Properties

Label 8018.2.a.j.1.19
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 1.19
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-0.764189 q^{3}\) \(+1.00000 q^{4}\) \(-0.445775 q^{5}\) \(-0.764189 q^{6}\) \(-0.938446 q^{7}\) \(+1.00000 q^{8}\) \(-2.41602 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-0.764189 q^{3}\) \(+1.00000 q^{4}\) \(-0.445775 q^{5}\) \(-0.764189 q^{6}\) \(-0.938446 q^{7}\) \(+1.00000 q^{8}\) \(-2.41602 q^{9}\) \(-0.445775 q^{10}\) \(+2.33898 q^{11}\) \(-0.764189 q^{12}\) \(-6.49743 q^{13}\) \(-0.938446 q^{14}\) \(+0.340656 q^{15}\) \(+1.00000 q^{16}\) \(+1.93985 q^{17}\) \(-2.41602 q^{18}\) \(-1.00000 q^{19}\) \(-0.445775 q^{20}\) \(+0.717150 q^{21}\) \(+2.33898 q^{22}\) \(+3.50222 q^{23}\) \(-0.764189 q^{24}\) \(-4.80128 q^{25}\) \(-6.49743 q^{26}\) \(+4.13886 q^{27}\) \(-0.938446 q^{28}\) \(-1.31075 q^{29}\) \(+0.340656 q^{30}\) \(+4.83737 q^{31}\) \(+1.00000 q^{32}\) \(-1.78742 q^{33}\) \(+1.93985 q^{34}\) \(+0.418336 q^{35}\) \(-2.41602 q^{36}\) \(+2.27726 q^{37}\) \(-1.00000 q^{38}\) \(+4.96526 q^{39}\) \(-0.445775 q^{40}\) \(-8.03117 q^{41}\) \(+0.717150 q^{42}\) \(-2.86373 q^{43}\) \(+2.33898 q^{44}\) \(+1.07700 q^{45}\) \(+3.50222 q^{46}\) \(+2.15639 q^{47}\) \(-0.764189 q^{48}\) \(-6.11932 q^{49}\) \(-4.80128 q^{50}\) \(-1.48241 q^{51}\) \(-6.49743 q^{52}\) \(+3.08544 q^{53}\) \(+4.13886 q^{54}\) \(-1.04266 q^{55}\) \(-0.938446 q^{56}\) \(+0.764189 q^{57}\) \(-1.31075 q^{58}\) \(+1.71699 q^{59}\) \(+0.340656 q^{60}\) \(+2.46308 q^{61}\) \(+4.83737 q^{62}\) \(+2.26730 q^{63}\) \(+1.00000 q^{64}\) \(+2.89639 q^{65}\) \(-1.78742 q^{66}\) \(+4.61290 q^{67}\) \(+1.93985 q^{68}\) \(-2.67636 q^{69}\) \(+0.418336 q^{70}\) \(+8.01255 q^{71}\) \(-2.41602 q^{72}\) \(+10.4169 q^{73}\) \(+2.27726 q^{74}\) \(+3.66909 q^{75}\) \(-1.00000 q^{76}\) \(-2.19501 q^{77}\) \(+4.96526 q^{78}\) \(+0.375799 q^{79}\) \(-0.445775 q^{80}\) \(+4.08518 q^{81}\) \(-8.03117 q^{82}\) \(+6.21956 q^{83}\) \(+0.717150 q^{84}\) \(-0.864734 q^{85}\) \(-2.86373 q^{86}\) \(+1.00166 q^{87}\) \(+2.33898 q^{88}\) \(+14.0546 q^{89}\) \(+1.07700 q^{90}\) \(+6.09749 q^{91}\) \(+3.50222 q^{92}\) \(-3.69666 q^{93}\) \(+2.15639 q^{94}\) \(+0.445775 q^{95}\) \(-0.764189 q^{96}\) \(-16.8131 q^{97}\) \(-6.11932 q^{98}\) \(-5.65101 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.764189 −0.441205 −0.220602 0.975364i \(-0.570802\pi\)
−0.220602 + 0.975364i \(0.570802\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.445775 −0.199357 −0.0996783 0.995020i \(-0.531781\pi\)
−0.0996783 + 0.995020i \(0.531781\pi\)
\(6\) −0.764189 −0.311979
\(7\) −0.938446 −0.354699 −0.177350 0.984148i \(-0.556752\pi\)
−0.177350 + 0.984148i \(0.556752\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.41602 −0.805338
\(10\) −0.445775 −0.140966
\(11\) 2.33898 0.705229 0.352615 0.935769i \(-0.385293\pi\)
0.352615 + 0.935769i \(0.385293\pi\)
\(12\) −0.764189 −0.220602
\(13\) −6.49743 −1.80206 −0.901031 0.433755i \(-0.857188\pi\)
−0.901031 + 0.433755i \(0.857188\pi\)
\(14\) −0.938446 −0.250810
\(15\) 0.340656 0.0879570
\(16\) 1.00000 0.250000
\(17\) 1.93985 0.470482 0.235241 0.971937i \(-0.424412\pi\)
0.235241 + 0.971937i \(0.424412\pi\)
\(18\) −2.41602 −0.569460
\(19\) −1.00000 −0.229416
\(20\) −0.445775 −0.0996783
\(21\) 0.717150 0.156495
\(22\) 2.33898 0.498672
\(23\) 3.50222 0.730263 0.365132 0.930956i \(-0.381024\pi\)
0.365132 + 0.930956i \(0.381024\pi\)
\(24\) −0.764189 −0.155989
\(25\) −4.80128 −0.960257
\(26\) −6.49743 −1.27425
\(27\) 4.13886 0.796524
\(28\) −0.938446 −0.177350
\(29\) −1.31075 −0.243400 −0.121700 0.992567i \(-0.538835\pi\)
−0.121700 + 0.992567i \(0.538835\pi\)
\(30\) 0.340656 0.0621950
\(31\) 4.83737 0.868816 0.434408 0.900716i \(-0.356958\pi\)
0.434408 + 0.900716i \(0.356958\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.78742 −0.311150
\(34\) 1.93985 0.332681
\(35\) 0.418336 0.0707116
\(36\) −2.41602 −0.402669
\(37\) 2.27726 0.374380 0.187190 0.982324i \(-0.440062\pi\)
0.187190 + 0.982324i \(0.440062\pi\)
\(38\) −1.00000 −0.162221
\(39\) 4.96526 0.795078
\(40\) −0.445775 −0.0704832
\(41\) −8.03117 −1.25426 −0.627129 0.778916i \(-0.715770\pi\)
−0.627129 + 0.778916i \(0.715770\pi\)
\(42\) 0.717150 0.110659
\(43\) −2.86373 −0.436715 −0.218358 0.975869i \(-0.570070\pi\)
−0.218358 + 0.975869i \(0.570070\pi\)
\(44\) 2.33898 0.352615
\(45\) 1.07700 0.160549
\(46\) 3.50222 0.516374
\(47\) 2.15639 0.314542 0.157271 0.987556i \(-0.449730\pi\)
0.157271 + 0.987556i \(0.449730\pi\)
\(48\) −0.764189 −0.110301
\(49\) −6.11932 −0.874188
\(50\) −4.80128 −0.679004
\(51\) −1.48241 −0.207579
\(52\) −6.49743 −0.901031
\(53\) 3.08544 0.423818 0.211909 0.977289i \(-0.432032\pi\)
0.211909 + 0.977289i \(0.432032\pi\)
\(54\) 4.13886 0.563227
\(55\) −1.04266 −0.140592
\(56\) −0.938446 −0.125405
\(57\) 0.764189 0.101219
\(58\) −1.31075 −0.172109
\(59\) 1.71699 0.223534 0.111767 0.993734i \(-0.464349\pi\)
0.111767 + 0.993734i \(0.464349\pi\)
\(60\) 0.340656 0.0439785
\(61\) 2.46308 0.315365 0.157682 0.987490i \(-0.449598\pi\)
0.157682 + 0.987490i \(0.449598\pi\)
\(62\) 4.83737 0.614346
\(63\) 2.26730 0.285653
