Properties

Label 8018.2.a.j.1.7
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.41559 q^{3}\) \(+1.00000 q^{4}\) \(+0.828405 q^{5}\) \(-2.41559 q^{6}\) \(+0.635145 q^{7}\) \(+1.00000 q^{8}\) \(+2.83509 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.41559 q^{3}\) \(+1.00000 q^{4}\) \(+0.828405 q^{5}\) \(-2.41559 q^{6}\) \(+0.635145 q^{7}\) \(+1.00000 q^{8}\) \(+2.83509 q^{9}\) \(+0.828405 q^{10}\) \(+4.76175 q^{11}\) \(-2.41559 q^{12}\) \(+1.33861 q^{13}\) \(+0.635145 q^{14}\) \(-2.00109 q^{15}\) \(+1.00000 q^{16}\) \(+4.13113 q^{17}\) \(+2.83509 q^{18}\) \(-1.00000 q^{19}\) \(+0.828405 q^{20}\) \(-1.53425 q^{21}\) \(+4.76175 q^{22}\) \(+8.13489 q^{23}\) \(-2.41559 q^{24}\) \(-4.31374 q^{25}\) \(+1.33861 q^{26}\) \(+0.398357 q^{27}\) \(+0.635145 q^{28}\) \(-3.53077 q^{29}\) \(-2.00109 q^{30}\) \(+6.81222 q^{31}\) \(+1.00000 q^{32}\) \(-11.5024 q^{33}\) \(+4.13113 q^{34}\) \(+0.526157 q^{35}\) \(+2.83509 q^{36}\) \(+0.803490 q^{37}\) \(-1.00000 q^{38}\) \(-3.23353 q^{39}\) \(+0.828405 q^{40}\) \(+9.53625 q^{41}\) \(-1.53425 q^{42}\) \(+0.674754 q^{43}\) \(+4.76175 q^{44}\) \(+2.34860 q^{45}\) \(+8.13489 q^{46}\) \(-3.36611 q^{47}\) \(-2.41559 q^{48}\) \(-6.59659 q^{49}\) \(-4.31374 q^{50}\) \(-9.97912 q^{51}\) \(+1.33861 q^{52}\) \(+6.15273 q^{53}\) \(+0.398357 q^{54}\) \(+3.94466 q^{55}\) \(+0.635145 q^{56}\) \(+2.41559 q^{57}\) \(-3.53077 q^{58}\) \(+6.64260 q^{59}\) \(-2.00109 q^{60}\) \(-1.12180 q^{61}\) \(+6.81222 q^{62}\) \(+1.80069 q^{63}\) \(+1.00000 q^{64}\) \(+1.10891 q^{65}\) \(-11.5024 q^{66}\) \(-1.28127 q^{67}\) \(+4.13113 q^{68}\) \(-19.6506 q^{69}\) \(+0.526157 q^{70}\) \(+2.12031 q^{71}\) \(+2.83509 q^{72}\) \(-11.7665 q^{73}\) \(+0.803490 q^{74}\) \(+10.4203 q^{75}\) \(-1.00000 q^{76}\) \(+3.02440 q^{77}\) \(-3.23353 q^{78}\) \(-0.475054 q^{79}\) \(+0.828405 q^{80}\) \(-9.46754 q^{81}\) \(+9.53625 q^{82}\) \(-4.38717 q^{83}\) \(-1.53425 q^{84}\) \(+3.42225 q^{85}\) \(+0.674754 q^{86}\) \(+8.52890 q^{87}\) \(+4.76175 q^{88}\) \(+6.45159 q^{89}\) \(+2.34860 q^{90}\) \(+0.850209 q^{91}\) \(+8.13489 q^{92}\) \(-16.4555 q^{93}\) \(-3.36611 q^{94}\) \(-0.828405 q^{95}\) \(-2.41559 q^{96}\) \(+1.33445 q^{97}\) \(-6.59659 q^{98}\) \(+13.5000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.41559 −1.39464 −0.697322 0.716758i \(-0.745625\pi\)
−0.697322 + 0.716758i \(0.745625\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.828405 0.370474 0.185237 0.982694i \(-0.440695\pi\)
0.185237 + 0.982694i \(0.440695\pi\)
\(6\) −2.41559 −0.986162
\(7\) 0.635145 0.240062 0.120031 0.992770i \(-0.461701\pi\)
0.120031 + 0.992770i \(0.461701\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.83509 0.945030
\(10\) 0.828405 0.261965
\(11\) 4.76175 1.43572 0.717860 0.696187i \(-0.245122\pi\)
0.717860 + 0.696187i \(0.245122\pi\)
\(12\) −2.41559 −0.697322
\(13\) 1.33861 0.371263 0.185631 0.982619i \(-0.440567\pi\)
0.185631 + 0.982619i \(0.440567\pi\)
\(14\) 0.635145 0.169750
\(15\) −2.00109 −0.516679
\(16\) 1.00000 0.250000
\(17\) 4.13113 1.00195 0.500973 0.865463i \(-0.332976\pi\)
0.500973 + 0.865463i \(0.332976\pi\)
\(18\) 2.83509 0.668237
\(19\) −1.00000 −0.229416
\(20\) 0.828405 0.185237
\(21\) −1.53425 −0.334801
\(22\) 4.76175 1.01521
\(23\) 8.13489 1.69624 0.848121 0.529803i \(-0.177734\pi\)
0.848121 + 0.529803i \(0.177734\pi\)
\(24\) −2.41559 −0.493081
\(25\) −4.31374 −0.862749
\(26\) 1.33861 0.262522
\(27\) 0.398357 0.0766639
\(28\) 0.635145 0.120031
\(29\) −3.53077 −0.655647 −0.327824 0.944739i \(-0.606315\pi\)
−0.327824 + 0.944739i \(0.606315\pi\)
\(30\) −2.00109 −0.365347
\(31\) 6.81222 1.22351 0.611755 0.791047i \(-0.290464\pi\)
0.611755 + 0.791047i \(0.290464\pi\)
\(32\) 1.00000 0.176777
\(33\) −11.5024 −2.00232
\(34\) 4.13113 0.708482
\(35\) 0.526157 0.0889368
\(36\) 2.83509 0.472515
\(37\) 0.803490 0.132093 0.0660464 0.997817i \(-0.478961\pi\)
0.0660464 + 0.997817i \(0.478961\pi\)
\(38\) −1.00000 −0.162221
\(39\) −3.23353 −0.517779
\(40\) 0.828405 0.130982
\(41\) 9.53625 1.48931 0.744656 0.667448i \(-0.232613\pi\)
0.744656 + 0.667448i \(0.232613\pi\)
\(42\) −1.53425 −0.236740
\(43\) 0.674754 0.102899 0.0514495 0.998676i \(-0.483616\pi\)
0.0514495 + 0.998676i \(0.483616\pi\)
\(44\) 4.76175 0.717860
\(45\) 2.34860 0.350109
\(46\) 8.13489 1.19942
\(47\) −3.36611 −0.490997 −0.245499 0.969397i \(-0.578952\pi\)
−0.245499 + 0.969397i \(0.578952\pi\)
\(48\) −2.41559 −0.348661
\(49\) −6.59659 −0.942370
\(50\) −4.31374 −0.610056
\(51\) −9.97912 −1.39736
\(52\) 1.33861 0.185631
\(53\) 6.15273 0.845142 0.422571 0.906330i \(-0.361128\pi\)
0.422571 + 0.906330i \(0.361128\pi\)
\(54\) 0.398357 0.0542096
\(55\) 3.94466 0.531897
\(56\) 0.635145 0.0848748
\(57\) 2.41559 0.319953
\(58\) −3.53077 −0.463613
\(59\) 6.64260 0.864793 0.432397 0.901684i \(-0.357668\pi\)
0.432397 + 0.901684i \(0.357668\pi\)
\(60\) −2.00109 −0.258340
\(61\) −1.12180 −0.143631 −0.0718157 0.997418i \(-0.522879\pi\)
−0.0718157 + 0.997418i \(0.522879\pi\)
\(62\) 6.81222 0.865152
\(63\) 1.80069 0.226866
\(64\) 1.00000 0.125000
\(65\) 1.10891 0.137543
\(66\) −11.5024 −1.41585
