Properties

Label 6026.2.a.h.1.16
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.11947 q^{3}\) \(+1.00000 q^{4}\) \(+1.71773 q^{5}\) \(-1.11947 q^{6}\) \(+3.78646 q^{7}\) \(-1.00000 q^{8}\) \(-1.74680 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.11947 q^{3}\) \(+1.00000 q^{4}\) \(+1.71773 q^{5}\) \(-1.11947 q^{6}\) \(+3.78646 q^{7}\) \(-1.00000 q^{8}\) \(-1.74680 q^{9}\) \(-1.71773 q^{10}\) \(-5.02853 q^{11}\) \(+1.11947 q^{12}\) \(-1.13725 q^{13}\) \(-3.78646 q^{14}\) \(+1.92293 q^{15}\) \(+1.00000 q^{16}\) \(-2.02110 q^{17}\) \(+1.74680 q^{18}\) \(-3.45188 q^{19}\) \(+1.71773 q^{20}\) \(+4.23882 q^{21}\) \(+5.02853 q^{22}\) \(-1.00000 q^{23}\) \(-1.11947 q^{24}\) \(-2.04942 q^{25}\) \(+1.13725 q^{26}\) \(-5.31387 q^{27}\) \(+3.78646 q^{28}\) \(+3.63249 q^{29}\) \(-1.92293 q^{30}\) \(-2.60130 q^{31}\) \(-1.00000 q^{32}\) \(-5.62926 q^{33}\) \(+2.02110 q^{34}\) \(+6.50411 q^{35}\) \(-1.74680 q^{36}\) \(+6.85095 q^{37}\) \(+3.45188 q^{38}\) \(-1.27311 q^{39}\) \(-1.71773 q^{40}\) \(+0.0708493 q^{41}\) \(-4.23882 q^{42}\) \(-10.0539 q^{43}\) \(-5.02853 q^{44}\) \(-3.00052 q^{45}\) \(+1.00000 q^{46}\) \(+9.72463 q^{47}\) \(+1.11947 q^{48}\) \(+7.33731 q^{49}\) \(+2.04942 q^{50}\) \(-2.26255 q^{51}\) \(-1.13725 q^{52}\) \(+4.37827 q^{53}\) \(+5.31387 q^{54}\) \(-8.63764 q^{55}\) \(-3.78646 q^{56}\) \(-3.86426 q^{57}\) \(-3.63249 q^{58}\) \(-4.09523 q^{59}\) \(+1.92293 q^{60}\) \(-7.58965 q^{61}\) \(+2.60130 q^{62}\) \(-6.61419 q^{63}\) \(+1.00000 q^{64}\) \(-1.95348 q^{65}\) \(+5.62926 q^{66}\) \(+6.77221 q^{67}\) \(-2.02110 q^{68}\) \(-1.11947 q^{69}\) \(-6.50411 q^{70}\) \(+7.67491 q^{71}\) \(+1.74680 q^{72}\) \(+0.694157 q^{73}\) \(-6.85095 q^{74}\) \(-2.29425 q^{75}\) \(-3.45188 q^{76}\) \(-19.0403 q^{77}\) \(+1.27311 q^{78}\) \(-6.56104 q^{79}\) \(+1.71773 q^{80}\) \(-0.708306 q^{81}\) \(-0.0708493 q^{82}\) \(-6.10921 q^{83}\) \(+4.23882 q^{84}\) \(-3.47170 q^{85}\) \(+10.0539 q^{86}\) \(+4.06644 q^{87}\) \(+5.02853 q^{88}\) \(+0.281878 q^{89}\) \(+3.00052 q^{90}\) \(-4.30614 q^{91}\) \(-1.00000 q^{92}\) \(-2.91207 q^{93}\) \(-9.72463 q^{94}\) \(-5.92938 q^{95}\) \(-1.11947 q^{96}\) \(-5.35678 q^{97}\) \(-7.33731 q^{98}\) \(+8.78382 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.11947 0.646324 0.323162 0.946344i \(-0.395254\pi\)
0.323162 + 0.946344i \(0.395254\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.71773 0.768190 0.384095 0.923294i \(-0.374513\pi\)
0.384095 + 0.923294i \(0.374513\pi\)
\(6\) −1.11947 −0.457020
\(7\) 3.78646 1.43115 0.715574 0.698536i \(-0.246165\pi\)
0.715574 + 0.698536i \(0.246165\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.74680 −0.582266
\(10\) −1.71773 −0.543193
\(11\) −5.02853 −1.51616 −0.758079 0.652162i \(-0.773862\pi\)
−0.758079 + 0.652162i \(0.773862\pi\)
\(12\) 1.11947 0.323162
\(13\) −1.13725 −0.315415 −0.157708 0.987486i \(-0.550410\pi\)
−0.157708 + 0.987486i \(0.550410\pi\)
\(14\) −3.78646 −1.01198
\(15\) 1.92293 0.496500
\(16\) 1.00000 0.250000
\(17\) −2.02110 −0.490189 −0.245095 0.969499i \(-0.578819\pi\)
−0.245095 + 0.969499i \(0.578819\pi\)
\(18\) 1.74680 0.411724
\(19\) −3.45188 −0.791915 −0.395958 0.918269i \(-0.629587\pi\)
−0.395958 + 0.918269i \(0.629587\pi\)
\(20\) 1.71773 0.384095
\(21\) 4.23882 0.924985
\(22\) 5.02853 1.07209
\(23\) −1.00000 −0.208514
\(24\) −1.11947 −0.228510
\(25\) −2.04942 −0.409884
\(26\) 1.13725 0.223032
\(27\) −5.31387 −1.02266
\(28\) 3.78646 0.715574
\(29\) 3.63249 0.674536 0.337268 0.941409i \(-0.390497\pi\)
0.337268 + 0.941409i \(0.390497\pi\)
\(30\) −1.92293 −0.351078
\(31\) −2.60130 −0.467208 −0.233604 0.972332i \(-0.575052\pi\)
−0.233604 + 0.972332i \(0.575052\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.62926 −0.979929
\(34\) 2.02110 0.346616
\(35\) 6.50411 1.09939
\(36\) −1.74680 −0.291133
\(37\) 6.85095 1.12629 0.563145 0.826358i \(-0.309591\pi\)
0.563145 + 0.826358i \(0.309591\pi\)
\(38\) 3.45188 0.559969
\(39\) −1.27311 −0.203860
\(40\) −1.71773 −0.271596
\(41\) 0.0708493 0.0110648 0.00553240 0.999985i \(-0.498239\pi\)
0.00553240 + 0.999985i \(0.498239\pi\)
\(42\) −4.23882 −0.654063
\(43\) −10.0539 −1.53321 −0.766604 0.642120i \(-0.778055\pi\)
−0.766604 + 0.642120i \(0.778055\pi\)
\(44\) −5.02853 −0.758079
\(45\) −3.00052 −0.447291
\(46\) 1.00000 0.147442
\(47\) 9.72463 1.41848 0.709241 0.704966i \(-0.249038\pi\)
0.709241 + 0.704966i \(0.249038\pi\)
\(48\) 1.11947 0.161581
\(49\) 7.33731 1.04819
\(50\) 2.04942 0.289831
\(51\) −2.26255 −0.316821
\(52\) −1.13725 −0.157708
\(53\) 4.37827 0.601402 0.300701 0.953718i \(-0.402779\pi\)
0.300701 + 0.953718i \(0.402779\pi\)
\(54\) 5.31387 0.723127
\(55\) −8.63764 −1.16470
\(56\) −3.78646 −0.505988
\(57\) −3.86426 −0.511834
\(58\) −3.63249 −0.476969
\(59\) −4.09523 −0.533153 −0.266577 0.963814i \(-0.585893\pi\)
−0.266577 + 0.963814i \(0.585893\pi\)
\(60\) 1.92293 0.248250
\(61\) −7.58965 −0.971755 −0.485877 0.874027i \(-0.661500\pi\)
−0.485877 + 0.874027i \(0.661500\pi\)
\(62\) 2.60130 0.330366
\(63\) −6.61419 −0.833309
\(64\) 1.00000 0.125000
\(65\) −1.95348 −0.242299
\(66\) 5.62926 0.692915