\(64\) 1.00000 0.125000
\(65\) 2.89639 0.359253
\(66\) −1.78742 −0.220017
\(67\) 4.61290 0.563555 0.281778 0.959480i \(-0.409076\pi\)
0.281778 + 0.959480i \(0.409076\pi\)
\(68\) 1.93985 0.235241
\(69\) −2.67636 −0.322196
\(70\) 0.418336 0.0500007
\(71\) 8.01255 0.950915 0.475457 0.879739i \(-0.342283\pi\)
0.475457 + 0.879739i \(0.342283\pi\)
\(72\) −2.41602 −0.284730
\(73\) 10.4169 1.21921 0.609605 0.792705i \(-0.291328\pi\)
0.609605 + 0.792705i \(0.291328\pi\)
\(74\) 2.27726 0.264726
\(75\) 3.66909 0.423670
\(76\) −1.00000 −0.114708
\(77\) −2.19501 −0.250144
\(78\) 4.96526 0.562205
\(79\) 0.375799 0.0422807 0.0211403 0.999777i \(-0.493270\pi\)
0.0211403 + 0.999777i \(0.493270\pi\)
\(80\) −0.445775 −0.0498391
\(81\) 4.08518 0.453908
\(82\) −8.03117 −0.886894
\(83\) 6.21956 0.682685 0.341343 0.939939i \(-0.389118\pi\)
0.341343 + 0.939939i \(0.389118\pi\)
\(84\) 0.717150 0.0782475
\(85\) −0.864734 −0.0937936
\(86\) −2.86373 −0.308804
\(87\) 1.00166 0.107389
\(88\) 2.33898 0.249336
\(89\) 14.0546 1.48978 0.744890 0.667187i \(-0.232502\pi\)
0.744890 + 0.667187i \(0.232502\pi\)
\(90\) 1.07700 0.113526
\(91\) 6.09749 0.639190
\(92\) 3.50222 0.365132
\(93\) −3.69666 −0.383326
\(94\) 2.15639 0.222414
\(95\) 0.445775 0.0457355
\(96\) −0.764189 −0.0779947
\(97\) −16.8131 −1.70711 −0.853557 0.520999i \(-0.825560\pi\)
−0.853557 + 0.520999i \(0.825560\pi\)
\(98\) −6.11932 −0.618145
\(99\) −5.65101 −0.567948
\(100\) −4.80128 −0.480128
\(101\) −7.61087 −0.757309 −0.378655 0.925538i \(-0.623613\pi\)
−0.378655 + 0.925538i \(0.623613\pi\)
\(102\) −1.48241 −0.146780
\(103\) −2.78620 −0.274533 −0.137266 0.990534i \(-0.543832\pi\)
−0.137266 + 0.990534i \(0.543832\pi\)
\(104\) −6.49743 −0.637125
\(105\) −0.319687 −0.0311983
\(106\) 3.08544 0.299685
\(107\) 3.42104 0.330725 0.165362 0.986233i \(-0.447121\pi\)
0.165362 + 0.986233i \(0.447121\pi\)
\(108\) 4.13886 0.398262
\(109\) −9.39884 −0.900246 −0.450123 0.892967i \(-0.648620\pi\)
−0.450123 + 0.892967i \(0.648620\pi\)
\(110\) −1.04266 −0.0994136
\(111\) −1.74026 −0.165178
\(112\) −0.938446 −0.0886748
\(113\) 5.98637 0.563151 0.281575 0.959539i \(-0.409143\pi\)
0.281575 + 0.959539i \(0.409143\pi\)
\(114\) 0.764189 0.0715729
\(115\) −1.56120 −0.145583
\(116\) −1.31075 −0.121700
\(117\) 15.6979 1.45127
\(118\) 1.71699 0.158062
\(119\) −1.82044 −0.166879
\(120\) 0.340656 0.0310975
\(121\) −5.52917 −0.502652
\(122\) 2.46308 0.222997
\(123\) 6.13733 0.553384
\(124\) 4.83737 0.434408
\(125\) 4.36917 0.390790
\(126\) 2.26730 0.201987
\(127\) 3.86438 0.342908 0.171454 0.985192i \(-0.445153\pi\)
0.171454 + 0.985192i \(0.445153\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.18843 0.192681
\(130\) 2.89639 0.254030
\(131\) 18.3402 1.60239 0.801197 0.598400i \(-0.204197\pi\)
0.801197 + 0.598400i \(0.204197\pi\)
\(132\) −1.78742 −0.155575
\(133\) 0.938446 0.0813736
\(134\) 4.61290 0.398494
\(135\) −1.84500 −0.158792
\(136\) 1.93985 0.166340
\(137\) −11.4988 −0.982412 −0.491206 0.871043i \(-0.663444\pi\)
−0.491206 + 0.871043i \(0.663444\pi\)
\(138\) −2.67636 −0.227827
\(139\) 4.45298 0.377697 0.188848 0.982006i \(-0.439525\pi\)
0.188848 + 0.982006i \(0.439525\pi\)
\(140\) 0.418336 0.0353558
\(141\) −1.64789 −0.138777
\(142\) 8.01255 0.672398
\(143\) −15.1974 −1.27087
\(144\) −2.41602 −0.201335
\(145\) 0.584298 0.0485233
\(146\) 10.4169 0.862112
\(147\) 4.67632 0.385696
\(148\) 2.27726 0.187190
\(149\) 8.24566 0.675511 0.337755 0.941234i \(-0.390332\pi\)
0.337755 + 0.941234i \(0.390332\pi\)
\(150\) 3.66909 0.299580
\(151\) 15.8642 1.29101 0.645505 0.763756i \(-0.276647\pi\)
0.645505 + 0.763756i \(0.276647\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −4.68670 −0.378897
\(154\) −2.19501 −0.176879
\(155\) −2.15638 −0.173204
\(156\) 4.96526 0.397539
\(157\) −0.995625 −0.0794595 −0.0397298 0.999210i \(-0.512650\pi\)
−0.0397298 + 0.999210i \(0.512650\pi\)
\(158\) 0.375799 0.0298969
\(159\) −2.35786 −0.186991
\(160\) −0.445775 −0.0352416
\(161\) −3.28664 −0.259024
\(162\) 4.08518 0.320962
\(163\) 7.80212 0.611109 0.305555 0.952175i \(-0.401158\pi\)
0.305555 + 0.952175i \(0.401158\pi\)
\(164\) −8.03117 −0.627129
\(165\) 0.796788 0.0620299
\(166\) 6.21956 0.482731
\(167\) 23.4783 1.81680 0.908402 0.418098i \(-0.137303\pi\)
0.908402 + 0.418098i \(0.137303\pi\)
\(168\) 0.717150 0.0553293
\(169\) 29.2166 2.24743
\(170\) −0.864734 −0.0663221
\(171\) 2.41602 0.184757
\(172\) −2.86373 −0.218358
\(173\) 25.8598 1.96609 0.983044 0.183372i \(-0.0587013\pi\)
0.983044 + 0.183372i \(0.0587013\pi\)
\(174\) 1.00166 0.0759355
\(175\) 4.50575 0.340602
\(176\) 2.33898 0.176307
\(177\) −1.31211 −0.0986241
\(178\) 14.0546 1.05343
\(179\) −8.61773 −0.644120 −0.322060 0.946719i \(-0.604375\pi\)
−0.322060 + 0.946719i \(0.604375\pi\)
\(180\) 1.07700 0.0802747
\(181\) −14.8729 −1.10549 −0.552746 0.833350i \(-0.686420\pi\)
−0.552746 + 0.833350i \(0.686420\pi\)
\(182\) 6.09749 0.451976
\(183\) −1.88226 −0.139140
\(184\) 3.50222 0.258187
\(185\) −1.01515 −0.0746351
\(186\) −3.69666 −0.271052
\(187\) 4.53726 0.331797
\(188\) 2.15639 0.157271
\(189\) −3.88410 −0.282526
\(190\) 0.445775 0.0323399
\(191\) 26.5713 1.92263 0.961316 0.275448i \(-0.0888261\pi\)
