Properties

Label 6010.2.a.c.1.10
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
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 1.10
Root \(1.27770\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+0.277700 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+0.277700 q^{6}\) \(+2.55233 q^{7}\) \(+1.00000 q^{8}\) \(-2.92288 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+0.277700 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+0.277700 q^{6}\) \(+2.55233 q^{7}\) \(+1.00000 q^{8}\) \(-2.92288 q^{9}\) \(+1.00000 q^{10}\) \(-4.94159 q^{11}\) \(+0.277700 q^{12}\) \(+4.28763 q^{13}\) \(+2.55233 q^{14}\) \(+0.277700 q^{15}\) \(+1.00000 q^{16}\) \(-3.28799 q^{17}\) \(-2.92288 q^{18}\) \(-3.94209 q^{19}\) \(+1.00000 q^{20}\) \(+0.708781 q^{21}\) \(-4.94159 q^{22}\) \(-6.03884 q^{23}\) \(+0.277700 q^{24}\) \(+1.00000 q^{25}\) \(+4.28763 q^{26}\) \(-1.64479 q^{27}\) \(+2.55233 q^{28}\) \(-7.47038 q^{29}\) \(+0.277700 q^{30}\) \(-4.60144 q^{31}\) \(+1.00000 q^{32}\) \(-1.37228 q^{33}\) \(-3.28799 q^{34}\) \(+2.55233 q^{35}\) \(-2.92288 q^{36}\) \(-1.65521 q^{37}\) \(-3.94209 q^{38}\) \(+1.19068 q^{39}\) \(+1.00000 q^{40}\) \(-8.01358 q^{41}\) \(+0.708781 q^{42}\) \(+1.78175 q^{43}\) \(-4.94159 q^{44}\) \(-2.92288 q^{45}\) \(-6.03884 q^{46}\) \(-3.33231 q^{47}\) \(+0.277700 q^{48}\) \(-0.485632 q^{49}\) \(+1.00000 q^{50}\) \(-0.913075 q^{51}\) \(+4.28763 q^{52}\) \(-8.76375 q^{53}\) \(-1.64479 q^{54}\) \(-4.94159 q^{55}\) \(+2.55233 q^{56}\) \(-1.09472 q^{57}\) \(-7.47038 q^{58}\) \(+6.61220 q^{59}\) \(+0.277700 q^{60}\) \(+10.0369 q^{61}\) \(-4.60144 q^{62}\) \(-7.46015 q^{63}\) \(+1.00000 q^{64}\) \(+4.28763 q^{65}\) \(-1.37228 q^{66}\) \(-5.12837 q^{67}\) \(-3.28799 q^{68}\) \(-1.67699 q^{69}\) \(+2.55233 q^{70}\) \(+2.50077 q^{71}\) \(-2.92288 q^{72}\) \(+2.44565 q^{73}\) \(-1.65521 q^{74}\) \(+0.277700 q^{75}\) \(-3.94209 q^{76}\) \(-12.6126 q^{77}\) \(+1.19068 q^{78}\) \(+10.1143 q^{79}\) \(+1.00000 q^{80}\) \(+8.31189 q^{81}\) \(-8.01358 q^{82}\) \(+1.46001 q^{83}\) \(+0.708781 q^{84}\) \(-3.28799 q^{85}\) \(+1.78175 q^{86}\) \(-2.07453 q^{87}\) \(-4.94159 q^{88}\) \(-7.59665 q^{89}\) \(-2.92288 q^{90}\) \(+10.9434 q^{91}\) \(-6.03884 q^{92}\) \(-1.27782 q^{93}\) \(-3.33231 q^{94}\) \(-3.94209 q^{95}\) \(+0.277700 q^{96}\) \(-0.655528 q^{97}\) \(-0.485632 q^{98}\) \(+14.4437 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.277700 0.160330 0.0801651 0.996782i \(-0.474455\pi\)
0.0801651 + 0.996782i \(0.474455\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 0.277700 0.113371
\(7\) 2.55233 0.964689 0.482344 0.875982i \(-0.339785\pi\)
0.482344 + 0.875982i \(0.339785\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.92288 −0.974294
\(10\) 1.00000 0.316228
\(11\) −4.94159 −1.48995 −0.744973 0.667094i \(-0.767538\pi\)
−0.744973 + 0.667094i \(0.767538\pi\)
\(12\) 0.277700 0.0801651
\(13\) 4.28763 1.18918 0.594588 0.804031i \(-0.297315\pi\)
0.594588 + 0.804031i \(0.297315\pi\)
\(14\) 2.55233 0.682138
\(15\) 0.277700 0.0717019
\(16\) 1.00000 0.250000
\(17\) −3.28799 −0.797455 −0.398727 0.917070i \(-0.630548\pi\)
−0.398727 + 0.917070i \(0.630548\pi\)
\(18\) −2.92288 −0.688930
\(19\) −3.94209 −0.904377 −0.452189 0.891922i \(-0.649357\pi\)
−0.452189 + 0.891922i \(0.649357\pi\)
\(20\) 1.00000 0.223607
\(21\) 0.708781 0.154669
\(22\) −4.94159 −1.05355
\(23\) −6.03884 −1.25918 −0.629592 0.776926i \(-0.716778\pi\)
−0.629592 + 0.776926i \(0.716778\pi\)
\(24\) 0.277700 0.0566853
\(25\) 1.00000 0.200000
\(26\) 4.28763 0.840874
\(27\) −1.64479 −0.316539
\(28\) 2.55233 0.482344
\(29\) −7.47038 −1.38721 −0.693607 0.720353i \(-0.743980\pi\)
−0.693607 + 0.720353i \(0.743980\pi\)
\(30\) 0.277700 0.0507009
\(31\) −4.60144 −0.826443 −0.413222 0.910630i \(-0.635597\pi\)
−0.413222 + 0.910630i \(0.635597\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.37228 −0.238884
\(34\) −3.28799 −0.563886
\(35\) 2.55233 0.431422
\(36\) −2.92288 −0.487147
\(37\) −1.65521 −0.272115 −0.136058 0.990701i \(-0.543443\pi\)
−0.136058 + 0.990701i \(0.543443\pi\)
\(38\) −3.94209 −0.639491
\(39\) 1.19068 0.190661
\(40\) 1.00000 0.158114
\(41\) −8.01358 −1.25151 −0.625755 0.780019i \(-0.715209\pi\)
−0.625755 + 0.780019i \(0.715209\pi\)
\(42\) 0.708781 0.109367
\(43\) 1.78175 0.271715 0.135857 0.990728i \(-0.456621\pi\)
0.135857 + 0.990728i \(0.456621\pi\)
\(44\) −4.94159 −0.744973
\(45\) −2.92288 −0.435718
\(46\) −6.03884 −0.890378
\(47\) −3.33231 −0.486068 −0.243034 0.970018i \(-0.578143\pi\)
−0.243034 + 0.970018i \(0.578143\pi\)
\(48\) 0.277700 0.0400826
\(49\) −0.485632 −0.0693761
\(50\) 1.00000 0.141421
\(51\) −0.913075 −0.127856
\(52\) 4.28763 0.594588
\(53\) −8.76375 −1.20379 −0.601896 0.798574i \(-0.705588\pi\)
−0.601896 + 0.798574i \(0.705588\pi\)
\(54\) −1.64479 −0.223827
\(55\) −4.94159 −0.666324
\(56\) 2.55233 0.341069
\(57\) −1.09472 −0.144999
\(58\) −7.47038 −0.980909
\(59\) 6.61220 0.860836 0.430418 0.902630i \(-0.358366\pi\)
0.430418 + 0.902630i \(0.358366\pi\)
\(60\) 0.277700 0.0358509
\(61\) 10.0369 1.28509 0.642547 0.766246i \(-0.277878\pi\)
0.642547 + 0.766246i \(0.277878\pi\)
\(62\) −4.60144 −0.584384