\(67\) 6.77221 0.827357 0.413678 0.910423i \(-0.364244\pi\)
0.413678 + 0.910423i \(0.364244\pi\)
\(68\) −2.02110 −0.245095
\(69\) −1.11947 −0.134768
\(70\) −6.50411 −0.777389
\(71\) 7.67491 0.910844 0.455422 0.890276i \(-0.349488\pi\)
0.455422 + 0.890276i \(0.349488\pi\)
\(72\) 1.74680 0.205862
\(73\) 0.694157 0.0812449 0.0406224 0.999175i \(-0.487066\pi\)
0.0406224 + 0.999175i \(0.487066\pi\)
\(74\) −6.85095 −0.796407
\(75\) −2.29425 −0.264917
\(76\) −3.45188 −0.395958
\(77\) −19.0403 −2.16985
\(78\) 1.27311 0.144151
\(79\) −6.56104 −0.738175 −0.369087 0.929395i \(-0.620330\pi\)
−0.369087 + 0.929395i \(0.620330\pi\)
\(80\) 1.71773 0.192048
\(81\) −0.708306 −0.0787007
\(82\) −0.0708493 −0.00782400
\(83\) −6.10921 −0.670572 −0.335286 0.942116i \(-0.608833\pi\)
−0.335286 + 0.942116i \(0.608833\pi\)
\(84\) 4.23882 0.462493
\(85\) −3.47170 −0.376558
\(86\) 10.0539 1.08414
\(87\) 4.06644 0.435968
\(88\) 5.02853 0.536043
\(89\) 0.281878 0.0298790 0.0149395 0.999888i \(-0.495244\pi\)
0.0149395 + 0.999888i \(0.495244\pi\)
\(90\) 3.00052 0.316282
\(91\) −4.30614 −0.451406
\(92\) −1.00000 −0.104257
\(93\) −2.91207 −0.301967
\(94\) −9.72463 −1.00302
\(95\) −5.92938 −0.608342
\(96\) −1.11947 −0.114255
\(97\) −5.35678 −0.543899 −0.271949 0.962312i \(-0.587668\pi\)
−0.271949 + 0.962312i \(0.587668\pi\)
\(98\) −7.33731 −0.741180
\(99\) 8.78382 0.882807
\(100\) −2.04942 −0.204942
\(101\) −0.757584 −0.0753825 −0.0376912 0.999289i \(-0.512000\pi\)
−0.0376912 + 0.999289i \(0.512000\pi\)
\(102\) 2.26255 0.224026
\(103\) −4.62928 −0.456137 −0.228068 0.973645i \(-0.573241\pi\)
−0.228068 + 0.973645i \(0.573241\pi\)
\(104\) 1.13725 0.111516
\(105\) 7.28112 0.710565
\(106\) −4.37827 −0.425256
\(107\) −20.5580 −1.98741 −0.993707 0.112009i \(-0.964271\pi\)
−0.993707 + 0.112009i \(0.964271\pi\)
\(108\) −5.31387 −0.511328
\(109\) −20.6989 −1.98260 −0.991299 0.131630i \(-0.957979\pi\)
−0.991299 + 0.131630i \(0.957979\pi\)
\(110\) 8.63764 0.823566
\(111\) 7.66940 0.727947
\(112\) 3.78646 0.357787
\(113\) 4.74818 0.446671 0.223336 0.974742i \(-0.428305\pi\)
0.223336 + 0.974742i \(0.428305\pi\)
\(114\) 3.86426 0.361921
\(115\) −1.71773 −0.160179
\(116\) 3.63249 0.337268
\(117\) 1.98654 0.183656
\(118\) 4.09523 0.376996
\(119\) −7.65283 −0.701534
\(120\) −1.92293 −0.175539
\(121\) 14.2861 1.29874
\(122\) 7.58965 0.687134
\(123\) 0.0793133 0.00715144
\(124\) −2.60130 −0.233604
\(125\) −12.1090 −1.08306
\(126\) 6.61419 0.589239
\(127\) −13.2591 −1.17655 −0.588276 0.808660i \(-0.700193\pi\)
−0.588276 + 0.808660i \(0.700193\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −11.2550 −0.990949
\(130\) 1.95348 0.171331
\(131\) −1.00000 −0.0873704
\(132\) −5.62926 −0.489965
\(133\) −13.0704 −1.13335
\(134\) −6.77221 −0.585030
\(135\) −9.12778 −0.785594
\(136\) 2.02110 0.173308
\(137\) 2.57060 0.219621 0.109810 0.993953i \(-0.464976\pi\)
0.109810 + 0.993953i \(0.464976\pi\)
\(138\) 1.11947 0.0952952
\(139\) −22.8730 −1.94006 −0.970031 0.242980i \(-0.921875\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(140\) 6.50411 0.549697
\(141\) 10.8864 0.916799
\(142\) −7.67491 −0.644064
\(143\) 5.71868 0.478220
\(144\) −1.74680 −0.145566
\(145\) 6.23962 0.518172
\(146\) −0.694157 −0.0574488
\(147\) 8.21386 0.677468
\(148\) 6.85095 0.563145
\(149\) 17.0135 1.39380 0.696899 0.717170i \(-0.254563\pi\)
0.696899 + 0.717170i \(0.254563\pi\)
\(150\) 2.29425 0.187325
\(151\) −17.0823 −1.39013 −0.695067 0.718945i \(-0.744626\pi\)
−0.695067 + 0.718945i \(0.744626\pi\)
\(152\) 3.45188 0.279984
\(153\) 3.53045 0.285420
\(154\) 19.0403 1.53432
\(155\) −4.46832 −0.358904
\(156\) −1.27311 −0.101930
\(157\) −9.07778 −0.724486 −0.362243 0.932084i \(-0.617989\pi\)
−0.362243 + 0.932084i \(0.617989\pi\)
\(158\) 6.56104 0.521968
\(159\) 4.90133 0.388700
\(160\) −1.71773 −0.135798
\(161\) −3.78646 −0.298415
\(162\) 0.708306 0.0556498
\(163\) −9.73473 −0.762483 −0.381242 0.924475i \(-0.624503\pi\)
−0.381242 + 0.924475i \(0.624503\pi\)
\(164\) 0.0708493 0.00553240
\(165\) −9.66953 −0.752772
\(166\) 6.10921 0.474166
\(167\) 8.15347 0.630934 0.315467 0.948936i \(-0.397839\pi\)
0.315467 + 0.948936i \(0.397839\pi\)
\(168\) −4.23882 −0.327032
\(169\) −11.7067 −0.900513
\(170\) 3.47170 0.266267
\(171\) 6.02973 0.461105
\(172\) −10.0539 −0.766604
\(173\) −10.9776 −0.834609 −0.417305 0.908767i \(-0.637025\pi\)
−0.417305 + 0.908767i \(0.637025\pi\)
\(174\) −4.06644 −0.308276
\(175\) −7.76005 −0.586605
\(176\) −5.02853 −0.379040
\(177\) −4.58446 −0.344589
\(178\) −0.281878 −0.0211276
\(179\) 10.2656 0.767287 0.383644 0.923481i \(-0.374669\pi\)
0.383644 + 0.923481i \(0.374669\pi\)
\(180\) −3.00052 −0.223645
\(181\) −17.1571 −1.27528 −0.637639 0.770335i \(-0.720089\pi\)
−0.637639 + 0.770335i \(0.720089\pi\)
\(182\) 4.30614 0.319193
\(183\) −8.49634 −0.628068
\(184\) 1.00000 0.0737210
\(185\) 11.7681 0.865204
\(186\) 2.91207 0.213523
\(187\) 10.1632 0.743204
\(188\) 9.72463 0.709241
\(189\) −20.1208 −1.46357
\(190\) 5.92938 0.430163
\(191\) −9.30577 −0.673342 −0.336671 0.941622i \(-0.609301\pi\)
−0.336671 + 0.941622i \(0.609301\pi\)
\(192\) 1.11947 0.0807904
