.567825 0.823149i \(-0.307785\pi\)
0.567825 + 0.823149i \(0.307785\pi\)
\(332\) −3.97674 −0.218252
\(333\) 0.542704 0.0297400
\(334\) −12.6294 −0.691049
\(335\) −14.0758 −0.769042
\(336\) −2.39003 −0.130387
\(337\) 34.9396 1.90328 0.951640 0.307216i \(-0.0993976\pi\)
0.951640 + 0.307216i \(0.0993976\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 6.56362 0.356487
\(340\) 11.4333 0.620058
\(341\) 30.0674 1.62824
\(342\) −1.39003 −0.0751641
\(343\) −19.8080 −1.06953
\(344\) 12.5305 0.675599
\(345\) −1.13667 −0.0611962
\(346\) 0.502612 0.0270206
\(347\) 30.1347 1.61771 0.808857 0.588005i \(-0.200086\pi\)
0.808857 + 0.588005i \(0.200086\pi\)
\(348\) 7.21542 0.386787
\(349\) −1.84054 −0.0985216 −0.0492608 0.998786i \(-0.515687\pi\)
−0.0492608 + 0.998786i \(0.515687\pi\)
\(350\) 4.86541 0.260067
\(351\) −1.00000 −0.0533761
\(352\) 4.25377 0.226727
\(353\) −4.55407 −0.242389 −0.121194 0.992629i \(-0.538672\pi\)
−0.121194 + 0.992629i \(0.538672\pi\)
\(354\) 0.644743 0.0342677
\(355\) 2.09196 0.111030
\(356\) −12.3981 −0.657099
\(357\) −15.8714 −0.840003
\(358\) −2.79727 −0.147841
\(359\) 0.674029 0.0355739 0.0177869 0.999842i \(-0.494338\pi\)
0.0177869 + 0.999842i \(0.494338\pi\)
\(360\) −1.72171 −0.0907421
\(361\) −17.0678 −0.898306
\(362\) 21.0300 1.10531
\(363\) −7.09460 −0.372370
\(364\) 2.39003 0.125272
\(365\) −2.09615 −0.109717
\(366\) 7.01661 0.366764
\(367\) 19.6521 1.02583 0.512916 0.858439i \(-0.328565\pi\)
0.512916 + 0.858439i \(0.328565\pi\)
\(368\) 0.660198 0.0344152
\(369\) 6.29089 0.327491
\(370\) −0.934379 −0.0485760
\(371\) 7.56942 0.392985
\(372\) 7.06840 0.366480
\(373\) −25.0095 −1.29494 −0.647472 0.762090i \(-0.724174\pi\)
−0.647472 + 0.762090i \(0.724174\pi\)
\(374\) 28.2479 1.46066
\(375\) 12.1135 0.625536
\(376\) 5.06122 0.261012
\(377\) −7.21542 −0.371613
\(378\) 2.39003 0.122930
\(379\) −15.4257 −0.792363 −0.396181 0.918172i \(-0.629665\pi\)
−0.396181 + 0.918172i \(0.629665\pi\)
\(380\) 2.39323 0.122770
\(381\) 18.3701 0.941129
\(382\) 14.3576 0.734600
\(383\) −22.4939 −1.14938 −0.574692 0.818370i \(-0.694878\pi\)
−0.574692 + 0.818370i \(0.694878\pi\)
\(384\) 1.00000 0.0510310
\(385\) −17.5040 −0.892087
\(386\) −8.89416 −0.452701
\(387\) −12.5305 −0.636961
\(388\) −18.4985 −0.939120
\(389\) 13.6967 0.694451 0.347226 0.937782i \(-0.387124\pi\)
0.347226 + 0.937782i \(0.387124\pi\)
\(390\) 1.72171 0.0871822
\(391\) 4.38415 0.221716
\(392\) 1.28777 0.0650420
\(393\) −19.5981 −0.988595
\(394\) −18.5418 −0.934124
\(395\) −8.89016 −0.447312
\(396\) −4.25377 −0.213760
\(397\) −26.2443 −1.31716 −0.658582 0.752509i \(-0.728843\pi\)
−0.658582 + 0.752509i \(0.728843\pi\)
\(398\) −8.13646 −0.407844
\(399\) −3.32221 −0.166318
\(400\) −2.03571 −0.101786
\(401\) 11.9508 0.596796 0.298398 0.954441i \(-0.403548\pi\)
0.298398 + 0.954441i \(0.403548\pi\)
\(402\) −8.17546 −0.407755
\(403\) −7.06840 −0.352102
\(404\) 18.3579 0.913338
\(405\) 1.72171 0.0855525
\(406\) 17.2451 0.855858
\(407\) −2.30854 −0.114430
\(408\) 6.64067 0.328762
\(409\) 6.19764 0.306454 0.153227 0.988191i \(-0.451033\pi\)
0.153227 + 0.988191i \(0.451033\pi\)
\(410\) −10.8311 −0.534909
\(411\) −9.23862 −0.455707