\(63\) −7.46015 −0.939890
\(64\) 1.00000 0.125000
\(65\) 4.28763 0.531816
\(66\) −1.37228 −0.168916
\(67\) −5.12837 −0.626530 −0.313265 0.949666i \(-0.601423\pi\)
−0.313265 + 0.949666i \(0.601423\pi\)
\(68\) −3.28799 −0.398727
\(69\) −1.67699 −0.201885
\(70\) 2.55233 0.305061
\(71\) 2.50077 0.296787 0.148394 0.988928i \(-0.452590\pi\)
0.148394 + 0.988928i \(0.452590\pi\)
\(72\) −2.92288 −0.344465
\(73\) 2.44565 0.286241 0.143121 0.989705i \(-0.454286\pi\)
0.143121 + 0.989705i \(0.454286\pi\)
\(74\) −1.65521 −0.192415
\(75\) 0.277700 0.0320661
\(76\) −3.94209 −0.452189
\(77\) −12.6126 −1.43733
\(78\) 1.19068 0.134818
\(79\) 10.1143 1.13795 0.568975 0.822355i \(-0.307340\pi\)
0.568975 + 0.822355i \(0.307340\pi\)
\(80\) 1.00000 0.111803
\(81\) 8.31189 0.923543
\(82\) −8.01358 −0.884952
\(83\) 1.46001 0.160257 0.0801287 0.996785i \(-0.474467\pi\)
0.0801287 + 0.996785i \(0.474467\pi\)
\(84\) 0.708781 0.0773344
\(85\) −3.28799 −0.356633
\(86\) 1.78175 0.192131
\(87\) −2.07453 −0.222412
\(88\) −4.94159 −0.526776
\(89\) −7.59665 −0.805243 −0.402622 0.915367i \(-0.631901\pi\)
−0.402622 + 0.915367i \(0.631901\pi\)
\(90\) −2.92288 −0.308099
\(91\) 10.9434 1.14718
\(92\) −6.03884 −0.629592
\(93\) −1.27782 −0.132504
\(94\) −3.33231 −0.343702
\(95\) −3.94209 −0.404450
\(96\) 0.277700 0.0283427
\(97\) −0.655528 −0.0665588 −0.0332794 0.999446i \(-0.510595\pi\)
−0.0332794 + 0.999446i \(0.510595\pi\)
\(98\) −0.485632 −0.0490563
\(99\) 14.4437 1.45165
\(100\) 1.00000 0.100000
\(101\) −6.14651 −0.611601 −0.305800 0.952096i \(-0.598924\pi\)
−0.305800 + 0.952096i \(0.598924\pi\)
\(102\) −0.913075 −0.0904079
\(103\) −2.00406 −0.197465 −0.0987327 0.995114i \(-0.531479\pi\)
−0.0987327 + 0.995114i \(0.531479\pi\)
\(104\) 4.28763 0.420437
\(105\) 0.708781 0.0691700
\(106\) −8.76375 −0.851210
\(107\) −5.83270 −0.563869 −0.281934 0.959434i \(-0.590976\pi\)
−0.281934 + 0.959434i \(0.590976\pi\)
\(108\) −1.64479 −0.158270
\(109\) 2.38596 0.228534 0.114267 0.993450i \(-0.463548\pi\)
0.114267 + 0.993450i \(0.463548\pi\)
\(110\) −4.94159 −0.471162
\(111\) −0.459653 −0.0436283
\(112\) 2.55233 0.241172
\(113\) 2.53256 0.238243 0.119121 0.992880i \(-0.461992\pi\)
0.119121 + 0.992880i \(0.461992\pi\)
\(114\) −1.09472 −0.102530
\(115\) −6.03884 −0.563125
\(116\) −7.47038 −0.693607
\(117\) −12.5323 −1.15861
\(118\) 6.61220 0.608703
\(119\) −8.39202 −0.769295
\(120\) 0.277700 0.0253504
\(121\) 13.4193 1.21994
\(122\) 10.0369 0.908699
\(123\) −2.22537 −0.200655
\(124\) −4.60144 −0.413222
\(125\) 1.00000 0.0894427
\(126\) −7.46015 −0.664603
\(127\) 4.39330 0.389842 0.194921 0.980819i \(-0.437555\pi\)
0.194921 + 0.980819i \(0.437555\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.494793 0.0435641
\(130\) 4.28763 0.376050
\(131\) 12.5579 1.09719 0.548596 0.836087i \(-0.315162\pi\)
0.548596 + 0.836087i \(0.315162\pi\)
\(132\) −1.37228 −0.119442
\(133\) −10.0615 −0.872442
\(134\) −5.12837 −0.443024
\(135\) −1.64479 −0.141561
\(136\) −3.28799 −0.281943
\(137\) 6.12044 0.522905 0.261452 0.965216i \(-0.415799\pi\)
0.261452 + 0.965216i \(0.415799\pi\)
\(138\) −1.67699 −0.142755
\(139\) 8.54580 0.724846 0.362423 0.932014i \(-0.381950\pi\)
0.362423 + 0.932014i \(0.381950\pi\)
\(140\) 2.55233 0.215711
\(141\) −0.925383 −0.0779313
\(142\) 2.50077 0.209860
\(143\) −21.1877 −1.77181
\(144\) −2.92288 −0.243574
\(145\) −7.47038 −0.620381
\(146\) 2.44565 0.202403
\(147\) −0.134860 −0.0111231
\(148\) −1.65521 −0.136058
\(149\) 4.25428 0.348524 0.174262 0.984699i \(-0.444246\pi\)
0.174262 + 0.984699i \(0.444246\pi\)
\(150\) 0.277700 0.0226741
\(151\) −1.20287 −0.0978879 −0.0489440 0.998802i \(-0.515586\pi\)
−0.0489440 + 0.998802i \(0.515586\pi\)
\(152\) −3.94209 −0.319746
\(153\) 9.61041 0.776955
\(154\) −12.6126 −1.01635
\(155\) −4.60144 −0.369597
\(156\) 1.19068 0.0953304
\(157\) −10.1536 −0.810349 −0.405175 0.914239i \(-0.632789\pi\)
−0.405175 + 0.914239i \(0.632789\pi\)
\(158\) 10.1143 0.804652
\(159\) −2.43369 −0.193004
\(160\) 1.00000 0.0790569
\(161\) −15.4131 −1.21472
\(162\) 8.31189 0.653044
\(163\) −7.04820 −0.552058 −0.276029 0.961149i \(-0.589019\pi\)
−0.276029 + 0.961149i \(0.589019\pi\)
\(164\) −8.01358 −0.625755
\(165\) −1.37228 −0.106832
\(166\) 1.46001 0.113319
\(167\) 13.1292 1.01597 0.507984 0.861367i \(-0.330391\pi\)
0.507984 + 0.861367i \(0.330391\pi\)
\(168\) 0.708781 0.0546837
\(169\) 5.38380 0.414139
\(170\) −3.28799 −0.252177
\(171\) 11.5223 0.881129
\(172\) 1.78175 0.135857
\(173\) 9.66095 0.734508 0.367254 0.930121i \(-0.380298\pi\)
0.367254 + 0.930121i \(0.380298\pi\)
\(174\) −2.07453 −0.157269
\(175\) 2.55233 0.192938
\(176\) −4.94159 −0.372487
\(177\) 1.83621 0.138018
\(178\) −7.59665 −0.569393
\(179\) −12.4660 −0.931756 −0.465878 0.884849i \(-0.654261\pi\)
−0.465878 + 0.884849i \(0.654261\pi\)
\(180\) −2.92288 −0.217859
\(181\) −5.60337 −0.416495 −0.208248 0.978076i \(-0.566776\pi\)
−0.208248 + 0.978076i \(0.566776\pi\)
\(182\) 10.9434 0.811182
\(183\) 2.78725 0.206039
\(184\) −6.03884 −0.445189
\(185\) −1.65521 −0.121694
\(186\) −1.27782 −0.0936944
\(187\) 16.2479 1.18816
\(188\) −3.33231 −0.243034
\(189\) −4.19803 −0.305362