0.961316 + 0.275448i \(0.0888261\pi\)
\(192\) −0.764189 −0.0551506
\(193\) 9.14555 0.658311 0.329155 0.944276i \(-0.393236\pi\)
0.329155 + 0.944276i \(0.393236\pi\)
\(194\) −16.8131 −1.20711
\(195\) −2.21339 −0.158504
\(196\) −6.11932 −0.437094
\(197\) −6.29190 −0.448280 −0.224140 0.974557i \(-0.571957\pi\)
−0.224140 + 0.974557i \(0.571957\pi\)
\(198\) −5.65101 −0.401600
\(199\) 12.9988 0.921461 0.460730 0.887540i \(-0.347588\pi\)
0.460730 + 0.887540i \(0.347588\pi\)
\(200\) −4.80128 −0.339502
\(201\) −3.52513 −0.248643
\(202\) −7.61087 −0.535499
\(203\) 1.23007 0.0863336
\(204\) −1.48241 −0.103789
\(205\) 3.58009 0.250044
\(206\) −2.78620 −0.194124
\(207\) −8.46141 −0.588109
\(208\) −6.49743 −0.450515
\(209\) −2.33898 −0.161791
\(210\) −0.319687 −0.0220605
\(211\) −1.00000 −0.0688428
\(212\) 3.08544 0.211909
\(213\) −6.12310 −0.419548
\(214\) 3.42104 0.233858
\(215\) 1.27658 0.0870620
\(216\) 4.13886 0.281614
\(217\) −4.53961 −0.308169
\(218\) −9.39884 −0.636570
\(219\) −7.96051 −0.537922
\(220\) −1.04266 −0.0702960
\(221\) −12.6040 −0.847837
\(222\) −1.74026 −0.116799
\(223\) −7.52754 −0.504081 −0.252041 0.967717i \(-0.581102\pi\)
−0.252041 + 0.967717i \(0.581102\pi\)
\(224\) −0.938446 −0.0627026
\(225\) 11.6000 0.773332
\(226\) 5.98637 0.398208
\(227\) 14.5955 0.968741 0.484370 0.874863i \(-0.339049\pi\)
0.484370 + 0.874863i \(0.339049\pi\)
\(228\) 0.764189 0.0506096
\(229\) 0.825160 0.0545281 0.0272641 0.999628i \(-0.491321\pi\)
0.0272641 + 0.999628i \(0.491321\pi\)
\(230\) −1.56120 −0.102943
\(231\) 1.67740 0.110365
\(232\) −1.31075 −0.0860547
\(233\) −3.32946 −0.218120 −0.109060 0.994035i \(-0.534784\pi\)
−0.109060 + 0.994035i \(0.534784\pi\)
\(234\) 15.6979 1.02620
\(235\) −0.961264 −0.0627059
\(236\) 1.71699 0.111767
\(237\) −0.287181 −0.0186544
\(238\) −1.82044 −0.118002
\(239\) 25.7371 1.66479 0.832397 0.554179i \(-0.186968\pi\)
0.832397 + 0.554179i \(0.186968\pi\)
\(240\) 0.340656 0.0219893
\(241\) −16.2372 −1.04593 −0.522964 0.852355i \(-0.675174\pi\)
−0.522964 + 0.852355i \(0.675174\pi\)
\(242\) −5.52917 −0.355429
\(243\) −15.5384 −0.996790
\(244\) 2.46308 0.157682
\(245\) 2.72784 0.174275
\(246\) 6.13733 0.391302
\(247\) 6.49743 0.413421
\(248\) 4.83737 0.307173
\(249\) −4.75292 −0.301204
\(250\) 4.36917 0.276330
\(251\) 21.4672 1.35499 0.677497 0.735525i \(-0.263065\pi\)
0.677497 + 0.735525i \(0.263065\pi\)
\(252\) 2.26730 0.142826
\(253\) 8.19162 0.515003
\(254\) 3.86438 0.242473
\(255\) 0.660820 0.0413822
\(256\) 1.00000 0.0625000
\(257\) −13.1660 −0.821273 −0.410636 0.911799i \(-0.634693\pi\)
−0.410636 + 0.911799i \(0.634693\pi\)
\(258\) 2.18843 0.136246
\(259\) −2.13709 −0.132792
\(260\) 2.89639 0.179626
\(261\) 3.16678 0.196019
\(262\) 18.3402 1.13306
\(263\) −20.5440 −1.26680 −0.633399 0.773826i \(-0.718341\pi\)
−0.633399 + 0.773826i \(0.718341\pi\)
\(264\) −1.78742 −0.110008
\(265\) −1.37541 −0.0844909
\(266\) 0.938446 0.0575398
\(267\) −10.7403 −0.657298
\(268\) 4.61290 0.281778
\(269\) 15.2113 0.927450 0.463725 0.885979i \(-0.346513\pi\)
0.463725 + 0.885979i \(0.346513\pi\)
\(270\) −1.84500 −0.112283
\(271\) −28.2783 −1.71779 −0.858893 0.512156i \(-0.828847\pi\)
−0.858893 + 0.512156i \(0.828847\pi\)
\(272\) 1.93985 0.117620
\(273\) −4.65963 −0.282014
\(274\) −11.4988 −0.694670
\(275\) −11.2301 −0.677201
\(276\) −2.67636 −0.161098
\(277\) 4.85219 0.291540 0.145770 0.989319i \(-0.453434\pi\)
0.145770 + 0.989319i \(0.453434\pi\)
\(278\) 4.45298 0.267072
\(279\) −11.6871 −0.699691
\(280\) 0.418336 0.0250003
\(281\) 17.6581 1.05339 0.526697 0.850053i \(-0.323430\pi\)
0.526697 + 0.850053i \(0.323430\pi\)
\(282\) −1.64789 −0.0981303
\(283\) −16.3055 −0.969259 −0.484630 0.874719i \(-0.661046\pi\)
−0.484630 + 0.874719i \(0.661046\pi\)
\(284\) 8.01255 0.475457
\(285\) −0.340656 −0.0201787
\(286\) −15.1974 −0.898638
\(287\) 7.53682 0.444884
\(288\) −2.41602 −0.142365
\(289\) −13.2370 −0.778647
\(290\) 0.584298 0.0343111
\(291\) 12.8484 0.753187
\(292\) 10.4169 0.609605
\(293\) −13.4661 −0.786699 −0.393350 0.919389i \(-0.628684\pi\)
−0.393350 + 0.919389i \(0.628684\pi\)
\(294\) 4.67632 0.272728
\(295\) −0.765393 −0.0445629
\(296\) 2.27726 0.132363
\(297\) 9.68071 0.561732
\(298\) 8.24566 0.477658
\(299\) −22.7554 −1.31598
\(300\) 3.66909 0.211835
\(301\) 2.68746 0.154903
\(302\) 15.8642 0.912882
\(303\) 5.81614 0.334128
\(304\) −1.00000 −0.0573539
\(305\) −1.09798 −0.0628700
\(306\) −4.68670 −0.267921
\(307\) 22.3795 1.27727 0.638633 0.769511i \(-0.279500\pi\)
0.638633 + 0.769511i \(0.279500\pi\)
\(308\) −2.19501 −0.125072
\(309\) 2.12919 0.121125
\(310\) −2.15638 −0.122474
\(311\) −2.35198 −0.133369 −0.0666844 0.997774i \(-0.521242\pi\)
−0.0666844 + 0.997774i \(0.521242\pi\)
\(312\) 4.96526 0.281103
\(313\) −6.37098 −0.360109 −0.180054 0.983657i \(-0.557627\pi\)
−0.180054 + 0.983657i \(0.557627\pi\)
\(314\) −0.995625 −0.0561864
\(315\) −1.01071 −0.0569468
\(316\) 0.375799 0.0211403
\(317\) 17.7481 0.996831 0.498415 0.866938i \(-0.333915\pi\)
0.498415 + 0.866938i \(0.333915\pi\)
\(318\) −2.35786 −0.132222
\(319\) −3.06581 −0.171652
\(320\) −0.445775 −0.0249196