\(412\) 1.00000 0.0492665
\(413\) 1.54095 0.0758254
\(414\) −0.660198 −0.0324469
\(415\) −6.84679 −0.336096
\(416\) −1.00000 −0.0490290
\(417\) 16.8128 0.823325
\(418\) 5.91287 0.289208
\(419\) 14.6735 0.716850 0.358425 0.933559i \(-0.383314\pi\)
0.358425 + 0.933559i \(0.383314\pi\)
\(420\) −4.11494 −0.200788
\(421\) 34.3333 1.67330 0.836650 0.547738i \(-0.184511\pi\)
0.836650 + 0.547738i \(0.184511\pi\)
\(422\) −15.3277 −0.746142
\(423\) −5.06122 −0.246085
\(424\) −3.16708 −0.153807
\(425\) −13.5185 −0.655744
\(426\) 1.21505 0.0588692
\(427\) 16.7699 0.811552
\(428\) −14.1501 −0.683971
\(429\) 4.25377 0.205374
\(430\) 21.5739 1.04038
\(431\) −7.64446 −0.368221 −0.184110 0.982906i \(-0.558940\pi\)
−0.184110 + 0.982906i \(0.558940\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −12.6684 −0.608807 −0.304403 0.952543i \(-0.598457\pi\)
−0.304403 + 0.952543i \(0.598457\pi\)
\(434\) 16.8937 0.810923
\(435\) 12.4229 0.595630
\(436\) 1.16806 0.0559400
\(437\) 0.917693 0.0438992
\(438\) −1.21748 −0.0581734
\(439\) 31.1964 1.48892 0.744461 0.667666i \(-0.232706\pi\)
0.744461 + 0.667666i \(0.232706\pi\)
\(440\) 7.32377 0.349147
\(441\) −1.28777 −0.0613222
\(442\) −6.64067 −0.315864
\(443\) −5.89484 −0.280072 −0.140036 0.990146i \(-0.544722\pi\)
−0.140036 + 0.990146i \(0.544722\pi\)
\(444\) −0.542704 −0.0257556
\(445\) −21.3460 −1.01190
\(446\) −15.4713 −0.732588
\(447\) −3.72254 −0.176070
\(448\) 2.39003 0.112918
\(449\) 21.1771 0.999411 0.499706 0.866195i \(-0.333441\pi\)
0.499706 + 0.866195i \(0.333441\pi\)
\(450\) 2.03571 0.0959645
\(451\) −26.7600 −1.26008
\(452\) −6.56362 −0.308726
\(453\) 15.0853 0.708769
\(454\) −12.8564 −0.603382
\(455\) 4.11494 0.192911
\(456\) 1.39003 0.0650940
\(457\) 17.4405 0.815833 0.407916 0.913019i \(-0.366255\pi\)
0.407916 + 0.913019i \(0.366255\pi\)
\(458\) −18.6495 −0.871432
\(459\) −6.64067 −0.309960
\(460\) 1.13667 0.0529975
\(461\) 17.9659 0.836754 0.418377 0.908274i \(-0.362599\pi\)
0.418377 + 0.908274i \(0.362599\pi\)
\(462\) −10.1666 −0.472995
\(463\) 6.96127 0.323518 0.161759 0.986830i \(-0.448283\pi\)
0.161759 + 0.986830i \(0.448283\pi\)
\(464\) −7.21542 −0.334967
\(465\) 12.1697 0.564358
\(466\) 24.7604 1.14700
\(467\) −19.2176 −0.889285 −0.444642 0.895708i \(-0.646669\pi\)
−0.444642 + 0.895708i \(0.646669\pi\)
\(468\) 1.00000 0.0462250
\(469\) −19.5396 −0.902254
\(470\) 8.71395 0.401944
\(471\) 22.4610 1.03495
\(472\) −0.644743 −0.0296767
\(473\) 53.3019 2.45082
\(474\) −5.16356 −0.237170
\(475\) −2.82970 −0.129836
\(476\) 15.8714 0.727464
\(477\) 3.16708 0.145011
\(478\) −6.41094 −0.293229
\(479\) 8.05490 0.368038 0.184019 0.982923i \(-0.441089\pi\)
0.184019 + 0.982923i \(0.441089\pi\)
\(480\) 1.72171 0.0785850
\(481\) 0.542704 0.0247452
\(482\) 9.82599 0.447562
\(483\) −1.57789 −0.0717965
\(484\) 7.09460 0.322482
\(485\) −31.8491 −1.44619
\(486\) 1.00000 0.0453609
\(487\) −37.2525 −1.68807 −0.844036 0.536286i \(-0.819827\pi\)
−0.844036 + 0.536286i \(0.819827\pi\)
\(488\) −7.01661 −0.317627
\(489\) −15.9747 −0.722399
\(490\) 2.21716 0.100161
\(491\) −33.0779 −1.49279 −0.746393 0.665505i \(-0.768216\pi\)
−0.746393 + 0.665505i \(0.768216\pi\)
\(492\) −6.29089 −0.283615