\(67\) −1.28127 −0.156532 −0.0782659 0.996933i \(-0.524938\pi\)
−0.0782659 + 0.996933i \(0.524938\pi\)
\(68\) 4.13113 0.500973
\(69\) −19.6506 −2.36565
\(70\) 0.526157 0.0628878
\(71\) 2.12031 0.251634 0.125817 0.992053i \(-0.459845\pi\)
0.125817 + 0.992053i \(0.459845\pi\)
\(72\) 2.83509 0.334118
\(73\) −11.7665 −1.37717 −0.688583 0.725158i \(-0.741767\pi\)
−0.688583 + 0.725158i \(0.741767\pi\)
\(74\) 0.803490 0.0934038
\(75\) 10.4203 1.20323
\(76\) −1.00000 −0.114708
\(77\) 3.02440 0.344662
\(78\) −3.23353 −0.366125
\(79\) −0.475054 −0.0534478 −0.0267239 0.999643i \(-0.508507\pi\)
−0.0267239 + 0.999643i \(0.508507\pi\)
\(80\) 0.828405 0.0926185
\(81\) −9.46754 −1.05195
\(82\) 9.53625 1.05310
\(83\) −4.38717 −0.481555 −0.240777 0.970580i \(-0.577402\pi\)
−0.240777 + 0.970580i \(0.577402\pi\)
\(84\) −1.53425 −0.167401
\(85\) 3.42225 0.371195
\(86\) 0.674754 0.0727606
\(87\) 8.52890 0.914394
\(88\) 4.76175 0.507604
\(89\) 6.45159 0.683867 0.341933 0.939724i \(-0.388918\pi\)
0.341933 + 0.939724i \(0.388918\pi\)
\(90\) 2.34860 0.247565
\(91\) 0.850209 0.0891261
\(92\) 8.13489 0.848121
\(93\) −16.4555 −1.70636
\(94\) −3.36611 −0.347188
\(95\) −0.828405 −0.0849926
\(96\) −2.41559 −0.246540
\(97\) 1.33445 0.135493 0.0677463 0.997703i \(-0.478419\pi\)
0.0677463 + 0.997703i \(0.478419\pi\)
\(98\) −6.59659 −0.666356
\(99\) 13.5000 1.35680
\(100\) −4.31374 −0.431374
\(101\) 3.18561 0.316980 0.158490 0.987361i \(-0.449337\pi\)
0.158490 + 0.987361i \(0.449337\pi\)
\(102\) −9.97912 −0.988080
\(103\) −11.1322 −1.09689 −0.548446 0.836186i \(-0.684780\pi\)
−0.548446 + 0.836186i \(0.684780\pi\)
\(104\) 1.33861 0.131261
\(105\) −1.27098 −0.124035
\(106\) 6.15273 0.597606
\(107\) −9.35251 −0.904141 −0.452071 0.891982i \(-0.649314\pi\)
−0.452071 + 0.891982i \(0.649314\pi\)
\(108\) 0.398357 0.0383319
\(109\) −2.99989 −0.287337 −0.143669 0.989626i \(-0.545890\pi\)
−0.143669 + 0.989626i \(0.545890\pi\)
\(110\) 3.94466 0.376108
\(111\) −1.94090 −0.184222
\(112\) 0.635145 0.0600155
\(113\) 2.04492 0.192370 0.0961851 0.995363i \(-0.469336\pi\)
0.0961851 + 0.995363i \(0.469336\pi\)
\(114\) 2.41559 0.226241
\(115\) 6.73898 0.628414
\(116\) −3.53077 −0.327824
\(117\) 3.79507 0.350854
\(118\) 6.64260 0.611501
\(119\) 2.62386 0.240529
\(120\) −2.00109 −0.182674
\(121\) 11.6742 1.06129
\(122\) −1.12180 −0.101563
\(123\) −23.0357 −2.07706
\(124\) 6.81222 0.611755
\(125\) −7.71556 −0.690100
\(126\) 1.80069 0.160418
\(127\) −0.791022 −0.0701918 −0.0350959 0.999384i \(-0.511174\pi\)
−0.0350959 + 0.999384i \(0.511174\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.62993 −0.143507
\(130\) 1.10891 0.0972578
\(131\) 3.06716 0.267979 0.133989 0.990983i \(-0.457221\pi\)
0.133989 + 0.990983i \(0.457221\pi\)
\(132\) −11.5024 −1.00116
\(133\) −0.635145 −0.0550740
\(134\) −1.28127 −0.110685
\(135\) 0.330001 0.0284020
\(136\) 4.13113 0.354241
\(137\) 8.27758 0.707201 0.353601 0.935397i \(-0.384957\pi\)
0.353601 + 0.935397i \(0.384957\pi\)
\(138\) −19.6506 −1.67277
\(139\) −15.4336 −1.30906 −0.654530 0.756036i \(-0.727134\pi\)
−0.654530 + 0.756036i \(0.727134\pi\)
\(140\) 0.526157 0.0444684
\(141\) 8.13115 0.684766
\(142\) 2.12031 0.177932
\(143\) 6.37411 0.533030
\(144\) 2.83509 0.236257
\(145\) −2.92491 −0.242900
\(146\) −11.7665 −0.973803
\(147\) 15.9347 1.31427
\(148\) 0.803490 0.0660464
\(149\) 6.93021 0.567745 0.283872 0.958862i \(-0.408381\pi\)
0.283872 + 0.958862i \(0.408381\pi\)
\(150\) 10.4203 0.850810
\(151\) −0.709930 −0.0577733 −0.0288866 0.999583i \(-0.509196\pi\)
−0.0288866 + 0.999583i \(0.509196\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 11.7121 0.946868
\(154\) 3.02440 0.243713
\(155\) 5.64328 0.453279
\(156\) −3.23353 −0.258890
\(157\) 10.5903 0.845199 0.422599 0.906317i \(-0.361118\pi\)
0.422599 + 0.906317i \(0.361118\pi\)
\(158\) −0.475054 −0.0377933
\(159\) −14.8625 −1.17867
\(160\) 0.828405 0.0654912
\(161\) 5.16683 0.407203
\(162\) −9.46754 −0.743840
\(163\) −20.8815 −1.63556 −0.817781 0.575530i \(-0.804796\pi\)
−0.817781 + 0.575530i \(0.804796\pi\)
\(164\) 9.53625 0.744656
\(165\) −9.52868 −0.741807
\(166\) −4.38717 −0.340511
\(167\) −5.79451 −0.448393 −0.224196 0.974544i \(-0.571976\pi\)
−0.224196 + 0.974544i \(0.571976\pi\)
\(168\) −1.53425 −0.118370
\(169\) −11.2081 −0.862164
\(170\) 3.42225 0.262474
\(171\) −2.83509 −0.216805
\(172\) 0.674754 0.0514495
\(173\) 6.43491 0.489237 0.244618 0.969619i \(-0.421337\pi\)
0.244618 + 0.969619i \(0.421337\pi\)
\(174\) 8.52890 0.646574
\(175\) −2.73985 −0.207113
\(176\) 4.76175 0.358930
\(177\) −16.0458 −1.20608
\(178\) 6.45159 0.483567
\(179\) 6.94931 0.519416 0.259708 0.965687i \(-0.416374\pi\)
0.259708 + 0.965687i \(0.416374\pi\)
\(180\) 2.34860 0.175055
\(181\) 7.34646 0.546058 0.273029 0.962006i \(-0.411974\pi\)
0.273029 + 0.962006i \(0.411974\pi\)
\(182\) 0.850209 0.0630217
\(183\) 2.70981 0.200315
\(184\) 8.13489 0.599712
\(185\) 0.665615 0.0489370
\(186\) −16.4555 −1.20658
\(187\) 19.6714 1.43851
\(188\) −3.36611 −0.245499
\(189\) 0.253015 0.0184041
\(190\) −0.828405 −0.0600988
\(191\) −16.3578 −1.18361 −0.591806 0.806081i \(-0.701585\pi\)
−0.591806 + 0.806081i \(0.701585\pi\)