\(321\) −2.61432 −0.145917
\(322\) −3.28664 −0.183158
\(323\) −1.93985 −0.107936
\(324\) 4.08518 0.226954
\(325\) 31.1960 1.73044
\(326\) 7.80212 0.432119
\(327\) 7.18249 0.397193
\(328\) −8.03117 −0.443447
\(329\) −2.02365 −0.111568
\(330\) 0.796788 0.0438617
\(331\) 33.0567 1.81696 0.908481 0.417926i \(-0.137243\pi\)
0.908481 + 0.417926i \(0.137243\pi\)
\(332\) 6.21956 0.341343
\(333\) −5.50190 −0.301502
\(334\) 23.4783 1.28467
\(335\) −2.05631 −0.112348
\(336\) 0.717150 0.0391237
\(337\) 14.7689 0.804512 0.402256 0.915527i \(-0.368226\pi\)
0.402256 + 0.915527i \(0.368226\pi\)
\(338\) 29.2166 1.58917
\(339\) −4.57472 −0.248465
\(340\) −0.864734 −0.0468968
\(341\) 11.3145 0.612715
\(342\) 2.41602 0.130643
\(343\) 12.3118 0.664773
\(344\) −2.86373 −0.154402
\(345\) 1.19305 0.0642318
\(346\) 25.8598 1.39023
\(347\) 4.30574 0.231144 0.115572 0.993299i \(-0.463130\pi\)
0.115572 + 0.993299i \(0.463130\pi\)
\(348\) 1.00166 0.0536945
\(349\) −18.1302 −0.970486 −0.485243 0.874379i \(-0.661269\pi\)
−0.485243 + 0.874379i \(0.661269\pi\)
\(350\) 4.50575 0.240842
\(351\) −26.8919 −1.43539
\(352\) 2.33898 0.124668
\(353\) 2.85803 0.152118 0.0760589 0.997103i \(-0.475766\pi\)
0.0760589 + 0.997103i \(0.475766\pi\)
\(354\) −1.31211 −0.0697378
\(355\) −3.57179 −0.189571
\(356\) 14.0546 0.744890
\(357\) 1.39116 0.0736280
\(358\) −8.61773 −0.455461
\(359\) −6.66319 −0.351670 −0.175835 0.984420i \(-0.556262\pi\)
−0.175835 + 0.984420i \(0.556262\pi\)
\(360\) 1.07700 0.0567628
\(361\) 1.00000 0.0526316
\(362\) −14.8729 −0.781701
\(363\) 4.22533 0.221772
\(364\) 6.09749 0.319595
\(365\) −4.64361 −0.243058
\(366\) −1.88226 −0.0983871
\(367\) −36.3545 −1.89769 −0.948844 0.315746i \(-0.897745\pi\)
−0.948844 + 0.315746i \(0.897745\pi\)
\(368\) 3.50222 0.182566
\(369\) 19.4034 1.01010
\(370\) −1.01515 −0.0527750
\(371\) −2.89552 −0.150328
\(372\) −3.69666 −0.191663
\(373\) −15.6955 −0.812681 −0.406340 0.913722i \(-0.633195\pi\)
−0.406340 + 0.913722i \(0.633195\pi\)
\(374\) 4.53726 0.234616
\(375\) −3.33887 −0.172418
\(376\) 2.15639 0.111207
\(377\) 8.51648 0.438621
\(378\) −3.88410 −0.199776
\(379\) −28.0313 −1.43987 −0.719934 0.694042i \(-0.755828\pi\)
−0.719934 + 0.694042i \(0.755828\pi\)
\(380\) 0.445775 0.0228678
\(381\) −2.95311 −0.151293
\(382\) 26.5713 1.35951
\(383\) 8.23090 0.420579 0.210290 0.977639i \(-0.432559\pi\)
0.210290 + 0.977639i \(0.432559\pi\)
\(384\) −0.764189 −0.0389974
\(385\) 0.978479 0.0498679
\(386\) 9.14555 0.465496
\(387\) 6.91882 0.351704
\(388\) −16.8131 −0.853557
\(389\) −5.79423 −0.293779 −0.146890 0.989153i \(-0.546926\pi\)
−0.146890 + 0.989153i \(0.546926\pi\)
\(390\) −2.21339 −0.112079
\(391\) 6.79376 0.343575
\(392\) −6.11932 −0.309072
\(393\) −14.0154 −0.706984
\(394\) −6.29190 −0.316982
\(395\) −0.167522 −0.00842893
\(396\) −5.65101 −0.283974
\(397\) −1.96987 −0.0988648 −0.0494324 0.998777i \(-0.515741\pi\)
−0.0494324 + 0.998777i \(0.515741\pi\)
\(398\) 12.9988 0.651571
\(399\) −0.717150 −0.0359024
\(400\) −4.80128 −0.240064
\(401\) −15.0980 −0.753957 −0.376978 0.926222i \(-0.623037\pi\)
−0.376978 + 0.926222i \(0.623037\pi\)
\(402\) −3.52513 −0.175817
\(403\) −31.4304 −1.56566
\(404\) −7.61087 −0.378655
\(405\) −1.82107 −0.0904896
\(406\) 1.23007 0.0610471
\(407\) 5.32647 0.264024
\(408\) −1.48241 −0.0733901
\(409\) −10.4789 −0.518147 −0.259074 0.965858i \(-0.583417\pi\)
−0.259074 + 0.965858i \(0.583417\pi\)
\(410\) 3.58009 0.176808
\(411\) 8.78729 0.433445
\(412\) −2.78620 −0.137266
\(413\) −1.61131 −0.0792872
\(414\) −8.46141 −0.415856
\(415\) −2.77252 −0.136098
\(416\) −6.49743 −0.318563
\(417\) −3.40292 −0.166642
\(418\) −2.33898 −0.114403
\(419\) 3.20378 0.156515 0.0782574 0.996933i \(-0.475064\pi\)
0.0782574 + 0.996933i \(0.475064\pi\)
\(420\) −0.319687 −0.0155992
\(421\) 3.79862 0.185133 0.0925667 0.995706i \(-0.470493\pi\)
0.0925667 + 0.995706i \(0.470493\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −5.20987 −0.253312
\(424\) 3.08544 0.149842
\(425\) −9.31375 −0.451783
\(426\) −6.12310 −0.296665
\(427\) −2.31147 −0.111860
\(428\) 3.42104 0.165362
\(429\) 11.6137 0.560712
\(430\) 1.27658 0.0615621
\(431\) 27.0164 1.30134 0.650668 0.759362i \(-0.274489\pi\)
0.650668 + 0.759362i \(0.274489\pi\)
\(432\) 4.13886 0.199131
\(433\) −13.8771 −0.666891 −0.333445 0.942769i \(-0.608211\pi\)
−0.333445 + 0.942769i \(0.608211\pi\)
\(434\) −4.53961 −0.217908
\(435\) −0.446514 −0.0214087
\(436\) −9.39884 −0.450123
\(437\) −3.50222 −0.167534
\(438\) −7.96051 −0.380368
\(439\) 3.16248 0.150937 0.0754684 0.997148i \(-0.475955\pi\)
0.0754684 + 0.997148i \(0.475955\pi\)
\(440\) −1.04266 −0.0497068
\(441\) 14.7844 0.704018
\(442\) −12.6040 −0.599511
\(443\) 5.99833 0.284989 0.142495 0.989796i \(-0.454488\pi\)
0.142495 + 0.989796i \(0.454488\pi\)
\(444\) −1.74026 −0.0825891
\(445\) −6.26517 −0.296997
\(446\) −7.52754 −0.356439
\(447\) −6.30124 −0.298038
\(448\) −0.938446 −0.0443374
\(449\) 37.6856 1.77850 0.889248 0.457426i \(-0.151229\pi\)
0.889248 + 0.457426i \(0.151229\pi\)
\(450\) 11.6000 0.546828
\(451\) −18.7847 −0.884539
\(452\) 5.98637 0.281575
\(453\) −12.1232 −0.569599
\(454\) 14.5955 0.685003