\(493\) −47.9152 −2.15799
\(494\) −1.39003 −0.0625403
\(495\) −7.32377 −0.329179
\(496\) −7.06840 −0.317381
\(497\) 2.90400 0.130262
\(498\) −3.97674 −0.178202
\(499\) 20.3427 0.910666 0.455333 0.890321i \(-0.349520\pi\)
0.455333 + 0.890321i \(0.349520\pi\)
\(500\) −12.1135 −0.541730
\(501\) −12.6294 −0.564239
\(502\) −0.529566 −0.0236357
\(503\) 10.9249 0.487119 0.243559 0.969886i \(-0.421685\pi\)
0.243559 + 0.969886i \(0.421685\pi\)
\(504\) −2.39003 −0.106460
\(505\) 31.6069 1.40649
\(506\) 2.80833 0.124846
\(507\) −1.00000 −0.0444116
\(508\) −18.3701 −0.815042
\(509\) −5.17386 −0.229327 −0.114664 0.993404i \(-0.536579\pi\)
−0.114664 + 0.993404i \(0.536579\pi\)
\(510\) 11.4333 0.506275
\(511\) −2.90981 −0.128722
\(512\) −1.00000 −0.0441942
\(513\) −1.39003 −0.0613712
\(514\) 16.9954 0.749633
\(515\) 1.72171 0.0758676
\(516\) 12.5305 0.551624
\(517\) 21.5293 0.946856
\(518\) −1.29708 −0.0569903
\(519\) 0.502612 0.0220622
\(520\) −1.72171 −0.0755020
\(521\) −24.0410 −1.05326 −0.526629 0.850095i \(-0.676544\pi\)
−0.526629 + 0.850095i \(0.676544\pi\)
\(522\) 7.21542 0.315810
\(523\) −36.8960 −1.61335 −0.806676 0.590994i \(-0.798736\pi\)
−0.806676 + 0.590994i \(0.798736\pi\)
\(524\) 19.5981 0.856149
\(525\) 4.86541 0.212344
\(526\) 20.0780 0.875441
\(527\) −46.9389 −2.04469
\(528\) 4.25377 0.185122
\(529\) −22.5641 −0.981050
\(530\) −5.45280 −0.236854
\(531\) 0.644743 0.0279795
\(532\) 3.32221 0.144036
\(533\) 6.29089 0.272489
\(534\) −12.3981 −0.536519
\(535\) −24.3624 −1.05328
\(536\) 8.17546 0.353126
\(537\) −2.79727 −0.120711
\(538\) −9.40162 −0.405333
\(539\) 5.47787 0.235948
\(540\) −1.72171 −0.0740906
\(541\) 0.662284 0.0284738 0.0142369 0.999899i \(-0.495468\pi\)
0.0142369 + 0.999899i \(0.495468\pi\)
\(542\) 19.3124 0.829540
\(543\) 21.0300 0.902484
\(544\) −6.64067 −0.284716
\(545\) 2.01106 0.0861446
\(546\) 2.39003 0.102284
\(547\) 7.57319 0.323806 0.161903 0.986807i \(-0.448237\pi\)
0.161903 + 0.986807i \(0.448237\pi\)
\(548\) 9.23862 0.394654
\(549\) 7.01661 0.299461
\(550\) −8.65947 −0.369241
\(551\) −10.0296 −0.427277
\(552\) 0.660198 0.0280999
\(553\) −12.3411 −0.524795
\(554\) −30.6289 −1.30130
\(555\) −0.934379 −0.0396622
\(556\) −16.8128 −0.713020
\(557\) 17.0626 0.722965 0.361483 0.932379i \(-0.382271\pi\)
0.361483 + 0.932379i \(0.382271\pi\)
\(558\) 7.06840 0.299229
\(559\) −12.5305 −0.529983
\(560\) 4.11494 0.173888
\(561\) 28.2479 1.19263
\(562\) 18.9263 0.798358
\(563\) 30.7787 1.29717 0.648583 0.761144i \(-0.275362\pi\)
0.648583 + 0.761144i \(0.275362\pi\)
\(564\) 5.06122 0.213116
\(565\) −11.3006 −0.475422
\(566\) −28.5045 −1.19813
\(567\) 2.39003 0.100372
\(568\) −1.21505 −0.0509823
\(569\) 12.0641 0.505753 0.252876 0.967499i \(-0.418623\pi\)
0.252876 + 0.967499i \(0.418623\pi\)
\(570\) 2.39323 0.100241
\(571\) −8.17714 −0.342203 −0.171101 0.985253i \(-0.554733\pi\)
−0.171101 + 0.985253i \(0.554733\pi\)
\(572\) −4.25377 −0.177859
\(573\) 14.3576 0.599799
\(574\) −15.0354 −0.627566
\(575\) −1.34397 −0.0560476
\(576\) 1.00000 0.0416667
\(577\) 0.163804 0.00681926 0.00340963 0.999994i \(-0.498915\pi\)
0.00340963 + 0.999994i \(0.498915\pi\)
\(578\) −27.0985 −1.12715