\(192\) −2.41559 −0.174330
\(193\) 9.39884 0.676543 0.338272 0.941049i \(-0.390158\pi\)
0.338272 + 0.941049i \(0.390158\pi\)
\(194\) 1.33445 0.0958077
\(195\) −2.67867 −0.191824
\(196\) −6.59659 −0.471185
\(197\) 21.2194 1.51182 0.755908 0.654677i \(-0.227196\pi\)
0.755908 + 0.654677i \(0.227196\pi\)
\(198\) 13.5000 0.959401
\(199\) −27.9566 −1.98179 −0.990896 0.134626i \(-0.957017\pi\)
−0.990896 + 0.134626i \(0.957017\pi\)
\(200\) −4.31374 −0.305028
\(201\) 3.09502 0.218306
\(202\) 3.18561 0.224139
\(203\) −2.24255 −0.157396
\(204\) −9.97912 −0.698678
\(205\) 7.89988 0.551752
\(206\) −11.1322 −0.775620
\(207\) 23.0631 1.60300
\(208\) 1.33861 0.0928157
\(209\) −4.76175 −0.329377
\(210\) −1.27098 −0.0877061
\(211\) −1.00000 −0.0688428
\(212\) 6.15273 0.422571
\(213\) −5.12179 −0.350940
\(214\) −9.35251 −0.639324
\(215\) 0.558970 0.0381214
\(216\) 0.398357 0.0271048
\(217\) 4.32674 0.293719
\(218\) −2.99989 −0.203178
\(219\) 28.4231 1.92065
\(220\) 3.94466 0.265949
\(221\) 5.52995 0.371985
\(222\) −1.94090 −0.130265
\(223\) −6.03373 −0.404049 −0.202024 0.979381i \(-0.564752\pi\)
−0.202024 + 0.979381i \(0.564752\pi\)
\(224\) 0.635145 0.0424374
\(225\) −12.2299 −0.815323
\(226\) 2.04492 0.136026
\(227\) 2.85447 0.189458 0.0947291 0.995503i \(-0.469802\pi\)
0.0947291 + 0.995503i \(0.469802\pi\)
\(228\) 2.41559 0.159977
\(229\) 7.52528 0.497284 0.248642 0.968595i \(-0.420016\pi\)
0.248642 + 0.968595i \(0.420016\pi\)
\(230\) 6.73898 0.444355
\(231\) −7.30572 −0.480681
\(232\) −3.53077 −0.231806
\(233\) −9.44916 −0.619035 −0.309517 0.950894i \(-0.600168\pi\)
−0.309517 + 0.950894i \(0.600168\pi\)
\(234\) 3.79507 0.248091
\(235\) −2.78850 −0.181902
\(236\) 6.64260 0.432397
\(237\) 1.14754 0.0745406
\(238\) 2.62386 0.170080
\(239\) 8.19763 0.530260 0.265130 0.964213i \(-0.414585\pi\)
0.265130 + 0.964213i \(0.414585\pi\)
\(240\) −2.00109 −0.129170
\(241\) 10.5796 0.681494 0.340747 0.940155i \(-0.389320\pi\)
0.340747 + 0.940155i \(0.389320\pi\)
\(242\) 11.6742 0.750448
\(243\) 21.6746 1.39043
\(244\) −1.12180 −0.0718157
\(245\) −5.46465 −0.349124
\(246\) −23.0357 −1.46870
\(247\) −1.33861 −0.0851735
\(248\) 6.81222 0.432576
\(249\) 10.5976 0.671597
\(250\) −7.71556 −0.487975
\(251\) 0.109849 0.00693359 0.00346680 0.999994i \(-0.498896\pi\)
0.00346680 + 0.999994i \(0.498896\pi\)
\(252\) 1.80069 0.113433
\(253\) 38.7363 2.43533
\(254\) −0.791022 −0.0496331
\(255\) −8.26676 −0.517684
\(256\) 1.00000 0.0625000
\(257\) 7.86185 0.490409 0.245204 0.969471i \(-0.421145\pi\)
0.245204 + 0.969471i \(0.421145\pi\)
\(258\) −1.62993 −0.101475
\(259\) 0.510332 0.0317105
\(260\) 1.10891 0.0687716
\(261\) −10.0100 −0.619606
\(262\) 3.06716 0.189490
\(263\) 21.6422 1.33452 0.667259 0.744826i \(-0.267467\pi\)
0.667259 + 0.744826i \(0.267467\pi\)
\(264\) −11.5024 −0.707926
\(265\) 5.09695 0.313103
\(266\) −0.635145 −0.0389432
\(267\) −15.5844 −0.953750
\(268\) −1.28127 −0.0782659
\(269\) −4.79940 −0.292624 −0.146312 0.989238i \(-0.546740\pi\)
−0.146312 + 0.989238i \(0.546740\pi\)
\(270\) 0.330001 0.0200832
\(271\) −8.60356 −0.522629 −0.261314 0.965254i \(-0.584156\pi\)
−0.261314 + 0.965254i \(0.584156\pi\)
\(272\) 4.13113 0.250486
\(273\) −2.05376 −0.124299
\(274\) 8.27758 0.500067
\(275\) −20.5410 −1.23867
\(276\) −19.6506 −1.18283
\(277\) 19.9564 1.19906 0.599531 0.800351i \(-0.295354\pi\)
0.599531 + 0.800351i \(0.295354\pi\)
\(278\) −15.4336 −0.925645
\(279\) 19.3132 1.15625
\(280\) 0.526157 0.0314439
\(281\) 17.7987 1.06178 0.530889 0.847441i \(-0.321858\pi\)
0.530889 + 0.847441i \(0.321858\pi\)
\(282\) 8.13115 0.484203
\(283\) 30.0238 1.78473 0.892366 0.451312i \(-0.149044\pi\)
0.892366 + 0.451312i \(0.149044\pi\)
\(284\) 2.12031 0.125817
\(285\) 2.00109 0.118534
\(286\) 6.37411 0.376909
\(287\) 6.05690 0.357528
\(288\) 2.83509 0.167059
\(289\) 0.0661984 0.00389403
\(290\) −2.92491 −0.171757
\(291\) −3.22348 −0.188964
\(292\) −11.7665 −0.688583
\(293\) 18.3876 1.07421 0.537107 0.843514i \(-0.319517\pi\)
0.537107 + 0.843514i \(0.319517\pi\)
\(294\) 15.9347 0.929329
\(295\) 5.50277 0.320384
\(296\) 0.803490 0.0467019
\(297\) 1.89688 0.110068
\(298\) 6.93021 0.401456
\(299\) 10.8894 0.629751
\(300\) 10.4203 0.601613
\(301\) 0.428566 0.0247022
\(302\) −0.709930 −0.0408519
\(303\) −7.69513 −0.442074
\(304\) −1.00000 −0.0573539
\(305\) −0.929303 −0.0532117
\(306\) 11.7121 0.669537
\(307\) −20.7591 −1.18479 −0.592393 0.805649i \(-0.701817\pi\)
−0.592393 + 0.805649i \(0.701817\pi\)
\(308\) 3.02440 0.172331
\(309\) 26.8909 1.52977
\(310\) 5.64328 0.320517
\(311\) −24.9991 −1.41757 −0.708786 0.705424i \(-0.750757\pi\)
−0.708786 + 0.705424i \(0.750757\pi\)
\(312\) −3.23353 −0.183063
\(313\) −16.4582 −0.930273 −0.465136 0.885239i \(-0.653995\pi\)
−0.465136 + 0.885239i \(0.653995\pi\)
\(314\) 10.5903 0.597646
\(315\) 1.49170 0.0840480
\(316\) −0.475054 −0.0267239
\(317\) 11.8239 0.664097 0.332048 0.943262i \(-0.392260\pi\)
0.332048 + 0.943262i \(0.392260\pi\)
\(318\) −14.8625 −0.833447
\(319\) −16.8126 −0.941326
\(320\) 0.828405 0.0463093
\(321\) 22.5919 1.26095
\(322\) 5.16683 0.287936
\(323\) −4.13113 −0.229862
