Properties

Label 8023.2.a.c.1.6
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.73131 q^{2}\) \(-2.15430 q^{3}\) \(+5.46003 q^{4}\) \(-2.36711 q^{5}\) \(+5.88407 q^{6}\) \(-3.03890 q^{7}\) \(-9.45041 q^{8}\) \(+1.64103 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.73131 q^{2}\) \(-2.15430 q^{3}\) \(+5.46003 q^{4}\) \(-2.36711 q^{5}\) \(+5.88407 q^{6}\) \(-3.03890 q^{7}\) \(-9.45041 q^{8}\) \(+1.64103 q^{9}\) \(+6.46530 q^{10}\) \(-1.23686 q^{11}\) \(-11.7626 q^{12}\) \(+0.935944 q^{13}\) \(+8.30017 q^{14}\) \(+5.09947 q^{15}\) \(+14.8919 q^{16}\) \(+3.71828 q^{17}\) \(-4.48215 q^{18}\) \(+6.12994 q^{19}\) \(-12.9245 q^{20}\) \(+6.54672 q^{21}\) \(+3.37824 q^{22}\) \(-3.46566 q^{23}\) \(+20.3591 q^{24}\) \(+0.603200 q^{25}\) \(-2.55635 q^{26}\) \(+2.92764 q^{27}\) \(-16.5925 q^{28}\) \(-5.46018 q^{29}\) \(-13.9282 q^{30}\) \(+4.47779 q^{31}\) \(-21.7735 q^{32}\) \(+2.66457 q^{33}\) \(-10.1558 q^{34}\) \(+7.19341 q^{35}\) \(+8.96007 q^{36}\) \(-1.25753 q^{37}\) \(-16.7427 q^{38}\) \(-2.01631 q^{39}\) \(+22.3701 q^{40}\) \(-5.00276 q^{41}\) \(-17.8811 q^{42}\) \(-8.04498 q^{43}\) \(-6.75330 q^{44}\) \(-3.88449 q^{45}\) \(+9.46578 q^{46}\) \(-11.1410 q^{47}\) \(-32.0817 q^{48}\) \(+2.23492 q^{49}\) \(-1.64752 q^{50}\) \(-8.01031 q^{51}\) \(+5.11029 q^{52}\) \(+1.52281 q^{53}\) \(-7.99628 q^{54}\) \(+2.92778 q^{55}\) \(+28.7189 q^{56}\) \(-13.2058 q^{57}\) \(+14.9134 q^{58}\) \(-2.78143 q^{59}\) \(+27.8433 q^{60}\) \(-10.6917 q^{61}\) \(-12.2302 q^{62}\) \(-4.98692 q^{63}\) \(+29.6864 q^{64}\) \(-2.21548 q^{65}\) \(-7.27777 q^{66}\) \(-5.50665 q^{67}\) \(+20.3019 q^{68}\) \(+7.46609 q^{69}\) \(-19.6474 q^{70}\) \(-1.00000 q^{71}\) \(-15.5084 q^{72}\) \(-7.75902 q^{73}\) \(+3.43469 q^{74}\) \(-1.29948 q^{75}\) \(+33.4697 q^{76}\) \(+3.75869 q^{77}\) \(+5.50716 q^{78}\) \(+12.1551 q^{79}\) \(-35.2508 q^{80}\) \(-11.2301 q^{81}\) \(+13.6641 q^{82}\) \(-1.58835 q^{83}\) \(+35.7453 q^{84}\) \(-8.80157 q^{85}\) \(+21.9733 q^{86}\) \(+11.7629 q^{87}\) \(+11.6888 q^{88}\) \(+16.4018 q^{89}\) \(+10.6097 q^{90}\) \(-2.84424 q^{91}\) \(-18.9226 q^{92}\) \(-9.64653 q^{93}\) \(+30.4296 q^{94}\) \(-14.5102 q^{95}\) \(+46.9068 q^{96}\) \(+8.08872 q^{97}\) \(-6.10424 q^{98}\) \(-2.02972 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73131 −1.93133 −0.965663 0.259799i \(-0.916344\pi\)
−0.965663 + 0.259799i \(0.916344\pi\)
\(3\) −2.15430 −1.24379 −0.621894 0.783101i \(-0.713637\pi\)
−0.621894 + 0.783101i \(0.713637\pi\)
\(4\) 5.46003 2.73002
\(5\) −2.36711 −1.05860 −0.529301 0.848434i \(-0.677546\pi\)
−0.529301 + 0.848434i \(0.677546\pi\)
\(6\) 5.88407 2.40216
\(7\) −3.03890 −1.14860 −0.574298 0.818646i \(-0.694725\pi\)
−0.574298 + 0.818646i \(0.694725\pi\)
\(8\) −9.45041 −3.34123
\(9\) 1.64103 0.547010
\(10\) 6.46530 2.04451
\(11\) −1.23686 −0.372927 −0.186464 0.982462i \(-0.559703\pi\)
−0.186464 + 0.982462i \(0.559703\pi\)
\(12\) −11.7626 −3.39556
\(13\) 0.935944 0.259584 0.129792 0.991541i \(-0.458569\pi\)
0.129792 + 0.991541i \(0.458569\pi\)
\(14\) 8.30017 2.21831
\(15\) 5.09947 1.31668
\(16\) 14.8919 3.72298
\(17\) 3.71828 0.901815 0.450908 0.892571i \(-0.351100\pi\)
0.450908 + 0.892571i \(0.351100\pi\)
\(18\) −4.48215 −1.05645
\(19\) 6.12994 1.40631 0.703153 0.711039i \(-0.251775\pi\)
0.703153 + 0.711039i \(0.251775\pi\)
\(20\) −12.9245 −2.89000
\(21\) 6.54672 1.42861
\(22\) 3.37824 0.720244
\(23\) −3.46566 −0.722640 −0.361320 0.932442i \(-0.617674\pi\)
−0.361320 + 0.932442i \(0.617674\pi\)
\(24\) 20.3591 4.15578
\(25\) 0.603200 0.120640
\(26\) −2.55635 −0.501341
\(27\) 2.92764 0.563424
\(28\) −16.5925 −3.13569
\(29\) −5.46018 −1.01393 −0.506965 0.861967i \(-0.669233\pi\)
−0.506965 + 0.861967i \(0.669233\pi\)
\(30\) −13.9282 −2.54293
\(31\) 4.47779 0.804236 0.402118 0.915588i \(-0.368274\pi\)
0.402118 + 0.915588i \(0.368274\pi\)
\(32\) −21.7735 −3.84905
\(33\) 2.66457 0.463843
\(34\) −10.1558 −1.74170
\(35\) 7.19341 1.21591
\(36\) 8.96007 1.49335
\(37\) −1.25753 −0.206736 −0.103368 0.994643i \(-0.532962\pi\)
−0.103368 + 0.994643i \(0.532962\pi\)
\(38\) −16.7427 −2.71603
\(39\) −2.01631 −0.322868
\(40\) 22.3701 3.53703
\(41\) −5.00276 −0.781300 −0.390650 0.920539i \(-0.627750\pi\)
−0.390650 + 0.920539i \(0.627750\pi\)
\(42\) −17.8811 −2.75911
\(43\) −8.04498 −1.22685 −0.613424 0.789754i \(-0.710208\pi\)
−0.613424 + 0.789754i \(0.710208\pi\)
\(44\) −6.75330 −1.01810
\(45\) −3.88449 −0.579066
\(46\) 9.46578 1.39565
\(47\) −11.1410 −1.62509 −0.812544 0.582900i \(-0.801918\pi\)
−0.812544 + 0.582900i \(0.801918\pi\)
\(48\) −32.0817 −4.63060
\(49\) 2.23492 0.319274
\(50\) −1.64752 −0.232995
\(51\) −8.01031 −1.12167
\(52\) 5.11029 0.708669
\(53\) 1.52281 0.209174 0.104587 0.994516i \(-0.466648\pi\)
0.104587 + 0.994516i \(0.466648\pi\)
\(54\) −7.99628 −1.08816
\(55\) 2.92778 0.394782
\(56\) 28.7189 3.83772
\(57\) −13.2058 −1.74915
\(58\) 14.9134 1.95823
\(59\) −2.78143 −0.362111 −0.181056 0.983473i \(-0.557951\pi\)
−0.181056 + 0.983473i \(0.557951\pi\)
\(60\) 27.8433 3.59455
\(61\) −10.6917 −1.36893 −0.684466 0.729044i \(-0.739965\pi\)