\(455\) −2.71811 −0.127427
\(456\) 0.764189 0.0357864
\(457\) 30.0152 1.40405 0.702026 0.712151i \(-0.252279\pi\)
0.702026 + 0.712151i \(0.252279\pi\)
\(458\) 0.825160 0.0385572
\(459\) 8.02875 0.374750
\(460\) −1.56120 −0.0727914
\(461\) 20.8735 0.972177 0.486089 0.873910i \(-0.338423\pi\)
0.486089 + 0.873910i \(0.338423\pi\)
\(462\) 1.67740 0.0780397
\(463\) 1.49128 0.0693056 0.0346528 0.999399i \(-0.488967\pi\)
0.0346528 + 0.999399i \(0.488967\pi\)
\(464\) −1.31075 −0.0608499
\(465\) 1.64788 0.0764185
\(466\) −3.32946 −0.154234
\(467\) 30.5393 1.41319 0.706595 0.707618i \(-0.250230\pi\)
0.706595 + 0.707618i \(0.250230\pi\)
\(468\) 15.6979 0.725635
\(469\) −4.32896 −0.199893
\(470\) −0.961264 −0.0443398
\(471\) 0.760846 0.0350579
\(472\) 1.71699 0.0790311
\(473\) −6.69822 −0.307984
\(474\) −0.287181 −0.0131907
\(475\) 4.80128 0.220298
\(476\) −1.82044 −0.0834397
\(477\) −7.45448 −0.341317
\(478\) 25.7371 1.17719
\(479\) −9.83352 −0.449305 −0.224652 0.974439i \(-0.572125\pi\)
−0.224652 + 0.974439i \(0.572125\pi\)
\(480\) 0.340656 0.0155488
\(481\) −14.7964 −0.674656
\(482\) −16.2372 −0.739583
\(483\) 2.51162 0.114283
\(484\) −5.52917 −0.251326
\(485\) 7.49487 0.340324
\(486\) −15.5384 −0.704837
\(487\) 35.4027 1.60425 0.802125 0.597156i \(-0.203703\pi\)
0.802125 + 0.597156i \(0.203703\pi\)
\(488\) 2.46308 0.111498
\(489\) −5.96229 −0.269624
\(490\) 2.72784 0.123231
\(491\) 40.3906 1.82280 0.911400 0.411521i \(-0.135002\pi\)
0.911400 + 0.411521i \(0.135002\pi\)
\(492\) 6.13733 0.276692
\(493\) −2.54265 −0.114515
\(494\) 6.49743 0.292333
\(495\) 2.51908 0.113224
\(496\) 4.83737 0.217204
\(497\) −7.51935 −0.337289
\(498\) −4.75292 −0.212983
\(499\) −39.7386 −1.77894 −0.889472 0.456989i \(-0.848928\pi\)
−0.889472 + 0.456989i \(0.848928\pi\)
\(500\) 4.36917 0.195395
\(501\) −17.9418 −0.801582
\(502\) 21.4672 0.958126
\(503\) −15.4051 −0.686878 −0.343439 0.939175i \(-0.611592\pi\)
−0.343439 + 0.939175i \(0.611592\pi\)
\(504\) 2.26730 0.100994
\(505\) 3.39273 0.150975
\(506\) 8.19162 0.364162
\(507\) −22.3270 −0.991576
\(508\) 3.86438 0.171454
\(509\) 14.8372 0.657649 0.328824 0.944391i \(-0.393348\pi\)
0.328824 + 0.944391i \(0.393348\pi\)
\(510\) 0.660820 0.0292616
\(511\) −9.77574 −0.432453
\(512\) 1.00000 0.0441942
\(513\) −4.13886 −0.182735
\(514\) −13.1660 −0.580728
\(515\) 1.24202 0.0547299
\(516\) 2.18843 0.0963404
\(517\) 5.04375 0.221824
\(518\) −2.13709 −0.0938983
\(519\) −19.7618 −0.867447
\(520\) 2.89639 0.127015
\(521\) 2.03437 0.0891275 0.0445637 0.999007i \(-0.485810\pi\)
0.0445637 + 0.999007i \(0.485810\pi\)
\(522\) 3.16678 0.138606
\(523\) −25.5625 −1.11777 −0.558885 0.829245i \(-0.688771\pi\)
−0.558885 + 0.829245i \(0.688771\pi\)
\(524\) 18.3402 0.801197
\(525\) −3.44324 −0.150275
\(526\) −20.5440 −0.895761
\(527\) 9.38374 0.408762
\(528\) −1.78742 −0.0777876
\(529\) −10.7345 −0.466716
\(530\) −1.37541 −0.0597441
\(531\) −4.14829 −0.180020
\(532\) 0.938446 0.0406868
\(533\) 52.1819 2.26025
\(534\) −10.7403 −0.464780
\(535\) −1.52501 −0.0659321
\(536\) 4.61290 0.199247
\(537\) 6.58558 0.284189
\(538\) 15.2113 0.655806
\(539\) −14.3130 −0.616503
\(540\) −1.84500 −0.0793961
\(541\) 38.6920 1.66350 0.831749 0.555152i \(-0.187340\pi\)
0.831749 + 0.555152i \(0.187340\pi\)
\(542\) −28.2783 −1.21466
\(543\) 11.3657 0.487748
\(544\) 1.93985 0.0831702
\(545\) 4.18977 0.179470
\(546\) −4.65963 −0.199414
\(547\) −9.98396 −0.426883 −0.213442 0.976956i \(-0.568467\pi\)
−0.213442 + 0.976956i \(0.568467\pi\)
\(548\) −11.4988 −0.491206
\(549\) −5.95083 −0.253975
\(550\) −11.2301 −0.478854
\(551\) 1.31075 0.0558397
\(552\) −2.67636 −0.113913
\(553\) −0.352667 −0.0149969
\(554\) 4.85219 0.206150
\(555\) 0.775764 0.0329293
\(556\) 4.45298 0.188848
\(557\) 3.96418 0.167968 0.0839839 0.996467i \(-0.473236\pi\)
0.0839839 + 0.996467i \(0.473236\pi\)
\(558\) −11.6871 −0.494756
\(559\) 18.6069 0.786988
\(560\) 0.418336 0.0176779
\(561\) −3.46732 −0.146391
\(562\) 17.6581 0.744862
\(563\) −22.5379 −0.949858 −0.474929 0.880024i \(-0.657526\pi\)
−0.474929 + 0.880024i \(0.657526\pi\)
\(564\) −1.64789 −0.0693886
\(565\) −2.66857 −0.112268
\(566\) −16.3055 −0.685370
\(567\) −3.83372 −0.161001
\(568\) 8.01255 0.336199
\(569\) 14.9334 0.626040 0.313020 0.949747i \(-0.398659\pi\)
0.313020 + 0.949747i \(0.398659\pi\)
\(570\) −0.340656 −0.0142685
\(571\) −1.25242 −0.0524120 −0.0262060 0.999657i \(-0.508343\pi\)
−0.0262060 + 0.999657i \(0.508343\pi\)
\(572\) −15.1974 −0.635433
\(573\) −20.3055 −0.848274
\(574\) 7.53682 0.314581
\(575\) −16.8152 −0.701240
\(576\) −2.41602 −0.100667
\(577\) 6.93416 0.288673 0.144336 0.989529i \(-0.453895\pi\)
0.144336 + 0.989529i \(0.453895\pi\)
\(578\) −13.2370 −0.550587
\(579\) −6.98893 −0.290450
\(580\) 0.584298 0.0242616
\(581\) −5.83672 −0.242148
\(582\) 12.8484 0.532584
\(583\) 7.21679 0.298889
\(584\) 10.4169 0.431056
\(585\) −6.99772 −0.289320
\(586\) −13.4661 −0.556280
\(587\) 18.2346 0.752624 0.376312 0.926493i \(-0.377192\pi\)
0.376312 + 0.926493i \(0.377192\pi\)
\(588\) 4.67632 0.192848
\(589\) −4.83737 −0.199320
\(590\) −0.765393 −0.0315107
\(591\) 4.80820 0.197783
\(592\) 2.27726 0.0935949