\(324\) −9.46754 −0.525974
\(325\) −5.77441 −0.320307
\(326\) −20.8815 −1.15652
\(327\) 7.24651 0.400733
\(328\) 9.53625 0.526551
\(329\) −2.13797 −0.117870
\(330\) −9.52868 −0.524537
\(331\) 3.97060 0.218244 0.109122 0.994028i \(-0.465196\pi\)
0.109122 + 0.994028i \(0.465196\pi\)
\(332\) −4.38717 −0.240777
\(333\) 2.27796 0.124832
\(334\) −5.79451 −0.317062
\(335\) −1.06141 −0.0579910
\(336\) −1.53425 −0.0837003
\(337\) 7.60288 0.414155 0.207078 0.978325i \(-0.433605\pi\)
0.207078 + 0.978325i \(0.433605\pi\)
\(338\) −11.2081 −0.609642
\(339\) −4.93970 −0.268288
\(340\) 3.42225 0.185597
\(341\) 32.4380 1.75662
\(342\) −2.83509 −0.153304
\(343\) −8.63580 −0.466290
\(344\) 0.674754 0.0363803
\(345\) −16.2786 −0.876413
\(346\) 6.43491 0.345943
\(347\) −3.74842 −0.201226 −0.100613 0.994926i \(-0.532080\pi\)
−0.100613 + 0.994926i \(0.532080\pi\)
\(348\) 8.52890 0.457197
\(349\) 1.47489 0.0789489 0.0394745 0.999221i \(-0.487432\pi\)
0.0394745 + 0.999221i \(0.487432\pi\)
\(350\) −2.73985 −0.146451
\(351\) 0.533244 0.0284624
\(352\) 4.76175 0.253802
\(353\) 1.60152 0.0852403 0.0426202 0.999091i \(-0.486429\pi\)
0.0426202 + 0.999091i \(0.486429\pi\)
\(354\) −16.0458 −0.852826
\(355\) 1.75647 0.0932239
\(356\) 6.45159 0.341933
\(357\) −6.33818 −0.335452
\(358\) 6.94931 0.367283
\(359\) 28.5063 1.50450 0.752252 0.658876i \(-0.228968\pi\)
0.752252 + 0.658876i \(0.228968\pi\)
\(360\) 2.34860 0.123782
\(361\) 1.00000 0.0526316
\(362\) 7.34646 0.386122
\(363\) −28.2002 −1.48013
\(364\) 0.850209 0.0445631
\(365\) −9.74744 −0.510204
\(366\) 2.70981 0.141644
\(367\) −33.4257 −1.74481 −0.872404 0.488786i \(-0.837440\pi\)
−0.872404 + 0.488786i \(0.837440\pi\)
\(368\) 8.13489 0.424060
\(369\) 27.0361 1.40744
\(370\) 0.665615 0.0346037
\(371\) 3.90787 0.202887
\(372\) −16.4555 −0.853180
\(373\) 26.1707 1.35507 0.677534 0.735491i \(-0.263049\pi\)
0.677534 + 0.735491i \(0.263049\pi\)
\(374\) 19.6714 1.01718
\(375\) 18.6376 0.962444
\(376\) −3.36611 −0.173594
\(377\) −4.72631 −0.243417
\(378\) 0.253015 0.0130137
\(379\) −0.979375 −0.0503071 −0.0251536 0.999684i \(-0.508007\pi\)
−0.0251536 + 0.999684i \(0.508007\pi\)
\(380\) −0.828405 −0.0424963
\(381\) 1.91079 0.0978926
\(382\) −16.3578 −0.836940
\(383\) 19.6342 1.00326 0.501631 0.865082i \(-0.332733\pi\)
0.501631 + 0.865082i \(0.332733\pi\)
\(384\) −2.41559 −0.123270
\(385\) 2.50543 0.127688
\(386\) 9.39884 0.478388
\(387\) 1.91299 0.0972426
\(388\) 1.33445 0.0677463
\(389\) −13.1836 −0.668435 −0.334218 0.942496i \(-0.608472\pi\)
−0.334218 + 0.942496i \(0.608472\pi\)
\(390\) −2.67867 −0.135640
\(391\) 33.6062 1.69954
\(392\) −6.59659 −0.333178
\(393\) −7.40900 −0.373735
\(394\) 21.2194 1.06902
\(395\) −0.393538 −0.0198010
\(396\) 13.5000 0.678399
\(397\) −13.2270 −0.663844 −0.331922 0.943307i \(-0.607697\pi\)
−0.331922 + 0.943307i \(0.607697\pi\)
\(398\) −27.9566 −1.40134
\(399\) 1.53425 0.0768086
\(400\) −4.31374 −0.215687
\(401\) −10.2977 −0.514245 −0.257122 0.966379i \(-0.582774\pi\)
−0.257122 + 0.966379i \(0.582774\pi\)
\(402\) 3.09502 0.154366
\(403\) 9.11888 0.454244
\(404\) 3.18561 0.158490
\(405\) −7.84296 −0.389720
\(406\) −2.24255 −0.111296
\(407\) 3.82601 0.189648
\(408\) −9.97912 −0.494040
\(409\) −21.2666 −1.05157 −0.525783 0.850619i \(-0.676228\pi\)
−0.525783 + 0.850619i \(0.676228\pi\)
\(410\) 7.89988 0.390147
\(411\) −19.9953 −0.986293
\(412\) −11.1322 −0.548446
\(413\) 4.21901 0.207604
\(414\) 23.0631 1.13349
\(415\) −3.63436 −0.178404
\(416\) 1.33861 0.0656306
\(417\) 37.2813 1.82567
\(418\) −4.76175 −0.232905
\(419\) 20.5713 1.00497 0.502486 0.864585i \(-0.332419\pi\)
0.502486 + 0.864585i \(0.332419\pi\)
\(420\) −1.27098 −0.0620176
\(421\) 26.4209 1.28767 0.643837 0.765163i \(-0.277342\pi\)
0.643837 + 0.765163i \(0.277342\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −9.54322 −0.464007
\(424\) 6.15273 0.298803
\(425\) −17.8206 −0.864427
\(426\) −5.12179 −0.248152
\(427\) −0.712504 −0.0344805
\(428\) −9.35251 −0.452071
\(429\) −15.3972 −0.743386
\(430\) 0.558970 0.0269559
\(431\) 28.1887 1.35780 0.678900 0.734231i \(-0.262457\pi\)
0.678900 + 0.734231i \(0.262457\pi\)
\(432\) 0.398357 0.0191660
\(433\) −28.8739 −1.38759 −0.693796 0.720171i \(-0.744063\pi\)
−0.693796 + 0.720171i \(0.744063\pi\)
\(434\) 4.32674 0.207690
\(435\) 7.06539 0.338759
\(436\) −2.99989 −0.143669
\(437\) −8.13489 −0.389144
\(438\) 28.4231 1.35811
\(439\) 10.1732 0.485540 0.242770 0.970084i \(-0.421944\pi\)
0.242770 + 0.970084i \(0.421944\pi\)
\(440\) 3.94466 0.188054
\(441\) −18.7019 −0.890568
\(442\) 5.52995 0.263033
\(443\) 14.1030 0.670053 0.335026 0.942209i \(-0.391255\pi\)
0.335026 + 0.942209i \(0.391255\pi\)
\(444\) −1.94090 −0.0921112
\(445\) 5.34453 0.253355
\(446\) −6.03373 −0.285705
\(447\) −16.7406 −0.791801
\(448\) 0.635145 0.0300078
\(449\) 0.195234 0.00921368 0.00460684 0.999989i \(-0.498534\pi\)
0.00460684 + 0.999989i \(0.498534\pi\)
\(450\) −12.2299 −0.576521
\(451\) 45.4092 2.13824
\(452\) 2.04492 0.0961851
\(453\) 1.71490 0.0805731
\(454\) 2.85447 0.133967
\(455\) 0.704318 0.0330189
\(456\) 2.41559 0.113121