−0.684466 + 0.729044i \(0.739965\pi\)
\(62\) −12.2302 −1.55324
\(63\) −4.98692 −0.628293
\(64\) 29.6864 3.71080
\(65\) −2.21548 −0.274797
\(66\) −7.27777 −0.895831
\(67\) −5.50665 −0.672745 −0.336372 0.941729i \(-0.609200\pi\)
−0.336372 + 0.941729i \(0.609200\pi\)
\(68\) 20.3019 2.46197
\(69\) 7.46609 0.898811
\(70\) −19.6474 −2.34831
\(71\) −1.00000 −0.118678
\(72\) −15.5084 −1.82768
\(73\) −7.75902 −0.908124 −0.454062 0.890970i \(-0.650026\pi\)
−0.454062 + 0.890970i \(0.650026\pi\)
\(74\) 3.43469 0.399274
\(75\) −1.29948 −0.150051
\(76\) 33.4697 3.83924
\(77\) 3.75869 0.428343
\(78\) 5.50716 0.623563
\(79\) 12.1551 1.36755 0.683776 0.729692i \(-0.260336\pi\)
0.683776 + 0.729692i \(0.260336\pi\)
\(80\) −35.2508 −3.94115
\(81\) −11.2301 −1.24779
\(82\) 13.6641 1.50894
\(83\) −1.58835 −0.174344 −0.0871719 0.996193i \(-0.527783\pi\)
−0.0871719 + 0.996193i \(0.527783\pi\)
\(84\) 35.7453 3.90013
\(85\) −8.80157 −0.954664
\(86\) 21.9733 2.36944
\(87\) 11.7629 1.26111
\(88\) 11.6888 1.24603
\(89\) 16.4018 1.73859 0.869293 0.494296i \(-0.164574\pi\)
0.869293 + 0.494296i \(0.164574\pi\)
\(90\) 10.6097 1.11836
\(91\) −2.84424 −0.298157
\(92\) −18.9226 −1.97282
\(93\) −9.64653 −1.00030
\(94\) 30.4296 3.13857
\(95\) −14.5102 −1.48872
\(96\) 46.9068 4.78741
\(97\) 8.08872 0.821285 0.410643 0.911796i \(-0.365304\pi\)
0.410643 + 0.911796i \(0.365304\pi\)
\(98\) −6.10424 −0.616622
\(99\) −2.02972 −0.203995
\(100\) 3.29349 0.329349
\(101\) 7.11014 0.707486 0.353743 0.935343i \(-0.384909\pi\)
0.353743 + 0.935343i \(0.384909\pi\)
\(102\) 21.8786 2.16630
\(103\) 19.9876 1.96943 0.984716 0.174166i \(-0.0557230\pi\)
0.984716 + 0.174166i \(0.0557230\pi\)
\(104\) −8.84506 −0.867329
\(105\) −15.4968 −1.51233
\(106\) −4.15926 −0.403983
\(107\) −14.9027 −1.44070 −0.720351 0.693610i \(-0.756019\pi\)
−0.720351 + 0.693610i \(0.756019\pi\)
\(108\) 15.9850 1.53816
\(109\) 15.8787 1.52090 0.760450 0.649396i \(-0.224978\pi\)
0.760450 + 0.649396i \(0.224978\pi\)
\(110\) −7.99667 −0.762452
\(111\) 2.70909 0.257136
\(112\) −45.2550 −4.27620
\(113\) −1.00000 −0.0940721
\(114\) 36.0690 3.37817
\(115\) 8.20359 0.764989
\(116\) −29.8128 −2.76805
\(117\) 1.53591 0.141995
\(118\) 7.59694 0.699355
\(119\) −11.2995 −1.03582
\(120\) −48.1921 −4.39932
\(121\) −9.47018 −0.860925
\(122\) 29.2023 2.64385
\(123\) 10.7775 0.971772
\(124\) 24.4489 2.19558
\(125\) 10.4077 0.930893
\(126\) 13.6208 1.21344
\(127\) 19.1330 1.69778 0.848889 0.528571i \(-0.177272\pi\)
0.848889 + 0.528571i \(0.177272\pi\)
\(128\) −37.5355 −3.31770
\(129\) 17.3313 1.52594
\(130\) 6.05116 0.530721
\(131\) 0.763075 0.0666702 0.0333351 0.999444i \(-0.489387\pi\)
0.0333351 + 0.999444i \(0.489387\pi\)
\(132\) 14.5487 1.26630
\(133\) −18.6283 −1.61528
\(134\) 15.0404 1.29929
\(135\) −6.93004 −0.596443
\(136\) −35.1393 −3.01317
\(137\) 2.64401 0.225893 0.112946 0.993601i \(-0.463971\pi\)
0.112946 + 0.993601i \(0.463971\pi\)
\(138\) −20.3922 −1.73590
\(139\) 12.7257 1.07938 0.539690 0.841864i \(-0.318541\pi\)
0.539690 + 0.841864i \(0.318541\pi\)
\(140\) 39.2762 3.31945
\(141\) 24.0012 2.02127
\(142\) 2.73131 0.229206
\(143\) −1.15763 −0.0968060
\(144\) 24.4380 2.03650
\(145\) 12.9248 1.07335
\(146\) 21.1923 1.75388
\(147\) −4.81469 −0.397109
\(148\) −6.86613 −0.564392
\(149\) 9.38599 0.768930 0.384465 0.923140i \(-0.374386\pi\)
0.384465 + 0.923140i \(0.374386\pi\)
\(150\) 3.54927 0.289796
\(151\) −19.1757 −1.56050 −0.780249 0.625469i \(-0.784908\pi\)
−0.780249 + 0.625469i \(0.784908\pi\)
\(152\) −57.9305 −4.69878
\(153\) 6.10180 0.493302
\(154\) −10.2661 −0.827270
\(155\) −10.5994 −0.851366
\(156\) −11.0091 −0.881435
\(157\) −12.4573 −0.994201 −0.497101 0.867693i \(-0.665602\pi\)
−0.497101 + 0.867693i \(0.665602\pi\)
\(158\) −33.1992 −2.64119
\(159\) −3.28060 −0.260168
\(160\) 51.5403 4.07462
\(161\) 10.5318 0.830022
\(162\) 30.6729 2.40989
\(163\) 5.12401 0.401343 0.200672 0.979659i \(-0.435688\pi\)
0.200672 + 0.979659i \(0.435688\pi\)
\(164\) −27.3152 −2.13296
\(165\) −6.30733 −0.491025
\(166\) 4.33826 0.336714
\(167\) 7.07034 0.547119 0.273560 0.961855i \(-0.411799\pi\)
0.273560 + 0.961855i \(0.411799\pi\)
\(168\) −61.8692 −4.77331
\(169\) −12.1240 −0.932616
\(170\) 24.0398 1.84377
\(171\) 10.0594 0.769262
\(172\) −43.9259 −3.34932
\(173\) 17.0444 1.29586 0.647930 0.761700i \(-0.275635\pi\)
0.647930 + 0.761700i \(0.275635\pi\)
\(174\) −32.1281 −2.43562
\(175\) −1.83306 −0.138567
\(176\) −18.4192 −1.38840
\(177\) 5.99205 0.450390
\(178\) −44.7983 −3.35778
\(179\) 12.4273 0.928863 0.464432 0.885609i \(-0.346259\pi\)
0.464432 + 0.885609i \(0.346259\pi\)
\(180\) −21.2095 −1.58086
\(181\) 24.8628 1.84803 0.924017 0.382351i \(-0.124885\pi\)
0.924017 + 0.382351i \(0.124885\pi\)
\(182\) 7.76849 0.575839
\(183\) 23.0332 1.70266
\(184\) 32.7519 2.41450
\(185\) 2.97670 0.218851
\(186\) 26.3476 1.93190
\(187\) −4.59899 −0.336312
\(188\) −60.8305 −4.43652
\(189\) −8.89680 −0.647147
\(190\) 39.6319 2.87520
\(191\) 7.44465 0.538676 0.269338 0.963046i \(-0.413195\pi\)
0.269338 + 0.963046i \(0.413195\pi\)