\(193\) 10.0038 0.720092 0.360046 0.932935i \(-0.382761\pi\)
0.360046 + 0.932935i \(0.382761\pi\)
\(194\) 5.35678 0.384594
\(195\) −2.18685 −0.156604
\(196\) 7.33731 0.524094
\(197\) 6.72942 0.479451 0.239726 0.970841i \(-0.422943\pi\)
0.239726 + 0.970841i \(0.422943\pi\)
\(198\) −8.78382 −0.624239
\(199\) 8.96908 0.635801 0.317901 0.948124i \(-0.397022\pi\)
0.317901 + 0.948124i \(0.397022\pi\)
\(200\) 2.04942 0.144916
\(201\) 7.58125 0.534740
\(202\) 0.757584 0.0533034
\(203\) 13.7543 0.965361
\(204\) −2.26255 −0.158410
\(205\) 0.121700 0.00849987
\(206\) 4.62928 0.322537
\(207\) 1.74680 0.121411
\(208\) −1.13725 −0.0788538
\(209\) 17.3579 1.20067
\(210\) −7.28112 −0.502445
\(211\) 9.91161 0.682344 0.341172 0.940001i \(-0.389176\pi\)
0.341172 + 0.940001i \(0.389176\pi\)
\(212\) 4.37827 0.300701
\(213\) 8.59180 0.588700
\(214\) 20.5580 1.40531
\(215\) −17.2699 −1.17780
\(216\) 5.31387 0.361563
\(217\) −9.84974 −0.668644
\(218\) 20.6989 1.40191
\(219\) 0.777084 0.0525105
\(220\) −8.63764 −0.582349
\(221\) 2.29849 0.154613
\(222\) −7.66940 −0.514736
\(223\) −6.93130 −0.464154 −0.232077 0.972697i \(-0.574552\pi\)
−0.232077 + 0.972697i \(0.574552\pi\)
\(224\) −3.78646 −0.252994
\(225\) 3.57992 0.238661
\(226\) −4.74818 −0.315844
\(227\) −22.3660 −1.48448 −0.742241 0.670133i \(-0.766237\pi\)
−0.742241 + 0.670133i \(0.766237\pi\)
\(228\) −3.86426 −0.255917
\(229\) −6.96193 −0.460057 −0.230029 0.973184i \(-0.573882\pi\)
−0.230029 + 0.973184i \(0.573882\pi\)
\(230\) 1.71773 0.113263
\(231\) −21.3150 −1.40242
\(232\) −3.63249 −0.238484
\(233\) −14.4881 −0.949146 −0.474573 0.880216i \(-0.657398\pi\)
−0.474573 + 0.880216i \(0.657398\pi\)
\(234\) −1.98654 −0.129864
\(235\) 16.7042 1.08966
\(236\) −4.09523 −0.266577
\(237\) −7.34486 −0.477100
\(238\) 7.65283 0.496059
\(239\) −0.437654 −0.0283095 −0.0141547 0.999900i \(-0.504506\pi\)
−0.0141547 + 0.999900i \(0.504506\pi\)
\(240\) 1.92293 0.124125
\(241\) 14.7766 0.951842 0.475921 0.879488i \(-0.342115\pi\)
0.475921 + 0.879488i \(0.342115\pi\)
\(242\) −14.2861 −0.918346
\(243\) 15.1487 0.971790
\(244\) −7.58965 −0.485877
\(245\) 12.6035 0.805207
\(246\) −0.0793133 −0.00505683
\(247\) 3.92564 0.249782
\(248\) 2.60130 0.165183
\(249\) −6.83904 −0.433407
\(250\) 12.1090 0.765838
\(251\) 26.6680 1.68327 0.841634 0.540049i \(-0.181594\pi\)
0.841634 + 0.540049i \(0.181594\pi\)
\(252\) −6.61419 −0.416655
\(253\) 5.02853 0.316141
\(254\) 13.2591 0.831947
\(255\) −3.88644 −0.243379
\(256\) 1.00000 0.0625000
\(257\) −1.63010 −0.101683 −0.0508415 0.998707i \(-0.516190\pi\)
−0.0508415 + 0.998707i \(0.516190\pi\)
\(258\) 11.2550 0.700707
\(259\) 25.9409 1.61189
\(260\) −1.95348 −0.121150
\(261\) −6.34522 −0.392759
\(262\) 1.00000 0.0617802
\(263\) −10.6468 −0.656512 −0.328256 0.944589i \(-0.606461\pi\)
−0.328256 + 0.944589i \(0.606461\pi\)
\(264\) 5.62926 0.346457
\(265\) 7.52067 0.461991
\(266\) 13.0704 0.801399
\(267\) 0.315553 0.0193115
\(268\) 6.77221 0.413678
\(269\) −3.27243 −0.199523 −0.0997617 0.995011i \(-0.531808\pi\)
−0.0997617 + 0.995011i \(0.531808\pi\)
\(270\) 9.12778 0.555499
\(271\) 30.6593 1.86242 0.931211 0.364482i \(-0.118754\pi\)
0.931211 + 0.364482i \(0.118754\pi\)
\(272\) −2.02110 −0.122547
\(273\) −4.82058 −0.291755
\(274\) −2.57060 −0.155295
\(275\) 10.3056 0.621449
\(276\) −1.11947 −0.0673839
\(277\) 2.46610 0.148174 0.0740869 0.997252i \(-0.476396\pi\)
0.0740869 + 0.997252i \(0.476396\pi\)
\(278\) 22.8730 1.37183
\(279\) 4.54395 0.272039
\(280\) −6.50411 −0.388695
\(281\) 22.4296 1.33804 0.669020 0.743245i \(-0.266714\pi\)
0.669020 + 0.743245i \(0.266714\pi\)
\(282\) −10.8864 −0.648275
\(283\) 1.27092 0.0755486 0.0377743 0.999286i \(-0.487973\pi\)
0.0377743 + 0.999286i \(0.487973\pi\)
\(284\) 7.67491 0.455422
\(285\) −6.63774 −0.393186
\(286\) −5.71868 −0.338152
\(287\) 0.268268 0.0158354
\(288\) 1.74680 0.102931
\(289\) −12.9152 −0.759715
\(290\) −6.23962 −0.366403
\(291\) −5.99673 −0.351535
\(292\) 0.694157 0.0406224
\(293\) 8.38624 0.489929 0.244965 0.969532i \(-0.421224\pi\)
0.244965 + 0.969532i \(0.421224\pi\)
\(294\) −8.21386 −0.479042
\(295\) −7.03448 −0.409563
\(296\) −6.85095 −0.398203
\(297\) 26.7210 1.55051
\(298\) −17.0135 −0.985564
\(299\) 1.13725 0.0657687
\(300\) −2.29425 −0.132459
\(301\) −38.0688 −2.19425
\(302\) 17.0823 0.982974
\(303\) −0.848089 −0.0487215
\(304\) −3.45188 −0.197979
\(305\) −13.0369 −0.746492
\(306\) −3.53045 −0.201823
\(307\) −0.219042 −0.0125014 −0.00625069 0.999980i \(-0.501990\pi\)
−0.00625069 + 0.999980i \(0.501990\pi\)
\(308\) −19.0403 −1.08492
\(309\) −5.18232 −0.294812
\(310\) 4.46832 0.253784
\(311\) 19.9608 1.13188 0.565938 0.824448i \(-0.308514\pi\)
0.565938 + 0.824448i \(0.308514\pi\)
\(312\) 1.27311 0.0720755
\(313\) −8.10032 −0.457857 −0.228928 0.973443i \(-0.573522\pi\)
−0.228928 + 0.973443i \(0.573522\pi\)
\(314\) 9.07778 0.512289
\(315\) −11.3614 −0.640140
\(316\) −6.56104 −0.369087
\(317\) 26.9094 1.51138 0.755690 0.654929i \(-0.227302\pi\)
0.755690 + 0.654929i \(0.227302\pi\)
\(318\) −4.90133 −0.274853
\(319\) −18.2661 −1.02270
\(320\) 1.71773 0.0960238
\(321\) −23.0139 −1.28451