\(457\) 26.1327 1.22243 0.611217 0.791463i \(-0.290680\pi\)
0.611217 + 0.791463i \(0.290680\pi\)
\(458\) 7.52528 0.351633
\(459\) 1.64566 0.0768130
\(460\) 6.73898 0.314207
\(461\) −5.41612 −0.252254 −0.126127 0.992014i \(-0.540255\pi\)
−0.126127 + 0.992014i \(0.540255\pi\)
\(462\) −7.30572 −0.339893
\(463\) 25.7914 1.19863 0.599314 0.800514i \(-0.295440\pi\)
0.599314 + 0.800514i \(0.295440\pi\)
\(464\) −3.53077 −0.163912
\(465\) −13.6319 −0.632162
\(466\) −9.44916 −0.437724
\(467\) −15.5157 −0.717981 −0.358991 0.933341i \(-0.616879\pi\)
−0.358991 + 0.933341i \(0.616879\pi\)
\(468\) 3.79507 0.175427
\(469\) −0.813791 −0.0375774
\(470\) −2.78850 −0.128624
\(471\) −25.5819 −1.17875
\(472\) 6.64260 0.305751
\(473\) 3.21301 0.147734
\(474\) 1.14754 0.0527082
\(475\) 4.31374 0.197928
\(476\) 2.62386 0.120265
\(477\) 17.4435 0.798684
\(478\) 8.19763 0.374951
\(479\) −2.13221 −0.0974231 −0.0487116 0.998813i \(-0.515512\pi\)
−0.0487116 + 0.998813i \(0.515512\pi\)
\(480\) −2.00109 −0.0913369
\(481\) 1.07556 0.0490412
\(482\) 10.5796 0.481889
\(483\) −12.4810 −0.567903
\(484\) 11.6742 0.530647
\(485\) 1.10546 0.0501965
\(486\) 21.6746 0.983182
\(487\) −10.0437 −0.455124 −0.227562 0.973764i \(-0.573075\pi\)
−0.227562 + 0.973764i \(0.573075\pi\)
\(488\) −1.12180 −0.0507814
\(489\) 50.4411 2.28102
\(490\) −5.46465 −0.246868
\(491\) −25.2523 −1.13962 −0.569811 0.821776i \(-0.692984\pi\)
−0.569811 + 0.821776i \(0.692984\pi\)
\(492\) −23.0357 −1.03853
\(493\) −14.5860 −0.656923
\(494\) −1.33861 −0.0602268
\(495\) 11.1835 0.502659
\(496\) 6.81222 0.305878
\(497\) 1.34670 0.0604078
\(498\) 10.5976 0.474891
\(499\) −12.2963 −0.550456 −0.275228 0.961379i \(-0.588753\pi\)
−0.275228 + 0.961379i \(0.588753\pi\)
\(500\) −7.71556 −0.345050
\(501\) 13.9972 0.625348
\(502\) 0.109849 0.00490279
\(503\) 25.4968 1.13684 0.568422 0.822737i \(-0.307554\pi\)
0.568422 + 0.822737i \(0.307554\pi\)
\(504\) 1.80069 0.0802092
\(505\) 2.63898 0.117433
\(506\) 38.7363 1.72204
\(507\) 27.0743 1.20241
\(508\) −0.791022 −0.0350959
\(509\) −18.1913 −0.806314 −0.403157 0.915131i \(-0.632087\pi\)
−0.403157 + 0.915131i \(0.632087\pi\)
\(510\) −8.26676 −0.366058
\(511\) −7.47344 −0.330605
\(512\) 1.00000 0.0441942
\(513\) −0.398357 −0.0175879
\(514\) 7.86185 0.346771
\(515\) −9.22200 −0.406370
\(516\) −1.62993 −0.0717537
\(517\) −16.0286 −0.704935
\(518\) 0.510332 0.0224227
\(519\) −15.5441 −0.682311
\(520\) 1.10891 0.0486289
\(521\) 30.4690 1.33487 0.667437 0.744667i \(-0.267392\pi\)
0.667437 + 0.744667i \(0.267392\pi\)
\(522\) −10.0100 −0.438128
\(523\) −13.2742 −0.580440 −0.290220 0.956960i \(-0.593728\pi\)
−0.290220 + 0.956960i \(0.593728\pi\)
\(524\) 3.06716 0.133989
\(525\) 6.61837 0.288849
\(526\) 21.6422 0.943647
\(527\) 28.1421 1.22589
\(528\) −11.5024 −0.500579
\(529\) 43.1764 1.87723
\(530\) 5.09695 0.221397
\(531\) 18.8324 0.817255
\(532\) −0.635145 −0.0275370
\(533\) 12.7653 0.552926
\(534\) −15.5844 −0.674403
\(535\) −7.74767 −0.334961
\(536\) −1.28127 −0.0553424
\(537\) −16.7867 −0.724400
\(538\) −4.79940 −0.206917
\(539\) −31.4113 −1.35298
\(540\) 0.330001 0.0142010
\(541\) −3.45816 −0.148678 −0.0743391 0.997233i \(-0.523685\pi\)
−0.0743391 + 0.997233i \(0.523685\pi\)
\(542\) −8.60356 −0.369554
\(543\) −17.7461 −0.761557
\(544\) 4.13113 0.177121
\(545\) −2.48512 −0.106451
\(546\) −2.05376 −0.0878928
\(547\) −43.6707 −1.86722 −0.933612 0.358285i \(-0.883362\pi\)
−0.933612 + 0.358285i \(0.883362\pi\)
\(548\) 8.27758 0.353601
\(549\) −3.18040 −0.135736
\(550\) −20.5410 −0.875869
\(551\) 3.53077 0.150416
\(552\) −19.6506 −0.836384
\(553\) −0.301728 −0.0128308
\(554\) 19.9564 0.847865
\(555\) −1.60786 −0.0682497
\(556\) −15.4336 −0.654530
\(557\) 40.7250 1.72557 0.862787 0.505568i \(-0.168717\pi\)
0.862787 + 0.505568i \(0.168717\pi\)
\(558\) 19.3132 0.817595
\(559\) 0.903230 0.0382026
\(560\) 0.526157 0.0222342
\(561\) −47.5180 −2.00621
\(562\) 17.7987 0.750791
\(563\) −1.28414 −0.0541199 −0.0270599 0.999634i \(-0.508615\pi\)
−0.0270599 + 0.999634i \(0.508615\pi\)
\(564\) 8.13115 0.342383
\(565\) 1.69403 0.0712682
\(566\) 30.0238 1.26200
\(567\) −6.01326 −0.252533
\(568\) 2.12031 0.0889660
\(569\) 38.4213 1.61071 0.805353 0.592796i \(-0.201976\pi\)
0.805353 + 0.592796i \(0.201976\pi\)
\(570\) 2.00109 0.0838164
\(571\) −22.3930 −0.937119 −0.468559 0.883432i \(-0.655227\pi\)
−0.468559 + 0.883432i \(0.655227\pi\)
\(572\) 6.37411 0.266515
\(573\) 39.5139 1.65072
\(574\) 6.05690 0.252810
\(575\) −35.0918 −1.46343
\(576\) 2.83509 0.118129
\(577\) 0.391406 0.0162945 0.00814723 0.999967i \(-0.497407\pi\)
0.00814723 + 0.999967i \(0.497407\pi\)
\(578\) 0.0661984 0.00275349
\(579\) −22.7038 −0.943536
\(580\) −2.92491 −0.121450
\(581\) −2.78649 −0.115603
\(582\) −3.22348 −0.133618
\(583\) 29.2977 1.21339
\(584\) −11.7665 −0.486902
\(585\) 3.14386 0.129982
\(586\) 18.3876 0.759584
\(587\) 33.0618 1.36461 0.682303 0.731069i \(-0.260978\pi\)
0.682303 + 0.731069i \(0.260978\pi\)
\(588\) 15.9347 0.657135
\(589\) −6.81222 −0.280693
\(590\) 5.50277 0.226545
\(591\) −51.2573 −2.10845
\(592\) 0.803490 0.0330232
\(593\) −28.2077 −1.15835 −0.579175 0.815203i \(-0.696625\pi\)