\(192\) −63.9535 −4.61545
\(193\) −16.3689 −1.17826 −0.589128 0.808040i \(-0.700529\pi\)
−0.589128 + 0.808040i \(0.700529\pi\)
\(194\) −22.0928 −1.58617
\(195\) 4.77282 0.341789
\(196\) 12.2027 0.871623
\(197\) −12.0292 −0.857044 −0.428522 0.903531i \(-0.640966\pi\)
−0.428522 + 0.903531i \(0.640966\pi\)
\(198\) 5.54379 0.393980
\(199\) −8.12373 −0.575876 −0.287938 0.957649i \(-0.592970\pi\)
−0.287938 + 0.957649i \(0.592970\pi\)
\(200\) −5.70049 −0.403085
\(201\) 11.8630 0.836752
\(202\) −19.4200 −1.36638
\(203\) 16.5929 1.16460
\(204\) −43.7366 −3.06217
\(205\) 11.8421 0.827086
\(206\) −54.5921 −3.80361
\(207\) −5.68725 −0.395291
\(208\) 13.9380 0.966426
\(209\) −7.58188 −0.524450
\(210\) 42.3265 2.92080
\(211\) 25.7925 1.77563 0.887813 0.460204i \(-0.152224\pi\)
0.887813 + 0.460204i \(0.152224\pi\)
\(212\) 8.31459 0.571049
\(213\) 2.15430 0.147611
\(214\) 40.7039 2.78246
\(215\) 19.0433 1.29875
\(216\) −27.6674 −1.88253
\(217\) −13.6076 −0.923742
\(218\) −43.3695 −2.93735
\(219\) 16.7153 1.12951
\(220\) 15.9858 1.07776
\(221\) 3.48010 0.234097
\(222\) −7.39936 −0.496613
\(223\) 1.06724 0.0714674 0.0357337 0.999361i \(-0.488623\pi\)
0.0357337 + 0.999361i \(0.488623\pi\)
\(224\) 66.1676 4.42101
\(225\) 0.989868 0.0659912
\(226\) 2.73131 0.181684
\(227\) −23.0156 −1.52760 −0.763798 0.645455i \(-0.776668\pi\)
−0.763798 + 0.645455i \(0.776668\pi\)
\(228\) −72.1039 −4.77520
\(229\) 2.63761 0.174298 0.0871492 0.996195i \(-0.472224\pi\)
0.0871492 + 0.996195i \(0.472224\pi\)
\(230\) −22.4065 −1.47744
\(231\) −8.09737 −0.532768
\(232\) 51.6010 3.38777
\(233\) 16.4544 1.07796 0.538981 0.842318i \(-0.318810\pi\)
0.538981 + 0.842318i \(0.318810\pi\)
\(234\) −4.19504 −0.274239
\(235\) 26.3721 1.72032
\(236\) −15.1867 −0.988570
\(237\) −26.1857 −1.70095
\(238\) 30.8624 2.00051
\(239\) −22.5202 −1.45671 −0.728356 0.685199i \(-0.759715\pi\)
−0.728356 + 0.685199i \(0.759715\pi\)
\(240\) 75.9409 4.90196
\(241\) 5.06501 0.326266 0.163133 0.986604i \(-0.447840\pi\)
0.163133 + 0.986604i \(0.447840\pi\)
\(242\) 25.8660 1.66273
\(243\) 15.4102 0.988563
\(244\) −58.3771 −3.73721
\(245\) −5.29029 −0.337984
\(246\) −29.4366 −1.87681
\(247\) 5.73728 0.365055
\(248\) −42.3170 −2.68713
\(249\) 3.42178 0.216847
\(250\) −28.4266 −1.79786
\(251\) 0.702492 0.0443409 0.0221704 0.999754i \(-0.492942\pi\)
0.0221704 + 0.999754i \(0.492942\pi\)
\(252\) −27.2288 −1.71525
\(253\) 4.28654 0.269492
\(254\) −52.2581 −3.27896
\(255\) 18.9613 1.18740
\(256\) 43.1483 2.69677
\(257\) −8.68978 −0.542054 −0.271027 0.962572i \(-0.587363\pi\)
−0.271027 + 0.962572i \(0.587363\pi\)
\(258\) −47.3372 −2.94709
\(259\) 3.82149 0.237456
\(260\) −12.0966 −0.750199
\(261\) −8.96031 −0.554629
\(262\) −2.08419 −0.128762
\(263\) −17.5100 −1.07972 −0.539858 0.841756i \(-0.681522\pi\)
−0.539858 + 0.841756i \(0.681522\pi\)
\(264\) −25.1813 −1.54980
\(265\) −3.60466 −0.221432
\(266\) 50.8795 3.11963
\(267\) −35.3345 −2.16243
\(268\) −30.0665 −1.83660
\(269\) −17.9562 −1.09481 −0.547406 0.836867i \(-0.684385\pi\)
−0.547406 + 0.836867i \(0.684385\pi\)
\(270\) 18.9281 1.15192
\(271\) −1.01763 −0.0618164 −0.0309082 0.999522i \(-0.509840\pi\)
−0.0309082 + 0.999522i \(0.509840\pi\)
\(272\) 55.3723 3.35744
\(273\) 6.12736 0.370845
\(274\) −7.22159 −0.436272
\(275\) −0.746073 −0.0449899
\(276\) 40.7651 2.45377
\(277\) 27.5483 1.65521 0.827607 0.561307i \(-0.189701\pi\)
0.827607 + 0.561307i \(0.189701\pi\)
\(278\) −34.7578 −2.08464
\(279\) 7.34819 0.439924
\(280\) −67.9807 −4.06262
\(281\) 14.4506 0.862048 0.431024 0.902341i \(-0.358153\pi\)
0.431024 + 0.902341i \(0.358153\pi\)
\(282\) −65.5546 −3.90372
\(283\) 13.2348 0.786730 0.393365 0.919382i \(-0.371311\pi\)
0.393365 + 0.919382i \(0.371311\pi\)
\(284\) −5.46003 −0.323993
\(285\) 31.2595 1.85165
\(286\) 3.16185 0.186964
\(287\) 15.2029 0.897398
\(288\) −35.7310 −2.10547
\(289\) −3.17439 −0.186729
\(290\) −35.3017 −2.07299
\(291\) −17.4256 −1.02151
\(292\) −42.3645 −2.47920
\(293\) 14.9887 0.875648 0.437824 0.899061i \(-0.355749\pi\)
0.437824 + 0.899061i \(0.355749\pi\)
\(294\) 13.1504 0.766947
\(295\) 6.58395 0.383332
\(296\) 11.8841 0.690751
\(297\) −3.62108 −0.210116
\(298\) −25.6360 −1.48505
\(299\) −3.24366 −0.187586
\(300\) −7.09518 −0.409640
\(301\) 24.4479 1.40915
\(302\) 52.3748 3.01383
\(303\) −15.3174 −0.879962
\(304\) 91.2865 5.23564
\(305\) 25.3084 1.44916
\(306\) −16.6659 −0.952726
\(307\) 21.4218 1.22260 0.611302 0.791397i \(-0.290646\pi\)
0.611302 + 0.791397i \(0.290646\pi\)
\(308\) 20.5226 1.16938
\(309\) −43.0593 −2.44956
\(310\) 28.9503 1.64426
\(311\) 20.8186 1.18051 0.590257 0.807215i \(-0.299026\pi\)
0.590257 + 0.807215i \(0.299026\pi\)
\(312\) 19.0550 1.07877
\(313\) 2.42545 0.137094 0.0685472 0.997648i \(-0.478164\pi\)
0.0685472 + 0.997648i \(0.478164\pi\)
\(314\) 34.0247 1.92013
\(315\) 11.8046 0.665113
\(316\) 66.3671 3.73344
\(317\) −12.9570 −0.727736 −0.363868 0.931451i \(-0.618544\pi\)
−0.363868 + 0.931451i \(0.618544\pi\)
\(318\) 8.96031 0.502469
\(319\) 6.75348 0.378122
\(320\) −70.2709 −3.92826