\(593\) 13.8580 0.569082 0.284541 0.958664i \(-0.408159\pi\)
0.284541 + 0.958664i \(0.408159\pi\)
\(594\) 9.68071 0.397204
\(595\) 0.811506 0.0332685
\(596\) 8.24566 0.337755
\(597\) −9.93354 −0.406553
\(598\) −22.7554 −0.930538
\(599\) −25.1617 −1.02808 −0.514040 0.857766i \(-0.671852\pi\)
−0.514040 + 0.857766i \(0.671852\pi\)
\(600\) 3.66909 0.149790
\(601\) −9.12976 −0.372411 −0.186205 0.982511i \(-0.559619\pi\)
−0.186205 + 0.982511i \(0.559619\pi\)
\(602\) 2.68746 0.109533
\(603\) −11.1448 −0.453853
\(604\) 15.8642 0.645505
\(605\) 2.46476 0.100207
\(606\) 5.81614 0.236265
\(607\) 45.7800 1.85815 0.929076 0.369889i \(-0.120604\pi\)
0.929076 + 0.369889i \(0.120604\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −0.940002 −0.0380908
\(610\) −1.09798 −0.0444558
\(611\) −14.0110 −0.566823
\(612\) −4.68670 −0.189448
\(613\) 36.8334 1.48769 0.743844 0.668353i \(-0.233001\pi\)
0.743844 + 0.668353i \(0.233001\pi\)
\(614\) 22.3795 0.903163
\(615\) −2.73587 −0.110321
\(616\) −2.19501 −0.0884394
\(617\) −9.04274 −0.364047 −0.182023 0.983294i \(-0.558265\pi\)
−0.182023 + 0.983294i \(0.558265\pi\)
\(618\) 2.12919 0.0856484
\(619\) −6.06037 −0.243587 −0.121793 0.992555i \(-0.538865\pi\)
−0.121793 + 0.992555i \(0.538865\pi\)
\(620\) −2.15638 −0.0866021
\(621\) 14.4952 0.581672
\(622\) −2.35198 −0.0943059
\(623\) −13.1894 −0.528424
\(624\) 4.96526 0.198770
\(625\) 22.0588 0.882350
\(626\) −6.37098 −0.254635
\(627\) 1.78742 0.0713828
\(628\) −0.995625 −0.0397298
\(629\) 4.41754 0.176139
\(630\) −1.01071 −0.0402675
\(631\) −7.79035 −0.310129 −0.155064 0.987904i \(-0.549559\pi\)
−0.155064 + 0.987904i \(0.549559\pi\)
\(632\) 0.375799 0.0149485
\(633\) 0.764189 0.0303738
\(634\) 17.7481 0.704866
\(635\) −1.72264 −0.0683610
\(636\) −2.35786 −0.0934953
\(637\) 39.7598 1.57534
\(638\) −3.06581 −0.121377
\(639\) −19.3584 −0.765808
\(640\) −0.445775 −0.0176208
\(641\) −28.5563 −1.12791 −0.563953 0.825807i \(-0.690720\pi\)
−0.563953 + 0.825807i \(0.690720\pi\)
\(642\) −2.61432 −0.103179
\(643\) −22.4503 −0.885353 −0.442677 0.896681i \(-0.645971\pi\)
−0.442677 + 0.896681i \(0.645971\pi\)
\(644\) −3.28664 −0.129512
\(645\) −0.975548 −0.0384122
\(646\) −1.93985 −0.0763222
\(647\) −17.4199 −0.684848 −0.342424 0.939545i \(-0.611248\pi\)
−0.342424 + 0.939545i \(0.611248\pi\)
\(648\) 4.08518 0.160481
\(649\) 4.01602 0.157642
\(650\) 31.1960 1.22361
\(651\) 3.46912 0.135965
\(652\) 7.80212 0.305555
\(653\) −10.3451 −0.404835 −0.202417 0.979299i \(-0.564880\pi\)
−0.202417 + 0.979299i \(0.564880\pi\)
\(654\) 7.18249 0.280858
\(655\) −8.17562 −0.319448
\(656\) −8.03117 −0.313564
\(657\) −25.1675 −0.981877
\(658\) −2.02365 −0.0788903
\(659\) 27.4899 1.07085 0.535427 0.844582i \(-0.320151\pi\)
0.535427 + 0.844582i \(0.320151\pi\)
\(660\) 0.796788 0.0310149
\(661\) −7.29822 −0.283868 −0.141934 0.989876i \(-0.545332\pi\)
−0.141934 + 0.989876i \(0.545332\pi\)
\(662\) 33.0567 1.28479
\(663\) 9.63184 0.374070
\(664\) 6.21956 0.241366
\(665\) −0.418336 −0.0162224
\(666\) −5.50190 −0.213194
\(667\) −4.59052 −0.177746
\(668\) 23.4783 0.908402
\(669\) 5.75246 0.222403
\(670\) −2.05631 −0.0794423
\(671\) 5.76109 0.222404
\(672\) 0.717150 0.0276647
\(673\) 39.0761 1.50627 0.753137 0.657863i \(-0.228540\pi\)
0.753137 + 0.657863i \(0.228540\pi\)
\(674\) 14.7689 0.568876
\(675\) −19.8718 −0.764868
\(676\) 29.2166 1.12371
\(677\) 14.2293 0.546878 0.273439 0.961889i \(-0.411839\pi\)
0.273439 + 0.961889i \(0.411839\pi\)
\(678\) −4.57472 −0.175691
\(679\) 15.7782 0.605512
\(680\) −0.864734 −0.0331610
\(681\) −11.1538 −0.427413
\(682\) 11.3145 0.433255
\(683\) −31.5817 −1.20844 −0.604220 0.796817i \(-0.706515\pi\)
−0.604220 + 0.796817i \(0.706515\pi\)
\(684\) 2.41602 0.0923787
\(685\) 5.12589 0.195850
\(686\) 12.3118 0.470066
\(687\) −0.630578 −0.0240581
\(688\) −2.86373 −0.109179
\(689\) −20.0474 −0.763746
\(690\) 1.19305 0.0454187
\(691\) 31.9590 1.21578 0.607889 0.794022i \(-0.292016\pi\)
0.607889 + 0.794022i \(0.292016\pi\)
\(692\) 25.8598 0.983044
\(693\) 5.30317 0.201451
\(694\) 4.30574 0.163444
\(695\) −1.98503 −0.0752963
\(696\) 1.00166 0.0379678
\(697\) −15.5792 −0.590105
\(698\) −18.1302 −0.686237
\(699\) 2.54434 0.0962357
\(700\) 4.50575 0.170301
\(701\) 30.4045 1.14836 0.574180 0.818729i \(-0.305321\pi\)
0.574180 + 0.818729i \(0.305321\pi\)
\(702\) −26.8919 −1.01497
\(703\) −2.27726 −0.0858886
\(704\) 2.33898 0.0881536
\(705\) 0.734587 0.0276661
\(706\) 2.85803 0.107564
\(707\) 7.14239 0.268617
\(708\) −1.31211 −0.0493121
\(709\) −29.4007 −1.10417 −0.552083 0.833789i \(-0.686167\pi\)
−0.552083 + 0.833789i \(0.686167\pi\)
\(710\) −3.57179 −0.134047
\(711\) −0.907936 −0.0340502
\(712\) 14.0546 0.526717
\(713\) 16.9415 0.634465
\(714\) 1.39116 0.0520629
\(715\) 6.77460 0.253356
\(716\) −8.61773 −0.322060
\(717\) −19.6680 −0.734515
\(718\) −6.66319 −0.248668
\(719\) −41.7483 −1.55695 −0.778475 0.627675i \(-0.784007\pi\)
−0.778475 + 0.627675i \(0.784007\pi\)
\(720\) 1.07700 0.0401374
\(721\) 2.61470 0.0973766
\(722\) 1.00000 0.0372161
\(723\) 12.4083 0.461468
\(724\) −14.8729 −0.552746
\(725\) 6.29327 0.233726
\(726\) 4.22533 0.156817
