Properties

Label 8023.2.a.c.1.4
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.74732 q^{2}\) \(+2.10960 q^{3}\) \(+5.54775 q^{4}\) \(+3.39073 q^{5}\) \(-5.79574 q^{6}\) \(-0.0705501 q^{7}\) \(-9.74679 q^{8}\) \(+1.45041 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.74732 q^{2}\) \(+2.10960 q^{3}\) \(+5.54775 q^{4}\) \(+3.39073 q^{5}\) \(-5.79574 q^{6}\) \(-0.0705501 q^{7}\) \(-9.74679 q^{8}\) \(+1.45041 q^{9}\) \(-9.31541 q^{10}\) \(-4.86039 q^{11}\) \(+11.7035 q^{12}\) \(+2.06905 q^{13}\) \(+0.193823 q^{14}\) \(+7.15308 q^{15}\) \(+15.6820 q^{16}\) \(-2.52700 q^{17}\) \(-3.98473 q^{18}\) \(-5.74187 q^{19}\) \(+18.8109 q^{20}\) \(-0.148832 q^{21}\) \(+13.3530 q^{22}\) \(+6.77197 q^{23}\) \(-20.5618 q^{24}\) \(+6.49705 q^{25}\) \(-5.68433 q^{26}\) \(-3.26902 q^{27}\) \(-0.391394 q^{28}\) \(-4.60912 q^{29}\) \(-19.6518 q^{30}\) \(+5.42280 q^{31}\) \(-23.5899 q^{32}\) \(-10.2535 q^{33}\) \(+6.94248 q^{34}\) \(-0.239216 q^{35}\) \(+8.04651 q^{36}\) \(+10.4954 q^{37}\) \(+15.7747 q^{38}\) \(+4.36486 q^{39}\) \(-33.0487 q^{40}\) \(-7.49278 q^{41}\) \(+0.408890 q^{42}\) \(-5.59125 q^{43}\) \(-26.9642 q^{44}\) \(+4.91795 q^{45}\) \(-18.6047 q^{46}\) \(-12.9389 q^{47}\) \(+33.0828 q^{48}\) \(-6.99502 q^{49}\) \(-17.8495 q^{50}\) \(-5.33097 q^{51}\) \(+11.4786 q^{52}\) \(+6.07795 q^{53}\) \(+8.98102 q^{54}\) \(-16.4803 q^{55}\) \(+0.687637 q^{56}\) \(-12.1130 q^{57}\) \(+12.6627 q^{58}\) \(-4.42794 q^{59}\) \(+39.6835 q^{60}\) \(-7.53661 q^{61}\) \(-14.8982 q^{62}\) \(-0.102327 q^{63}\) \(+33.4449 q^{64}\) \(+7.01558 q^{65}\) \(+28.1696 q^{66}\) \(-13.6186 q^{67}\) \(-14.0192 q^{68}\) \(+14.2861 q^{69}\) \(+0.657203 q^{70}\) \(-1.00000 q^{71}\) \(-14.1368 q^{72}\) \(-13.5795 q^{73}\) \(-28.8343 q^{74}\) \(+13.7062 q^{75}\) \(-31.8545 q^{76}\) \(+0.342901 q^{77}\) \(-11.9917 q^{78}\) \(+9.27609 q^{79}\) \(+53.1735 q^{80}\) \(-11.2475 q^{81}\) \(+20.5850 q^{82}\) \(-5.20125 q^{83}\) \(-0.825685 q^{84}\) \(-8.56839 q^{85}\) \(+15.3609 q^{86}\) \(-9.72341 q^{87}\) \(+47.3732 q^{88}\) \(-15.9877 q^{89}\) \(-13.5112 q^{90}\) \(-0.145972 q^{91}\) \(+37.5692 q^{92}\) \(+11.4399 q^{93}\) \(+35.5471 q^{94}\) \(-19.4691 q^{95}\) \(-49.7652 q^{96}\) \(+15.8297 q^{97}\) \(+19.2175 q^{98}\) \(-7.04956 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74732 −1.94265 −0.971323 0.237763i \(-0.923586\pi\)
−0.971323 + 0.237763i \(0.923586\pi\)
\(3\) 2.10960 1.21798 0.608989 0.793179i \(-0.291575\pi\)
0.608989 + 0.793179i \(0.291575\pi\)
\(4\) 5.54775 2.77387
\(5\) 3.39073 1.51638 0.758190 0.652033i \(-0.226084\pi\)
0.758190 + 0.652033i \(0.226084\pi\)
\(6\) −5.79574 −2.36610
\(7\) −0.0705501 −0.0266654 −0.0133327 0.999911i \(-0.504244\pi\)
−0.0133327 + 0.999911i \(0.504244\pi\)
\(8\) −9.74679 −3.44601
\(9\) 1.45041 0.483470
\(10\) −9.31541 −2.94579
\(11\) −4.86039 −1.46546 −0.732732 0.680518i \(-0.761755\pi\)
−0.732732 + 0.680518i \(0.761755\pi\)
\(12\) 11.7035 3.37852
\(13\) 2.06905 0.573851 0.286925 0.957953i \(-0.407367\pi\)
0.286925 + 0.957953i \(0.407367\pi\)
\(14\) 0.193823 0.0518015
\(15\) 7.15308 1.84692
\(16\) 15.6820 3.92050
\(17\) −2.52700 −0.612889 −0.306444 0.951889i \(-0.599139\pi\)
−0.306444 + 0.951889i \(0.599139\pi\)
\(18\) −3.98473 −0.939211
\(19\) −5.74187 −1.31728 −0.658638 0.752460i \(-0.728867\pi\)
−0.658638 + 0.752460i \(0.728867\pi\)
\(20\) 18.8109 4.20625
\(21\) −0.148832 −0.0324779
\(22\) 13.3530 2.84688
\(23\) 6.77197 1.41205 0.706026 0.708186i \(-0.250486\pi\)
0.706026 + 0.708186i \(0.250486\pi\)
\(24\) −20.5618 −4.19716
\(25\) 6.49705 1.29941
\(26\) −5.68433 −1.11479
\(27\) −3.26902 −0.629122
\(28\) −0.391394 −0.0739666
\(29\) −4.60912 −0.855893 −0.427946 0.903804i \(-0.640763\pi\)
−0.427946 + 0.903804i \(0.640763\pi\)
\(30\) −19.6518 −3.58791