\(321\) 32.1050 1.79193
\(322\) −28.7656 −1.60304
\(323\) 22.7928 1.26823
\(324\) −61.3168 −3.40649
\(325\) 0.564561 0.0313162
\(326\) −13.9952 −0.775124
\(327\) −34.2075 −1.89168
\(328\) 47.2782 2.61050
\(329\) 33.8565 1.86657
\(330\) 17.2273 0.948329
\(331\) −12.0179 −0.660562 −0.330281 0.943883i \(-0.607144\pi\)
−0.330281 + 0.943883i \(0.607144\pi\)
\(332\) −8.67243 −0.475961
\(333\) −2.06363 −0.113086
\(334\) −19.3113 −1.05666
\(335\) 13.0348 0.712169
\(336\) 97.4931 5.31869
\(337\) −15.0255 −0.818492 −0.409246 0.912424i \(-0.634208\pi\)
−0.409246 + 0.912424i \(0.634208\pi\)
\(338\) 33.1144 1.80118
\(339\) 2.15430 0.117006
\(340\) −48.0569 −2.60625
\(341\) −5.53840 −0.299921
\(342\) −27.4753 −1.48570
\(343\) 14.4806 0.781880
\(344\) 76.0284 4.09918
\(345\) −17.6730 −0.951484
\(346\) −46.5534 −2.50273
\(347\) −25.1866 −1.35209 −0.676043 0.736862i \(-0.736307\pi\)
−0.676043 + 0.736862i \(0.736307\pi\)
\(348\) 64.2258 3.44286
\(349\) −24.6754 −1.32084 −0.660422 0.750894i \(-0.729623\pi\)
−0.660422 + 0.750894i \(0.729623\pi\)
\(350\) 5.00666 0.267617
\(351\) 2.74011 0.146256
\(352\) 26.9308 1.43542
\(353\) 26.1979 1.39438 0.697188 0.716889i \(-0.254434\pi\)
0.697188 + 0.716889i \(0.254434\pi\)
\(354\) −16.3661 −0.869850
\(355\) 2.36711 0.125633
\(356\) 89.5544 4.74637
\(357\) 24.3425 1.28834
\(358\) −33.9429 −1.79394
\(359\) 17.8907 0.944236 0.472118 0.881535i \(-0.343490\pi\)
0.472118 + 0.881535i \(0.343490\pi\)
\(360\) 36.7101 1.93479
\(361\) 18.5762 0.977694
\(362\) −67.9078 −3.56916
\(363\) 20.4016 1.07081
\(364\) −15.5297 −0.813975
\(365\) 18.3664 0.961343
\(366\) −62.9107 −3.28840
\(367\) 20.3121 1.06028 0.530142 0.847909i \(-0.322138\pi\)
0.530142 + 0.847909i \(0.322138\pi\)
\(368\) −51.6103 −2.69037
\(369\) −8.20967 −0.427379
\(370\) −8.13027 −0.422673
\(371\) −4.62767 −0.240257
\(372\) −52.6704 −2.73083
\(373\) −22.9192 −1.18671 −0.593356 0.804940i \(-0.702197\pi\)
−0.593356 + 0.804940i \(0.702197\pi\)
\(374\) 12.5613 0.649527
\(375\) −22.4214 −1.15783
\(376\) 105.287 5.42979
\(377\) −5.11042 −0.263200
\(378\) 24.2999 1.24985
\(379\) 4.09003 0.210091 0.105045 0.994467i \(-0.466501\pi\)
0.105045 + 0.994467i \(0.466501\pi\)
\(380\) −79.2264 −4.06423
\(381\) −41.2183 −2.11168
\(382\) −20.3336 −1.04036
\(383\) 9.79989 0.500751 0.250376 0.968149i \(-0.419446\pi\)
0.250376 + 0.968149i \(0.419446\pi\)
\(384\) 80.8629 4.12652
\(385\) −8.89724 −0.453445
\(386\) 44.7084 2.27560
\(387\) −13.2020 −0.671098
\(388\) 44.1647 2.24212
\(389\) −31.9861 −1.62176 −0.810881 0.585211i \(-0.801012\pi\)
−0.810881 + 0.585211i \(0.801012\pi\)
\(390\) −13.0360 −0.660105
\(391\) −12.8863 −0.651688
\(392\) −21.1209 −1.06677
\(393\) −1.64390 −0.0829236
\(394\) 32.8554 1.65523
\(395\) −28.7724 −1.44770
\(396\) −11.0824 −0.556909
\(397\) 2.08595 0.104691 0.0523453 0.998629i \(-0.483330\pi\)
0.0523453 + 0.998629i \(0.483330\pi\)
\(398\) 22.1884 1.11220
\(399\) 40.1310 2.00906
\(400\) 8.98279 0.449140
\(401\) −4.66681 −0.233049 −0.116525 0.993188i \(-0.537175\pi\)
−0.116525 + 0.993188i \(0.537175\pi\)
\(402\) −32.4015 −1.61604
\(403\) 4.19096 0.208767
\(404\) 38.8216 1.93145
\(405\) 26.5829 1.32091
\(406\) −45.3204 −2.24921
\(407\) 1.55538 0.0770974
\(408\) 75.7007 3.74774
\(409\) 33.5809 1.66047 0.830234 0.557414i \(-0.188207\pi\)
0.830234 + 0.557414i \(0.188207\pi\)
\(410\) −32.3443 −1.59737
\(411\) −5.69600 −0.280963
\(412\) 109.133 5.37658
\(413\) 8.45249 0.415920
\(414\) 15.5336 0.763435
\(415\) 3.75979 0.184561
\(416\) −20.3788 −0.999153
\(417\) −27.4151 −1.34252
\(418\) 20.7084 1.01288
\(419\) 37.4391 1.82902 0.914509 0.404565i \(-0.132577\pi\)
0.914509 + 0.404565i \(0.132577\pi\)
\(420\) −84.6130 −4.12869
\(421\) 16.7445 0.816075 0.408038 0.912965i \(-0.366213\pi\)
0.408038 + 0.912965i \(0.366213\pi\)
\(422\) −70.4471 −3.42931
\(423\) −18.2828 −0.888939
\(424\) −14.3912 −0.698898
\(425\) 2.24287 0.108795
\(426\) −5.88407 −0.285084
\(427\) 32.4910 1.57235
\(428\) −81.3694 −3.93314
\(429\) 2.49389 0.120406
\(430\) −52.0132 −2.50830
\(431\) −18.3487 −0.883825 −0.441912 0.897058i \(-0.645700\pi\)
−0.441912 + 0.897058i \(0.645700\pi\)
\(432\) 43.5981 2.09762
\(433\) 3.11096 0.149503 0.0747516 0.997202i \(-0.476184\pi\)
0.0747516 + 0.997202i \(0.476184\pi\)
\(434\) 37.1664 1.78405
\(435\) −27.8440 −1.33502
\(436\) 86.6981 4.15209
\(437\) −21.2443 −1.01625
\(438\) −45.6546 −2.18146
\(439\) −9.54411 −0.455515 −0.227758 0.973718i \(-0.573139\pi\)
−0.227758 + 0.973718i \(0.573139\pi\)
\(440\) −27.6687 −1.31906
\(441\) 3.66756 0.174646
\(442\) −9.50523 −0.452117
\(443\) 31.0567 1.47555 0.737773 0.675048i \(-0.235877\pi\)
0.737773 + 0.675048i \(0.235877\pi\)
\(444\) 14.7917 0.701985
\(445\) −38.8248 −1.84047
\(446\) −2.91495 −0.138027
\(447\) −20.2203 −0.956386
\(448\) −90.2139 −4.26221
\(449\) −23.3840 −1.10356 −0.551781 0.833989i \(-0.686051\pi\)
−0.551781 + 0.833989i \(0.686051\pi\)
\(450\) −2.70363 −0.127450
\(451\) 6.18772 0.291368
\(452\) −5.46003 −0.256818
\(453\) 41.3104 1.94093
\(454\) 62.8626 2.95029
\(455\) 6.73262 0.315630