\(190\) −3.94209 −0.285989
\(191\) 13.5010 0.976895 0.488448 0.872593i \(-0.337563\pi\)
0.488448 + 0.872593i \(0.337563\pi\)
\(192\) 0.277700 0.0200413
\(193\) 0.481989 0.0346943 0.0173472 0.999850i \(-0.494478\pi\)
0.0173472 + 0.999850i \(0.494478\pi\)
\(194\) −0.655528 −0.0470642
\(195\) 1.19068 0.0852661
\(196\) −0.485632 −0.0346880
\(197\) −9.40948 −0.670397 −0.335199 0.942147i \(-0.608803\pi\)
−0.335199 + 0.942147i \(0.608803\pi\)
\(198\) 14.4437 1.02647
\(199\) 18.8322 1.33498 0.667490 0.744619i \(-0.267369\pi\)
0.667490 + 0.744619i \(0.267369\pi\)
\(200\) 1.00000 0.0707107
\(201\) −1.42415 −0.100452
\(202\) −6.14651 −0.432467
\(203\) −19.0668 −1.33823
\(204\) −0.913075 −0.0639281
\(205\) −8.01358 −0.559693
\(206\) −2.00406 −0.139629
\(207\) 17.6508 1.22682
\(208\) 4.28763 0.297294
\(209\) 19.4802 1.34747
\(210\) 0.708781 0.0489106
\(211\) −0.421081 −0.0289884 −0.0144942 0.999895i \(-0.504614\pi\)
−0.0144942 + 0.999895i \(0.504614\pi\)
\(212\) −8.76375 −0.601896
\(213\) 0.694465 0.0475840
\(214\) −5.83270 −0.398715
\(215\) 1.78175 0.121514
\(216\) −1.64479 −0.111913
\(217\) −11.7444 −0.797260
\(218\) 2.38596 0.161598
\(219\) 0.679157 0.0458932
\(220\) −4.94159 −0.333162
\(221\) −14.0977 −0.948314
\(222\) −0.459653 −0.0308499
\(223\) 7.75783 0.519503 0.259751 0.965676i \(-0.416359\pi\)
0.259751 + 0.965676i \(0.416359\pi\)
\(224\) 2.55233 0.170534
\(225\) −2.92288 −0.194859
\(226\) 2.53256 0.168463
\(227\) −1.26402 −0.0838958 −0.0419479 0.999120i \(-0.513356\pi\)
−0.0419479 + 0.999120i \(0.513356\pi\)
\(228\) −1.09472 −0.0724995
\(229\) 17.1590 1.13390 0.566950 0.823752i \(-0.308123\pi\)
0.566950 + 0.823752i \(0.308123\pi\)
\(230\) −6.03884 −0.398189
\(231\) −3.50251 −0.230448
\(232\) −7.47038 −0.490454
\(233\) −11.0937 −0.726769 −0.363385 0.931639i \(-0.618379\pi\)
−0.363385 + 0.931639i \(0.618379\pi\)
\(234\) −12.5323 −0.819259
\(235\) −3.33231 −0.217376
\(236\) 6.61220 0.430418
\(237\) 2.80875 0.182448
\(238\) −8.39202 −0.543974
\(239\) −12.0870 −0.781845 −0.390922 0.920424i \(-0.627844\pi\)
−0.390922 + 0.920424i \(0.627844\pi\)
\(240\) 0.277700 0.0179255
\(241\) −25.6218 −1.65044 −0.825222 0.564809i \(-0.808950\pi\)
−0.825222 + 0.564809i \(0.808950\pi\)
\(242\) 13.4193 0.862628
\(243\) 7.24257 0.464611
\(244\) 10.0369 0.642547
\(245\) −0.485632 −0.0310259
\(246\) −2.22537 −0.141885
\(247\) −16.9022 −1.07546
\(248\) −4.60144 −0.292192
\(249\) 0.405446 0.0256941
\(250\) 1.00000 0.0632456
\(251\) −18.7449 −1.18317 −0.591583 0.806244i \(-0.701497\pi\)
−0.591583 + 0.806244i \(0.701497\pi\)
\(252\) −7.46015 −0.469945
\(253\) 29.8415 1.87612
\(254\) 4.39330 0.275660
\(255\) −0.913075 −0.0571790
\(256\) 1.00000 0.0625000
\(257\) −11.5427 −0.720015 −0.360008 0.932949i \(-0.617226\pi\)
−0.360008 + 0.932949i \(0.617226\pi\)
\(258\) 0.494793 0.0308045
\(259\) −4.22464 −0.262506
\(260\) 4.28763 0.265908
\(261\) 21.8350 1.35156
\(262\) 12.5579 0.775832
\(263\) −1.04321 −0.0643271 −0.0321635 0.999483i \(-0.510240\pi\)
−0.0321635 + 0.999483i \(0.510240\pi\)
\(264\) −1.37228 −0.0844581
\(265\) −8.76375 −0.538353
\(266\) −10.0615 −0.616910
\(267\) −2.10959 −0.129105
\(268\) −5.12837 −0.313265
\(269\) 2.08721 0.127260 0.0636299 0.997974i \(-0.479732\pi\)
0.0636299 + 0.997974i \(0.479732\pi\)
\(270\) −1.64479 −0.100098
\(271\) 32.6766 1.98496 0.992480 0.122405i \(-0.0390607\pi\)
0.992480 + 0.122405i \(0.0390607\pi\)
\(272\) −3.28799 −0.199364
\(273\) 3.03900 0.183928
\(274\) 6.12044 0.369749
\(275\) −4.94159 −0.297989
\(276\) −1.67699 −0.100943
\(277\) −22.1396 −1.33024 −0.665120 0.746737i \(-0.731620\pi\)
−0.665120 + 0.746737i \(0.731620\pi\)
\(278\) 8.54580 0.512543
\(279\) 13.4495 0.805199
\(280\) 2.55233 0.152531
\(281\) 8.01321 0.478028 0.239014 0.971016i \(-0.423176\pi\)
0.239014 + 0.971016i \(0.423176\pi\)
\(282\) −0.925383 −0.0551058
\(283\) 23.1815 1.37799 0.688997 0.724764i \(-0.258051\pi\)
0.688997 + 0.724764i \(0.258051\pi\)
\(284\) 2.50077 0.148394
\(285\) −1.09472 −0.0648455
\(286\) −21.1877 −1.25286
\(287\) −20.4533 −1.20732
\(288\) −2.92288 −0.172233
\(289\) −6.18912 −0.364066
\(290\) −7.47038 −0.438676
\(291\) −0.182040 −0.0106714
\(292\) 2.44565 0.143121
\(293\) 2.75354 0.160864 0.0804319 0.996760i \(-0.474370\pi\)
0.0804319 + 0.996760i \(0.474370\pi\)
\(294\) −0.134860 −0.00786521
\(295\) 6.61220 0.384977
\(296\) −1.65521 −0.0962073
\(297\) 8.12786 0.471626
\(298\) 4.25428 0.246444
\(299\) −25.8923 −1.49739
\(300\) 0.277700 0.0160330
\(301\) 4.54761 0.262120
\(302\) −1.20287 −0.0692172
\(303\) −1.70689 −0.0980581
\(304\) −3.94209 −0.226094
\(305\) 10.0369 0.574712
\(306\) 9.61041 0.549390
\(307\) −10.2302 −0.583866 −0.291933 0.956439i \(-0.594298\pi\)
−0.291933 + 0.956439i \(0.594298\pi\)
\(308\) −12.6126 −0.718667
\(309\) −0.556527 −0.0316597
\(310\) −4.60144 −0.261344
\(311\) −2.39920 −0.136046 −0.0680231 0.997684i \(-0.521669\pi\)
−0.0680231 + 0.997684i \(0.521669\pi\)
\(312\) 1.19068 0.0674088
\(313\) −15.1268 −0.855015 −0.427508 0.904012i \(-0.640608\pi\)
−0.427508 + 0.904012i \(0.640608\pi\)
\(314\) −10.1536 −0.573003
\(315\) −7.46015 −0.420332
\(316\) 10.1143 0.568975
\(317\) −20.8116 −1.16890 −0.584448 0.811431i \(-0.698689\pi\)