\(31\) 5.42280 0.973964 0.486982 0.873412i \(-0.338098\pi\)
0.486982 + 0.873412i \(0.338098\pi\)
\(32\) −23.5899 −4.17014
\(33\) −10.2535 −1.78490
\(34\) 6.94248 1.19063
\(35\) −0.239216 −0.0404350
\(36\) 8.04651 1.34108
\(37\) 10.4954 1.72544 0.862719 0.505684i \(-0.168760\pi\)
0.862719 + 0.505684i \(0.168760\pi\)
\(38\) 15.7747 2.55900
\(39\) 4.36486 0.698937
\(40\) −33.0487 −5.22546
\(41\) −7.49278 −1.17018 −0.585088 0.810970i \(-0.698940\pi\)
−0.585088 + 0.810970i \(0.698940\pi\)
\(42\) 0.408890 0.0630931
\(43\) −5.59125 −0.852657 −0.426328 0.904568i \(-0.640193\pi\)
−0.426328 + 0.904568i \(0.640193\pi\)
\(44\) −26.9642 −4.06501
\(45\) 4.91795 0.733124
\(46\) −18.6047 −2.74312
\(47\) −12.9389 −1.88733 −0.943663 0.330907i \(-0.892645\pi\)
−0.943663 + 0.330907i \(0.892645\pi\)
\(48\) 33.0828 4.77509
\(49\) −6.99502 −0.999289
\(50\) −17.8495 −2.52430
\(51\) −5.33097 −0.746485
\(52\) 11.4786 1.59179
\(53\) 6.07795 0.834871 0.417436 0.908707i \(-0.362929\pi\)
0.417436 + 0.908707i \(0.362929\pi\)
\(54\) 8.98102 1.22216
\(55\) −16.4803 −2.22220
\(56\) 0.687637 0.0918894
\(57\) −12.1130 −1.60441
\(58\) 12.6627 1.66270
\(59\) −4.42794 −0.576469 −0.288234 0.957560i \(-0.593068\pi\)
−0.288234 + 0.957560i \(0.593068\pi\)
\(60\) 39.6835 5.12312
\(61\) −7.53661 −0.964964 −0.482482 0.875906i \(-0.660265\pi\)
−0.482482 + 0.875906i \(0.660265\pi\)
\(62\) −14.8982 −1.89207
\(63\) −0.102327 −0.0128919
\(64\) 33.4449 4.18061
\(65\) 7.01558 0.870176
\(66\) 28.1696 3.46743
\(67\) −13.6186 −1.66378 −0.831888 0.554944i \(-0.812740\pi\)
−0.831888 + 0.554944i \(0.812740\pi\)
\(68\) −14.0192 −1.70008
\(69\) 14.2861 1.71985
\(70\) 0.657203 0.0785508
\(71\) −1.00000 −0.118678
\(72\) −14.1368 −1.66604
\(73\) −13.5795 −1.58936 −0.794682 0.607026i \(-0.792362\pi\)
−0.794682 + 0.607026i \(0.792362\pi\)
\(74\) −28.8343 −3.35191
\(75\) 13.7062 1.58265
\(76\) −31.8545 −3.65396
\(77\) 0.342901 0.0390772
\(78\) −11.9917 −1.35779
\(79\) 9.27609 1.04364 0.521821 0.853055i \(-0.325253\pi\)
0.521821 + 0.853055i \(0.325253\pi\)
\(80\) 53.1735 5.94498
\(81\) −11.2475 −1.24973
\(82\) 20.5850 2.27324
\(83\) −5.20125 −0.570912 −0.285456 0.958392i \(-0.592145\pi\)
−0.285456 + 0.958392i \(0.592145\pi\)
\(84\) −0.825685 −0.0900896
\(85\) −8.56839 −0.929373
\(86\) 15.3609 1.65641
\(87\) −9.72341 −1.04246
\(88\) 47.3732 5.05000
\(89\) −15.9877 −1.69469 −0.847345 0.531042i \(-0.821800\pi\)
−0.847345 + 0.531042i \(0.821800\pi\)
\(90\) −13.5112 −1.42420
\(91\) −0.145972 −0.0153020
\(92\) 37.5692 3.91686
\(93\) 11.4399 1.18627
\(94\) 35.5471 3.66641
\(95\) −19.4691 −1.99749
\(96\) −49.7652 −5.07914
\(97\) 15.8297 1.60726 0.803632 0.595126i \(-0.202898\pi\)
0.803632 + 0.595126i \(0.202898\pi\)
\(98\) 19.2175 1.94126
\(99\) −7.04956 −0.708507
\(100\) 36.0440 3.60440
\(101\) −13.0662 −1.30013 −0.650066 0.759878i \(-0.725259\pi\)
−0.650066 + 0.759878i \(0.725259\pi\)
\(102\) 14.6459 1.45016
\(103\) 0.223196 0.0219921 0.0109961 0.999940i \(-0.496500\pi\)
0.0109961 + 0.999940i \(0.496500\pi\)
\(104\) −20.1666 −1.97750
\(105\) −0.504651 −0.0492489
\(106\) −16.6981 −1.62186
\(107\) 15.6841 1.51624 0.758120 0.652115i \(-0.226118\pi\)
0.758120 + 0.652115i \(0.226118\pi\)
\(108\) −18.1357 −1.74511
\(109\) 3.18412 0.304984 0.152492 0.988305i \(-0.451270\pi\)
0.152492 + 0.988305i \(0.451270\pi\)
\(110\) 45.2766 4.31695
\(111\) 22.1411 2.10154
\(112\) −1.10637 −0.104542
\(113\) −1.00000 −0.0940721
\(114\) 33.2784 3.11681
\(115\) 22.9619 2.14121
\(116\) −25.5703 −2.37414
\(117\) 3.00097 0.277439
\(118\) 12.1649 1.11987
\(119\) 0.178280 0.0163429
\(120\) −69.7196 −6.36450
\(121\) 12.6234 1.14758
\(122\) 20.7055 1.87458
\(123\) −15.8068 −1.42525
\(124\) 30.0844 2.70165
\(125\) 5.07611 0.454021
\(126\) 0.281123 0.0250445