\(322\) 3.78646 0.211011
\(323\) 6.97660 0.388188
\(324\) −0.708306 −0.0393503
\(325\) 2.33069 0.129284
\(326\) 9.73473 0.539157
\(327\) −23.1717 −1.28140
\(328\) −0.0708493 −0.00391200
\(329\) 36.8220 2.03006
\(330\) 9.66953 0.532290
\(331\) 5.70687 0.313678 0.156839 0.987624i \(-0.449870\pi\)
0.156839 + 0.987624i \(0.449870\pi\)
\(332\) −6.10921 −0.335286
\(333\) −11.9672 −0.655800
\(334\) −8.15347 −0.446138
\(335\) 11.6328 0.635568
\(336\) 4.23882 0.231246
\(337\) −31.2307 −1.70125 −0.850623 0.525775i \(-0.823775\pi\)
−0.850623 + 0.525775i \(0.823775\pi\)
\(338\) 11.7067 0.636759
\(339\) 5.31542 0.288694
\(340\) −3.47170 −0.188279
\(341\) 13.0807 0.708361
\(342\) −6.02973 −0.326051
\(343\) 1.27722 0.0689632
\(344\) 10.0539 0.542071
\(345\) −1.92293 −0.103527
\(346\) 10.9776 0.590158
\(347\) 12.5198 0.672098 0.336049 0.941845i \(-0.390909\pi\)
0.336049 + 0.941845i \(0.390909\pi\)
\(348\) 4.06644 0.217984
\(349\) 2.28939 0.122548 0.0612740 0.998121i \(-0.480484\pi\)
0.0612740 + 0.998121i \(0.480484\pi\)
\(350\) 7.76005 0.414792
\(351\) 6.04319 0.322561
\(352\) 5.02853 0.268022
\(353\) 22.7168 1.20909 0.604546 0.796570i \(-0.293355\pi\)
0.604546 + 0.796570i \(0.293355\pi\)
\(354\) 4.58446 0.243662
\(355\) 13.1834 0.699702
\(356\) 0.281878 0.0149395
\(357\) −8.56707 −0.453418
\(358\) −10.2656 −0.542554
\(359\) 5.00987 0.264411 0.132206 0.991222i \(-0.457794\pi\)
0.132206 + 0.991222i \(0.457794\pi\)
\(360\) 3.00052 0.158141
\(361\) −7.08453 −0.372870
\(362\) 17.1571 0.901758
\(363\) 15.9928 0.839405
\(364\) −4.30614 −0.225703
\(365\) 1.19237 0.0624115
\(366\) 8.49634 0.444111
\(367\) 12.1325 0.633310 0.316655 0.948541i \(-0.397440\pi\)
0.316655 + 0.948541i \(0.397440\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −0.123759 −0.00644266
\(370\) −11.7681 −0.611792
\(371\) 16.5782 0.860696
\(372\) −2.91207 −0.150984
\(373\) −30.6721 −1.58814 −0.794071 0.607825i \(-0.792042\pi\)
−0.794071 + 0.607825i \(0.792042\pi\)
\(374\) −10.1632 −0.525525
\(375\) −13.5556 −0.700007
\(376\) −9.72463 −0.501509
\(377\) −4.13103 −0.212759
\(378\) 20.1208 1.03490
\(379\) 3.25289 0.167089 0.0835447 0.996504i \(-0.473376\pi\)
0.0835447 + 0.996504i \(0.473376\pi\)
\(380\) −5.92938 −0.304171
\(381\) −14.8431 −0.760433
\(382\) 9.30577 0.476125
\(383\) −25.1366 −1.28442 −0.642209 0.766529i \(-0.721982\pi\)
−0.642209 + 0.766529i \(0.721982\pi\)
\(384\) −1.11947 −0.0571275
\(385\) −32.7061 −1.66686
\(386\) −10.0038 −0.509182
\(387\) 17.5622 0.892735
\(388\) −5.35678 −0.271949
\(389\) −2.28504 −0.115856 −0.0579282 0.998321i \(-0.518449\pi\)
−0.0579282 + 0.998321i \(0.518449\pi\)
\(390\) 2.18685 0.110735
\(391\) 2.02110 0.102211
\(392\) −7.33731 −0.370590
\(393\) −1.11947 −0.0564696
\(394\) −6.72942 −0.339023
\(395\) −11.2701 −0.567059
\(396\) 8.78382 0.441404
\(397\) −6.23194 −0.312772 −0.156386 0.987696i \(-0.549984\pi\)
−0.156386 + 0.987696i \(0.549984\pi\)
\(398\) −8.96908 −0.449579
\(399\) −14.6319 −0.732510
\(400\) −2.04942 −0.102471
\(401\) 3.09289 0.154452 0.0772258 0.997014i \(-0.475394\pi\)
0.0772258 + 0.997014i \(0.475394\pi\)
\(402\) −7.58125 −0.378118
\(403\) 2.95832 0.147364
\(404\) −0.757584 −0.0376912
\(405\) −1.21668 −0.0604571
\(406\) −13.7543 −0.682614
\(407\) −34.4502 −1.70763
\(408\) 2.26255 0.112013
\(409\) 35.2669 1.74384 0.871918 0.489652i \(-0.162876\pi\)
0.871918 + 0.489652i \(0.162876\pi\)
\(410\) −0.121700 −0.00601032
\(411\) 2.87769 0.141946
\(412\) −4.62928 −0.228068
\(413\) −15.5064 −0.763022
\(414\) −1.74680 −0.0858504
\(415\) −10.4939 −0.515127
\(416\) 1.13725 0.0557581
\(417\) −25.6055 −1.25391
\(418\) −17.3579 −0.849002
\(419\) −5.18691 −0.253397 −0.126698 0.991941i \(-0.540438\pi\)
−0.126698 + 0.991941i \(0.540438\pi\)
\(420\) 7.28112 0.355282
\(421\) 22.7698 1.10973 0.554867 0.831939i \(-0.312769\pi\)
0.554867 + 0.831939i \(0.312769\pi\)
\(422\) −9.91161 −0.482490
\(423\) −16.9870 −0.825934
\(424\) −4.37827 −0.212628
\(425\) 4.14208 0.200920
\(426\) −8.59180 −0.416274
\(427\) −28.7379 −1.39073
\(428\) −20.5580 −0.993707
\(429\) 6.40186 0.309085
\(430\) 17.2699 0.832827
\(431\) 27.2797 1.31402 0.657009 0.753882i \(-0.271821\pi\)
0.657009 + 0.753882i \(0.271821\pi\)
\(432\) −5.31387 −0.255664
\(433\) 0.185277 0.00890385 0.00445193 0.999990i \(-0.498583\pi\)
0.00445193 + 0.999990i \(0.498583\pi\)
\(434\) 9.84974 0.472802
\(435\) 6.98503 0.334907
\(436\) −20.6989 −0.991299
\(437\) 3.45188 0.165126
\(438\) −0.777084 −0.0371305
\(439\) 8.48840 0.405129 0.202565 0.979269i \(-0.435072\pi\)
0.202565 + 0.979269i \(0.435072\pi\)
\(440\) 8.63764 0.411783
\(441\) −12.8168 −0.610324
\(442\) −2.29849 −0.109328
\(443\) −8.73848 −0.415178 −0.207589 0.978216i \(-0.566562\pi\)
−0.207589 + 0.978216i \(0.566562\pi\)
\(444\) 7.66940 0.363974
\(445\) 0.484189 0.0229528
\(446\) 6.93130 0.328206
\(447\) 19.0460 0.900844
\(448\) 3.78646 0.178894
\(449\) −34.5338 −1.62975 −0.814875 0.579636i \(-0.803195\pi\)
−0.814875 + 0.579636i \(0.803195\pi\)
\(450\) −3.57992 −0.168759
\(451\) −0.356268 −0.0167760
\(452\) 4.74818 0.223336
\(453\) −19.1230 −0.898477
\(454\) 22.3660 1.04969
\(455\) −7.39677 −0.346766