−0.584448 + 0.811431i \(0.698689\pi\)
\(318\) −2.43369 −0.136475
\(319\) 36.9156 2.06688
\(320\) 1.00000 0.0559017
\(321\) −1.61974 −0.0904052
\(322\) −15.4131 −0.858938
\(323\) 12.9615 0.721200
\(324\) 8.31189 0.461772
\(325\) 4.28763 0.237835
\(326\) −7.04820 −0.390364
\(327\) 0.662583 0.0366409
\(328\) −8.01358 −0.442476
\(329\) −8.50514 −0.468904
\(330\) −1.37228 −0.0755416
\(331\) −8.14597 −0.447743 −0.223872 0.974619i \(-0.571870\pi\)
−0.223872 + 0.974619i \(0.571870\pi\)
\(332\) 1.46001 0.0801287
\(333\) 4.83799 0.265120
\(334\) 13.1292 0.718398
\(335\) −5.12837 −0.280193
\(336\) 0.708781 0.0386672
\(337\) −9.14403 −0.498107 −0.249053 0.968490i \(-0.580119\pi\)
−0.249053 + 0.968490i \(0.580119\pi\)
\(338\) 5.38380 0.292840
\(339\) 0.703291 0.0381975
\(340\) −3.28799 −0.178316
\(341\) 22.7385 1.23136
\(342\) 11.5223 0.623053
\(343\) −19.1058 −1.03161
\(344\) 1.78175 0.0960656
\(345\) −1.67699 −0.0902859
\(346\) 9.66095 0.519376
\(347\) −5.88331 −0.315833 −0.157916 0.987452i \(-0.550478\pi\)
−0.157916 + 0.987452i \(0.550478\pi\)
\(348\) −2.07453 −0.111206
\(349\) 3.32250 0.177850 0.0889248 0.996038i \(-0.471657\pi\)
0.0889248 + 0.996038i \(0.471657\pi\)
\(350\) 2.55233 0.136428
\(351\) −7.05224 −0.376421
\(352\) −4.94159 −0.263388
\(353\) 22.7150 1.20900 0.604499 0.796606i \(-0.293373\pi\)
0.604499 + 0.796606i \(0.293373\pi\)
\(354\) 1.83621 0.0975935
\(355\) 2.50077 0.132727
\(356\) −7.59665 −0.402622
\(357\) −2.33047 −0.123341
\(358\) −12.4660 −0.658851
\(359\) 15.2694 0.805888 0.402944 0.915225i \(-0.367987\pi\)
0.402944 + 0.915225i \(0.367987\pi\)
\(360\) −2.92288 −0.154049
\(361\) −3.45994 −0.182102
\(362\) −5.60337 −0.294507
\(363\) 3.72656 0.195593
\(364\) 10.9434 0.573592
\(365\) 2.44565 0.128011
\(366\) 2.78725 0.145692
\(367\) 26.3432 1.37511 0.687553 0.726134i \(-0.258685\pi\)
0.687553 + 0.726134i \(0.258685\pi\)
\(368\) −6.03884 −0.314796
\(369\) 23.4227 1.21934
\(370\) −1.65521 −0.0860504
\(371\) −22.3679 −1.16129
\(372\) −1.27782 −0.0662519
\(373\) 25.4950 1.32008 0.660040 0.751230i \(-0.270539\pi\)
0.660040 + 0.751230i \(0.270539\pi\)
\(374\) 16.2479 0.840159
\(375\) 0.277700 0.0143404
\(376\) −3.33231 −0.171851
\(377\) −32.0302 −1.64964
\(378\) −4.19803 −0.215923
\(379\) −19.8048 −1.01730 −0.508652 0.860972i \(-0.669856\pi\)
−0.508652 + 0.860972i \(0.669856\pi\)
\(380\) −3.94209 −0.202225
\(381\) 1.22002 0.0625035
\(382\) 13.5010 0.690769
\(383\) −12.7968 −0.653884 −0.326942 0.945044i \(-0.606018\pi\)
−0.326942 + 0.945044i \(0.606018\pi\)
\(384\) 0.277700 0.0141713
\(385\) −12.6126 −0.642795
\(386\) 0.481989 0.0245326
\(387\) −5.20785 −0.264730
\(388\) −0.655528 −0.0332794
\(389\) 1.10510 0.0560307 0.0280154 0.999607i \(-0.491081\pi\)
0.0280154 + 0.999607i \(0.491081\pi\)
\(390\) 1.19068 0.0602923
\(391\) 19.8556 1.00414
\(392\) −0.485632 −0.0245281
\(393\) 3.48734 0.175913
\(394\) −9.40948 −0.474043
\(395\) 10.1143 0.508906
\(396\) 14.4437 0.725823
\(397\) −10.7718 −0.540619 −0.270310 0.962773i \(-0.587126\pi\)
−0.270310 + 0.962773i \(0.587126\pi\)
\(398\) 18.8322 0.943973
\(399\) −2.79408 −0.139879
\(400\) 1.00000 0.0500000
\(401\) −4.30494 −0.214978 −0.107489 0.994206i \(-0.534281\pi\)
−0.107489 + 0.994206i \(0.534281\pi\)
\(402\) −1.42415 −0.0710301
\(403\) −19.7293 −0.982786
\(404\) −6.14651 −0.305800
\(405\) 8.31189 0.413021
\(406\) −19.0668 −0.946271
\(407\) 8.17939 0.405437
\(408\) −0.913075 −0.0452040
\(409\) 28.0375 1.38636 0.693182 0.720763i \(-0.256208\pi\)
0.693182 + 0.720763i \(0.256208\pi\)
\(410\) −8.01358 −0.395762
\(411\) 1.69965 0.0838374
\(412\) −2.00406 −0.0987327
\(413\) 16.8765 0.830438
\(414\) 17.6508 0.867490
\(415\) 1.46001 0.0716693
\(416\) 4.28763 0.210219
\(417\) 2.37317 0.116215
\(418\) 19.4802 0.952808
\(419\) 9.83699 0.480569 0.240284 0.970703i \(-0.422759\pi\)
0.240284 + 0.970703i \(0.422759\pi\)
\(420\) 0.708781 0.0345850
\(421\) −11.3117 −0.551296 −0.275648 0.961259i \(-0.588892\pi\)
−0.275648 + 0.961259i \(0.588892\pi\)
\(422\) −0.421081 −0.0204979
\(423\) 9.73995 0.473573
\(424\) −8.76375 −0.425605
\(425\) −3.28799 −0.159491
\(426\) 0.694465 0.0336469
\(427\) 25.6175 1.23972
\(428\) −5.83270 −0.281934
\(429\) −5.88384 −0.284074
\(430\) 1.78175 0.0859237
\(431\) −20.3784 −0.981594 −0.490797 0.871274i \(-0.663294\pi\)
−0.490797 + 0.871274i \(0.663294\pi\)
\(432\) −1.64479 −0.0791348
\(433\) −16.2983 −0.783246 −0.391623 0.920126i \(-0.628086\pi\)
−0.391623 + 0.920126i \(0.628086\pi\)
\(434\) −11.7444 −0.563748
\(435\) −2.07453 −0.0994659
\(436\) 2.38596 0.114267
\(437\) 23.8056 1.13878
\(438\) 0.679157 0.0324514
\(439\) 16.3355 0.779650 0.389825 0.920889i \(-0.372535\pi\)
0.389825 + 0.920889i \(0.372535\pi\)
\(440\) −4.94159 −0.235581
\(441\) 1.41945 0.0675927
\(442\) −14.0977 −0.670559
\(443\) −30.3955 −1.44413 −0.722066 0.691824i \(-0.756807\pi\)
−0.722066 + 0.691824i \(0.756807\pi\)
\(444\) −0.459653 −0.0218142
\(445\) −7.59665 −0.360116
\(446\) 7.75783 0.367344
\(447\) 1.18141 0.0558789
\(448\) 2.55233 0.120586
\(449\) 11.9134 0.562230 0.281115 0.959674i \(-0.409296\pi\)
0.281115 + 0.959674i \(0.409296\pi\)
\(450\) −2.92288 −0.137786