\(127\) 0.560148 0.0497051 0.0248526 0.999691i \(-0.492088\pi\)
0.0248526 + 0.999691i \(0.492088\pi\)
\(128\) −44.7039 −3.95130
\(129\) −11.7953 −1.03852
\(130\) −19.2740 −1.69044
\(131\) 14.5177 1.26842 0.634209 0.773162i \(-0.281326\pi\)
0.634209 + 0.773162i \(0.281326\pi\)
\(132\) −56.8837 −4.95109
\(133\) 0.405090 0.0351257
\(134\) 37.4146 3.23213
\(135\) −11.0844 −0.953989
\(136\) 24.6302 2.11202
\(137\) 2.73647 0.233792 0.116896 0.993144i \(-0.462706\pi\)
0.116896 + 0.993144i \(0.462706\pi\)
\(138\) −39.2485 −3.34106
\(139\) −3.26153 −0.276640 −0.138320 0.990388i \(-0.544170\pi\)
−0.138320 + 0.990388i \(0.544170\pi\)
\(140\) −1.32711 −0.112161
\(141\) −27.2958 −2.29872
\(142\) 2.74732 0.230550
\(143\) −10.0564 −0.840957
\(144\) 22.7453 1.89545
\(145\) −15.6283 −1.29786
\(146\) 37.3073 3.08757
\(147\) −14.7567 −1.21711
\(148\) 58.2260 4.78615
\(149\) −20.2705 −1.66062 −0.830312 0.557299i \(-0.811838\pi\)
−0.830312 + 0.557299i \(0.811838\pi\)
\(150\) −37.6552 −3.07454
\(151\) 10.0843 0.820645 0.410323 0.911940i \(-0.365416\pi\)
0.410323 + 0.911940i \(0.365416\pi\)
\(152\) 55.9648 4.53935
\(153\) −3.66519 −0.296313
\(154\) −0.942058 −0.0759132
\(155\) 18.3873 1.47690
\(156\) 24.2152 1.93876
\(157\) 3.76686 0.300628 0.150314 0.988638i \(-0.451972\pi\)
0.150314 + 0.988638i \(0.451972\pi\)
\(158\) −25.4844 −2.02743
\(159\) 12.8220 1.01685
\(160\) −79.9870 −6.32353
\(161\) −0.477763 −0.0376530
\(162\) 30.9006 2.42778
\(163\) −2.70915 −0.212197 −0.106099 0.994356i \(-0.533836\pi\)
−0.106099 + 0.994356i \(0.533836\pi\)
\(164\) −41.5681 −3.24592
\(165\) −34.7668 −2.70659
\(166\) 14.2895 1.10908
\(167\) −7.94152 −0.614533 −0.307267 0.951623i \(-0.599414\pi\)
−0.307267 + 0.951623i \(0.599414\pi\)
\(168\) 1.45064 0.111919
\(169\) −8.71904 −0.670695
\(170\) 23.5401 1.80544
\(171\) −8.32806 −0.636863
\(172\) −31.0188 −2.36516
\(173\) 14.3204 1.08876 0.544380 0.838839i \(-0.316765\pi\)
0.544380 + 0.838839i \(0.316765\pi\)
\(174\) 26.7133 2.02513
\(175\) −0.458368 −0.0346494
\(176\) −76.2208 −5.74536
\(177\) −9.34118 −0.702126
\(178\) 43.9232 3.29218
\(179\) 14.4205 1.07784 0.538920 0.842357i \(-0.318832\pi\)
0.538920 + 0.842357i \(0.318832\pi\)
\(180\) 27.2835 2.03359
\(181\) −15.4170 −1.14594 −0.572968 0.819578i \(-0.694208\pi\)
−0.572968 + 0.819578i \(0.694208\pi\)
\(182\) 0.401030 0.0297263
\(183\) −15.8992 −1.17530
\(184\) −66.0049 −4.86595
\(185\) 35.5872 2.61642
\(186\) −31.4291 −2.30450
\(187\) 12.2822 0.898166
\(188\) −71.7815 −5.23521
\(189\) 0.230629 0.0167758
\(190\) 53.4879 3.88042
\(191\) 16.6125 1.20204 0.601020 0.799234i \(-0.294761\pi\)
0.601020 + 0.799234i \(0.294761\pi\)
\(192\) 70.5553 5.09189
\(193\) 4.20881 0.302957 0.151478 0.988461i \(-0.451597\pi\)
0.151478 + 0.988461i \(0.451597\pi\)
\(194\) −43.4892 −3.12235
\(195\) 14.8001 1.05986
\(196\) −38.8066 −2.77190
\(197\) −10.1778 −0.725139 −0.362569 0.931957i \(-0.618100\pi\)
−0.362569 + 0.931957i \(0.618100\pi\)
\(198\) 19.3674 1.37638
\(199\) −3.60505 −0.255555 −0.127778 0.991803i \(-0.540784\pi\)
−0.127778 + 0.991803i \(0.540784\pi\)
\(200\) −63.3254 −4.47778
\(201\) −28.7298 −2.02644
\(202\) 35.8969 2.52570
\(203\) 0.325174 0.0228228
\(204\) −29.5749 −2.07066
\(205\) −25.4060 −1.77443
\(206\) −0.613189 −0.0427229
\(207\) 9.82212 0.682685
\(208\) 32.4469 2.24978
\(209\) 27.9078 1.93042
\(210\) 1.38644 0.0956731
\(211\) 2.90904 0.200267 0.100133 0.994974i \(-0.468073\pi\)
0.100133 + 0.994974i \(0.468073\pi\)
\(212\) 33.7190 2.31583
\(213\) −2.10960 −0.144547
\(214\) −43.0892 −2.94552
\(215\) −18.9584 −1.29295
\(216\) 31.8624 2.16796
\(217\) −0.382579 −0.0259712
\(218\) −8.74780 −0.592475
\(219\) −28.6474 −1.93581
\(220\) −91.4285 −6.16411
\(221\) −5.22849 −0.351707
\(222\) −60.8287 −4.08256