\(579\) −8.89416 −0.369629
\(580\) −12.4229 −0.515831
\(581\) −9.50452 −0.394314
\(582\) −18.4985 −0.766788
\(583\) −13.4721 −0.557955
\(584\) 1.21748 0.0503796
\(585\) 1.72171 0.0711840
\(586\) −1.45581 −0.0601390
\(587\) −3.42990 −0.141567 −0.0707835 0.997492i \(-0.522550\pi\)
−0.0707835 + 0.997492i \(0.522550\pi\)
\(588\) 1.28777 0.0531066
\(589\) −9.82528 −0.404844
\(590\) −1.11006 −0.0457005
\(591\) −18.5418 −0.762709
\(592\) 0.542704 0.0223050
\(593\) 5.84030 0.239832 0.119916 0.992784i \(-0.461737\pi\)
0.119916 + 0.992784i \(0.461737\pi\)
\(594\) −4.25377 −0.174534
\(595\) 27.3259 1.12025
\(596\) 3.72254 0.152481
\(597\) −8.13646 −0.333003
\(598\) −0.660198 −0.0269975
\(599\) −45.4221 −1.85590 −0.927948 0.372709i \(-0.878429\pi\)
−0.927948 + 0.372709i \(0.878429\pi\)
\(600\) −2.03571 −0.0831077
\(601\) −38.8873 −1.58625 −0.793123 0.609062i \(-0.791546\pi\)
−0.793123 + 0.609062i \(0.791546\pi\)
\(602\) 29.9482 1.22060
\(603\) −8.17546 −0.332931
\(604\) −15.0853 −0.613812
\(605\) 12.2148 0.496604
\(606\) 18.3579 0.745738
\(607\) −20.0091 −0.812143 −0.406072 0.913841i \(-0.633102\pi\)
−0.406072 + 0.913841i \(0.633102\pi\)
\(608\) −1.39003 −0.0563731
\(609\) 17.2451 0.698805
\(610\) −12.0806 −0.489128
\(611\) −5.06122 −0.204755
\(612\) 6.64067 0.268433
\(613\) −43.4642 −1.75550 −0.877751 0.479117i \(-0.840957\pi\)
−0.877751 + 0.479117i \(0.840957\pi\)
\(614\) 11.7328 0.473497
\(615\) −10.8311 −0.436752
\(616\) 10.1666 0.409626
\(617\) −38.4997 −1.54994 −0.774969 0.631999i \(-0.782235\pi\)
−0.774969 + 0.631999i \(0.782235\pi\)
\(618\) 1.00000 0.0402259
\(619\) −26.8467 −1.07906 −0.539530 0.841966i \(-0.681398\pi\)
−0.539530 + 0.841966i \(0.681398\pi\)
\(620\) −12.1697 −0.488749
\(621\) −0.660198 −0.0264928
\(622\) 18.1845 0.729131
\(623\) −29.6318 −1.18717
\(624\) −1.00000 −0.0400320
\(625\) −10.6773 −0.427092
\(626\) 4.10088 0.163904
\(627\) 5.91287 0.236137
\(628\) −22.4610 −0.896292
\(629\) 3.60391 0.143697
\(630\) −4.11494 −0.163943
\(631\) −41.5903 −1.65568 −0.827841 0.560963i \(-0.810431\pi\)
−0.827841 + 0.560963i \(0.810431\pi\)
\(632\) 5.16356 0.205395
\(633\) −15.3277 −0.609223
\(634\) −5.55377 −0.220568
\(635\) −31.6280 −1.25512
\(636\) −3.16708 −0.125583
\(637\) −1.28777 −0.0510232
\(638\) −30.6928 −1.21514
\(639\) 1.21505 0.0480665
\(640\) −1.72171 −0.0680566
\(641\) −7.32445 −0.289298 −0.144649 0.989483i \(-0.546205\pi\)
−0.144649 + 0.989483i \(0.546205\pi\)
\(642\) −14.1501 −0.558460
\(643\) −28.6820 −1.13111 −0.565554 0.824711i \(-0.691338\pi\)
−0.565554 + 0.824711i \(0.691338\pi\)
\(644\) 1.57789 0.0621776
\(645\) 21.5739 0.849471
\(646\) −9.23071 −0.363178
\(647\) −47.4197 −1.86426 −0.932130 0.362124i \(-0.882052\pi\)
−0.932130 + 0.362124i \(0.882052\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −2.74259 −0.107656
\(650\) 2.03571 0.0798473
\(651\) 16.8937 0.662116
\(652\) 15.9747 0.625616
\(653\) 30.5387 1.19507 0.597536 0.801842i \(-0.296147\pi\)
0.597536 + 0.801842i \(0.296147\pi\)
\(654\) 1.16806 0.0456749
\(655\) 33.7423 1.31842
\(656\) 6.29089 0.245618
\(657\) −1.21748 −0.0474984
\(658\) 12.0965 0.471569
\(659\) −14.5640 −0.567334 −0.283667 0.958923i \(-0.591551\pi\)