\(456\) 3.86426 0.180960
\(457\) 5.56670 0.260399 0.130200 0.991488i \(-0.458438\pi\)
0.130200 + 0.991488i \(0.458438\pi\)
\(458\) 6.96193 0.325310
\(459\) 10.7399 0.501295
\(460\) −1.71773 −0.0800894
\(461\) −21.3007 −0.992072 −0.496036 0.868302i \(-0.665212\pi\)
−0.496036 + 0.868302i \(0.665212\pi\)
\(462\) 21.3150 0.991664
\(463\) 8.04899 0.374068 0.187034 0.982353i \(-0.440113\pi\)
0.187034 + 0.982353i \(0.440113\pi\)
\(464\) 3.63249 0.168634
\(465\) −5.00213 −0.231968
\(466\) 14.4881 0.671148
\(467\) 22.2400 1.02914 0.514572 0.857447i \(-0.327951\pi\)
0.514572 + 0.857447i \(0.327951\pi\)
\(468\) 1.98654 0.0918278
\(469\) 25.6427 1.18407
\(470\) −16.7042 −0.770509
\(471\) −10.1623 −0.468252
\(472\) 4.09523 0.188498
\(473\) 50.5564 2.32459
\(474\) 7.34486 0.337360
\(475\) 7.07434 0.324593
\(476\) −7.65283 −0.350767
\(477\) −7.64796 −0.350176
\(478\) 0.437654 0.0200178
\(479\) −40.1900 −1.83633 −0.918165 0.396199i \(-0.870329\pi\)
−0.918165 + 0.396199i \(0.870329\pi\)
\(480\) −1.92293 −0.0877695
\(481\) −7.79122 −0.355249
\(482\) −14.7766 −0.673054
\(483\) −4.23882 −0.192873
\(484\) 14.2861 0.649369
\(485\) −9.20148 −0.417818
\(486\) −15.1487 −0.687159
\(487\) −17.3281 −0.785212 −0.392606 0.919707i \(-0.628426\pi\)
−0.392606 + 0.919707i \(0.628426\pi\)
\(488\) 7.58965 0.343567
\(489\) −10.8977 −0.492811
\(490\) −12.6035 −0.569368
\(491\) −22.9947 −1.03774 −0.518868 0.854854i \(-0.673646\pi\)
−0.518868 + 0.854854i \(0.673646\pi\)
\(492\) 0.0793133 0.00357572
\(493\) −7.34162 −0.330650
\(494\) −3.92564 −0.176623
\(495\) 15.0882 0.678164
\(496\) −2.60130 −0.116802
\(497\) 29.0608 1.30355
\(498\) 6.83904 0.306465
\(499\) 4.50534 0.201687 0.100843 0.994902i \(-0.467846\pi\)
0.100843 + 0.994902i \(0.467846\pi\)
\(500\) −12.1090 −0.541529
\(501\) 9.12753 0.407788
\(502\) −26.6680 −1.19025
\(503\) 8.98902 0.400801 0.200400 0.979714i \(-0.435776\pi\)
0.200400 + 0.979714i \(0.435776\pi\)
\(504\) 6.61419 0.294619
\(505\) −1.30132 −0.0579081
\(506\) −5.02853 −0.223545
\(507\) −13.1052 −0.582023
\(508\) −13.2591 −0.588276
\(509\) −8.99235 −0.398579 −0.199290 0.979941i \(-0.563863\pi\)
−0.199290 + 0.979941i \(0.563863\pi\)
\(510\) 3.88644 0.172095
\(511\) 2.62840 0.116274
\(512\) −1.00000 −0.0441942
\(513\) 18.3429 0.809857
\(514\) 1.63010 0.0719008
\(515\) −7.95184 −0.350400
\(516\) −11.2550 −0.495474
\(517\) −48.9006 −2.15065
\(518\) −25.9409 −1.13978
\(519\) −12.2890 −0.539428
\(520\) 1.95348 0.0856657
\(521\) −9.42103 −0.412743 −0.206371 0.978474i \(-0.566166\pi\)
−0.206371 + 0.978474i \(0.566166\pi\)
\(522\) 6.34522 0.277723
\(523\) 1.08623 0.0474973 0.0237487 0.999718i \(-0.492440\pi\)
0.0237487 + 0.999718i \(0.492440\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −8.68710 −0.379136
\(526\) 10.6468 0.464224
\(527\) 5.25749 0.229020
\(528\) −5.62926 −0.244982
\(529\) 1.00000 0.0434783
\(530\) −7.52067 −0.326677
\(531\) 7.15353 0.310437
\(532\) −13.0704 −0.566674
\(533\) −0.0805731 −0.00349001
\(534\) −0.315553 −0.0136553
\(535\) −35.3130 −1.52671
\(536\) −6.77221 −0.292515
\(537\) 11.4920 0.495916
\(538\) 3.27243 0.141084
\(539\) −36.8959 −1.58922
\(540\) −9.12778 −0.392797
\(541\) 43.9183 1.88819 0.944097 0.329669i \(-0.106937\pi\)
0.944097 + 0.329669i \(0.106937\pi\)
\(542\) −30.6593 −1.31693
\(543\) −19.2068 −0.824242
\(544\) 2.02110 0.0866540
\(545\) −35.5551 −1.52301
\(546\) 4.82058 0.206302
\(547\) −9.03578 −0.386342 −0.193171 0.981165i \(-0.561877\pi\)
−0.193171 + 0.981165i \(0.561877\pi\)
\(548\) 2.57060 0.109810
\(549\) 13.2576 0.565819
\(550\) −10.3056 −0.439431
\(551\) −12.5389 −0.534175
\(552\) 1.11947 0.0476476
\(553\) −24.8431 −1.05644
\(554\) −2.46610 −0.104775
\(555\) 13.1739 0.559202
\(556\) −22.8730 −0.970031
\(557\) 8.51279 0.360698 0.180349 0.983603i \(-0.442277\pi\)
0.180349 + 0.983603i \(0.442277\pi\)
\(558\) −4.54395 −0.192361
\(559\) 11.4338 0.483597
\(560\) 6.50411 0.274849
\(561\) 11.3773 0.480351
\(562\) −22.4296 −0.946137
\(563\) 9.95255 0.419450 0.209725 0.977760i \(-0.432743\pi\)
0.209725 + 0.977760i \(0.432743\pi\)
\(564\) 10.8864 0.458399
\(565\) 8.15607 0.343128
\(566\) −1.27092 −0.0534209
\(567\) −2.68198 −0.112632
\(568\) −7.67491 −0.322032
\(569\) −22.5982 −0.947365 −0.473682 0.880696i \(-0.657076\pi\)
−0.473682 + 0.880696i \(0.657076\pi\)
\(570\) 6.63774 0.278024
\(571\) 25.0524 1.04841 0.524205 0.851592i \(-0.324362\pi\)
0.524205 + 0.851592i \(0.324362\pi\)
\(572\) 5.71868 0.239110
\(573\) −10.4175 −0.435197
\(574\) −0.268268 −0.0111973
\(575\) 2.04942 0.0854666
\(576\) −1.74680 −0.0727832
\(577\) 31.6088 1.31589 0.657946 0.753065i \(-0.271425\pi\)
0.657946 + 0.753065i \(0.271425\pi\)
\(578\) 12.9152 0.537199
\(579\) 11.1990 0.465413
\(580\) 6.23962 0.259086
\(581\) −23.1323 −0.959689
\(582\) 5.99673 0.248572
\(583\) −22.0163 −0.911821
\(584\) −0.694157 −0.0287244
\(585\) 3.41233 0.141082
\(586\) −8.38624 −0.346432
\(587\) −5.66913 −0.233990 −0.116995 0.993133i \(-0.537326\pi\)
−0.116995 + 0.993133i \(0.537326\pi\)
\(588\) 8.21386 0.338734
\(589\) 8.97938 0.369989
\(590\) 7.03448 0.289605
\(591\) 7.53335 0.309881
\(592\) 6.85095 0.281572