\(223\) −5.94964 −0.398418 −0.199209 0.979957i \(-0.563837\pi\)
−0.199209 + 0.979957i \(0.563837\pi\)
\(224\) 1.66427 0.111199
\(225\) 9.42339 0.628226
\(226\) 2.74732 0.182749
\(227\) 7.06787 0.469111 0.234556 0.972103i \(-0.424637\pi\)
0.234556 + 0.972103i \(0.424637\pi\)
\(228\) −67.2002 −4.45044
\(229\) −22.0972 −1.46023 −0.730114 0.683326i \(-0.760533\pi\)
−0.730114 + 0.683326i \(0.760533\pi\)
\(230\) −63.0837 −4.15961
\(231\) 0.723384 0.0475952
\(232\) 44.9242 2.94942
\(233\) −23.2399 −1.52250 −0.761248 0.648460i \(-0.775413\pi\)
−0.761248 + 0.648460i \(0.775413\pi\)
\(234\) −8.24460 −0.538967
\(235\) −43.8722 −2.86191
\(236\) −24.5651 −1.59905
\(237\) 19.5688 1.27113
\(238\) −0.489793 −0.0317486
\(239\) −10.4329 −0.674846 −0.337423 0.941353i \(-0.609555\pi\)
−0.337423 + 0.941353i \(0.609555\pi\)
\(240\) 112.175 7.24085
\(241\) 22.4864 1.44848 0.724238 0.689550i \(-0.242192\pi\)
0.724238 + 0.689550i \(0.242192\pi\)
\(242\) −34.6805 −2.22935
\(243\) −13.9208 −0.893017
\(244\) −41.8112 −2.67669
\(245\) −23.7182 −1.51530
\(246\) 43.4262 2.76875
\(247\) −11.8802 −0.755920
\(248\) −52.8549 −3.35629
\(249\) −10.9726 −0.695358
\(250\) −13.9457 −0.882002
\(251\) 6.05768 0.382357 0.191179 0.981555i \(-0.438769\pi\)
0.191179 + 0.981555i \(0.438769\pi\)
\(252\) −0.567682 −0.0357606
\(253\) −32.9144 −2.06931
\(254\) −1.53890 −0.0965594
\(255\) −18.0759 −1.13196
\(256\) 55.9259 3.49537
\(257\) −15.4251 −0.962194 −0.481097 0.876667i \(-0.659762\pi\)
−0.481097 + 0.876667i \(0.659762\pi\)
\(258\) 32.4054 2.01747
\(259\) −0.740453 −0.0460095
\(260\) 38.9207 2.41376
\(261\) −6.68512 −0.413798
\(262\) −39.8847 −2.46409
\(263\) 19.3766 1.19481 0.597405 0.801940i \(-0.296198\pi\)
0.597405 + 0.801940i \(0.296198\pi\)
\(264\) 99.9385 6.15079
\(265\) 20.6087 1.26598
\(266\) −1.11291 −0.0682369
\(267\) −33.7276 −2.06410
\(268\) −75.5525 −4.61510
\(269\) −9.60622 −0.585701 −0.292851 0.956158i \(-0.594604\pi\)
−0.292851 + 0.956158i \(0.594604\pi\)
\(270\) 30.4522 1.85326
\(271\) 24.8514 1.50962 0.754808 0.655945i \(-0.227730\pi\)
0.754808 + 0.655945i \(0.227730\pi\)
\(272\) −39.6285 −2.40283
\(273\) −0.307942 −0.0186375
\(274\) −7.51794 −0.454176
\(275\) −31.5782 −1.90424
\(276\) 79.2559 4.77064
\(277\) 9.29688 0.558595 0.279298 0.960205i \(-0.409898\pi\)
0.279298 + 0.960205i \(0.409898\pi\)
\(278\) 8.96046 0.537413
\(279\) 7.86528 0.470882
\(280\) 2.33159 0.139339
\(281\) 7.19069 0.428961 0.214480 0.976728i \(-0.431194\pi\)
0.214480 + 0.976728i \(0.431194\pi\)
\(282\) 74.9902 4.46560
\(283\) 28.8931 1.71751 0.858757 0.512383i \(-0.171237\pi\)
0.858757 + 0.512383i \(0.171237\pi\)
\(284\) −5.54775 −0.329198
\(285\) −41.0721 −2.43290
\(286\) 27.6281 1.63368
\(287\) 0.528616 0.0312032
\(288\) −34.2150 −2.01614
\(289\) −10.6142 −0.624367
\(290\) 42.9359 2.52128
\(291\) 33.3944 1.95761
\(292\) −75.3358 −4.40869
\(293\) −9.86677 −0.576423 −0.288212 0.957567i \(-0.593061\pi\)
−0.288212 + 0.957567i \(0.593061\pi\)
\(294\) 40.5413 2.36442
\(295\) −15.0139 −0.874146
\(296\) −102.297 −5.94588
\(297\) 15.8887 0.921956
\(298\) 55.6895 3.22600
\(299\) 14.0115 0.810307
\(300\) 76.0384 4.39008
\(301\) 0.394463 0.0227365
\(302\) −27.7047 −1.59422
\(303\) −27.5644 −1.58353
\(304\) −90.0441 −5.16439
\(305\) −25.5546 −1.46325
\(306\) 10.0694 0.575632
\(307\) −6.05059 −0.345326 −0.172663 0.984981i \(-0.555237\pi\)
−0.172663 + 0.984981i \(0.555237\pi\)
\(308\) 1.90233 0.108395
\(309\) 0.470854 0.0267859
\(310\) −50.5156 −2.86910
\(311\) −31.6751 −1.79613 −0.898066 0.439860i \(-0.855028\pi\)
−0.898066 + 0.439860i \(0.855028\pi\)
\(312\) −42.5434 −2.40855
\(313\) 1.83352 0.103637 0.0518183 0.998657i \(-0.483498\pi\)
0.0518183 + 0.998657i \(0.483498\pi\)
\(314\) −10.3487 −0.584014