−0.283667 + 0.958923i \(0.591551\pi\)
\(660\) 7.32377 0.285077
\(661\) −42.6428 −1.65861 −0.829307 0.558793i \(-0.811265\pi\)
−0.829307 + 0.558793i \(0.811265\pi\)
\(662\) −20.6613 −0.803026
\(663\) −6.64067 −0.257902
\(664\) 3.97674 0.154327
\(665\) 5.71988 0.221807
\(666\) −0.542704 −0.0210293
\(667\) −4.76360 −0.184447
\(668\) 12.6294 0.488645
\(669\) −15.4713 −0.598155
\(670\) 14.0758 0.543795
\(671\) −29.8471 −1.15223
\(672\) 2.39003 0.0921973
\(673\) −13.8465 −0.533742 −0.266871 0.963732i \(-0.585990\pi\)
−0.266871 + 0.963732i \(0.585990\pi\)
\(674\) −34.9396 −1.34582
\(675\) 2.03571 0.0783547
\(676\) 1.00000 0.0384615
\(677\) −36.1681 −1.39005 −0.695027 0.718984i \(-0.744607\pi\)
−0.695027 + 0.718984i \(0.744607\pi\)
\(678\) −6.56362 −0.252074
\(679\) −44.2120 −1.69670
\(680\) −11.4333 −0.438447
\(681\) −12.8564 −0.492660
\(682\) −30.0674 −1.15134
\(683\) −9.23341 −0.353307 −0.176653 0.984273i \(-0.556527\pi\)
−0.176653 + 0.984273i \(0.556527\pi\)
\(684\) 1.39003 0.0531490
\(685\) 15.9062 0.607746
\(686\) 19.8080 0.756273
\(687\) −18.6495 −0.711522
\(688\) −12.5305 −0.477721
\(689\) 3.16708 0.120656
\(690\) 1.13667 0.0432722
\(691\) 1.26275 0.0480373 0.0240186 0.999712i \(-0.492354\pi\)
0.0240186 + 0.999712i \(0.492354\pi\)
\(692\) −0.502612 −0.0191064
\(693\) −10.1666 −0.386199
\(694\) −30.1347 −1.14390
\(695\) −28.9467 −1.09801
\(696\) −7.21542 −0.273500
\(697\) 41.7757 1.58237
\(698\) 1.84054 0.0696653
\(699\) 24.7604 0.936523
\(700\) −4.86541 −0.183895
\(701\) 48.9768 1.84983 0.924913 0.380178i \(-0.124137\pi\)
0.924913 + 0.380178i \(0.124137\pi\)
\(702\) 1.00000 0.0377426
\(703\) 0.754373 0.0284517
\(704\) −4.25377 −0.160320
\(705\) 8.71395 0.328186
\(706\) 4.55407 0.171395
\(707\) 43.8758 1.65012
\(708\) −0.644743 −0.0242309
\(709\) −38.6968 −1.45329 −0.726644 0.687014i \(-0.758921\pi\)
−0.726644 + 0.687014i \(0.758921\pi\)
\(710\) −2.09196 −0.0785099
\(711\) −5.16356 −0.193649
\(712\) 12.3981 0.464639
\(713\) −4.66654 −0.174763
\(714\) 15.8714 0.593971
\(715\) −7.32377 −0.273893
\(716\) 2.79727 0.104539
\(717\) −6.41094 −0.239421
\(718\) −0.674029 −0.0251545
\(719\) −6.34028 −0.236452 −0.118226 0.992987i \(-0.537721\pi\)
−0.118226 + 0.992987i \(0.537721\pi\)
\(720\) 1.72171 0.0641643
\(721\) 2.39003 0.0890093
\(722\) 17.0678 0.635199
\(723\) 9.82599 0.365432
\(724\) −21.0300 −0.781574
\(725\) 14.6885 0.545518
\(726\) 7.09460 0.263305
\(727\) 7.41722 0.275089 0.137545 0.990496i \(-0.456079\pi\)
0.137545 + 0.990496i \(0.456079\pi\)
\(728\) −2.39003 −0.0885803
\(729\) 1.00000 0.0370370
\(730\) 2.09615 0.0775818
\(731\) −83.2108 −3.07766
\(732\) −7.01661 −0.259341
\(733\) −2.41675 −0.0892648 −0.0446324 0.999003i \(-0.514212\pi\)
−0.0446324 + 0.999003i \(0.514212\pi\)
\(734\) −19.6521 −0.725373
\(735\) 2.21716 0.0817812
\(736\) −0.660198 −0.0243352
\(737\) 34.7766 1.28101
\(738\) −6.29089 −0.231571
\(739\) 18.7670 0.690356 0.345178 0.938537i \(-0.387818\pi\)
0.345178 + 0.938537i \(0.387818\pi\)
\(740\) 0.934379 0.0343484
\(741\) −1.39003 −0.0510640
\(742\) −7.56942 −0.277882
\(743\) 42.8482 1.57195 0.785973 0.618261i \(-0.212162\pi\)
0.785973 + 0.618261i \(0.212162\pi\)