\(451\) 39.5998 1.86468
\(452\) 2.53256 0.119121
\(453\) −0.334036 −0.0156944
\(454\) −1.26402 −0.0593233
\(455\) 10.9434 0.513036
\(456\) −1.09472 −0.0512649
\(457\) −35.3128 −1.65186 −0.825931 0.563771i \(-0.809350\pi\)
−0.825931 + 0.563771i \(0.809350\pi\)
\(458\) 17.1590 0.801788
\(459\) 5.40804 0.252426
\(460\) −6.03884 −0.281562
\(461\) 37.5505 1.74890 0.874450 0.485116i \(-0.161223\pi\)
0.874450 + 0.485116i \(0.161223\pi\)
\(462\) −3.50251 −0.162951
\(463\) 29.2633 1.35998 0.679992 0.733220i \(-0.261983\pi\)
0.679992 + 0.733220i \(0.261983\pi\)
\(464\) −7.47038 −0.346804
\(465\) −1.27782 −0.0592575
\(466\) −11.0937 −0.513904
\(467\) −2.05376 −0.0950366 −0.0475183 0.998870i \(-0.515131\pi\)
−0.0475183 + 0.998870i \(0.515131\pi\)
\(468\) −12.5323 −0.579303
\(469\) −13.0893 −0.604406
\(470\) −3.33231 −0.153708
\(471\) −2.81967 −0.129924
\(472\) 6.61220 0.304351
\(473\) −8.80469 −0.404840
\(474\) 2.80875 0.129010
\(475\) −3.94209 −0.180875
\(476\) −8.39202 −0.384648
\(477\) 25.6154 1.17285
\(478\) −12.0870 −0.552848
\(479\) −22.3022 −1.01901 −0.509506 0.860467i \(-0.670172\pi\)
−0.509506 + 0.860467i \(0.670172\pi\)
\(480\) 0.277700 0.0126752
\(481\) −7.09695 −0.323593
\(482\) −25.6218 −1.16704
\(483\) −4.28022 −0.194757
\(484\) 13.4193 0.609970
\(485\) −0.655528 −0.0297660
\(486\) 7.24257 0.328530
\(487\) −22.7781 −1.03218 −0.516088 0.856536i \(-0.672612\pi\)
−0.516088 + 0.856536i \(0.672612\pi\)
\(488\) 10.0369 0.454349
\(489\) −1.95729 −0.0885116
\(490\) −0.485632 −0.0219386
\(491\) −18.0674 −0.815372 −0.407686 0.913122i \(-0.633664\pi\)
−0.407686 + 0.913122i \(0.633664\pi\)
\(492\) −2.22537 −0.100328
\(493\) 24.5625 1.10624
\(494\) −16.9022 −0.760467
\(495\) 14.4437 0.649196
\(496\) −4.60144 −0.206611
\(497\) 6.38279 0.286307
\(498\) 0.405446 0.0181685
\(499\) −37.4965 −1.67857 −0.839286 0.543690i \(-0.817027\pi\)
−0.839286 + 0.543690i \(0.817027\pi\)
\(500\) 1.00000 0.0447214
\(501\) 3.64598 0.162890
\(502\) −18.7449 −0.836624
\(503\) 19.0805 0.850757 0.425378 0.905016i \(-0.360141\pi\)
0.425378 + 0.905016i \(0.360141\pi\)
\(504\) −7.46015 −0.332301
\(505\) −6.14651 −0.273516
\(506\) 29.8415 1.32662
\(507\) 1.49508 0.0663990
\(508\) 4.39330 0.194921
\(509\) −32.0076 −1.41871 −0.709356 0.704851i \(-0.751014\pi\)
−0.709356 + 0.704851i \(0.751014\pi\)
\(510\) −0.913075 −0.0404317
\(511\) 6.24209 0.276134
\(512\) 1.00000 0.0441942
\(513\) 6.48389 0.286271
\(514\) −11.5427 −0.509128
\(515\) −2.00406 −0.0883092
\(516\) 0.494793 0.0217820
\(517\) 16.4669 0.724215
\(518\) −4.22464 −0.185620
\(519\) 2.68285 0.117764
\(520\) 4.28763 0.188025
\(521\) −18.1180 −0.793765 −0.396882 0.917870i \(-0.629908\pi\)
−0.396882 + 0.917870i \(0.629908\pi\)
\(522\) 21.8350 0.955694
\(523\) −10.0446 −0.439219 −0.219610 0.975588i \(-0.570478\pi\)
−0.219610 + 0.975588i \(0.570478\pi\)
\(524\) 12.5579 0.548596
\(525\) 0.708781 0.0309338
\(526\) −1.04321 −0.0454861
\(527\) 15.1295 0.659051
\(528\) −1.37228 −0.0597209
\(529\) 13.4676 0.585546
\(530\) −8.76375 −0.380673
\(531\) −19.3267 −0.838707
\(532\) −10.0615 −0.436221
\(533\) −34.3593 −1.48827
\(534\) −2.10959 −0.0912909
\(535\) −5.83270 −0.252170
\(536\) −5.12837 −0.221512
\(537\) −3.46182 −0.149389
\(538\) 2.08721 0.0899862
\(539\) 2.39980 0.103367
\(540\) −1.64479 −0.0707803
\(541\) 13.4911 0.580028 0.290014 0.957022i \(-0.406340\pi\)
0.290014 + 0.957022i \(0.406340\pi\)
\(542\) 32.6766 1.40358
\(543\) −1.55606 −0.0667768
\(544\) −3.28799 −0.140971
\(545\) 2.38596 0.102203
\(546\) 3.03900 0.130057
\(547\) −12.1566 −0.519777 −0.259889 0.965639i \(-0.583686\pi\)
−0.259889 + 0.965639i \(0.583686\pi\)
\(548\) 6.12044 0.261452
\(549\) −29.3367 −1.25206
\(550\) −4.94159 −0.210710
\(551\) 29.4489 1.25456
\(552\) −1.67699 −0.0713773
\(553\) 25.8150 1.09777
\(554\) −22.1396 −0.940621
\(555\) −0.459653 −0.0195112
\(556\) 8.54580 0.362423
\(557\) −15.8398 −0.671152 −0.335576 0.942013i \(-0.608931\pi\)
−0.335576 + 0.942013i \(0.608931\pi\)
\(558\) 13.4495 0.569362
\(559\) 7.63950 0.323116
\(560\) 2.55233 0.107855
\(561\) 4.51205 0.190499
\(562\) 8.01321 0.338017
\(563\) 10.3672 0.436927 0.218464 0.975845i \(-0.429895\pi\)
0.218464 + 0.975845i \(0.429895\pi\)
\(564\) −0.925383 −0.0389657
\(565\) 2.53256 0.106545
\(566\) 23.1815 0.974389
\(567\) 21.2147 0.890932
\(568\) 2.50077 0.104930
\(569\) −30.1146 −1.26247 −0.631235 0.775592i \(-0.717452\pi\)
−0.631235 + 0.775592i \(0.717452\pi\)
\(570\) −1.09472 −0.0458527
\(571\) −30.8585 −1.29139 −0.645695 0.763596i \(-0.723432\pi\)
−0.645695 + 0.763596i \(0.723432\pi\)
\(572\) −21.1877 −0.885904
\(573\) 3.74922 0.156626
\(574\) −20.4533 −0.853703
\(575\) −6.03884 −0.251837
\(576\) −2.92288 −0.121787
\(577\) −25.0135 −1.04132 −0.520662 0.853763i \(-0.674315\pi\)
−0.520662 + 0.853763i \(0.674315\pi\)
\(578\) −6.18912 −0.257434
\(579\) 0.133848 0.00556255
\(580\) −7.47038 −0.310191
\(581\) 3.72643 0.154598
\(582\) −0.182040 −0.00754581
\(583\) 43.3069 1.79359
\(584\) 2.44565 0.101202
\(585\) −12.5323 −0.518145
\(586\) 2.75354 0.113748
\(587\) 11.1035 0.458291 0.229145 0.973392i \(-0.426407\pi\)
0.229145 + 0.973392i \(0.426407\pi\)
\(588\) −0.134860 −0.00556154