\(315\) −0.346962 −0.0195491
\(316\) 51.4614 2.89493
\(317\) 0.687550 0.0386167 0.0193083 0.999814i \(-0.493854\pi\)
0.0193083 + 0.999814i \(0.493854\pi\)
\(318\) −35.2262 −1.97539
\(319\) 22.4022 1.25428
\(320\) 113.403 6.33939
\(321\) 33.0872 1.84675
\(322\) 1.31257 0.0731465
\(323\) 14.5097 0.807344
\(324\) −62.3985 −3.46659
\(325\) 13.4427 0.745668
\(326\) 7.44290 0.412224
\(327\) 6.71722 0.371463
\(328\) 73.0305 4.03244
\(329\) 0.912838 0.0503264
\(330\) 95.5154 5.25795
\(331\) −16.7905 −0.922891 −0.461446 0.887168i \(-0.652669\pi\)
−0.461446 + 0.887168i \(0.652669\pi\)
\(332\) −28.8552 −1.58364
\(333\) 15.2227 0.834197
\(334\) 21.8179 1.19382
\(335\) −46.1770 −2.52292
\(336\) −2.33399 −0.127330
\(337\) −0.359970 −0.0196088 −0.00980441 0.999952i \(-0.503121\pi\)
−0.00980441 + 0.999952i \(0.503121\pi\)
\(338\) 23.9540 1.30292
\(339\) −2.10960 −0.114578
\(340\) −47.5353 −2.57796
\(341\) −26.3570 −1.42731
\(342\) 22.8798 1.23720
\(343\) 0.987350 0.0533119
\(344\) 54.4967 2.93826
\(345\) 48.4404 2.60795
\(346\) −39.3427 −2.11508
\(347\) 28.6773 1.53948 0.769739 0.638359i \(-0.220386\pi\)
0.769739 + 0.638359i \(0.220386\pi\)
\(348\) −53.9430 −2.89165
\(349\) 33.5987 1.79850 0.899250 0.437435i \(-0.144113\pi\)
0.899250 + 0.437435i \(0.144113\pi\)
\(350\) 1.25928 0.0673114
\(351\) −6.76375 −0.361022
\(352\) 114.656 6.11119
\(353\) 35.2677 1.87711 0.938556 0.345128i \(-0.112165\pi\)
0.938556 + 0.345128i \(0.112165\pi\)
\(354\) 25.6632 1.36398
\(355\) −3.39073 −0.179961
\(356\) −88.6956 −4.70086
\(357\) 0.376100 0.0199053
\(358\) −39.6177 −2.09386
\(359\) 14.2910 0.754251 0.377126 0.926162i \(-0.376912\pi\)
0.377126 + 0.926162i \(0.376912\pi\)
\(360\) −47.9342 −2.52635
\(361\) 13.9691 0.735216
\(362\) 42.3554 2.22615
\(363\) 26.6303 1.39773
\(364\) −0.809814 −0.0424458
\(365\) −46.0445 −2.41008
\(366\) 43.6802 2.28320
\(367\) 8.63696 0.450846 0.225423 0.974261i \(-0.427624\pi\)
0.225423 + 0.974261i \(0.427624\pi\)
\(368\) 106.198 5.53596
\(369\) −10.8676 −0.565744
\(370\) −97.7692 −5.08278
\(371\) −0.428800 −0.0222622
\(372\) 63.4659 3.29056
\(373\) −14.4634 −0.748889 −0.374444 0.927249i \(-0.622167\pi\)
−0.374444 + 0.927249i \(0.622167\pi\)
\(374\) −33.7432 −1.74482
\(375\) 10.7086 0.552987
\(376\) 126.112 6.50375
\(377\) −9.53650 −0.491155
\(378\) −0.633612 −0.0325895
\(379\) 24.0416 1.23494 0.617468 0.786596i \(-0.288159\pi\)
0.617468 + 0.786596i \(0.288159\pi\)
\(380\) −108.010 −5.54079
\(381\) 1.18169 0.0605397
\(382\) −45.6399 −2.33514
\(383\) −24.3095 −1.24216 −0.621079 0.783748i \(-0.713305\pi\)
−0.621079 + 0.783748i \(0.713305\pi\)
\(384\) −94.3072 −4.81260
\(385\) 1.16269 0.0592559
\(386\) −11.5629 −0.588538
\(387\) −8.10959 −0.412234
\(388\) 87.8193 4.45835
\(389\) 23.7805 1.20572 0.602860 0.797847i \(-0.294028\pi\)
0.602860 + 0.797847i \(0.294028\pi\)
\(390\) −40.6605 −2.05892
\(391\) −17.1128 −0.865431
\(392\) 68.1790 3.44356
\(393\) 30.6265 1.54491
\(394\) 27.9617 1.40869
\(395\) 31.4527 1.58256
\(396\) −39.1092 −1.96531
\(397\) −6.58099 −0.330291 −0.165145 0.986269i \(-0.552809\pi\)
−0.165145 + 0.986269i \(0.552809\pi\)
\(398\) 9.90422 0.496454
\(399\) 0.854577 0.0427824
\(400\) 101.887 5.09435
\(401\) −15.2578 −0.761938 −0.380969 0.924588i \(-0.624409\pi\)
−0.380969 + 0.924588i \(0.624409\pi\)
\(402\) 78.9298 3.93666
\(403\) 11.2200 0.558910
\(404\) −72.4878 −3.60640
\(405\) −38.1374 −1.89506
\(406\) −0.893357 −0.0443365
\(407\) −51.0119 −2.52857
\(408\) 51.9598 2.57239
\(409\) 3.98816 0.197202 0.0986009 0.995127i \(-0.468563\pi\)
0.0986009 + 0.995127i \(0.468563\pi\)
\(410\) 69.7983 3.44709
\(411\) 5.77285 0.284754
\(412\) 1.23823 0.0610034
\(413\) 0.312392 0.0153718
\(414\) −26.9845 −1.32621
\(415\) −17.6360 −0.865720
\(416\) −48.8086 −2.39304