\(456\) 124.800 5.84429
\(457\) −3.43198 −0.160541 −0.0802705 0.996773i \(-0.525578\pi\)
−0.0802705 + 0.996773i \(0.525578\pi\)
\(458\) −7.20413 −0.336627
\(459\) 10.8858 0.508105
\(460\) 44.7919 2.08843
\(461\) 5.27951 0.245891 0.122946 0.992413i \(-0.460766\pi\)
0.122946 + 0.992413i \(0.460766\pi\)
\(462\) 22.1164 1.02895
\(463\) −22.0355 −1.02408 −0.512039 0.858962i \(-0.671110\pi\)
−0.512039 + 0.858962i \(0.671110\pi\)
\(464\) −81.3125 −3.77484
\(465\) 22.8344 1.05892
\(466\) −44.9419 −2.08189
\(467\) 0.867223 0.0401303 0.0200651 0.999799i \(-0.493613\pi\)
0.0200651 + 0.999799i \(0.493613\pi\)
\(468\) 8.38613 0.387649
\(469\) 16.7342 0.772712
\(470\) −72.0302 −3.32250
\(471\) 26.8368 1.23658
\(472\) 26.2857 1.20990
\(473\) 9.95052 0.457525
\(474\) 71.5213 3.28508
\(475\) 3.69758 0.169657
\(476\) −61.6956 −2.82781
\(477\) 2.49897 0.114420
\(478\) 61.5096 2.81338
\(479\) 16.1246 0.736751 0.368376 0.929677i \(-0.379914\pi\)
0.368376 + 0.929677i \(0.379914\pi\)
\(480\) −111.034 −5.06796
\(481\) −1.17697 −0.0536654
\(482\) −13.8341 −0.630125
\(483\) −22.6887 −1.03237
\(484\) −51.7075 −2.35034
\(485\) −19.1469 −0.869415
\(486\) −42.0899 −1.90924
\(487\) −0.454083 −0.0205765 −0.0102882 0.999947i \(-0.503275\pi\)
−0.0102882 + 0.999947i \(0.503275\pi\)
\(488\) 101.041 4.57391
\(489\) −11.0387 −0.499186
\(490\) 14.4494 0.652757
\(491\) 25.4965 1.15064 0.575320 0.817928i \(-0.304877\pi\)
0.575320 + 0.817928i \(0.304877\pi\)
\(492\) 58.8454 2.65295
\(493\) −20.3025 −0.914378
\(494\) −15.6703 −0.705039
\(495\) 4.80457 0.215949
\(496\) 66.6829 2.99415
\(497\) 3.03890 0.136313
\(498\) −9.34594 −0.418802
\(499\) 22.7943 1.02041 0.510206 0.860052i \(-0.329569\pi\)
0.510206 + 0.860052i \(0.329569\pi\)
\(500\) 56.8264 2.54135
\(501\) −15.2317 −0.680500
\(502\) −1.91872 −0.0856367
\(503\) 11.6202 0.518119 0.259060 0.965861i \(-0.416587\pi\)
0.259060 + 0.965861i \(0.416587\pi\)
\(504\) 47.1285 2.09927
\(505\) −16.8305 −0.748946
\(506\) −11.7078 −0.520477
\(507\) 26.1188 1.15998
\(508\) 104.467 4.63496
\(509\) −17.7606 −0.787224 −0.393612 0.919277i \(-0.628775\pi\)
−0.393612 + 0.919277i \(0.628775\pi\)
\(510\) −51.7890 −2.29326
\(511\) 23.5789 1.04307
\(512\) −42.7801 −1.89063
\(513\) 17.9463 0.792346
\(514\) 23.7345 1.04688
\(515\) −47.3127 −2.08485
\(516\) 94.6297 4.16584
\(517\) 13.7799 0.606040
\(518\) −10.4377 −0.458605
\(519\) −36.7188 −1.61178
\(520\) 20.9372 0.918157
\(521\) 19.5249 0.855401 0.427700 0.903921i \(-0.359324\pi\)
0.427700 + 0.903921i \(0.359324\pi\)
\(522\) 24.4734 1.07117
\(523\) −39.6157 −1.73228 −0.866138 0.499806i \(-0.833405\pi\)
−0.866138 + 0.499806i \(0.833405\pi\)
\(524\) 4.16642 0.182011
\(525\) 3.94898 0.172347
\(526\) 47.8253 2.08528
\(527\) 16.6497 0.725272
\(528\) 39.6806 1.72688
\(529\) −10.9892 −0.477791
\(530\) 9.84542 0.427658
\(531\) −4.56441 −0.198078
\(532\) −101.711 −4.40973
\(533\) −4.68230 −0.202813
\(534\) 96.5093 4.17636
\(535\) 35.2764 1.52513
\(536\) 52.0401 2.24779
\(537\) −26.7723 −1.15531
\(538\) 49.0440 2.11444
\(539\) −2.76428 −0.119066
\(540\) −37.8382 −1.62830
\(541\) −14.9299 −0.641887 −0.320943 0.947098i \(-0.604000\pi\)
−0.320943 + 0.947098i \(0.604000\pi\)
\(542\) 2.77945 0.119388
\(543\) −53.5620 −2.29856
\(544\) −80.9601 −3.47114
\(545\) −37.5865 −1.61003
\(546\) −16.7357 −0.716222
\(547\) 27.1105 1.15916 0.579581 0.814915i \(-0.303216\pi\)
0.579581 + 0.814915i \(0.303216\pi\)
\(548\) 14.4364 0.616691
\(549\) −17.5454 −0.748819
\(550\) 2.03775 0.0868902
\(551\) −33.4706 −1.42590
\(552\) −70.5576 −3.00313
\(553\) −36.9381 −1.57077
\(554\) −75.2428 −3.19676
\(555\) −6.41271 −0.272205
\(556\) 69.4828 2.94673
\(557\) −21.9844 −0.931507 −0.465753 0.884915i \(-0.654217\pi\)
−0.465753 + 0.884915i \(0.654217\pi\)
\(558\) −20.0702 −0.849637
\(559\) −7.52965 −0.318470
\(560\) 107.124 4.52680
\(561\) 9.90763 0.418300
\(562\) −39.4689 −1.66489
\(563\) 13.6587 0.575646 0.287823 0.957684i \(-0.407069\pi\)
0.287823 + 0.957684i \(0.407069\pi\)
\(564\) 131.047 5.51809
\(565\) 2.36711 0.0995850
\(566\) −36.1484 −1.51943
\(567\) 34.1272 1.43321
\(568\) 9.45041 0.396531
\(569\) 0.482899 0.0202442 0.0101221 0.999949i \(-0.496778\pi\)
0.0101221 + 0.999949i \(0.496778\pi\)
\(570\) −85.3792 −3.57614
\(571\) −21.6107 −0.904382 −0.452191 0.891921i \(-0.649357\pi\)
−0.452191 + 0.891921i \(0.649357\pi\)
\(572\) −6.32071 −0.264282
\(573\) −16.0380 −0.669999
\(574\) −41.5238 −1.73317
\(575\) −2.09048 −0.0871792
\(576\) 48.7162 2.02984
\(577\) −22.6379 −0.942429 −0.471215 0.882019i \(-0.656184\pi\)
−0.471215 + 0.882019i \(0.656184\pi\)
\(578\) 8.67023 0.360634
\(579\) 35.2635 1.46550
\(580\) 70.5701 2.93026
\(581\) 4.82683 0.200251
\(582\) 47.5946 1.97286
\(583\) −1.88350 −0.0780067
\(584\) 73.3259 3.03425
\(585\) −3.63567 −0.150316
\(586\) −40.9387 −1.69116
\(587\) −19.7275 −0.814239 −0.407120 0.913375i \(-0.633467\pi\)
−0.407120 + 0.913375i \(0.633467\pi\)
\(588\) −26.2884 −1.08411
\(589\) 27.4486 1.13100
\(590\) −17.9828 −0.740339
\(591\) 25.9145 1.06598
\(592\) −18.7269 −0.769673