\(589\) 18.1393 0.747416
\(590\) 6.61220 0.272220
\(591\) −2.61301 −0.107485
\(592\) −1.65521 −0.0680288
\(593\) −12.1577 −0.499256 −0.249628 0.968342i \(-0.580308\pi\)
−0.249628 + 0.968342i \(0.580308\pi\)
\(594\) 8.12786 0.333490
\(595\) −8.39202 −0.344039
\(596\) 4.25428 0.174262
\(597\) 5.22971 0.214038
\(598\) −25.8923 −1.05882
\(599\) −44.2078 −1.80628 −0.903141 0.429345i \(-0.858744\pi\)
−0.903141 + 0.429345i \(0.858744\pi\)
\(600\) 0.277700 0.0113371
\(601\) −1.00000 −0.0407909
\(602\) 4.54761 0.185347
\(603\) 14.9896 0.610425
\(604\) −1.20287 −0.0489440
\(605\) 13.4193 0.545574
\(606\) −1.70689 −0.0693376
\(607\) −28.9368 −1.17451 −0.587255 0.809402i \(-0.699791\pi\)
−0.587255 + 0.809402i \(0.699791\pi\)
\(608\) −3.94209 −0.159873
\(609\) −5.29487 −0.214559
\(610\) 10.0369 0.406382
\(611\) −14.2877 −0.578020
\(612\) 9.61041 0.388478
\(613\) 3.16304 0.127754 0.0638770 0.997958i \(-0.479653\pi\)
0.0638770 + 0.997958i \(0.479653\pi\)
\(614\) −10.2302 −0.412856
\(615\) −2.22537 −0.0897357
\(616\) −12.6126 −0.508174
\(617\) 18.2934 0.736465 0.368232 0.929734i \(-0.379963\pi\)
0.368232 + 0.929734i \(0.379963\pi\)
\(618\) −0.556527 −0.0223868
\(619\) 0.884234 0.0355404 0.0177702 0.999842i \(-0.494343\pi\)
0.0177702 + 0.999842i \(0.494343\pi\)
\(620\) −4.60144 −0.184798
\(621\) 9.93259 0.398581
\(622\) −2.39920 −0.0961992
\(623\) −19.3891 −0.776809
\(624\) 1.19068 0.0476652
\(625\) 1.00000 0.0400000
\(626\) −15.1268 −0.604587
\(627\) 5.40965 0.216041
\(628\) −10.1536 −0.405175
\(629\) 5.44232 0.217000
\(630\) −7.46015 −0.297219
\(631\) −12.5644 −0.500183 −0.250091 0.968222i \(-0.580461\pi\)
−0.250091 + 0.968222i \(0.580461\pi\)
\(632\) 10.1143 0.402326
\(633\) −0.116934 −0.00464772
\(634\) −20.8116 −0.826534
\(635\) 4.39330 0.174343
\(636\) −2.43369 −0.0965022
\(637\) −2.08221 −0.0825003
\(638\) 36.9156 1.46150
\(639\) −7.30947 −0.289158
\(640\) 1.00000 0.0395285
\(641\) 4.36246 0.172307 0.0861535 0.996282i \(-0.472542\pi\)
0.0861535 + 0.996282i \(0.472542\pi\)
\(642\) −1.61974 −0.0639262
\(643\) 29.1984 1.15147 0.575736 0.817636i \(-0.304716\pi\)
0.575736 + 0.817636i \(0.304716\pi\)
\(644\) −15.4131 −0.607361
\(645\) 0.494793 0.0194824
\(646\) 12.9615 0.509965
\(647\) −32.3343 −1.27119 −0.635595 0.772022i \(-0.719245\pi\)
−0.635595 + 0.772022i \(0.719245\pi\)
\(648\) 8.31189 0.326522
\(649\) −32.6748 −1.28260
\(650\) 4.28763 0.168175
\(651\) −3.26142 −0.127825
\(652\) −7.04820 −0.276029
\(653\) 24.9559 0.976598 0.488299 0.872676i \(-0.337617\pi\)
0.488299 + 0.872676i \(0.337617\pi\)
\(654\) 0.662583 0.0259090
\(655\) 12.5579 0.490680
\(656\) −8.01358 −0.312878
\(657\) −7.14834 −0.278883
\(658\) −8.50514 −0.331565
\(659\) −44.1975 −1.72169 −0.860844 0.508868i \(-0.830064\pi\)
−0.860844 + 0.508868i \(0.830064\pi\)
\(660\) −1.37228 −0.0534160
\(661\) −25.1576 −0.978516 −0.489258 0.872139i \(-0.662732\pi\)
−0.489258 + 0.872139i \(0.662732\pi\)
\(662\) −8.14597 −0.316602
\(663\) −3.91493 −0.152043
\(664\) 1.46001 0.0566595
\(665\) −10.0615 −0.390168
\(666\) 4.83799 0.187468
\(667\) 45.1124 1.74676
\(668\) 13.1292 0.507984
\(669\) 2.15435 0.0832920
\(670\) −5.12837 −0.198126
\(671\) −49.5983 −1.91472
\(672\) 0.708781 0.0273418
\(673\) −13.0385 −0.502598 −0.251299 0.967910i \(-0.580858\pi\)
−0.251299 + 0.967910i \(0.580858\pi\)
\(674\) −9.14403 −0.352215
\(675\) −1.64479 −0.0633078
\(676\) 5.38380 0.207069
\(677\) 14.6706 0.563835 0.281918 0.959439i \(-0.409030\pi\)
0.281918 + 0.959439i \(0.409030\pi\)
\(678\) 0.703291 0.0270097
\(679\) −1.67312 −0.0642085
\(680\) −3.28799 −0.126089
\(681\) −0.351018 −0.0134510
\(682\) 22.7385 0.870701
\(683\) 23.0514 0.882039 0.441019 0.897498i \(-0.354617\pi\)
0.441019 + 0.897498i \(0.354617\pi\)
\(684\) 11.5223 0.440565
\(685\) 6.12044 0.233850
\(686\) −19.1058 −0.729462
\(687\) 4.76506 0.181798
\(688\) 1.78175 0.0679286
\(689\) −37.5757 −1.43152
\(690\) −1.67699 −0.0638418
\(691\) −12.3973 −0.471614 −0.235807 0.971800i \(-0.575773\pi\)
−0.235807 + 0.971800i \(0.575773\pi\)
\(692\) 9.66095 0.367254
\(693\) 36.8650 1.40039
\(694\) −5.88331 −0.223328
\(695\) 8.54580 0.324161
\(696\) −2.07453 −0.0786347
\(697\) 26.3486 0.998023
\(698\) 3.32250 0.125759
\(699\) −3.08071 −0.116523
\(700\) 2.55233 0.0964689
\(701\) 44.9218 1.69667 0.848337 0.529456i \(-0.177604\pi\)
0.848337 + 0.529456i \(0.177604\pi\)
\(702\) −7.05224 −0.266170
\(703\) 6.52499 0.246095
\(704\) −4.94159 −0.186243
\(705\) −0.925383 −0.0348520
\(706\) 22.7150 0.854891
\(707\) −15.6879 −0.590004
\(708\) 1.83621 0.0690090
\(709\) −10.9410 −0.410899 −0.205449 0.978668i \(-0.565866\pi\)
−0.205449 + 0.978668i \(0.565866\pi\)
\(710\) 2.50077 0.0938523
\(711\) −29.5630 −1.10870
\(712\) −7.59665 −0.284696
\(713\) 27.7874 1.04064
\(714\) −2.33047 −0.0872155
\(715\) −21.1877 −0.792377
\(716\) −12.4660 −0.465878
\(717\) −3.35657 −0.125353
\(718\) 15.2694 0.569849
\(719\) 15.7049 0.585693 0.292847 0.956159i \(-0.405397\pi\)
0.292847 + 0.956159i \(0.405397\pi\)
\(720\) −2.92288 −0.108929
\(721\) −5.11500 −0.190493
\(722\) −3.45994 −0.128766
\(723\) −7.11517 −0.264616
\(724\) −5.60337 −0.208248
\(725\) −7.47038 −0.277443