\(417\) −6.88053 −0.336941
\(418\) −76.6714 −3.75012
\(419\) −24.9568 −1.21922 −0.609610 0.792701i \(-0.708674\pi\)
−0.609610 + 0.792701i \(0.708674\pi\)
\(420\) −2.79968 −0.136610
\(421\) −25.8614 −1.26041 −0.630205 0.776429i \(-0.717029\pi\)
−0.630205 + 0.776429i \(0.717029\pi\)
\(422\) −7.99206 −0.389047
\(423\) −18.7666 −0.912465
\(424\) −59.2405 −2.87697
\(425\) −16.4181 −0.796394
\(426\) 5.79574 0.280804
\(427\) 0.531709 0.0257312
\(428\) 87.0115 4.20586
\(429\) −21.2149 −1.02427
\(430\) 52.0848 2.51175
\(431\) 5.08003 0.244697 0.122348 0.992487i \(-0.460957\pi\)
0.122348 + 0.992487i \(0.460957\pi\)
\(432\) −51.2648 −2.46648
\(433\) −6.42184 −0.308614 −0.154307 0.988023i \(-0.549314\pi\)
−0.154307 + 0.988023i \(0.549314\pi\)
\(434\) 1.05107 0.0504528
\(435\) −32.9694 −1.58076
\(436\) 17.6647 0.845987
\(437\) −38.8838 −1.86006
\(438\) 78.7034 3.76059
\(439\) −10.5406 −0.503078 −0.251539 0.967847i \(-0.580937\pi\)
−0.251539 + 0.967847i \(0.580937\pi\)
\(440\) 160.630 7.65773
\(441\) −10.1456 −0.483126
\(442\) 14.3643 0.683242
\(443\) −33.0925 −1.57227 −0.786136 0.618054i \(-0.787921\pi\)
−0.786136 + 0.618054i \(0.787921\pi\)
\(444\) 122.834 5.82942
\(445\) −54.2099 −2.56980
\(446\) 16.3456 0.773984
\(447\) −42.7626 −2.02260
\(448\) −2.35954 −0.111478
\(449\) 33.7618 1.59332 0.796659 0.604429i \(-0.206599\pi\)
0.796659 + 0.604429i \(0.206599\pi\)
\(450\) −25.8890 −1.22042
\(451\) 36.4178 1.71485
\(452\) −5.54775 −0.260944
\(453\) 21.2737 0.999528
\(454\) −19.4177 −0.911317
\(455\) −0.494950 −0.0232036
\(456\) 118.063 5.52882
\(457\) −8.64831 −0.404551 −0.202276 0.979329i \(-0.564834\pi\)
−0.202276 + 0.979329i \(0.564834\pi\)
\(458\) 60.7081 2.83670
\(459\) 8.26082 0.385582
\(460\) 127.387 5.93945
\(461\) −9.86146 −0.459294 −0.229647 0.973274i \(-0.573757\pi\)
−0.229647 + 0.973274i \(0.573757\pi\)
\(462\) −1.98737 −0.0924606
\(463\) 9.92849 0.461416 0.230708 0.973023i \(-0.425896\pi\)
0.230708 + 0.973023i \(0.425896\pi\)
\(464\) −72.2804 −3.35553
\(465\) 38.7898 1.79883
\(466\) 63.8474 2.95767
\(467\) −31.1371 −1.44085 −0.720427 0.693530i \(-0.756054\pi\)
−0.720427 + 0.693530i \(0.756054\pi\)
\(468\) 16.6486 0.769582
\(469\) 0.960793 0.0443653
\(470\) 120.531 5.55967
\(471\) 7.94656 0.366158
\(472\) 43.1582 1.98652
\(473\) 27.1756 1.24954
\(474\) −53.7618 −2.46936
\(475\) −37.3053 −1.71168
\(476\) 0.989055 0.0453333
\(477\) 8.81552 0.403635
\(478\) 28.6624 1.31099
\(479\) 3.21017 0.146676 0.0733382 0.997307i \(-0.476635\pi\)
0.0733382 + 0.997307i \(0.476635\pi\)
\(480\) −168.740 −7.70191
\(481\) 21.7155 0.990143
\(482\) −61.7772 −2.81388
\(483\) −1.00789 −0.0458605
\(484\) 70.0315 3.18325
\(485\) 53.6743 2.43722
\(486\) 38.2447 1.73482
\(487\) 35.6704 1.61638 0.808189 0.588923i \(-0.200448\pi\)
0.808189 + 0.588923i \(0.200448\pi\)
\(488\) 73.4578 3.32528
\(489\) −5.71523 −0.258452
\(490\) 65.1615 2.94370
\(491\) 15.2861 0.689854 0.344927 0.938629i \(-0.387904\pi\)
0.344927 + 0.938629i \(0.387904\pi\)
\(492\) −87.6919 −3.95346
\(493\) 11.6473 0.524567
\(494\) 32.6387 1.46848
\(495\) −23.9032 −1.07437
\(496\) 85.0405 3.81843
\(497\) 0.0705501 0.00316460
\(498\) 30.1451 1.35083
\(499\) 27.4267 1.22779 0.613893 0.789389i \(-0.289603\pi\)
0.613893 + 0.789389i \(0.289603\pi\)
\(500\) 28.1610 1.25940
\(501\) −16.7534 −0.748488
\(502\) −16.6424 −0.742785
\(503\) −27.3541 −1.21966 −0.609831 0.792532i \(-0.708762\pi\)
−0.609831 + 0.792532i \(0.708762\pi\)
\(504\) 0.997355 0.0444257
\(505\) −44.3038 −1.97149
\(506\) 90.4263 4.01994
\(507\) −18.3937 −0.816892
\(508\) 3.10756 0.137876
\(509\) 5.98267 0.265177 0.132589 0.991171i \(-0.457671\pi\)
0.132589 + 0.991171i \(0.457671\pi\)
\(510\) 49.6602 2.19899
\(511\) 0.958037 0.0423811
\(512\) −64.2385 −2.83897