\(593\) −38.3571 −1.57514 −0.787569 0.616226i \(-0.788661\pi\)
−0.787569 + 0.616226i \(0.788661\pi\)
\(594\) −26.7210 −1.09638
\(595\) −13.1455 −0.538911
\(596\) 17.0135 0.696899
\(597\) 10.0406 0.410933
\(598\) −1.13725 −0.0465055
\(599\) −31.7389 −1.29682 −0.648409 0.761292i \(-0.724565\pi\)
−0.648409 + 0.761292i \(0.724565\pi\)
\(600\) 2.29425 0.0936625
\(601\) 33.7116 1.37513 0.687563 0.726125i \(-0.258680\pi\)
0.687563 + 0.726125i \(0.258680\pi\)
\(602\) 38.0688 1.55157
\(603\) −11.8297 −0.481742
\(604\) −17.0823 −0.695067
\(605\) 24.5396 0.997678
\(606\) 0.848089 0.0344513
\(607\) 7.21595 0.292886 0.146443 0.989219i \(-0.453217\pi\)
0.146443 + 0.989219i \(0.453217\pi\)
\(608\) 3.45188 0.139992
\(609\) 15.3974 0.623936
\(610\) 13.0369 0.527850
\(611\) −11.0593 −0.447411
\(612\) 3.53045 0.142710
\(613\) 9.24872 0.373552 0.186776 0.982402i \(-0.440196\pi\)
0.186776 + 0.982402i \(0.440196\pi\)
\(614\) 0.219042 0.00883981
\(615\) 0.136239 0.00549367
\(616\) 19.0403 0.767158
\(617\) 30.4274 1.22496 0.612480 0.790486i \(-0.290172\pi\)
0.612480 + 0.790486i \(0.290172\pi\)
\(618\) 5.18232 0.208464
\(619\) 23.3222 0.937398 0.468699 0.883358i \(-0.344723\pi\)
0.468699 + 0.883358i \(0.344723\pi\)
\(620\) −4.46832 −0.179452
\(621\) 5.31387 0.213238
\(622\) −19.9608 −0.800357
\(623\) 1.06732 0.0427613
\(624\) −1.27311 −0.0509651
\(625\) −10.5528 −0.422112
\(626\) 8.10032 0.323754
\(627\) 19.4315 0.776021
\(628\) −9.07778 −0.362243
\(629\) −13.8465 −0.552095
\(630\) 11.3614 0.452647
\(631\) −5.85913 −0.233248 −0.116624 0.993176i \(-0.537207\pi\)
−0.116624 + 0.993176i \(0.537207\pi\)
\(632\) 6.56104 0.260984
\(633\) 11.0957 0.441015
\(634\) −26.9094 −1.06871
\(635\) −22.7754 −0.903815
\(636\) 4.90133 0.194350
\(637\) −8.34433 −0.330614
\(638\) 18.2661 0.723161
\(639\) −13.4065 −0.530353
\(640\) −1.71773 −0.0678991
\(641\) 36.3729 1.43664 0.718321 0.695712i \(-0.244911\pi\)
0.718321 + 0.695712i \(0.244911\pi\)
\(642\) 23.0139 0.908288
\(643\) −39.3201 −1.55063 −0.775317 0.631573i \(-0.782410\pi\)
−0.775317 + 0.631573i \(0.782410\pi\)
\(644\) −3.78646 −0.149208
\(645\) −19.3330 −0.761237
\(646\) −6.97660 −0.274491
\(647\) 42.1255 1.65612 0.828062 0.560637i \(-0.189444\pi\)
0.828062 + 0.560637i \(0.189444\pi\)
\(648\) 0.708306 0.0278249
\(649\) 20.5930 0.808345
\(650\) −2.33069 −0.0914173
\(651\) −11.0264 −0.432160
\(652\) −9.73473 −0.381242
\(653\) −28.4950 −1.11510 −0.557548 0.830145i \(-0.688258\pi\)
−0.557548 + 0.830145i \(0.688258\pi\)
\(654\) 23.1717 0.906086
\(655\) −1.71773 −0.0671171
\(656\) 0.0708493 0.00276620
\(657\) −1.21255 −0.0473061
\(658\) −36.8220 −1.43547
\(659\) 9.45400 0.368275 0.184138 0.982900i \(-0.441051\pi\)
0.184138 + 0.982900i \(0.441051\pi\)
\(660\) −9.66953 −0.376386
\(661\) −28.1789 −1.09603 −0.548016 0.836468i \(-0.684617\pi\)
−0.548016 + 0.836468i \(0.684617\pi\)
\(662\) −5.70687 −0.221804
\(663\) 2.57308 0.0999301
\(664\) 6.10921 0.237083
\(665\) −22.4514 −0.870628
\(666\) 11.9672 0.463720
\(667\) −3.63249 −0.140650
\(668\) 8.15347 0.315467
\(669\) −7.75934 −0.299994
\(670\) −11.6328 −0.449414
\(671\) 38.1648 1.47333
\(672\) −4.23882 −0.163516
\(673\) 26.0996 1.00607 0.503033 0.864267i \(-0.332217\pi\)
0.503033 + 0.864267i \(0.332217\pi\)
\(674\) 31.2307 1.20296
\(675\) 10.8904 0.419170
\(676\) −11.7067 −0.450257
\(677\) 4.70817 0.180950 0.0904749 0.995899i \(-0.471162\pi\)
0.0904749 + 0.995899i \(0.471162\pi\)
\(678\) −5.31542 −0.204137
\(679\) −20.2833 −0.778400
\(680\) 3.47170 0.133134
\(681\) −25.0379 −0.959456
\(682\) −13.0807 −0.500887
\(683\) −14.0487 −0.537560 −0.268780 0.963202i \(-0.586620\pi\)
−0.268780 + 0.963202i \(0.586620\pi\)
\(684\) 6.02973 0.230553
\(685\) 4.41558 0.168711
\(686\) −1.27722 −0.0487643
\(687\) −7.79364 −0.297346
\(688\) −10.0539 −0.383302
\(689\) −4.97918 −0.189692
\(690\) 1.92293 0.0732049
\(691\) 28.7587 1.09403 0.547017 0.837122i \(-0.315763\pi\)
0.547017 + 0.837122i \(0.315763\pi\)
\(692\) −10.9776 −0.417305
\(693\) 33.2596 1.26343
\(694\) −12.5198 −0.475245
\(695\) −39.2895 −1.49034
\(696\) −4.06644 −0.154138
\(697\) −0.143194 −0.00542385
\(698\) −2.28939 −0.0866545
\(699\) −16.2189 −0.613456
\(700\) −7.76005 −0.293302
\(701\) 18.8449 0.711763 0.355881 0.934531i \(-0.384181\pi\)
0.355881 + 0.934531i \(0.384181\pi\)
\(702\) −6.04319 −0.228085
\(703\) −23.6487 −0.891926
\(704\) −5.02853 −0.189520
\(705\) 18.6998 0.704276
\(706\) −22.7168 −0.854957
\(707\) −2.86857 −0.107884
\(708\) −4.58446 −0.172295
\(709\) 14.0089 0.526115 0.263057 0.964780i \(-0.415269\pi\)
0.263057 + 0.964780i \(0.415269\pi\)
\(710\) −13.1834 −0.494764
\(711\) 11.4608 0.429814
\(712\) −0.281878 −0.0105638
\(713\) 2.60130 0.0974195
\(714\) 8.56707 0.320615
\(715\) 9.82312 0.367364
\(716\) 10.2656 0.383644
\(717\) −0.489938 −0.0182971
\(718\) −5.00987 −0.186967
\(719\) 28.1173 1.04860 0.524299 0.851534i \(-0.324328\pi\)
0.524299 + 0.851534i \(0.324328\pi\)
\(720\) −3.00052 −0.111823
\(721\) −17.5286 −0.652800
\(722\) 7.08453 0.263659
\(723\) 16.5419 0.615198
\(724\) −17.1571 −0.637639
\(725\) −7.44449 −0.276481
\(726\) −15.9928 −0.593549