\(726\) 3.72656 0.138305
\(727\) −11.8864 −0.440841 −0.220421 0.975405i \(-0.570743\pi\)
−0.220421 + 0.975405i \(0.570743\pi\)
\(728\) 10.9434 0.405591
\(729\) −22.9244 −0.849052
\(730\) 2.44565 0.0905175
\(731\) −5.85838 −0.216680
\(732\) 2.78725 0.103020
\(733\) 45.6422 1.68583 0.842916 0.538045i \(-0.180837\pi\)
0.842916 + 0.538045i \(0.180837\pi\)
\(734\) 26.3432 0.972347
\(735\) −0.134860 −0.00497439
\(736\) −6.03884 −0.222595
\(737\) 25.3423 0.933497
\(738\) 23.4227 0.862203
\(739\) −11.0877 −0.407869 −0.203934 0.978985i \(-0.565373\pi\)
−0.203934 + 0.978985i \(0.565373\pi\)
\(740\) −1.65521 −0.0608468
\(741\) −4.69375 −0.172429
\(742\) −22.3679 −0.821153
\(743\) 11.3725 0.417217 0.208609 0.977999i \(-0.433107\pi\)
0.208609 + 0.977999i \(0.433107\pi\)
\(744\) −1.27782 −0.0468472
\(745\) 4.25428 0.155865
\(746\) 25.4950 0.933438
\(747\) −4.26745 −0.156138
\(748\) 16.2479 0.594082
\(749\) −14.8870 −0.543958
\(750\) 0.277700 0.0101402
\(751\) −3.67148 −0.133974 −0.0669870 0.997754i \(-0.521339\pi\)
−0.0669870 + 0.997754i \(0.521339\pi\)
\(752\) −3.33231 −0.121517
\(753\) −5.20545 −0.189697
\(754\) −32.0302 −1.16647
\(755\) −1.20287 −0.0437768
\(756\) −4.19803 −0.152681
\(757\) −11.4260 −0.415286 −0.207643 0.978205i \(-0.566579\pi\)
−0.207643 + 0.978205i \(0.566579\pi\)
\(758\) −19.8048 −0.719343
\(759\) 8.28699 0.300799
\(760\) −3.94209 −0.142995
\(761\) 22.6045 0.819414 0.409707 0.912217i \(-0.365631\pi\)
0.409707 + 0.912217i \(0.365631\pi\)
\(762\) 1.22002 0.0441967
\(763\) 6.08976 0.220464
\(764\) 13.5010 0.488448
\(765\) 9.61041 0.347465
\(766\) −12.7968 −0.462366
\(767\) 28.3507 1.02368
\(768\) 0.277700 0.0100206
\(769\) 0.658801 0.0237570 0.0118785 0.999929i \(-0.496219\pi\)
0.0118785 + 0.999929i \(0.496219\pi\)
\(770\) −12.6126 −0.454525
\(771\) −3.20542 −0.115440
\(772\) 0.481989 0.0173472
\(773\) −35.8459 −1.28929 −0.644644 0.764483i \(-0.722994\pi\)
−0.644644 + 0.764483i \(0.722994\pi\)
\(774\) −5.20785 −0.187192
\(775\) −4.60144 −0.165289
\(776\) −0.655528 −0.0235321
\(777\) −1.17318 −0.0420877
\(778\) 1.10510 0.0396197
\(779\) 31.5902 1.13184
\(780\) 1.19068 0.0426331
\(781\) −12.3578 −0.442197
\(782\) 19.8556 0.710036
\(783\) 12.2872 0.439108
\(784\) −0.485632 −0.0173440
\(785\) −10.1536 −0.362399
\(786\) 3.48734 0.124389
\(787\) 14.7576 0.526053 0.263026 0.964789i \(-0.415279\pi\)
0.263026 + 0.964789i \(0.415279\pi\)
\(788\) −9.40948 −0.335199
\(789\) −0.289700 −0.0103136
\(790\) 10.1143 0.359851
\(791\) 6.46391 0.229830
\(792\) 14.4437 0.513234
\(793\) 43.0346 1.52820
\(794\) −10.7718 −0.382275
\(795\) −2.43369 −0.0863142
\(796\) 18.8322 0.667490
\(797\) −3.04398 −0.107823 −0.0539116 0.998546i \(-0.517169\pi\)
−0.0539116 + 0.998546i \(0.517169\pi\)
\(798\) −2.79408 −0.0989093
\(799\) 10.9566 0.387617
\(800\) 1.00000 0.0353553
\(801\) 22.2041 0.784544
\(802\) −4.30494 −0.152013
\(803\) −12.0854 −0.426484
\(804\) −1.42415 −0.0502259
\(805\) −15.4131 −0.543240
\(806\) −19.7293 −0.694935
\(807\) 0.579620 0.0204036
\(808\) −6.14651 −0.216234
\(809\) 0.954037 0.0335422 0.0167711 0.999859i \(-0.494661\pi\)
0.0167711 + 0.999859i \(0.494661\pi\)
\(810\) 8.31189 0.292050
\(811\) −3.29009 −0.115531 −0.0577654 0.998330i \(-0.518398\pi\)
−0.0577654 + 0.998330i \(0.518398\pi\)
\(812\) −19.0668 −0.669115
\(813\) 9.07429 0.318249
\(814\) 8.17939 0.286687
\(815\) −7.04820 −0.246888
\(816\) −0.913075 −0.0319640
\(817\) −7.02382 −0.245732
\(818\) 28.0375 0.980307
\(819\) −31.9864 −1.11769
\(820\) −8.01358 −0.279846
\(821\) 23.2855 0.812670 0.406335 0.913724i \(-0.366807\pi\)
0.406335 + 0.913724i \(0.366807\pi\)
\(822\) 1.69965 0.0592820
\(823\) −40.0869 −1.39734 −0.698670 0.715444i \(-0.746225\pi\)
−0.698670 + 0.715444i \(0.746225\pi\)
\(824\) −2.00406 −0.0698146
\(825\) −1.37228 −0.0477767
\(826\) 16.8765 0.587208
\(827\) −17.1194 −0.595301 −0.297651 0.954675i \(-0.596203\pi\)
−0.297651 + 0.954675i \(0.596203\pi\)
\(828\) 17.6508 0.613408
\(829\) 6.44906 0.223985 0.111993 0.993709i \(-0.464277\pi\)
0.111993 + 0.993709i \(0.464277\pi\)
\(830\) 1.46001 0.0506778
\(831\) −6.14817 −0.213278
\(832\) 4.28763 0.148647
\(833\) 1.59675 0.0553243
\(834\) 2.37317 0.0821762
\(835\) 13.1292 0.454355
\(836\) 19.4802 0.673737
\(837\) 7.56839 0.261602
\(838\) 9.83699 0.339813
\(839\) −8.16787 −0.281986 −0.140993 0.990011i \(-0.545030\pi\)
−0.140993 + 0.990011i \(0.545030\pi\)
\(840\) 0.708781 0.0244553
\(841\) 26.8066 0.924364
\(842\) −11.3117 −0.389825
\(843\) 2.22527 0.0766424
\(844\) −0.421081 −0.0144942
\(845\) 5.38380 0.185209
\(846\) 9.73995 0.334867
\(847\) 34.2505 1.17686
\(848\) −8.76375 −0.300948
\(849\) 6.43749 0.220934
\(850\) −3.28799 −0.112777
\(851\) 9.99556 0.342643
\(852\) 0.694465 0.0237920
\(853\) 46.9574 1.60779 0.803895 0.594772i \(-0.202757\pi\)
0.803895 + 0.594772i \(0.202757\pi\)
\(854\) 25.6175 0.876611
\(855\) 11.5223 0.394053
\(856\) −5.83270 −0.199358
\(857\) 33.5470 1.14594 0.572971 0.819576i \(-0.305791\pi\)
0.572971 + 0.819576i \(0.305791\pi\)
\(858\) −5.88384 −0.200871
\(859\) 37.2655 1.27148 0.635741 0.771902i \(-0.280695\pi\)
0.635741 + 0.771902i \(0.280695\pi\)
\(860\) 1.78175 0.0607572