−0.579175 + 0.815203i \(0.696625\pi\)
\(594\) 1.89688 0.0778298
\(595\) 2.17362 0.0891098
\(596\) 6.93021 0.283872
\(597\) 67.5318 2.76389
\(598\) 10.8894 0.445301
\(599\) −1.46904 −0.0600235 −0.0300118 0.999550i \(-0.509554\pi\)
−0.0300118 + 0.999550i \(0.509554\pi\)
\(600\) 10.4203 0.425405
\(601\) 20.2253 0.825007 0.412504 0.910956i \(-0.364654\pi\)
0.412504 + 0.910956i \(0.364654\pi\)
\(602\) 0.428566 0.0174671
\(603\) −3.63251 −0.147927
\(604\) −0.709930 −0.0288866
\(605\) 9.67099 0.393182
\(606\) −7.69513 −0.312593
\(607\) −17.6276 −0.715483 −0.357741 0.933821i \(-0.616453\pi\)
−0.357741 + 0.933821i \(0.616453\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 5.41709 0.219511
\(610\) −0.929303 −0.0376264
\(611\) −4.50590 −0.182289
\(612\) 11.7121 0.473434
\(613\) −9.54693 −0.385597 −0.192798 0.981238i \(-0.561756\pi\)
−0.192798 + 0.981238i \(0.561756\pi\)
\(614\) −20.7591 −0.837771
\(615\) −19.0829 −0.769497
\(616\) 3.02440 0.121856
\(617\) 41.8651 1.68543 0.842713 0.538363i \(-0.180957\pi\)
0.842713 + 0.538363i \(0.180957\pi\)
\(618\) 26.8909 1.08171
\(619\) −40.5618 −1.63032 −0.815158 0.579239i \(-0.803350\pi\)
−0.815158 + 0.579239i \(0.803350\pi\)
\(620\) 5.64328 0.226639
\(621\) 3.24059 0.130040
\(622\) −24.9991 −1.00237
\(623\) 4.09769 0.164171
\(624\) −3.23353 −0.129445
\(625\) 15.1771 0.607085
\(626\) −16.4582 −0.657802
\(627\) 11.5024 0.459363
\(628\) 10.5903 0.422599
\(629\) 3.31932 0.132350
\(630\) 1.49170 0.0594309
\(631\) 7.83752 0.312007 0.156003 0.987757i \(-0.450139\pi\)
0.156003 + 0.987757i \(0.450139\pi\)
\(632\) −0.475054 −0.0188967
\(633\) 2.41559 0.0960112
\(634\) 11.8239 0.469587
\(635\) −0.655287 −0.0260043
\(636\) −14.8625 −0.589336
\(637\) −8.83024 −0.349867
\(638\) −16.8126 −0.665618
\(639\) 6.01125 0.237802
\(640\) 0.828405 0.0327456
\(641\) 22.5387 0.890226 0.445113 0.895474i \(-0.353163\pi\)
0.445113 + 0.895474i \(0.353163\pi\)
\(642\) 22.5919 0.891629
\(643\) −3.92059 −0.154613 −0.0773064 0.997007i \(-0.524632\pi\)
−0.0773064 + 0.997007i \(0.524632\pi\)
\(644\) 5.16683 0.203602
\(645\) −1.35024 −0.0531658
\(646\) −4.13113 −0.162537
\(647\) −16.0435 −0.630734 −0.315367 0.948970i \(-0.602128\pi\)
−0.315367 + 0.948970i \(0.602128\pi\)
\(648\) −9.46754 −0.371920
\(649\) 31.6304 1.24160
\(650\) −5.77441 −0.226491
\(651\) −10.4517 −0.409633
\(652\) −20.8815 −0.817781
\(653\) −45.0187 −1.76172 −0.880859 0.473378i \(-0.843035\pi\)
−0.880859 + 0.473378i \(0.843035\pi\)
\(654\) 7.24651 0.283361
\(655\) 2.54085 0.0992792
\(656\) 9.53625 0.372328
\(657\) −33.3591 −1.30146
\(658\) −2.13797 −0.0833466
\(659\) 30.5203 1.18890 0.594451 0.804132i \(-0.297370\pi\)
0.594451 + 0.804132i \(0.297370\pi\)
\(660\) −9.52868 −0.370904
\(661\) −0.115839 −0.00450563 −0.00225282 0.999997i \(-0.500717\pi\)
−0.00225282 + 0.999997i \(0.500717\pi\)
\(662\) 3.97060 0.154322
\(663\) −13.3581 −0.518786
\(664\) −4.38717 −0.170255
\(665\) −0.526157 −0.0204035
\(666\) 2.27796 0.0882693
\(667\) −28.7224 −1.11214
\(668\) −5.79451 −0.224196
\(669\) 14.5750 0.563504
\(670\) −1.06141 −0.0410058
\(671\) −5.34171 −0.206215
\(672\) −1.53425 −0.0591850
\(673\) −12.2830 −0.473477 −0.236738 0.971573i \(-0.576078\pi\)
−0.236738 + 0.971573i \(0.576078\pi\)
\(674\) 7.60288 0.292852
\(675\) −1.71841 −0.0661417
\(676\) −11.2081 −0.431082
\(677\) 14.6420 0.562738 0.281369 0.959600i \(-0.409212\pi\)
0.281369 + 0.959600i \(0.409212\pi\)
\(678\) −4.93970 −0.189708
\(679\) 0.847567 0.0325266
\(680\) 3.42225 0.131237
\(681\) −6.89525 −0.264226
\(682\) 32.4380 1.24212
\(683\) −11.6178 −0.444542 −0.222271 0.974985i \(-0.571347\pi\)
−0.222271 + 0.974985i \(0.571347\pi\)
\(684\) −2.83509 −0.108402
\(685\) 6.85719 0.262000
\(686\) −8.63580 −0.329717
\(687\) −18.1780 −0.693534
\(688\) 0.674754 0.0257248
\(689\) 8.23608 0.313770
\(690\) −16.2786 −0.619717
\(691\) 2.51172 0.0955504 0.0477752 0.998858i \(-0.484787\pi\)
0.0477752 + 0.998858i \(0.484787\pi\)
\(692\) 6.43491 0.244618
\(693\) 8.57444 0.325716
\(694\) −3.74842 −0.142288
\(695\) −12.7853 −0.484973
\(696\) 8.52890 0.323287
\(697\) 39.3955 1.49221
\(698\) 1.47489 0.0558253
\(699\) 22.8253 0.863333
\(700\) −2.73985 −0.103557
\(701\) −32.1166 −1.21303 −0.606513 0.795073i \(-0.707432\pi\)
−0.606513 + 0.795073i \(0.707432\pi\)
\(702\) 0.533244 0.0201260
\(703\) −0.803490 −0.0303042
\(704\) 4.76175 0.179465
\(705\) 6.73589 0.253688
\(706\) 1.60152 0.0602740
\(707\) 2.02332 0.0760949
\(708\) −16.0458 −0.603039
\(709\) 28.2421 1.06066 0.530328 0.847793i \(-0.322069\pi\)
0.530328 + 0.847793i \(0.322069\pi\)
\(710\) 1.75647 0.0659192
\(711\) −1.34682 −0.0505098
\(712\) 6.45159 0.241783
\(713\) 55.4166 2.07537
\(714\) −6.33818 −0.237201
\(715\) 5.28034 0.197474
\(716\) 6.94931 0.259708
\(717\) −19.8021 −0.739524
\(718\) 28.5063 1.06384
\(719\) 28.3906 1.05879 0.529395 0.848376i \(-0.322419\pi\)
0.529395 + 0.848376i \(0.322419\pi\)
\(720\) 2.34860 0.0875273
\(721\) −7.07058 −0.263322
\(722\) 1.00000 0.0372161
\(723\) −25.5561 −0.950441
\(724\) 7.34646 0.273029
\(725\) 15.2308 0.565659
\(726\) −28.2002 −1.04661
\(727\) −26.8529 −0.995920 −0.497960 0.867200i \(-0.665917\pi\)