\(727\) −7.63420 −0.283137 −0.141568 0.989928i \(-0.545215\pi\)
−0.141568 + 0.989928i \(0.545215\pi\)
\(728\) 4.30614 0.159596
\(729\) 19.0834 0.706791
\(730\) −1.19237 −0.0441316
\(731\) 20.3200 0.751562
\(732\) −8.49634 −0.314034
\(733\) 16.7518 0.618741 0.309371 0.950942i \(-0.399882\pi\)
0.309371 + 0.950942i \(0.399882\pi\)
\(734\) −12.1325 −0.447818
\(735\) 14.1092 0.520424
\(736\) 1.00000 0.0368605
\(737\) −34.0542 −1.25440
\(738\) 0.123759 0.00455565
\(739\) 34.9818 1.28683 0.643414 0.765519i \(-0.277518\pi\)
0.643414 + 0.765519i \(0.277518\pi\)
\(740\) 11.7681 0.432602
\(741\) 4.39461 0.161440
\(742\) −16.5782 −0.608604
\(743\) 11.4003 0.418238 0.209119 0.977890i \(-0.432940\pi\)
0.209119 + 0.977890i \(0.432940\pi\)
\(744\) 2.91207 0.106762
\(745\) 29.2245 1.07070
\(746\) 30.6721 1.12299
\(747\) 10.6715 0.390451
\(748\) 10.1632 0.371602
\(749\) −77.8420 −2.84429
\(750\) 13.5556 0.494979
\(751\) −2.70192 −0.0985946 −0.0492973 0.998784i \(-0.515698\pi\)
−0.0492973 + 0.998784i \(0.515698\pi\)
\(752\) 9.72463 0.354621
\(753\) 29.8539 1.08794
\(754\) 4.13103 0.150443
\(755\) −29.3426 −1.06789
\(756\) −20.1208 −0.731786
\(757\) −25.9273 −0.942344 −0.471172 0.882041i \(-0.656169\pi\)
−0.471172 + 0.882041i \(0.656169\pi\)
\(758\) −3.25289 −0.118150
\(759\) 5.62926 0.204329
\(760\) 5.92938 0.215081
\(761\) −1.33762 −0.0484887 −0.0242444 0.999706i \(-0.507718\pi\)
−0.0242444 + 0.999706i \(0.507718\pi\)
\(762\) 14.8431 0.537707
\(763\) −78.3758 −2.83739
\(764\) −9.30577 −0.336671
\(765\) 6.06435 0.219257
\(766\) 25.1366 0.908221
\(767\) 4.65728 0.168165
\(768\) 1.11947 0.0403952
\(769\) 40.5063 1.46069 0.730347 0.683076i \(-0.239358\pi\)
0.730347 + 0.683076i \(0.239358\pi\)
\(770\) 32.7061 1.17865
\(771\) −1.82484 −0.0657202
\(772\) 10.0038 0.360046
\(773\) 6.14112 0.220881 0.110440 0.993883i \(-0.464774\pi\)
0.110440 + 0.993883i \(0.464774\pi\)
\(774\) −17.5622 −0.631259
\(775\) 5.33115 0.191501
\(776\) 5.35678 0.192297
\(777\) 29.0399 1.04180
\(778\) 2.28504 0.0819228
\(779\) −0.244563 −0.00876239
\(780\) −2.18685 −0.0783018
\(781\) −38.5935 −1.38098
\(782\) −2.02110 −0.0722744
\(783\) −19.3026 −0.689818
\(784\) 7.33731 0.262047
\(785\) −15.5931 −0.556543
\(786\) 1.11947 0.0399300
\(787\) 55.5918 1.98163 0.990817 0.135212i \(-0.0431716\pi\)
0.990817 + 0.135212i \(0.0431716\pi\)
\(788\) 6.72942 0.239726
\(789\) −11.9188 −0.424319
\(790\) 11.2701 0.400971
\(791\) 17.9788 0.639253
\(792\) −8.78382 −0.312120
\(793\) 8.63130 0.306506
\(794\) 6.23194 0.221163
\(795\) 8.41913 0.298596
\(796\) 8.96908 0.317901
\(797\) 20.2170 0.716121 0.358061 0.933698i \(-0.383438\pi\)
0.358061 + 0.933698i \(0.383438\pi\)
\(798\) 14.6319 0.517963
\(799\) −19.6545 −0.695325
\(800\) 2.04942 0.0724579
\(801\) −0.492384 −0.0173975
\(802\) −3.09289 −0.109214
\(803\) −3.49059 −0.123180
\(804\) 7.58125 0.267370
\(805\) −6.50411 −0.229240
\(806\) −2.95832 −0.104202
\(807\) −3.66337 −0.128957
\(808\) 0.757584 0.0266517
\(809\) −23.0017 −0.808698 −0.404349 0.914605i \(-0.632502\pi\)
−0.404349 + 0.914605i \(0.632502\pi\)
\(810\) 1.21668 0.0427496
\(811\) 12.4913 0.438630 0.219315 0.975654i \(-0.429618\pi\)
0.219315 + 0.975654i \(0.429618\pi\)
\(812\) 13.7543 0.482681
\(813\) 34.3220 1.20373
\(814\) 34.4502 1.20748
\(815\) −16.7216 −0.585732
\(816\) −2.26255 −0.0792052
\(817\) 34.7049 1.21417
\(818\) −35.2669 −1.23308
\(819\) 7.52196 0.262839
\(820\) 0.121700 0.00424994
\(821\) −19.6664 −0.686362 −0.343181 0.939269i \(-0.611504\pi\)
−0.343181 + 0.939269i \(0.611504\pi\)
\(822\) −2.87769 −0.100371
\(823\) −30.0960 −1.04908 −0.524541 0.851385i \(-0.675763\pi\)
−0.524541 + 0.851385i \(0.675763\pi\)
\(824\) 4.62928 0.161269
\(825\) 11.5367 0.401657
\(826\) 15.5064 0.539538
\(827\) −15.6806 −0.545269 −0.272634 0.962118i \(-0.587895\pi\)
−0.272634 + 0.962118i \(0.587895\pi\)
\(828\) 1.74680 0.0607054
\(829\) −5.86794 −0.203802 −0.101901 0.994795i \(-0.532492\pi\)
−0.101901 + 0.994795i \(0.532492\pi\)
\(830\) 10.4939 0.364250
\(831\) 2.76072 0.0957683
\(832\) −1.13725 −0.0394269
\(833\) −14.8294 −0.513810
\(834\) 25.6055 0.886647
\(835\) 14.0054 0.484678
\(836\) 17.3579 0.600335
\(837\) 13.8230 0.477792
\(838\) 5.18691 0.179179
\(839\) 7.68218 0.265218 0.132609 0.991168i \(-0.457665\pi\)
0.132609 + 0.991168i \(0.457665\pi\)
\(840\) −7.28112 −0.251223
\(841\) −15.8050 −0.545001
\(842\) −22.7698 −0.784700
\(843\) 25.1092 0.864806
\(844\) 9.91161 0.341172
\(845\) −20.1088 −0.691765
\(846\) 16.9870 0.584024
\(847\) 54.0939 1.85869
\(848\) 4.37827 0.150351
\(849\) 1.42276 0.0488288
\(850\) −4.14208 −0.142072
\(851\) −6.85095 −0.234848
\(852\) 8.59180 0.294350
\(853\) −50.4283 −1.72663 −0.863315 0.504665i \(-0.831616\pi\)
−0.863315 + 0.504665i \(0.831616\pi\)
\(854\) 28.7379 0.983391
\(855\) 10.3574 0.354217
\(856\) 20.5580 0.702657
\(857\) −40.5583 −1.38544 −0.692722 0.721205i \(-0.743589\pi\)
−0.692722 + 0.721205i \(0.743589\pi\)
\(858\) −6.40186 −0.218556
\(859\) −24.8151 −0.846679 −0.423339 0.905971i \(-0.639142\pi\)
−0.423339 + 0.905971i \(0.639142\pi\)
\(860\) −17.2699 −0.588898
\(861\) 0.300317 0.0102348
\(862\) −27.2797 −0.929152