\(593\) −7.00780 −0.287776 −0.143888 0.989594i \(-0.545960\pi\)
−0.143888 + 0.989594i \(0.545960\pi\)
\(594\) 9.89028 0.405803
\(595\) 26.7471 1.09652
\(596\) 51.2478 2.09919
\(597\) 17.5010 0.716268
\(598\) 8.85944 0.362289
\(599\) 4.92010 0.201030 0.100515 0.994936i \(-0.467951\pi\)
0.100515 + 0.994936i \(0.467951\pi\)
\(600\) 12.2806 0.501353
\(601\) −25.5714 −1.04308 −0.521539 0.853227i \(-0.674642\pi\)
−0.521539 + 0.853227i \(0.674642\pi\)
\(602\) −66.7747 −2.72153
\(603\) −9.03657 −0.367998
\(604\) −104.700 −4.26019
\(605\) 22.4169 0.911378
\(606\) 41.8366 1.69949
\(607\) 36.0934 1.46499 0.732494 0.680774i \(-0.238356\pi\)
0.732494 + 0.680774i \(0.238356\pi\)
\(608\) −133.470 −5.41294
\(609\) −35.7463 −1.44851
\(610\) −69.1251 −2.79879
\(611\) −10.4274 −0.421847
\(612\) 33.3161 1.34672
\(613\) −24.1949 −0.977225 −0.488612 0.872501i \(-0.662497\pi\)
−0.488612 + 0.872501i \(0.662497\pi\)
\(614\) −58.5094 −2.36125
\(615\) −25.5114 −1.02872
\(616\) −35.5212 −1.43119
\(617\) −28.8112 −1.15990 −0.579948 0.814654i \(-0.696927\pi\)
−0.579948 + 0.814654i \(0.696927\pi\)
\(618\) 117.608 4.73089
\(619\) −16.4666 −0.661850 −0.330925 0.943657i \(-0.607361\pi\)
−0.330925 + 0.943657i \(0.607361\pi\)
\(620\) −57.8732 −2.32424
\(621\) −10.1462 −0.407153
\(622\) −56.8620 −2.27996
\(623\) −49.8434 −1.99693
\(624\) −30.0267 −1.20203
\(625\) −27.6521 −1.10609
\(626\) −6.62464 −0.264774
\(627\) 16.3337 0.652304
\(628\) −68.0173 −2.71419
\(629\) −4.67583 −0.186438
\(630\) −32.2419 −1.28455
\(631\) −20.6199 −0.820865 −0.410433 0.911891i \(-0.634622\pi\)
−0.410433 + 0.911891i \(0.634622\pi\)
\(632\) −114.870 −4.56930
\(633\) −55.5648 −2.20850
\(634\) 35.3895 1.40549
\(635\) −45.2899 −1.79727
\(636\) −17.9122 −0.710264
\(637\) 2.09176 0.0828784
\(638\) −18.4458 −0.730277
\(639\) −1.64103 −0.0649181
\(640\) 88.8506 3.51213
\(641\) −25.7511 −1.01711 −0.508553 0.861031i \(-0.669819\pi\)
−0.508553 + 0.861031i \(0.669819\pi\)
\(642\) −87.6887 −3.46080
\(643\) 13.8453 0.546006 0.273003 0.962013i \(-0.411983\pi\)
0.273003 + 0.962013i \(0.411983\pi\)
\(644\) 57.5040 2.26597
\(645\) −41.0252 −1.61536
\(646\) −62.2542 −2.44936
\(647\) −28.6234 −1.12530 −0.562651 0.826695i \(-0.690218\pi\)
−0.562651 + 0.826695i \(0.690218\pi\)
\(648\) 106.129 4.16915
\(649\) 3.44024 0.135041
\(650\) −1.54199 −0.0604818
\(651\) 29.3149 1.14894
\(652\) 27.9773 1.09567
\(653\) 20.6703 0.808892 0.404446 0.914562i \(-0.367464\pi\)
0.404446 + 0.914562i \(0.367464\pi\)
\(654\) 93.4312 3.65345
\(655\) −1.80628 −0.0705773
\(656\) −74.5007 −2.90876
\(657\) −12.7328 −0.496753
\(658\) −92.4725 −3.60495
\(659\) −50.1946 −1.95530 −0.977652 0.210230i \(-0.932579\pi\)
−0.977652 + 0.210230i \(0.932579\pi\)
\(660\) −34.4383 −1.34051
\(661\) 41.6228 1.61894 0.809469 0.587163i \(-0.199755\pi\)
0.809469 + 0.587163i \(0.199755\pi\)
\(662\) 32.8245 1.27576
\(663\) −7.49720 −0.291167
\(664\) 15.0105 0.582522
\(665\) 44.0952 1.70994
\(666\) 5.63642 0.218407
\(667\) 18.9231 0.732707
\(668\) 38.6043 1.49364
\(669\) −2.29915 −0.0888903
\(670\) −35.6021 −1.37543
\(671\) 13.2241 0.510512
\(672\) −142.545 −5.49880
\(673\) 31.1387 1.20031 0.600155 0.799884i \(-0.295106\pi\)
0.600155 + 0.799884i \(0.295106\pi\)
\(674\) 41.0393 1.58077
\(675\) 1.76595 0.0679715
\(676\) −66.1975 −2.54606
\(677\) −3.84088 −0.147617 −0.0738085 0.997272i \(-0.523515\pi\)
−0.0738085 + 0.997272i \(0.523515\pi\)
\(678\) −5.88407 −0.225976
\(679\) −24.5808 −0.943325
\(680\) 83.1785 3.18975
\(681\) 49.5825 1.90001
\(682\) 15.1271 0.579246
\(683\) 40.8975 1.56490 0.782450 0.622714i \(-0.213970\pi\)
0.782450 + 0.622714i \(0.213970\pi\)
\(684\) 54.9247 2.10010
\(685\) −6.25865 −0.239131
\(686\) −39.5510 −1.51006
\(687\) −5.68222 −0.216790
\(688\) −119.805 −4.56753
\(689\) 1.42526 0.0542983
\(690\) 48.2705 1.83763
\(691\) 18.0490 0.686615 0.343307 0.939223i \(-0.388453\pi\)
0.343307 + 0.939223i \(0.388453\pi\)
\(692\) 93.0629 3.53772
\(693\) 6.16813 0.234308
\(694\) 68.7922 2.61132
\(695\) −30.1231 −1.14264
\(696\) −111.164 −4.21367
\(697\) −18.6017 −0.704588
\(698\) 67.3961 2.55098
\(699\) −35.4477 −1.34076
\(700\) −10.0086 −0.378289
\(701\) 3.32529 0.125595 0.0627973 0.998026i \(-0.479998\pi\)
0.0627973 + 0.998026i \(0.479998\pi\)
\(702\) −7.48407 −0.282468
\(703\) −7.70856 −0.290734
\(704\) −36.7179 −1.38386
\(705\) −56.8134 −2.13972
\(706\) −71.5546 −2.69299
\(707\) −21.6070 −0.812616
\(708\) 32.7168 1.22957
\(709\) −40.5549 −1.52307 −0.761535 0.648123i \(-0.775554\pi\)
−0.761535 + 0.648123i \(0.775554\pi\)
\(710\) −6.46530 −0.242638
\(711\) 19.9468 0.748064
\(712\) −155.004 −5.80901
\(713\) −15.5185 −0.581173
\(714\) −66.4869 −2.48821
\(715\) 2.74024 0.102479
\(716\) 67.8537 2.53581
\(717\) 48.5154 1.81184
\(718\) −48.8650 −1.82363
\(719\) 40.5804 1.51339 0.756696 0.653767i \(-0.226812\pi\)
0.756696 + 0.653767i \(0.226812\pi\)
\(720\) −57.8475 −2.15585
\(721\) −60.7402 −2.26208
\(722\) −50.7372 −1.88824
\(723\) −10.9116 −0.405805
\(724\) 135.752 5.04517
\(725\) −3.29358 −0.122320
\(726\) −55.7231 −2.06808
\(727\) 25.0655 0.929629 0.464814 0.885408i \(-0.346121\pi\)