−0.497960 + 0.867200i \(0.665917\pi\)
\(728\) 0.850209 0.0315109
\(729\) −23.9545 −0.887204
\(730\) −9.74744 −0.360769
\(731\) 2.78749 0.103099
\(732\) 2.70981 0.100157
\(733\) −35.5174 −1.31187 −0.655933 0.754819i \(-0.727725\pi\)
−0.655933 + 0.754819i \(0.727725\pi\)
\(734\) −33.4257 −1.23377
\(735\) 13.2004 0.486903
\(736\) 8.13489 0.299856
\(737\) −6.10107 −0.224736
\(738\) 27.0361 0.995214
\(739\) 21.5191 0.791594 0.395797 0.918338i \(-0.370468\pi\)
0.395797 + 0.918338i \(0.370468\pi\)
\(740\) 0.665615 0.0244685
\(741\) 3.23353 0.118787
\(742\) 3.90787 0.143463
\(743\) 35.4893 1.30198 0.650988 0.759088i \(-0.274355\pi\)
0.650988 + 0.759088i \(0.274355\pi\)
\(744\) −16.4555 −0.603289
\(745\) 5.74102 0.210335
\(746\) 26.1707 0.958178
\(747\) −12.4380 −0.455084
\(748\) 19.6714 0.719257
\(749\) −5.94020 −0.217050
\(750\) 18.6376 0.680551
\(751\) −9.75862 −0.356097 −0.178049 0.984022i \(-0.556978\pi\)
−0.178049 + 0.984022i \(0.556978\pi\)
\(752\) −3.36611 −0.122749
\(753\) −0.265350 −0.00966989
\(754\) −4.72631 −0.172122
\(755\) −0.588110 −0.0214035
\(756\) 0.253015 0.00920205
\(757\) 23.0881 0.839150 0.419575 0.907721i \(-0.362179\pi\)
0.419575 + 0.907721i \(0.362179\pi\)
\(758\) −0.979375 −0.0355725
\(759\) −93.5711 −3.39641
\(760\) −0.828405 −0.0300494
\(761\) −42.4664 −1.53941 −0.769703 0.638402i \(-0.779596\pi\)
−0.769703 + 0.638402i \(0.779596\pi\)
\(762\) 1.91079 0.0692205
\(763\) −1.90536 −0.0689788
\(764\) −16.3578 −0.591806
\(765\) 9.70237 0.350790
\(766\) 19.6342 0.709414
\(767\) 8.89183 0.321066
\(768\) −2.41559 −0.0871652
\(769\) 12.4318 0.448303 0.224152 0.974554i \(-0.428039\pi\)
0.224152 + 0.974554i \(0.428039\pi\)
\(770\) 2.50543 0.0902894
\(771\) −18.9910 −0.683945
\(772\) 9.39884 0.338272
\(773\) −9.34414 −0.336085 −0.168043 0.985780i \(-0.553745\pi\)
−0.168043 + 0.985780i \(0.553745\pi\)
\(774\) 1.91299 0.0687609
\(775\) −29.3862 −1.05558
\(776\) 1.33445 0.0479039
\(777\) −1.23276 −0.0442248
\(778\) −13.1836 −0.472655
\(779\) −9.53625 −0.341672
\(780\) −2.67867 −0.0959119
\(781\) 10.0964 0.361276
\(782\) 33.6062 1.20176
\(783\) −1.40651 −0.0502645
\(784\) −6.59659 −0.235593
\(785\) 8.77307 0.313124
\(786\) −7.40900 −0.264270
\(787\) 8.52190 0.303773 0.151886 0.988398i \(-0.451465\pi\)
0.151886 + 0.988398i \(0.451465\pi\)
\(788\) 21.2194 0.755908
\(789\) −52.2788 −1.86118
\(790\) −0.393538 −0.0140014
\(791\) 1.29882 0.0461808
\(792\) 13.5000 0.479701
\(793\) −1.50165 −0.0533250
\(794\) −13.2270 −0.469409
\(795\) −12.3122 −0.436667
\(796\) −27.9566 −0.990896
\(797\) −27.7463 −0.982825 −0.491412 0.870927i \(-0.663519\pi\)
−0.491412 + 0.870927i \(0.663519\pi\)
\(798\) 1.53425 0.0543119
\(799\) −13.9058 −0.491953
\(800\) −4.31374 −0.152514
\(801\) 18.2908 0.646275
\(802\) −10.2977 −0.363626
\(803\) −56.0291 −1.97722
\(804\) 3.09502 0.109153
\(805\) 4.28023 0.150858
\(806\) 9.11888 0.321199
\(807\) 11.5934 0.408107
\(808\) 3.18561 0.112069
\(809\) −42.7861 −1.50428 −0.752139 0.659004i \(-0.770978\pi\)
−0.752139 + 0.659004i \(0.770978\pi\)
\(810\) −7.84296 −0.275573
\(811\) 21.6511 0.760272 0.380136 0.924931i \(-0.375877\pi\)
0.380136 + 0.924931i \(0.375877\pi\)
\(812\) −2.24255 −0.0786981
\(813\) 20.7827 0.728881
\(814\) 3.82601 0.134102
\(815\) −17.2983 −0.605933
\(816\) −9.97912 −0.349339
\(817\) −0.674754 −0.0236067
\(818\) −21.2666 −0.743570
\(819\) 2.41042 0.0842269
\(820\) 7.89988 0.275876
\(821\) −51.1735 −1.78597 −0.892984 0.450088i \(-0.851392\pi\)
−0.892984 + 0.450088i \(0.851392\pi\)
\(822\) −19.9953 −0.697415
\(823\) −17.4560 −0.608478 −0.304239 0.952596i \(-0.598402\pi\)
−0.304239 + 0.952596i \(0.598402\pi\)
\(824\) −11.1322 −0.387810
\(825\) 49.6186 1.72750
\(826\) 4.21901 0.146798
\(827\) −50.9896 −1.77308 −0.886541 0.462650i \(-0.846899\pi\)
−0.886541 + 0.462650i \(0.846899\pi\)
\(828\) 23.0631 0.801499
\(829\) −28.7988 −1.00022 −0.500111 0.865961i \(-0.666707\pi\)
−0.500111 + 0.865961i \(0.666707\pi\)
\(830\) −3.63436 −0.126150
\(831\) −48.2065 −1.67226
\(832\) 1.33861 0.0464078
\(833\) −27.2513 −0.944203
\(834\) 37.2813 1.29095
\(835\) −4.80021 −0.166118
\(836\) −4.76175 −0.164688
\(837\) 2.71370 0.0937991
\(838\) 20.5713 0.710623
\(839\) −10.4016 −0.359104 −0.179552 0.983748i \(-0.557465\pi\)
−0.179552 + 0.983748i \(0.557465\pi\)
\(840\) −1.27098 −0.0438530
\(841\) −16.5337 −0.570127
\(842\) 26.4209 0.910523
\(843\) −42.9943 −1.48080
\(844\) −1.00000 −0.0344214
\(845\) −9.28488 −0.319409
\(846\) −9.54322 −0.328103
\(847\) 7.41483 0.254776
\(848\) 6.15273 0.211286
\(849\) −72.5254 −2.48906
\(850\) −17.8206 −0.611242
\(851\) 6.53630 0.224061
\(852\) −5.12179 −0.175470
\(853\) 47.3750 1.62209 0.811045 0.584984i \(-0.198899\pi\)
0.811045 + 0.584984i \(0.198899\pi\)
\(854\) −0.712504 −0.0243814
\(855\) −2.34860 −0.0803205
\(856\) −9.35251 −0.319662
\(857\) 2.64304 0.0902845 0.0451422 0.998981i \(-0.485626\pi\)
0.0451422 + 0.998981i \(0.485626\pi\)
\(858\) −15.3972 −0.525653
\(859\) −19.9397 −0.680335 −0.340167 0.940365i \(-0.610484\pi\)
−0.340167 + 0.940365i \(0.610484\pi\)
\(860\) 0.558970 0.0190607
\(861\) −14.6310 −0.498623