\(513\) 18.7703 0.828728
\(514\) 42.3778 1.86920
\(515\) 0.756797 0.0333484
\(516\) −65.4373 −2.88072
\(517\) 62.8879 2.76581
\(518\) 2.03426 0.0893803
\(519\) 30.2103 1.32609
\(520\) −68.3794 −2.99864
\(521\) −23.9557 −1.04952 −0.524758 0.851251i \(-0.675844\pi\)
−0.524758 + 0.851251i \(0.675844\pi\)
\(522\) 18.3661 0.803864
\(523\) 39.7192 1.73680 0.868400 0.495864i \(-0.165149\pi\)
0.868400 + 0.495864i \(0.165149\pi\)
\(524\) 80.5406 3.51843
\(525\) −0.966973 −0.0422021
\(526\) −53.2336 −2.32109
\(527\) −13.7035 −0.596932
\(528\) −160.795 −6.99772
\(529\) 22.8595 0.993893
\(530\) −56.6186 −2.45936
\(531\) −6.42232 −0.278705
\(532\) 2.24734 0.0974344
\(533\) −15.5029 −0.671506
\(534\) 92.6604 4.00981
\(535\) 53.1806 2.29920
\(536\) 132.738 5.73339
\(537\) 30.4215 1.31279
\(538\) 26.3913 1.13781
\(539\) 33.9986 1.46442
\(540\) −61.4932 −2.64625
\(541\) −18.6229 −0.800659 −0.400330 0.916371i \(-0.631104\pi\)
−0.400330 + 0.916371i \(0.631104\pi\)
\(542\) −68.2747 −2.93265
\(543\) −32.5237 −1.39572
\(544\) 59.6118 2.55583
\(545\) 10.7965 0.462471
\(546\) 0.846013 0.0362060
\(547\) −19.5826 −0.837293 −0.418646 0.908149i \(-0.637495\pi\)
−0.418646 + 0.908149i \(0.637495\pi\)
\(548\) 15.1812 0.648510
\(549\) −10.9312 −0.466531
\(550\) 86.7554 3.69926
\(551\) 26.4650 1.12745
\(552\) −139.244 −5.92662
\(553\) −0.654429 −0.0278292
\(554\) −25.5415 −1.08515
\(555\) 75.0747 3.18674
\(556\) −18.0942 −0.767364
\(557\) −22.1231 −0.937384 −0.468692 0.883362i \(-0.655275\pi\)
−0.468692 + 0.883362i \(0.655275\pi\)
\(558\) −21.6084 −0.914758
\(559\) −11.5686 −0.489298
\(560\) −3.75140 −0.158525
\(561\) 25.9106 1.09395
\(562\) −19.7551 −0.833319
\(563\) 8.51277 0.358770 0.179385 0.983779i \(-0.442589\pi\)
0.179385 + 0.983779i \(0.442589\pi\)
\(564\) −151.430 −6.37637
\(565\) −3.39073 −0.142649
\(566\) −79.3784 −3.33652
\(567\) 0.793515 0.0333245
\(568\) 9.74679 0.408966
\(569\) 0.332793 0.0139514 0.00697571 0.999976i \(-0.497780\pi\)
0.00697571 + 0.999976i \(0.497780\pi\)
\(570\) 112.838 4.72626
\(571\) −38.5420 −1.61293 −0.806466 0.591280i \(-0.798623\pi\)
−0.806466 + 0.591280i \(0.798623\pi\)
\(572\) −55.7903 −2.33271
\(573\) 35.0458 1.46406
\(574\) −1.45228 −0.0606168
\(575\) 43.9978 1.83484
\(576\) 48.5087 2.02120
\(577\) −5.33205 −0.221976 −0.110988 0.993822i \(-0.535402\pi\)
−0.110988 + 0.993822i \(0.535402\pi\)
\(578\) 29.1607 1.21292
\(579\) 8.87890 0.368994
\(580\) −86.7019 −3.60010
\(581\) 0.366949 0.0152236
\(582\) −91.7449 −3.80295
\(583\) −29.5412 −1.22347
\(584\) 132.357 5.47696
\(585\) 10.1755 0.420704
\(586\) 27.1072 1.11979
\(587\) 10.8665 0.448508 0.224254 0.974531i \(-0.428005\pi\)
0.224254 + 0.974531i \(0.428005\pi\)
\(588\) −81.8664 −3.37611
\(589\) −31.1370 −1.28298
\(590\) 41.2481 1.69816
\(591\) −21.4711 −0.883203
\(592\) 164.589 6.76459
\(593\) −37.5761 −1.54306 −0.771532 0.636191i \(-0.780509\pi\)
−0.771532 + 0.636191i \(0.780509\pi\)
\(594\) −43.6513 −1.79103
\(595\) 0.604501 0.0247821
\(596\) −112.456 −4.60636
\(597\) −7.60522 −0.311261
\(598\) −38.4941 −1.57414
\(599\) −19.8467 −0.810915 −0.405457 0.914114i \(-0.632888\pi\)
−0.405457 + 0.914114i \(0.632888\pi\)
\(600\) −133.591 −5.45384
\(601\) 10.5686 0.431102 0.215551 0.976493i \(-0.430845\pi\)
0.215551 + 0.976493i \(0.430845\pi\)
\(602\) −1.08371 −0.0441689
\(603\) −19.7525 −0.804385
\(604\) 55.9449 2.27637
\(605\) 42.8026 1.74017
\(606\) 75.7280 3.07624
\(607\) −3.58851 −0.145653 −0.0728266 0.997345i \(-0.523202\pi\)
−0.0728266 + 0.997345i \(0.523202\pi\)
\(608\) 135.450 5.49323
\(609\) 0.685987 0.0277976
\(610\) 70.2066 2.84258
\(611\) −26.7711 −1.08304
\(612\) −20.3336 −0.821935
\(613\) 20.0533 0.809946 0.404973 0.914329i \(-0.367281\pi\)
0.404973 + 0.914329i \(0.367281\pi\)
\(614\) 16.6229 0.670845