\(744\) −7.06840 −0.259140
\(745\) 6.40913 0.234812
\(746\) 25.0095 0.915663
\(747\) −3.97674 −0.145501
\(748\) −28.2479 −1.03285
\(749\) −33.8191 −1.23572
\(750\) −12.1135 −0.442321
\(751\) −27.4564 −1.00190 −0.500949 0.865477i \(-0.667016\pi\)
−0.500949 + 0.865477i \(0.667016\pi\)
\(752\) −5.06122 −0.184564
\(753\) −0.529566 −0.0192985
\(754\) 7.21542 0.262770
\(755\) −25.9725 −0.945236
\(756\) −2.39003 −0.0869245
\(757\) −12.1256 −0.440713 −0.220357 0.975419i \(-0.570722\pi\)
−0.220357 + 0.975419i \(0.570722\pi\)
\(758\) 15.4257 0.560285
\(759\) 2.80833 0.101936
\(760\) −2.39323 −0.0868114
\(761\) −46.8246 −1.69739 −0.848696 0.528881i \(-0.822612\pi\)
−0.848696 + 0.528881i \(0.822612\pi\)
\(762\) −18.3701 −0.665479
\(763\) 2.79170 0.101066
\(764\) −14.3576 −0.519441
\(765\) 11.4333 0.413372
\(766\) 22.4939 0.812737
\(767\) 0.644743 0.0232803
\(768\) −1.00000 −0.0360844
\(769\) −2.71689 −0.0979736 −0.0489868 0.998799i \(-0.515599\pi\)
−0.0489868 + 0.998799i \(0.515599\pi\)
\(770\) 17.5040 0.630801
\(771\) 16.9954 0.612073
\(772\) 8.89416 0.320108
\(773\) 44.9781 1.61775 0.808875 0.587981i \(-0.200077\pi\)
0.808875 + 0.587981i \(0.200077\pi\)
\(774\) 12.5305 0.450399
\(775\) 14.3892 0.516877
\(776\) 18.4985 0.664058
\(777\) −1.29708 −0.0465324
\(778\) −13.6967 −0.491051
\(779\) 8.74451 0.313305
\(780\) −1.72171 −0.0616471
\(781\) −5.16854 −0.184945
\(782\) −4.38415 −0.156777
\(783\) 7.21542 0.257858
\(784\) −1.28777 −0.0459916
\(785\) −38.6714 −1.38024
\(786\) 19.5981 0.699042
\(787\) 17.0228 0.606797 0.303399 0.952864i \(-0.401879\pi\)
0.303399 + 0.952864i \(0.401879\pi\)
\(788\) 18.5418 0.660525
\(789\) 20.0780 0.714794
\(790\) 8.89016 0.316298
\(791\) −15.6872 −0.557773
\(792\) 4.25377 0.151151
\(793\) 7.01661 0.249167
\(794\) 26.2443 0.931376
\(795\) −5.45280 −0.193391
\(796\) 8.13646 0.288389
\(797\) 29.5539 1.04685 0.523427 0.852071i \(-0.324653\pi\)
0.523427 + 0.852071i \(0.324653\pi\)
\(798\) 3.32221 0.117605
\(799\) −33.6099 −1.18903
\(800\) 2.03571 0.0719734
\(801\) −12.3981 −0.438066
\(802\) −11.9508 −0.421999
\(803\) 5.17888 0.182759
\(804\) 8.17546 0.288326
\(805\) 2.71667 0.0957500
\(806\) 7.06840 0.248974
\(807\) −9.40162 −0.330953
\(808\) −18.3579 −0.645828
\(809\) 42.2616 1.48584 0.742920 0.669380i \(-0.233440\pi\)
0.742920 + 0.669380i \(0.233440\pi\)
\(810\) −1.72171 −0.0604947
\(811\) −36.5413 −1.28314 −0.641570 0.767065i \(-0.721717\pi\)
−0.641570 + 0.767065i \(0.721717\pi\)
\(812\) −17.2451 −0.605183
\(813\) 19.3124 0.677317
\(814\) 2.30854 0.0809143
\(815\) 27.5037 0.963414
\(816\) −6.64067 −0.232470
\(817\) −17.4177 −0.609369
\(818\) −6.19764 −0.216696
\(819\) 2.39003 0.0835143
\(820\) 10.8311 0.378238
\(821\) 27.6549 0.965162 0.482581 0.875851i \(-0.339699\pi\)
0.482581 + 0.875851i \(0.339699\pi\)
\(822\) 9.23862 0.322234
\(823\) 1.46514 0.0510716 0.0255358 0.999674i \(-0.491871\pi\)
0.0255358 + 0.999674i \(0.491871\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −8.65947 −0.301484
\(826\) −1.54095 −0.0536167
\(827\) 26.9118 0.935814 0.467907 0.883778i \(-0.345008\pi\)
0.467907 + 0.883778i \(0.345008\pi\)
\(828\) 0.660198 0.0229435