\(862\) 28.1887 0.960109
\(863\) −0.458199 −0.0155973 −0.00779864 0.999970i \(-0.502482\pi\)
−0.00779864 + 0.999970i \(0.502482\pi\)
\(864\) 0.398357 0.0135524
\(865\) 5.33071 0.181250
\(866\) −28.8739 −0.981176
\(867\) −0.159908 −0.00543078
\(868\) 4.32674 0.146859
\(869\) −2.26209 −0.0767361
\(870\) 7.06539 0.239539
\(871\) −1.71511 −0.0581144
\(872\) −2.99989 −0.101589
\(873\) 3.78328 0.128045
\(874\) −8.13489 −0.275167
\(875\) −4.90050 −0.165667
\(876\) 28.4231 0.960327
\(877\) 35.4313 1.19643 0.598216 0.801335i \(-0.295877\pi\)
0.598216 + 0.801335i \(0.295877\pi\)
\(878\) 10.1732 0.343328
\(879\) −44.4169 −1.49814
\(880\) 3.94466 0.132974
\(881\) −34.2584 −1.15419 −0.577097 0.816676i \(-0.695815\pi\)
−0.577097 + 0.816676i \(0.695815\pi\)
\(882\) −18.7019 −0.629727
\(883\) 7.96151 0.267926 0.133963 0.990986i \(-0.457230\pi\)
0.133963 + 0.990986i \(0.457230\pi\)
\(884\) 5.52995 0.185992
\(885\) −13.2924 −0.446821
\(886\) 14.1030 0.473799
\(887\) 7.28917 0.244746 0.122373 0.992484i \(-0.460950\pi\)
0.122373 + 0.992484i \(0.460950\pi\)
\(888\) −1.94090 −0.0651325
\(889\) −0.502413 −0.0168504
\(890\) 5.34453 0.179149
\(891\) −45.0820 −1.51030
\(892\) −6.03373 −0.202024
\(893\) 3.36611 0.112643
\(894\) −16.7406 −0.559888
\(895\) 5.75685 0.192430
\(896\) 0.635145 0.0212187
\(897\) −26.3044 −0.878278
\(898\) 0.195234 0.00651505
\(899\) −24.0524 −0.802191
\(900\) −12.2299 −0.407662
\(901\) 25.4177 0.846786
\(902\) 45.4092 1.51196
\(903\) −1.03524 −0.0344507
\(904\) 2.04492 0.0680131
\(905\) 6.08585 0.202301
\(906\) 1.71490 0.0569738
\(907\) 29.7969 0.989391 0.494695 0.869066i \(-0.335280\pi\)
0.494695 + 0.869066i \(0.335280\pi\)
\(908\) 2.85447 0.0947291
\(909\) 9.03149 0.299555
\(910\) 0.704318 0.0233479
\(911\) −24.2141 −0.802250 −0.401125 0.916023i \(-0.631381\pi\)
−0.401125 + 0.916023i \(0.631381\pi\)
\(912\) 2.41559 0.0799883
\(913\) −20.8906 −0.691378
\(914\) 26.1327 0.864391
\(915\) 2.24482 0.0742114
\(916\) 7.52528 0.248642
\(917\) 1.94809 0.0643315
\(918\) 1.64566 0.0543150
\(919\) 7.77547 0.256489 0.128244 0.991743i \(-0.459066\pi\)
0.128244 + 0.991743i \(0.459066\pi\)
\(920\) 6.73898 0.222178
\(921\) 50.1456 1.65235
\(922\) −5.41612 −0.178370
\(923\) 2.83826 0.0934223
\(924\) −7.30572 −0.240340
\(925\) −3.46605 −0.113963
\(926\) 25.7914 0.847557
\(927\) −31.5609 −1.03660
\(928\) −3.53077 −0.115903
\(929\) −16.8094 −0.551500 −0.275750 0.961229i \(-0.588926\pi\)
−0.275750 + 0.961229i \(0.588926\pi\)
\(930\) −13.6319 −0.447006
\(931\) 6.59659 0.216195
\(932\) −9.44916 −0.309517
\(933\) 60.3878 1.97701
\(934\) −15.5157 −0.507690
\(935\) 16.2959 0.532932
\(936\) 3.79507 0.124046
\(937\) 5.22852 0.170808 0.0854041 0.996346i \(-0.472782\pi\)
0.0854041 + 0.996346i \(0.472782\pi\)
\(938\) −0.813791 −0.0265712
\(939\) 39.7563 1.29740
\(940\) −2.78850 −0.0909509
\(941\) −13.3094 −0.433873 −0.216936 0.976186i \(-0.569606\pi\)
−0.216936 + 0.976186i \(0.569606\pi\)
\(942\) −25.5819 −0.833503
\(943\) 77.5763 2.52623
\(944\) 6.64260 0.216198
\(945\) 0.209599 0.00681824
\(946\) 3.21301 0.104464
\(947\) 27.6878 0.899733 0.449867 0.893096i \(-0.351472\pi\)
0.449867 + 0.893096i \(0.351472\pi\)
\(948\) 1.14754 0.0372703
\(949\) −15.7507 −0.511290
\(950\) 4.31374 0.139956
\(951\) −28.5617 −0.926178
\(952\) 2.62386 0.0850399
\(953\) −34.5165 −1.11810 −0.559050 0.829134i \(-0.688834\pi\)
−0.559050 + 0.829134i \(0.688834\pi\)
\(954\) 17.4435 0.564755
\(955\) −13.5509 −0.438497
\(956\) 8.19763 0.265130
\(957\) 40.6125 1.31281
\(958\) −2.13221 −0.0688885
\(959\) 5.25746 0.169772
\(960\) −2.00109 −0.0645849
\(961\) 15.4063 0.496977
\(962\) 1.07556 0.0346773
\(963\) −26.5152 −0.854440
\(964\) 10.5796 0.340747
\(965\) 7.78605 0.250642
\(966\) −12.4810 −0.401568
\(967\) −10.3428 −0.332601 −0.166300 0.986075i \(-0.553182\pi\)
−0.166300 + 0.986075i \(0.553182\pi\)
\(968\) 11.6742 0.375224
\(969\) 9.97912 0.320575
\(970\) 1.10546 0.0354943
\(971\) 28.7367 0.922206 0.461103 0.887347i \(-0.347454\pi\)
0.461103 + 0.887347i \(0.347454\pi\)
\(972\) 21.6746 0.695214
\(973\) −9.80257 −0.314256
\(974\) −10.0437 −0.321821
\(975\) 13.9486 0.446713
\(976\) −1.12180 −0.0359079
\(977\) 13.8581 0.443361 0.221680 0.975119i \(-0.428846\pi\)
0.221680 + 0.975119i \(0.428846\pi\)
\(978\) 50.4411 1.61293
\(979\) 30.7208 0.981842
\(980\) −5.46465 −0.174562
\(981\) −8.50495 −0.271542
\(982\) −25.2523 −0.805834
\(983\) 0.254699 0.00812363 0.00406181 0.999992i \(-0.498707\pi\)
0.00406181 + 0.999992i \(0.498707\pi\)
\(984\) −23.0357 −0.734351
\(985\) 17.5782 0.560089
\(986\) −14.5860 −0.464514
\(987\) 5.16446 0.164386
\(988\) −1.33861 −0.0425868
\(989\) 5.48905 0.174542
\(990\) 11.1835 0.355433
\(991\) 10.6407 0.338012 0.169006 0.985615i \(-0.445944\pi\)
0.169006 + 0.985615i \(0.445944\pi\)
\(992\) 6.81222 0.216288
\(993\) −9.59136 −0.304372
\(994\) 1.34670 0.0427148
\(995\) −23.1594 −0.734203
\(996\) 10.5976 0.335799
\(997\) −17.2498 −0.546305 −0.273153 0.961971i \(-0.588066\pi\)
−0.273153 + 0.961971i \(0.588066\pi\)
\(998\) −12.2963 −0.389231
\(999\) 0.320076 0.0101268
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 \(a_p\))