\(863\) 21.8192 0.742733 0.371366 0.928486i \(-0.378889\pi\)
0.371366 + 0.928486i \(0.378889\pi\)
\(864\) 5.31387 0.180782
\(865\) −18.8565 −0.641139
\(866\) −0.185277 −0.00629598
\(867\) −14.4581 −0.491022
\(868\) −9.84974 −0.334322
\(869\) 32.9924 1.11919
\(870\) −6.98503 −0.236815
\(871\) −7.70167 −0.260961
\(872\) 20.6989 0.700954
\(873\) 9.35721 0.316694
\(874\) −3.45188 −0.116762
\(875\) −45.8502 −1.55002
\(876\) 0.777084 0.0262552
\(877\) 22.5581 0.761733 0.380866 0.924630i \(-0.375626\pi\)
0.380866 + 0.924630i \(0.375626\pi\)
\(878\) −8.48840 −0.286470
\(879\) 9.38810 0.316653
\(880\) −8.63764 −0.291175
\(881\) −12.3252 −0.415248 −0.207624 0.978209i \(-0.566573\pi\)
−0.207624 + 0.978209i \(0.566573\pi\)
\(882\) 12.8168 0.431564
\(883\) −43.4179 −1.46113 −0.730564 0.682844i \(-0.760743\pi\)
−0.730564 + 0.682844i \(0.760743\pi\)
\(884\) 2.29849 0.0773066
\(885\) −7.87485 −0.264710
\(886\) 8.73848 0.293575
\(887\) −13.9255 −0.467572 −0.233786 0.972288i \(-0.575112\pi\)
−0.233786 + 0.972288i \(0.575112\pi\)
\(888\) −7.66940 −0.257368
\(889\) −50.2050 −1.68382
\(890\) −0.484189 −0.0162300
\(891\) 3.56174 0.119323
\(892\) −6.93130 −0.232077
\(893\) −33.5682 −1.12332
\(894\) −19.0460 −0.636993
\(895\) 17.6335 0.589423
\(896\) −3.78646 −0.126497
\(897\) 1.27311 0.0425078
\(898\) 34.5338 1.15241
\(899\) −9.44919 −0.315148
\(900\) 3.57992 0.119331
\(901\) −8.84894 −0.294801
\(902\) 0.356268 0.0118624
\(903\) −42.6167 −1.41820
\(904\) −4.74818 −0.157922
\(905\) −29.4712 −0.979656
\(906\) 19.1230 0.635319
\(907\) 1.73046 0.0574590 0.0287295 0.999587i \(-0.490854\pi\)
0.0287295 + 0.999587i \(0.490854\pi\)
\(908\) −22.3660 −0.742241
\(909\) 1.32335 0.0438926
\(910\) 7.39677 0.245201
\(911\) 1.21394 0.0402195 0.0201097 0.999798i \(-0.493598\pi\)
0.0201097 + 0.999798i \(0.493598\pi\)
\(912\) −3.86426 −0.127958
\(913\) 30.7203 1.01669
\(914\) −5.56670 −0.184130
\(915\) −14.5944 −0.482476
\(916\) −6.96193 −0.230029
\(917\) −3.78646 −0.125040
\(918\) −10.7399 −0.354469
\(919\) 0.857023 0.0282706 0.0141353 0.999900i \(-0.495500\pi\)
0.0141353 + 0.999900i \(0.495500\pi\)
\(920\) 1.71773 0.0566317
\(921\) −0.245210 −0.00807993
\(922\) 21.3007 0.701501
\(923\) −8.72826 −0.287294
\(924\) −21.3150 −0.701212
\(925\) −14.0405 −0.461648
\(926\) −8.04899 −0.264506
\(927\) 8.08642 0.265593
\(928\) −3.63249 −0.119242
\(929\) 34.7011 1.13851 0.569253 0.822162i \(-0.307232\pi\)
0.569253 + 0.822162i \(0.307232\pi\)
\(930\) 5.00213 0.164026
\(931\) −25.3275 −0.830076
\(932\) −14.4881 −0.474573
\(933\) 22.3455 0.731558
\(934\) −22.2400 −0.727715
\(935\) 17.4575 0.570922
\(936\) −1.98654 −0.0649321
\(937\) −7.49494 −0.244849 −0.122425 0.992478i \(-0.539067\pi\)
−0.122425 + 0.992478i \(0.539067\pi\)
\(938\) −25.6427 −0.837265
\(939\) −9.06802 −0.295924
\(940\) 16.7042 0.544832
\(941\) −13.0958 −0.426910 −0.213455 0.976953i \(-0.568472\pi\)
−0.213455 + 0.976953i \(0.568472\pi\)
\(942\) 10.1623 0.331104
\(943\) −0.0708493 −0.00230717
\(944\) −4.09523 −0.133288
\(945\) −34.5620 −1.12430
\(946\) −50.5564 −1.64373
\(947\) −4.96406 −0.161310 −0.0806551 0.996742i \(-0.525701\pi\)
−0.0806551 + 0.996742i \(0.525701\pi\)
\(948\) −7.34486 −0.238550
\(949\) −0.789427 −0.0256259
\(950\) −7.07434 −0.229522
\(951\) 30.1241 0.976841
\(952\) 7.65283 0.248030
\(953\) 57.0896 1.84931 0.924656 0.380803i \(-0.124352\pi\)
0.924656 + 0.380803i \(0.124352\pi\)
\(954\) 7.64796 0.247612
\(955\) −15.9848 −0.517255
\(956\) −0.437654 −0.0141547
\(957\) −20.4482 −0.660997
\(958\) 40.1900 1.29848
\(959\) 9.73347 0.314310
\(960\) 1.92293 0.0620624
\(961\) −24.2332 −0.781717
\(962\) 7.79122 0.251199
\(963\) 35.9106 1.15720
\(964\) 14.7766 0.475921
\(965\) 17.1839 0.553168
\(966\) 4.23882 0.136382
\(967\) −29.6492 −0.953455 −0.476728 0.879051i \(-0.658177\pi\)
−0.476728 + 0.879051i \(0.658177\pi\)
\(968\) −14.2861 −0.459173
\(969\) 7.81006 0.250895
\(970\) 9.20148 0.295442
\(971\) −7.32991 −0.235228 −0.117614 0.993059i \(-0.537525\pi\)
−0.117614 + 0.993059i \(0.537525\pi\)
\(972\) 15.1487 0.485895
\(973\) −86.6078 −2.77652
\(974\) 17.3281 0.555229
\(975\) 2.60913 0.0835590
\(976\) −7.58965 −0.242939
\(977\) 19.5965 0.626946 0.313473 0.949597i \(-0.398507\pi\)
0.313473 + 0.949597i \(0.398507\pi\)
\(978\) 10.8977 0.348470
\(979\) −1.41743 −0.0453013
\(980\) 12.6035 0.402604
\(981\) 36.1568 1.15440
\(982\) 22.9947 0.733790
\(983\) 36.0795 1.15076 0.575379 0.817887i \(-0.304854\pi\)
0.575379 + 0.817887i \(0.304854\pi\)
\(984\) −0.0793133 −0.00252842
\(985\) 11.5593 0.368310
\(986\) 7.34162 0.233805
\(987\) 41.2209 1.31208
\(988\) 3.92564 0.124891
\(989\) 10.0539 0.319696
\(990\) −15.0882 −0.479534
\(991\) −22.5818 −0.717334 −0.358667 0.933466i \(-0.616769\pi\)
−0.358667 + 0.933466i \(0.616769\pi\)
\(992\) 2.60130 0.0825914
\(993\) 6.38864 0.202737
\(994\) −29.0608 −0.921752
\(995\) 15.4064 0.488416
\(996\) −6.83904 −0.216703
\(997\) 8.62626 0.273196 0.136598 0.990627i \(-0.456383\pi\)
0.136598 + 0.990627i \(0.456383\pi\)
\(998\) −4.50534 −0.142614
\(999\) −36.4051 −1.15181
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 \(a_p\))