\(727\) −9.25790 −0.343356 −0.171678 0.985153i \(-0.554919\pi\)
−0.171678 + 0.985153i \(0.554919\pi\)
\(728\) 6.09749 0.225988
\(729\) −0.381235 −0.0141198
\(730\) −4.64361 −0.171868
\(731\) −5.55520 −0.205466
\(732\) −1.88226 −0.0695702
\(733\) −33.9445 −1.25377 −0.626884 0.779113i \(-0.715670\pi\)
−0.626884 + 0.779113i \(0.715670\pi\)
\(734\) −36.3545 −1.34187
\(735\) −2.08458 −0.0768910
\(736\) 3.50222 0.129094
\(737\) 10.7895 0.397435
\(738\) 19.4034 0.714250
\(739\) 23.5189 0.865156 0.432578 0.901597i \(-0.357604\pi\)
0.432578 + 0.901597i \(0.357604\pi\)
\(740\) −1.01515 −0.0373175
\(741\) −4.96526 −0.182403
\(742\) −2.89552 −0.106298
\(743\) 7.21153 0.264565 0.132283 0.991212i \(-0.457769\pi\)
0.132283 + 0.991212i \(0.457769\pi\)
\(744\) −3.69666 −0.135526
\(745\) −3.67571 −0.134667
\(746\) −15.6955 −0.574652
\(747\) −15.0266 −0.549793
\(748\) 4.53726 0.165899
\(749\) −3.21046 −0.117308
\(750\) −3.33887 −0.121918
\(751\) −21.2134 −0.774087 −0.387043 0.922062i \(-0.626504\pi\)
−0.387043 + 0.922062i \(0.626504\pi\)
\(752\) 2.15639 0.0786354
\(753\) −16.4050 −0.597830
\(754\) 8.51648 0.310152
\(755\) −7.07186 −0.257371
\(756\) −3.88410 −0.141263
\(757\) 30.4940 1.10832 0.554162 0.832409i \(-0.313039\pi\)
0.554162 + 0.832409i \(0.313039\pi\)
\(758\) −28.0313 −1.01814
\(759\) −6.25995 −0.227222
\(760\) 0.445775 0.0161700
\(761\) 26.2626 0.952019 0.476009 0.879440i \(-0.342083\pi\)
0.476009 + 0.879440i \(0.342083\pi\)
\(762\) −2.95311 −0.106980
\(763\) 8.82030 0.319316
\(764\) 26.5713 0.961316
\(765\) 2.08921 0.0755356
\(766\) 8.23090 0.297394
\(767\) −11.1560 −0.402822
\(768\) −0.764189 −0.0275753
\(769\) −9.83722 −0.354739 −0.177370 0.984144i \(-0.556759\pi\)
−0.177370 + 0.984144i \(0.556759\pi\)
\(770\) 0.978479 0.0352619
\(771\) 10.0613 0.362349
\(772\) 9.14555 0.329155
\(773\) −18.2383 −0.655986 −0.327993 0.944680i \(-0.606372\pi\)
−0.327993 + 0.944680i \(0.606372\pi\)
\(774\) 6.91882 0.248692
\(775\) −23.2256 −0.834287
\(776\) −16.8131 −0.603556
\(777\) 1.63314 0.0585886
\(778\) −5.79423 −0.207733
\(779\) 8.03117 0.287746
\(780\) −2.21339 −0.0792520
\(781\) 18.7412 0.670613
\(782\) 6.79376 0.242944
\(783\) −5.42500 −0.193874
\(784\) −6.11932 −0.218547
\(785\) 0.443825 0.0158408
\(786\) −14.0154 −0.499913
\(787\) −15.5519 −0.554366 −0.277183 0.960817i \(-0.589401\pi\)
−0.277183 + 0.960817i \(0.589401\pi\)
\(788\) −6.29190 −0.224140
\(789\) 15.6995 0.558917
\(790\) −0.167522 −0.00596015
\(791\) −5.61789 −0.199749
\(792\) −5.65101 −0.200800
\(793\) −16.0037 −0.568307
\(794\) −1.96987 −0.0699080
\(795\) 1.05107 0.0372778
\(796\) 12.9988 0.460730
\(797\) 35.2201 1.24756 0.623780 0.781600i \(-0.285596\pi\)
0.623780 + 0.781600i \(0.285596\pi\)
\(798\) −0.717150 −0.0253868
\(799\) 4.18306 0.147986
\(800\) −4.80128 −0.169751
\(801\) −33.9560 −1.19978
\(802\) −15.0980 −0.533128
\(803\) 24.3650 0.859823
\(804\) −3.52513 −0.124322
\(805\) 1.46510 0.0516381
\(806\) −31.4304 −1.10709
\(807\) −11.6243 −0.409195
\(808\) −7.61087 −0.267749
\(809\) −12.6627 −0.445197 −0.222599 0.974910i \(-0.571454\pi\)
−0.222599 + 0.974910i \(0.571454\pi\)
\(810\) −1.82107 −0.0639858
\(811\) −18.1668 −0.637922 −0.318961 0.947768i \(-0.603334\pi\)
−0.318961 + 0.947768i \(0.603334\pi\)
\(812\) 1.23007 0.0431668
\(813\) 21.6100 0.757895
\(814\) 5.32647 0.186693
\(815\) −3.47799 −0.121829
\(816\) −1.48241 −0.0518947
\(817\) 2.86373 0.100189
\(818\) −10.4789 −0.366386
\(819\) −14.7316 −0.514764
\(820\) 3.58009 0.125022
\(821\) −55.2483 −1.92818 −0.964090 0.265577i \(-0.914438\pi\)
−0.964090 + 0.265577i \(0.914438\pi\)
\(822\) 8.78729 0.306492
\(823\) −5.05842 −0.176326 −0.0881628 0.996106i \(-0.528100\pi\)
−0.0881628 + 0.996106i \(0.528100\pi\)
\(824\) −2.78620 −0.0970620
\(825\) 8.58193 0.298784
\(826\) −1.61131 −0.0560645
\(827\) −1.79636 −0.0624657 −0.0312328 0.999512i \(-0.509943\pi\)
−0.0312328 + 0.999512i \(0.509943\pi\)
\(828\) −8.46141 −0.294054
\(829\) 18.1787 0.631373 0.315686 0.948864i \(-0.397765\pi\)
0.315686 + 0.948864i \(0.397765\pi\)
\(830\) −2.77252 −0.0962357
\(831\) −3.70799 −0.128629
\(832\) −6.49743 −0.225258
\(833\) −11.8705 −0.411290
\(834\) −3.40292 −0.117833
\(835\) −10.4660 −0.362192
\(836\) −2.33898 −0.0808953
\(837\) 20.0212 0.692033
\(838\) 3.20378 0.110673
\(839\) 54.9632 1.89754 0.948770 0.315967i \(-0.102329\pi\)
0.948770 + 0.315967i \(0.102329\pi\)
\(840\) −0.319687 −0.0110303
\(841\) −27.2819 −0.940757
\(842\) 3.79862 0.130909
\(843\) −13.4941 −0.464762
\(844\) −1.00000 −0.0344214
\(845\) −13.0240 −0.448039
\(846\) −5.20987 −0.179119
\(847\) 5.18883 0.178290
\(848\) 3.08544 0.105955
\(849\) 12.4605 0.427642
\(850\) −9.31375 −0.319459
\(851\) 7.97547 0.273396
\(852\) −6.12310 −0.209774
\(853\) −49.1043 −1.68130 −0.840650 0.541579i \(-0.817827\pi\)
−0.840650 + 0.541579i \(0.817827\pi\)
\(854\) −2.31147 −0.0790967
\(855\) −1.07700 −0.0368326
\(856\) 3.42104 0.116929
\(857\) −3.95413 −0.135070 −0.0675352 0.997717i \(-0.521513\pi\)
−0.0675352 + 0.997717i \(0.521513\pi\)
\(858\) 11.6137 0.396483
\(859\) −25.5395 −0.871397 −0.435698 0.900093i \(-0.643499\pi\)
−0.435698 + 0.900093i \(0.643499\pi\)
\(860\) 1.27658 0.0435310