0.464814 + 0.885408i \(0.346121\pi\)
\(728\) 26.8793 0.996211
\(729\) 0.492142 0.0182275
\(730\) −50.1644 −1.85667
\(731\) −29.9135 −1.10639
\(732\) 125.762 4.64830
\(733\) −2.20054 −0.0812789 −0.0406395 0.999174i \(-0.512940\pi\)
−0.0406395 + 0.999174i \(0.512940\pi\)
\(734\) −55.4787 −2.04775
\(735\) 11.3969 0.420381
\(736\) 75.4597 2.78148
\(737\) 6.81096 0.250885
\(738\) 22.4231 0.825407
\(739\) −2.52192 −0.0927702 −0.0463851 0.998924i \(-0.514770\pi\)
−0.0463851 + 0.998924i \(0.514770\pi\)
\(740\) 16.2529 0.597467
\(741\) −12.3599 −0.454051
\(742\) 12.6396 0.464014
\(743\) −8.75925 −0.321346 −0.160673 0.987008i \(-0.551366\pi\)
−0.160673 + 0.987008i \(0.551366\pi\)
\(744\) 91.1637 3.34222
\(745\) −22.2176 −0.813992
\(746\) 62.5994 2.29193
\(747\) −2.60652 −0.0953677
\(748\) −25.1107 −0.918137
\(749\) 45.2879 1.65478
\(750\) 61.2396 2.23615
\(751\) 2.34396 0.0855324 0.0427662 0.999085i \(-0.486383\pi\)
0.0427662 + 0.999085i \(0.486383\pi\)
\(752\) −165.911 −6.05017
\(753\) −1.51338 −0.0551507
\(754\) 13.9581 0.508325
\(755\) 45.3910 1.65195
\(756\) −48.5768 −1.76672
\(757\) −28.3654 −1.03096 −0.515478 0.856903i \(-0.672386\pi\)
−0.515478 + 0.856903i \(0.672386\pi\)
\(758\) −11.1711 −0.405754
\(759\) −9.23450 −0.335191
\(760\) 137.128 4.97414
\(761\) −36.4088 −1.31982 −0.659909 0.751346i \(-0.729405\pi\)
−0.659909 + 0.751346i \(0.729405\pi\)
\(762\) 112.580 4.07834
\(763\) −48.2537 −1.74690
\(764\) 40.6481 1.47060
\(765\) −14.4436 −0.522211
\(766\) −26.7665 −0.967113
\(767\) −2.60326 −0.0939984
\(768\) −92.9545 −3.35421
\(769\) 20.1093 0.725159 0.362579 0.931953i \(-0.381896\pi\)
0.362579 + 0.931953i \(0.381896\pi\)
\(770\) 24.3011 0.875750
\(771\) 18.7204 0.674200
\(772\) −89.3745 −3.21666
\(773\) −16.5548 −0.595435 −0.297717 0.954654i \(-0.596225\pi\)
−0.297717 + 0.954654i \(0.596225\pi\)
\(774\) 36.0588 1.29611
\(775\) 2.70100 0.0970229
\(776\) −76.4418 −2.74410
\(777\) −8.23266 −0.295345
\(778\) 87.3639 3.13215
\(779\) −30.6666 −1.09875
\(780\) 26.0598 0.933089
\(781\) 1.23686 0.0442583
\(782\) 35.1964 1.25862
\(783\) −15.9854 −0.571273
\(784\) 33.2822 1.18865
\(785\) 29.4878 1.05246
\(786\) 4.48999 0.160152
\(787\) −13.9026 −0.495574 −0.247787 0.968815i \(-0.579703\pi\)
−0.247787 + 0.968815i \(0.579703\pi\)
\(788\) −65.6798 −2.33974
\(789\) 37.7220 1.34294
\(790\) 78.5862 2.79597
\(791\) 3.03890 0.108051
\(792\) 19.1817 0.681593
\(793\) −10.0068 −0.355353
\(794\) −5.69736 −0.202192
\(795\) 7.76553 0.275415
\(796\) −44.3558 −1.57215
\(797\) −21.7510 −0.770460 −0.385230 0.922820i \(-0.625878\pi\)
−0.385230 + 0.922820i \(0.625878\pi\)
\(798\) −109.610 −3.88015
\(799\) −41.4255 −1.46553
\(800\) −13.1338 −0.464349
\(801\) 26.9158 0.951024
\(802\) 12.7465 0.450094
\(803\) 9.59682 0.338664
\(804\) 64.7724 2.28435
\(805\) −24.9299 −0.878663
\(806\) −11.4468 −0.403197
\(807\) 38.6832 1.36171
\(808\) −67.1938 −2.36387
\(809\) 22.9969 0.808529 0.404264 0.914642i \(-0.367528\pi\)
0.404264 + 0.914642i \(0.367528\pi\)
\(810\) −72.6060 −2.55111
\(811\) −1.16332 −0.0408496 −0.0204248 0.999791i \(-0.506502\pi\)
−0.0204248 + 0.999791i \(0.506502\pi\)
\(812\) 90.5981 3.17937
\(813\) 2.19228 0.0768866
\(814\) −4.24823 −0.148900
\(815\) −12.1291 −0.424863
\(816\) −119.289 −4.17594
\(817\) −49.3153 −1.72532
\(818\) −91.7197 −3.20691
\(819\) −4.66748 −0.163095
\(820\) 64.6581 2.25796
\(821\) 48.8168 1.70372 0.851859 0.523771i \(-0.175475\pi\)
0.851859 + 0.523771i \(0.175475\pi\)
\(822\) 15.5575 0.542631
\(823\) 13.0705 0.455609 0.227805 0.973707i \(-0.426845\pi\)
0.227805 + 0.973707i \(0.426845\pi\)
\(824\) −188.891 −6.58032
\(825\) 1.60727 0.0559579
\(826\) −23.0863 −0.803277
\(827\) 46.6586 1.62248 0.811240 0.584713i \(-0.198793\pi\)
0.811240 + 0.584713i \(0.198793\pi\)
\(828\) −31.0526 −1.07915
\(829\) 29.9062 1.03869 0.519343 0.854566i \(-0.326177\pi\)
0.519343 + 0.854566i \(0.326177\pi\)
\(830\) −10.2691 −0.356447
\(831\) −59.3474 −2.05874
\(832\) 27.7848 0.963264
\(833\) 8.31005 0.287926
\(834\) 74.8789 2.59285
\(835\) −16.7362 −0.579182
\(836\) −41.3973 −1.43176
\(837\) 13.1094 0.453126
\(838\) −102.258 −3.53243
\(839\) 18.2890 0.631405 0.315702 0.948858i \(-0.397760\pi\)
0.315702 + 0.948858i \(0.397760\pi\)
\(840\) 146.451 5.05304
\(841\) 0.813577 0.0280544
\(842\) −45.7343 −1.57611
\(843\) −31.1309 −1.07220
\(844\) 140.828 4.84749
\(845\) 28.6988 0.987270
\(846\) 49.9358 1.71683
\(847\) 28.7789 0.988856
\(848\) 22.6775 0.778750
\(849\) −28.5119 −0.978526
\(850\) −6.12595 −0.210118
\(851\) 4.35815 0.149396
\(852\) 11.7626 0.402979
\(853\) 19.7229 0.675298 0.337649 0.941272i \(-0.390368\pi\)
0.337649 + 0.941272i \(0.390368\pi\)
\(854\) −88.7430 −3.03672
\(855\) −23.8117 −0.814343
\(856\) 140.837 4.81371
\(857\) 10.0471 0.343203 0.171602 0.985166i \(-0.445106\pi\)
0.171602 + 0.985166i \(0.445106\pi\)
\(858\) −6.81158 −0.232544
\(859\) 20.1108 0.686173 0.343086 0.939304i \(-0.388528\pi\)
0.343086 + 0.939304i \(0.388528\pi\)
\(860\) 103.977 3.54560
\(861\) −32.7517 −1.11617
\(862\) 50.1159 1.70695