\(861\) −5.67987 −0.193570
\(862\) −20.3784 −0.694092
\(863\) 24.6009 0.837425 0.418712 0.908119i \(-0.362482\pi\)
0.418712 + 0.908119i \(0.362482\pi\)
\(864\) −1.64479 −0.0559567
\(865\) 9.66095 0.328482
\(866\) −16.2983 −0.553839
\(867\) −1.71872 −0.0583708
\(868\) −11.7444 −0.398630
\(869\) −49.9808 −1.69548
\(870\) −2.07453 −0.0703330
\(871\) −21.9886 −0.745054
\(872\) 2.38596 0.0807989
\(873\) 1.91603 0.0648478
\(874\) 23.8056 0.805238
\(875\) 2.55233 0.0862844
\(876\) 0.679157 0.0229466
\(877\) −15.4347 −0.521194 −0.260597 0.965448i \(-0.583919\pi\)
−0.260597 + 0.965448i \(0.583919\pi\)
\(878\) 16.3355 0.551296
\(879\) 0.764660 0.0257913
\(880\) −4.94159 −0.166581
\(881\) 21.1992 0.714218 0.357109 0.934063i \(-0.383762\pi\)
0.357109 + 0.934063i \(0.383762\pi\)
\(882\) 1.41945 0.0477952
\(883\) −0.952077 −0.0320400 −0.0160200 0.999872i \(-0.505100\pi\)
−0.0160200 + 0.999872i \(0.505100\pi\)
\(884\) −14.0977 −0.474157
\(885\) 1.83621 0.0617235
\(886\) −30.3955 −1.02116
\(887\) 38.0504 1.27761 0.638804 0.769370i \(-0.279430\pi\)
0.638804 + 0.769370i \(0.279430\pi\)
\(888\) −0.459653 −0.0154249
\(889\) 11.2131 0.376076
\(890\) −7.59665 −0.254640
\(891\) −41.0740 −1.37603
\(892\) 7.75783 0.259751
\(893\) 13.1363 0.439588
\(894\) 1.18141 0.0395124
\(895\) −12.4660 −0.416694
\(896\) 2.55233 0.0852672
\(897\) −7.19030 −0.240077
\(898\) 11.9134 0.397556
\(899\) 34.3745 1.14645
\(900\) −2.92288 −0.0974294
\(901\) 28.8151 0.959970
\(902\) 39.5998 1.31853
\(903\) 1.26287 0.0420258
\(904\) 2.53256 0.0842316
\(905\) −5.60337 −0.186262
\(906\) −0.334036 −0.0110976
\(907\) −1.49117 −0.0495136 −0.0247568 0.999694i \(-0.507881\pi\)
−0.0247568 + 0.999694i \(0.507881\pi\)
\(908\) −1.26402 −0.0419479
\(909\) 17.9655 0.595879
\(910\) 10.9434 0.362771
\(911\) 40.7106 1.34880 0.674401 0.738365i \(-0.264402\pi\)
0.674401 + 0.738365i \(0.264402\pi\)
\(912\) −1.09472 −0.0362498
\(913\) −7.21480 −0.238775
\(914\) −35.3128 −1.16804
\(915\) 2.78725 0.0921437
\(916\) 17.1590 0.566950
\(917\) 32.0520 1.05845
\(918\) 5.40804 0.178492
\(919\) 35.6676 1.17656 0.588282 0.808655i \(-0.299804\pi\)
0.588282 + 0.808655i \(0.299804\pi\)
\(920\) −6.03884 −0.199095
\(921\) −2.84092 −0.0936114
\(922\) 37.5505 1.23666
\(923\) 10.7224 0.352932
\(924\) −3.50251 −0.115224
\(925\) −1.65521 −0.0544231
\(926\) 29.2633 0.961653
\(927\) 5.85762 0.192389
\(928\) −7.47038 −0.245227
\(929\) 35.6442 1.16945 0.584724 0.811232i \(-0.301203\pi\)
0.584724 + 0.811232i \(0.301203\pi\)
\(930\) −1.27782 −0.0419014
\(931\) 1.91441 0.0627421
\(932\) −11.0937 −0.363385
\(933\) −0.666259 −0.0218123
\(934\) −2.05376 −0.0672010
\(935\) 16.2479 0.531363
\(936\) −12.5323 −0.409629
\(937\) 4.74195 0.154913 0.0774564 0.996996i \(-0.475320\pi\)
0.0774564 + 0.996996i \(0.475320\pi\)
\(938\) −13.0893 −0.427380
\(939\) −4.20070 −0.137085
\(940\) −3.33231 −0.108688
\(941\) 17.7737 0.579407 0.289703 0.957116i \(-0.406443\pi\)
0.289703 + 0.957116i \(0.406443\pi\)
\(942\) −2.81967 −0.0918698
\(943\) 48.3927 1.57588
\(944\) 6.61220 0.215209
\(945\) −4.19803 −0.136562
\(946\) −8.80469 −0.286265
\(947\) 37.4217 1.21604 0.608020 0.793921i \(-0.291964\pi\)
0.608020 + 0.793921i \(0.291964\pi\)
\(948\) 2.80875 0.0912239
\(949\) 10.4860 0.340391
\(950\) −3.94209 −0.127898
\(951\) −5.77939 −0.187409
\(952\) −8.39202 −0.271987
\(953\) −9.13396 −0.295878 −0.147939 0.988997i \(-0.547264\pi\)
−0.147939 + 0.988997i \(0.547264\pi\)
\(954\) 25.6154 0.829329
\(955\) 13.5010 0.436881
\(956\) −12.0870 −0.390922
\(957\) 10.2515 0.331383
\(958\) −22.3022 −0.720550
\(959\) 15.6214 0.504440
\(960\) 0.277700 0.00896273
\(961\) −9.82673 −0.316991
\(962\) −7.09695 −0.228815
\(963\) 17.0483 0.549374
\(964\) −25.6218 −0.825222
\(965\) 0.481989 0.0155158
\(966\) −4.28022 −0.137714
\(967\) 43.0359 1.38394 0.691970 0.721926i \(-0.256743\pi\)
0.691970 + 0.721926i \(0.256743\pi\)
\(968\) 13.4193 0.431314
\(969\) 3.59942 0.115630
\(970\) −0.655528 −0.0210477
\(971\) 23.5469 0.755657 0.377829 0.925876i \(-0.376671\pi\)
0.377829 + 0.925876i \(0.376671\pi\)
\(972\) 7.24257 0.232306
\(973\) 21.8117 0.699250
\(974\) −22.7781 −0.729859
\(975\) 1.19068 0.0381322
\(976\) 10.0369 0.321274
\(977\) −43.6340 −1.39597 −0.697987 0.716110i \(-0.745921\pi\)
−0.697987 + 0.716110i \(0.745921\pi\)
\(978\) −1.95729 −0.0625872
\(979\) 37.5395 1.19977
\(980\) −0.485632 −0.0155130
\(981\) −6.97389 −0.222659
\(982\) −18.0674 −0.576555
\(983\) 17.4569 0.556790 0.278395 0.960467i \(-0.410198\pi\)
0.278395 + 0.960467i \(0.410198\pi\)
\(984\) −2.22537 −0.0709423
\(985\) −9.40948 −0.299811
\(986\) 24.5625 0.782230
\(987\) −2.36188 −0.0751795
\(988\) −16.9022 −0.537732
\(989\) −10.7597 −0.342139
\(990\) 14.4437 0.459051
\(991\) 23.6777 0.752146 0.376073 0.926590i \(-0.377274\pi\)
0.376073 + 0.926590i \(0.377274\pi\)
\(992\) −4.60144 −0.146096
\(993\) −2.26214 −0.0717868
\(994\) 6.38279 0.202450
\(995\) 18.8322 0.597021
\(996\) 0.405446 0.0128471
\(997\) −33.3445 −1.05603 −0.528015 0.849235i \(-0.677064\pi\)
−0.528015 + 0.849235i \(0.677064\pi\)
\(998\) −37.4965 −1.18693
\(999\) 2.72247 0.0861351
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 \(a_p\))