\(829\) 4.73394 0.164416 0.0822082 0.996615i \(-0.473803\pi\)
0.0822082 + 0.996615i \(0.473803\pi\)
\(830\) 6.84679 0.237656
\(831\) −30.6289 −1.06250
\(832\) 1.00000 0.0346688
\(833\) −8.55163 −0.296296
\(834\) −16.8128 −0.582178
\(835\) 21.7441 0.752487
\(836\) −5.91287 −0.204501
\(837\) 7.06840 0.244320
\(838\) −14.6735 −0.506889
\(839\) 24.6854 0.852236 0.426118 0.904668i \(-0.359881\pi\)
0.426118 + 0.904668i \(0.359881\pi\)
\(840\) 4.11494 0.141979
\(841\) 23.0623 0.795250
\(842\) −34.3333 −1.18320
\(843\) 18.9263 0.651857
\(844\) 15.3277 0.527602
\(845\) 1.72171 0.0592286
\(846\) 5.06122 0.174008
\(847\) 16.9563 0.582625
\(848\) 3.16708 0.108758
\(849\) −28.5045 −0.978271
\(850\) 13.5185 0.463681
\(851\) 0.358292 0.0122821
\(852\) −1.21505 −0.0416268
\(853\) 28.3671 0.971271 0.485635 0.874161i \(-0.338588\pi\)
0.485635 + 0.874161i \(0.338588\pi\)
\(854\) −16.7699 −0.573854
\(855\) 2.39323 0.0818466
\(856\) 14.1501 0.483641
\(857\) 25.3169 0.864807 0.432404 0.901680i \(-0.357666\pi\)
0.432404 + 0.901680i \(0.357666\pi\)
\(858\) −4.25377 −0.145221
\(859\) 54.4404 1.85748 0.928741 0.370729i \(-0.120892\pi\)
0.928741 + 0.370729i \(0.120892\pi\)
\(860\) −21.5739 −0.735663
\(861\) −15.0354 −0.512405
\(862\) 7.64446 0.260371
\(863\) −38.2577 −1.30231 −0.651153 0.758947i \(-0.725714\pi\)
−0.651153 + 0.758947i \(0.725714\pi\)
\(864\) 1.00000 0.0340207
\(865\) −0.865352 −0.0294228
\(866\) 12.6684 0.430491
\(867\) −27.0985 −0.920312
\(868\) −16.8937 −0.573409
\(869\) 21.9646 0.745099
\(870\) −12.4229 −0.421174
\(871\) −8.17546 −0.277015
\(872\) −1.16806 −0.0395556
\(873\) −18.4985 −0.626080
\(874\) −0.917693 −0.0310414
\(875\) −28.9515 −0.978740
\(876\) 1.21748 0.0411348
\(877\) −11.5755 −0.390875 −0.195438 0.980716i \(-0.562613\pi\)
−0.195438 + 0.980716i \(0.562613\pi\)
\(878\) −31.1964 −1.05283
\(879\) −1.45581 −0.0491033
\(880\) −7.32377 −0.246884
\(881\) −50.0849 −1.68740 −0.843701 0.536813i \(-0.819628\pi\)
−0.843701 + 0.536813i \(0.819628\pi\)
\(882\) 1.28777 0.0433613
\(883\) −9.54160 −0.321100 −0.160550 0.987028i \(-0.551327\pi\)
−0.160550 + 0.987028i \(0.551327\pi\)
\(884\) 6.64067 0.223350
\(885\) −1.11006 −0.0373143
\(886\) 5.89484 0.198041
\(887\) 14.7887 0.496557 0.248278 0.968689i \(-0.420135\pi\)
0.248278 + 0.968689i \(0.420135\pi\)
\(888\) 0.542704 0.0182119
\(889\) −43.9051 −1.47253
\(890\) 21.3460 0.715518
\(891\) −4.25377 −0.142507
\(892\) 15.4713 0.518018
\(893\) −7.03523 −0.235425
\(894\) 3.72254 0.124500
\(895\) 4.81609 0.160984
\(896\) −2.39003 −0.0798452
\(897\) −0.660198 −0.0220434
\(898\) −21.1771 −0.706691
\(899\) 51.0015 1.70099
\(900\) −2.03571 −0.0678571
\(901\) 21.0315 0.700662
\(902\) 26.7600 0.891011
\(903\) 29.9482 0.996615
\(904\) 6.56362 0.218303
\(905\) −36.2076 −1.20358
\(906\) −15.0853 −0.501175
\(907\) 19.9866 0.663644 0.331822 0.943342i \(-0.392337\pi\)
0.331822 + 0.943342i \(0.392337\pi\)
\(908\) 12.8564 0.426656
\(909\) 18.3579 0.608892
\(910\) −4.11494 −0.136409
\(911\) −22.1720 −0.734590 −0.367295 0.930104i \(-0.619716\pi\)
−0.367295 + 0.930104i \(0.619716\pi\)
\(912\) −1.39003 −0.0460284
\(913\) 16.9162 0.559843
\(914\) −17.4405 −0.576881
\(915\) −12.0806 −0.399371
\(916\) 18.6495 0.616196