\(863\) −6.02748 −0.205178 −0.102589 0.994724i \(-0.532713\pi\)
−0.102589 + 0.994724i \(0.532713\pi\)
\(864\) −63.7450 −2.16865
\(865\) −40.3459 −1.37180
\(866\) −8.49699 −0.288739
\(867\) 6.83860 0.232251
\(868\) −74.2978 −2.52183
\(869\) −15.0341 −0.509998
\(870\) 76.0506 2.57836
\(871\) −5.15392 −0.174634
\(872\) −150.060 −5.08167
\(873\) 13.2738 0.449251
\(874\) 58.0247 1.96271
\(875\) −31.6280 −1.06922
\(876\) 91.2661 3.08359
\(877\) 34.2354 1.15605 0.578023 0.816020i \(-0.303824\pi\)
0.578023 + 0.816020i \(0.303824\pi\)
\(878\) 26.0679 0.879748
\(879\) −32.2902 −1.08912
\(880\) 43.6002 1.46976
\(881\) 15.1195 0.509389 0.254695 0.967022i \(-0.418025\pi\)
0.254695 + 0.967022i \(0.418025\pi\)
\(882\) −10.0172 −0.337298
\(883\) 31.2169 1.05053 0.525265 0.850938i \(-0.323966\pi\)
0.525265 + 0.850938i \(0.323966\pi\)
\(884\) 19.0015 0.639089
\(885\) −14.1838 −0.476784
\(886\) −84.8253 −2.84976
\(887\) 4.70125 0.157852 0.0789262 0.996880i \(-0.474851\pi\)
0.0789262 + 0.996880i \(0.474851\pi\)
\(888\) −25.6020 −0.859148
\(889\) −58.1433 −1.95006
\(890\) 106.042 3.55455
\(891\) 13.8901 0.465335
\(892\) 5.82714 0.195107
\(893\) −68.2939 −2.28537
\(894\) 55.2278 1.84709
\(895\) −29.4169 −0.983297
\(896\) 114.067 3.81070
\(897\) 6.98784 0.233317
\(898\) 63.8690 2.13134
\(899\) −24.4496 −0.815439
\(900\) 5.40471 0.180157
\(901\) 5.66223 0.188636
\(902\) −16.9005 −0.562727
\(903\) −52.6682 −1.75269
\(904\) 9.45041 0.314316
\(905\) −58.8528 −1.95633
\(906\) −112.831 −3.74857
\(907\) −22.0554 −0.732339 −0.366170 0.930548i \(-0.619331\pi\)
−0.366170 + 0.930548i \(0.619331\pi\)
\(908\) −125.666 −4.17036
\(909\) 11.6679 0.387001
\(910\) −18.3889 −0.609585
\(911\) 35.0388 1.16089 0.580444 0.814300i \(-0.302879\pi\)
0.580444 + 0.814300i \(0.302879\pi\)
\(912\) −196.659 −6.51203
\(913\) 1.96456 0.0650175
\(914\) 9.37378 0.310057
\(915\) −54.5221 −1.80244
\(916\) 14.4015 0.475837
\(917\) −2.31891 −0.0765772
\(918\) −29.7324 −0.981316
\(919\) 29.6631 0.978495 0.489247 0.872145i \(-0.337272\pi\)
0.489247 + 0.872145i \(0.337272\pi\)
\(920\) −77.5273 −2.55600
\(921\) −46.1490 −1.52066
\(922\) −14.4200 −0.474896
\(923\) −0.935944 −0.0308070
\(924\) −44.2119 −1.45447
\(925\) −0.758539 −0.0249406
\(926\) 60.1857 1.97783
\(927\) 32.8002 1.07730
\(928\) 118.887 3.90267
\(929\) 3.28682 0.107837 0.0539185 0.998545i \(-0.482829\pi\)
0.0539185 + 0.998545i \(0.482829\pi\)
\(930\) −62.3677 −2.04512
\(931\) 13.6999 0.448996
\(932\) 89.8414 2.94285
\(933\) −44.8496 −1.46831
\(934\) −2.36865 −0.0775046
\(935\) 10.8863 0.356020
\(936\) −14.5150 −0.474437
\(937\) −0.832310 −0.0271904 −0.0135952 0.999908i \(-0.504328\pi\)
−0.0135952 + 0.999908i \(0.504328\pi\)
\(938\) −45.7061 −1.49236
\(939\) −5.22515 −0.170516
\(940\) 143.992 4.69651
\(941\) 4.22292 0.137663 0.0688316 0.997628i \(-0.478073\pi\)
0.0688316 + 0.997628i \(0.478073\pi\)
\(942\) −73.2996 −2.38823
\(943\) 17.3379 0.564599
\(944\) −41.4208 −1.34813
\(945\) 21.0597 0.685072
\(946\) −27.1779 −0.883630
\(947\) −0.415723 −0.0135092 −0.00675459 0.999977i \(-0.502150\pi\)
−0.00675459 + 0.999977i \(0.502150\pi\)
\(948\) −142.975 −4.64361
\(949\) −7.26201 −0.235735
\(950\) −10.0992 −0.327662
\(951\) 27.9133 0.905149
\(952\) 106.785 3.46092
\(953\) −20.1205 −0.651768 −0.325884 0.945410i \(-0.605662\pi\)
−0.325884 + 0.945410i \(0.605662\pi\)
\(954\) −6.82547 −0.220983
\(955\) −17.6223 −0.570244
\(956\) −122.961 −3.97685
\(957\) −14.5491 −0.470304
\(958\) −44.0412 −1.42291
\(959\) −8.03488 −0.259460
\(960\) 151.385 4.88592
\(961\) −10.9494 −0.353205
\(962\) 3.21467 0.103645
\(963\) −24.4558 −0.788078
\(964\) 27.6551 0.890711
\(965\) 38.7469 1.24731
\(966\) 61.9698 1.99385
\(967\) −14.3615 −0.461835 −0.230918 0.972973i \(-0.574173\pi\)
−0.230918 + 0.972973i \(0.574173\pi\)
\(968\) 89.4971 2.87655
\(969\) −49.1027 −1.57741
\(970\) 52.2960 1.67912
\(971\) −6.37382 −0.204545 −0.102273 0.994756i \(-0.532611\pi\)
−0.102273 + 0.994756i \(0.532611\pi\)
\(972\) 84.1400 2.69879
\(973\) −38.6722 −1.23977
\(974\) 1.24024 0.0397398
\(975\) −1.21624 −0.0389507
\(976\) −159.220 −5.09651
\(977\) 1.79537 0.0574389 0.0287194 0.999588i \(-0.490857\pi\)
0.0287194 + 0.999588i \(0.490857\pi\)
\(978\) 30.1500 0.964091
\(979\) −20.2867 −0.648367
\(980\) −28.8852 −0.922703
\(981\) 26.0574 0.831947
\(982\) −69.6387 −2.22226
\(983\) −27.1107 −0.864697 −0.432348 0.901707i \(-0.642315\pi\)
−0.432348 + 0.901707i \(0.642315\pi\)
\(984\) −101.852 −3.24691
\(985\) 28.4744 0.907269
\(986\) 55.4523 1.76596
\(987\) −72.9373 −2.32162
\(988\) 31.3258 0.996605
\(989\) 27.8812 0.886570
\(990\) −13.1228 −0.417069
\(991\) 18.1880 0.577762 0.288881 0.957365i \(-0.406717\pi\)
0.288881 + 0.957365i \(0.406717\pi\)
\(992\) −97.4974 −3.09555
\(993\) 25.8902 0.821600
\(994\) −8.30017 −0.263265
\(995\) 19.2297 0.609624
\(996\) 18.6831 0.591995
\(997\) 49.2180 1.55875 0.779375 0.626558i \(-0.215537\pi\)
0.779375 + 0.626558i \(0.215537\pi\)
\(998\) −62.2582 −1.97075
\(999\) −3.68158 −0.116480
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 \(a_p\))