\(861\) −5.75955 −0.196285
\(862\) 27.0164 0.920184
\(863\) −42.8897 −1.45998 −0.729990 0.683457i \(-0.760476\pi\)
−0.729990 + 0.683457i \(0.760476\pi\)
\(864\) 4.13886 0.140807
\(865\) −11.5277 −0.391952
\(866\) −13.8771 −0.471563
\(867\) 10.1156 0.343543
\(868\) −4.53961 −0.154084
\(869\) 0.878986 0.0298176
\(870\) −0.446514 −0.0151382
\(871\) −29.9720 −1.01556
\(872\) −9.39884 −0.318285
\(873\) 40.6208 1.37480
\(874\) −3.50222 −0.118464
\(875\) −4.10023 −0.138613
\(876\) −7.96051 −0.268961
\(877\) 13.6457 0.460782 0.230391 0.973098i \(-0.425999\pi\)
0.230391 + 0.973098i \(0.425999\pi\)
\(878\) 3.16248 0.106728
\(879\) 10.2907 0.347095
\(880\) −1.04266 −0.0351480
\(881\) −25.6699 −0.864840 −0.432420 0.901672i \(-0.642340\pi\)
−0.432420 + 0.901672i \(0.642340\pi\)
\(882\) 14.7844 0.497816
\(883\) 38.5043 1.29577 0.647887 0.761737i \(-0.275653\pi\)
0.647887 + 0.761737i \(0.275653\pi\)
\(884\) −12.6040 −0.423918
\(885\) 0.584905 0.0196614
\(886\) 5.99833 0.201518
\(887\) −37.6529 −1.26426 −0.632131 0.774862i \(-0.717819\pi\)
−0.632131 + 0.774862i \(0.717819\pi\)
\(888\) −1.74026 −0.0583993
\(889\) −3.62651 −0.121629
\(890\) −6.26517 −0.210009
\(891\) 9.55515 0.320109
\(892\) −7.52754 −0.252041
\(893\) −2.15639 −0.0721608
\(894\) −6.30124 −0.210745
\(895\) 3.84157 0.128409
\(896\) −0.938446 −0.0313513
\(897\) 17.3894 0.580616
\(898\) 37.6856 1.25759
\(899\) −6.34056 −0.211470
\(900\) 11.6000 0.386666
\(901\) 5.98528 0.199399
\(902\) −18.7847 −0.625464
\(903\) −2.05373 −0.0683437
\(904\) 5.98637 0.199104
\(905\) 6.62995 0.220387
\(906\) −12.1232 −0.402768
\(907\) 45.6997 1.51743 0.758716 0.651421i \(-0.225827\pi\)
0.758716 + 0.651421i \(0.225827\pi\)
\(908\) 14.5955 0.484370
\(909\) 18.3880 0.609890
\(910\) −2.71811 −0.0901043
\(911\) 28.6733 0.949988 0.474994 0.879989i \(-0.342450\pi\)
0.474994 + 0.879989i \(0.342450\pi\)
\(912\) 0.764189 0.0253048
\(913\) 14.5474 0.481450
\(914\) 30.0152 0.992815
\(915\) 0.839063 0.0277386
\(916\) 0.825160 0.0272641
\(917\) −17.2113 −0.568368
\(918\) 8.02875 0.264988
\(919\) −8.74883 −0.288597 −0.144299 0.989534i \(-0.546093\pi\)
−0.144299 + 0.989534i \(0.546093\pi\)
\(920\) −1.56120 −0.0514713
\(921\) −17.1022 −0.563536
\(922\) 20.8735 0.687433
\(923\) −52.0610 −1.71361
\(924\) 1.67740 0.0551824
\(925\) −10.9338 −0.359501
\(926\) 1.49128 0.0490065
\(927\) 6.73151 0.221092
\(928\) −1.31075 −0.0430274
\(929\) 36.8764 1.20987 0.604937 0.796273i \(-0.293198\pi\)
0.604937 + 0.796273i \(0.293198\pi\)
\(930\) 1.64788 0.0540361
\(931\) 6.11932 0.200553
\(932\) −3.32946 −0.109060
\(933\) 1.79736 0.0588429
\(934\) 30.5393 0.999276
\(935\) −2.02260 −0.0661460
\(936\) 15.6979 0.513101
\(937\) −3.28529 −0.107326 −0.0536629 0.998559i \(-0.517090\pi\)
−0.0536629 + 0.998559i \(0.517090\pi\)
\(938\) −4.32896 −0.141345
\(939\) 4.86863 0.158882
\(940\) −0.961264 −0.0313530
\(941\) −60.3501 −1.96736 −0.983678 0.179938i \(-0.942410\pi\)
−0.983678 + 0.179938i \(0.942410\pi\)
\(942\) 0.760846 0.0247897
\(943\) −28.1269 −0.915938
\(944\) 1.71699 0.0558834
\(945\) 1.73143 0.0563235
\(946\) −6.69822 −0.217778
\(947\) −28.3231 −0.920379 −0.460189 0.887821i \(-0.652218\pi\)
−0.460189 + 0.887821i \(0.652218\pi\)
\(948\) −0.287181 −0.00932722
\(949\) −67.6833 −2.19709
\(950\) 4.80128 0.155774
\(951\) −13.5629 −0.439807
\(952\) −1.82044 −0.0590008
\(953\) 11.0443 0.357761 0.178880 0.983871i \(-0.442753\pi\)
0.178880 + 0.983871i \(0.442753\pi\)
\(954\) −7.45448 −0.241348
\(955\) −11.8448 −0.383289
\(956\) 25.7371 0.832397
\(957\) 2.34286 0.0757339
\(958\) −9.83352 −0.317706
\(959\) 10.7910 0.348461
\(960\) 0.340656 0.0109946
\(961\) −7.59990 −0.245158
\(962\) −14.7964 −0.477054
\(963\) −8.26529 −0.266345
\(964\) −16.2372 −0.522964
\(965\) −4.07685 −0.131239
\(966\) 2.51162 0.0808100
\(967\) −33.5523 −1.07897 −0.539484 0.841996i \(-0.681381\pi\)
−0.539484 + 0.841996i \(0.681381\pi\)
\(968\) −5.52917 −0.177714
\(969\) 1.48241 0.0476218
\(970\) 7.49487 0.240646
\(971\) −25.7436 −0.826151 −0.413076 0.910697i \(-0.635545\pi\)
−0.413076 + 0.910697i \(0.635545\pi\)
\(972\) −15.5384 −0.498395
\(973\) −4.17888 −0.133969
\(974\) 35.4027 1.13438
\(975\) −23.8396 −0.763479
\(976\) 2.46308 0.0788412
\(977\) 61.1818 1.95738 0.978689 0.205349i \(-0.0658329\pi\)
0.978689 + 0.205349i \(0.0658329\pi\)
\(978\) −5.96229 −0.190653
\(979\) 32.8733 1.05064
\(980\) 2.72784 0.0871376
\(981\) 22.7077 0.725002
\(982\) 40.3906 1.28891
\(983\) 9.78730 0.312166 0.156083 0.987744i \(-0.450113\pi\)
0.156083 + 0.987744i \(0.450113\pi\)
\(984\) 6.13733 0.195651
\(985\) 2.80477 0.0893675
\(986\) −2.54265 −0.0809743
\(987\) 1.54645 0.0492242
\(988\) 6.49743 0.206711
\(989\) −10.0294 −0.318917
\(990\) 2.51908 0.0800616
\(991\) −23.9720 −0.761497 −0.380748 0.924679i \(-0.624334\pi\)
−0.380748 + 0.924679i \(0.624334\pi\)
\(992\) 4.83737 0.153586
\(993\) −25.2616 −0.801652
\(994\) −7.51935 −0.238499
\(995\) −5.79454 −0.183699
\(996\) −4.75292 −0.150602
\(997\) 37.4057 1.18465 0.592325 0.805699i \(-0.298210\pi\)
0.592325 + 0.805699i \(0.298210\pi\)
\(998\) −39.7386 −1.25790
\(999\) 9.42527 0.298202
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 \(a_p\))