\(917\) 46.8401 1.54680
\(918\) 6.64067 0.219175
\(919\) 19.1791 0.632659 0.316329 0.948649i \(-0.397550\pi\)
0.316329 + 0.948649i \(0.397550\pi\)
\(920\) −1.13667 −0.0374749
\(921\) 11.7328 0.386609
\(922\) −17.9659 −0.591674
\(923\) 1.21505 0.0399938
\(924\) 10.1666 0.334458
\(925\) −1.10479 −0.0363253
\(926\) −6.96127 −0.228762
\(927\) 1.00000 0.0328443
\(928\) 7.21542 0.236858
\(929\) −21.8824 −0.717938 −0.358969 0.933350i \(-0.616872\pi\)
−0.358969 + 0.933350i \(0.616872\pi\)
\(930\) −12.1697 −0.399062
\(931\) −1.79003 −0.0586659
\(932\) −24.7604 −0.811052
\(933\) 18.1845 0.595333
\(934\) 19.2176 0.628819
\(935\) −48.6347 −1.59052
\(936\) −1.00000 −0.0326860
\(937\) 18.7388 0.612170 0.306085 0.952004i \(-0.400981\pi\)
0.306085 + 0.952004i \(0.400981\pi\)
\(938\) 19.5396 0.637990
\(939\) 4.10088 0.133827
\(940\) −8.71395 −0.284218
\(941\) −28.1297 −0.917003 −0.458502 0.888694i \(-0.651614\pi\)
−0.458502 + 0.888694i \(0.651614\pi\)
\(942\) −22.4610 −0.731819
\(943\) 4.15323 0.135248
\(944\) 0.644743 0.0209846
\(945\) −4.11494 −0.133859
\(946\) −53.3019 −1.73299
\(947\) −26.4796 −0.860472 −0.430236 0.902716i \(-0.641570\pi\)
−0.430236 + 0.902716i \(0.641570\pi\)
\(948\) 5.16356 0.167705
\(949\) −1.21748 −0.0395210
\(950\) 2.82970 0.0918076
\(951\) −5.55377 −0.180093
\(952\) −15.8714 −0.514394
\(953\) 44.9734 1.45683 0.728415 0.685136i \(-0.240257\pi\)
0.728415 + 0.685136i \(0.240257\pi\)
\(954\) −3.16708 −0.102538
\(955\) −24.7197 −0.799910
\(956\) 6.41094 0.207345
\(957\) −30.6928 −0.992156
\(958\) −8.05490 −0.260242
\(959\) 22.0806 0.713018
\(960\) −1.72171 −0.0555680
\(961\) 18.9623 0.611688
\(962\) −0.542704 −0.0174975
\(963\) −14.1501 −0.455981
\(964\) −9.82599 −0.316474
\(965\) 15.3132 0.492948
\(966\) 1.57789 0.0507678
\(967\) −2.34236 −0.0753253 −0.0376626 0.999291i \(-0.511991\pi\)
−0.0376626 + 0.999291i \(0.511991\pi\)
\(968\) −7.09460 −0.228029
\(969\) −9.23071 −0.296533
\(970\) 31.8491 1.02261
\(971\) 37.9469 1.21777 0.608887 0.793257i \(-0.291616\pi\)
0.608887 + 0.793257i \(0.291616\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −40.1830 −1.28821
\(974\) 37.2525 1.19365
\(975\) 2.03571 0.0651950
\(976\) 7.01661 0.224596
\(977\) −1.93752 −0.0619867 −0.0309933 0.999520i \(-0.509867\pi\)
−0.0309933 + 0.999520i \(0.509867\pi\)
\(978\) 15.9747 0.510814
\(979\) 52.7388 1.68554
\(980\) −2.21716 −0.0708246
\(981\) 1.16806 0.0372934
\(982\) 33.0779 1.05556
\(983\) −16.3449 −0.521320 −0.260660 0.965431i \(-0.583940\pi\)
−0.260660 + 0.965431i \(0.583940\pi\)
\(984\) 6.29089 0.200546
\(985\) 31.9237 1.01717
\(986\) 47.9152 1.52593
\(987\) 12.0965 0.385034
\(988\) 1.39003 0.0442227
\(989\) −8.27260 −0.263053
\(990\) 7.32377 0.232765
\(991\) 5.85837 0.186097 0.0930486 0.995662i \(-0.470339\pi\)
0.0930486 + 0.995662i \(0.470339\pi\)
\(992\) 7.06840 0.224422
\(993\) −20.6613 −0.655668
\(994\) −2.90400 −0.0921092
\(995\) 14.0086 0.444104
\(996\) 3.97674 0.126008
\(997\) −37.3175 −1.18186 −0.590929 0.806724i \(-0.701239\pi\)
−0.590929 + 0.806724i \(0.701239\pi\)
\(998\) −20.3427 −0.643938
\(999\) −0.542704 −0.0171704
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 \(a_p\))