\(615\) −53.5965 −2.16122
\(616\) −3.34219 −0.134661
\(617\) −4.62763 −0.186301 −0.0931507 0.995652i \(-0.529694\pi\)
−0.0931507 + 0.995652i \(0.529694\pi\)
\(618\) −1.29358 −0.0520356
\(619\) −47.2965 −1.90101 −0.950504 0.310712i \(-0.899432\pi\)
−0.950504 + 0.310712i \(0.899432\pi\)
\(620\) 102.008 4.09674
\(621\) −22.1377 −0.888354
\(622\) 87.0216 3.48925
\(623\) 1.12793 0.0451897
\(624\) 68.4499 2.74019
\(625\) −15.2736 −0.610942
\(626\) −5.03725 −0.201329
\(627\) 58.8742 2.35121
\(628\) 20.8976 0.833904
\(629\) −26.5220 −1.05750
\(630\) 0.953214 0.0379769
\(631\) 11.1329 0.443193 0.221596 0.975138i \(-0.428873\pi\)
0.221596 + 0.975138i \(0.428873\pi\)
\(632\) −90.4121 −3.59640
\(633\) 6.13691 0.243920
\(634\) −1.88892 −0.0750185
\(635\) 1.89931 0.0753719
\(636\) 71.1335 2.82063
\(637\) −14.4730 −0.573443
\(638\) −61.5458 −2.43662
\(639\) −1.45041 −0.0573773
\(640\) −151.579 −5.99168
\(641\) −3.23752 −0.127874 −0.0639371 0.997954i \(-0.520366\pi\)
−0.0639371 + 0.997954i \(0.520366\pi\)
\(642\) −90.9010 −3.58758
\(643\) −32.8030 −1.29362 −0.646811 0.762650i \(-0.723898\pi\)
−0.646811 + 0.762650i \(0.723898\pi\)
\(644\) −2.65051 −0.104445
\(645\) −39.9946 −1.57479
\(646\) −39.8628 −1.56838
\(647\) 24.5601 0.965557 0.482778 0.875743i \(-0.339628\pi\)
0.482778 + 0.875743i \(0.339628\pi\)
\(648\) 109.627 4.30657
\(649\) 21.5215 0.844794
\(650\) −36.9314 −1.44857
\(651\) −0.807089 −0.0316323
\(652\) −15.0297 −0.588608
\(653\) −13.9745 −0.546864 −0.273432 0.961891i \(-0.588159\pi\)
−0.273432 + 0.961891i \(0.588159\pi\)
\(654\) −18.4543 −0.721622
\(655\) 49.2256 1.92340
\(656\) −117.502 −4.58768
\(657\) −19.6959 −0.768409
\(658\) −2.50785 −0.0977664
\(659\) 2.28226 0.0889043 0.0444522 0.999012i \(-0.485846\pi\)
0.0444522 + 0.999012i \(0.485846\pi\)
\(660\) −192.877 −7.50774
\(661\) −49.1212 −1.91059 −0.955296 0.295651i \(-0.904464\pi\)
−0.955296 + 0.295651i \(0.904464\pi\)
\(662\) 46.1289 1.79285
\(663\) −11.0300 −0.428371
\(664\) 50.6955 1.96737
\(665\) 1.37355 0.0532640
\(666\) −41.8215 −1.62055
\(667\) −31.2128 −1.20857
\(668\) −44.0576 −1.70464
\(669\) −12.5514 −0.485264
\(670\) 126.863 4.90114
\(671\) 36.6309 1.41412
\(672\) 3.51094 0.135438
\(673\) −4.02890 −0.155303 −0.0776513 0.996981i \(-0.524742\pi\)
−0.0776513 + 0.996981i \(0.524742\pi\)
\(674\) 0.988952 0.0380930
\(675\) −21.2390 −0.817488
\(676\) −48.3710 −1.86042
\(677\) −33.5593 −1.28979 −0.644895 0.764272i \(-0.723099\pi\)
−0.644895 + 0.764272i \(0.723099\pi\)
\(678\) 5.79574 0.222584
\(679\) −1.11679 −0.0428584
\(680\) 83.5143 3.20263
\(681\) 14.9104 0.571367
\(682\) 72.4109 2.77276
\(683\) 46.5275 1.78033 0.890163 0.455643i \(-0.150591\pi\)
0.890163 + 0.455643i \(0.150591\pi\)
\(684\) −46.2020 −1.76658
\(685\) 9.27863 0.354518
\(686\) −2.71256 −0.103566
\(687\) −46.6163 −1.77852
\(688\) −87.6820 −3.34285
\(689\) 12.5756 0.479091
\(690\) −133.081 −5.06632
\(691\) −16.8527 −0.641108 −0.320554 0.947230i \(-0.603869\pi\)
−0.320554 + 0.947230i \(0.603869\pi\)
\(692\) 79.4460 3.02008
\(693\) 0.497347 0.0188927
\(694\) −78.7856 −2.99066
\(695\) −11.0590 −0.419491
\(696\) 94.7720 3.59232
\(697\) 18.9343 0.717187
\(698\) −92.3064 −3.49385
\(699\) −49.0269 −1.85437
\(700\) −2.54291 −0.0961130
\(701\) −2.05005 −0.0774295 −0.0387147 0.999250i \(-0.512326\pi\)
−0.0387147 + 0.999250i \(0.512326\pi\)
\(702\) 18.5822 0.701339
\(703\) −60.2634 −2.27288
\(704\) −162.555 −6.12653
\(705\) −92.5527 −3.48574
\(706\) −96.8916 −3.64656
\(707\) 0.921819 0.0346686
\(708\) −51.8225 −1.94761
\(709\) 27.2969 1.02516 0.512579 0.858640i \(-0.328690\pi\)
0.512579 + 0.858640i \(0.328690\pi\)
\(710\) 9.31541 0.349601
\(711\) 13.4541 0.504569
\(712\) 155.829 5.83992
\(713\) 36.7231 1.37529
\(714\) −1.03327 −0.0386690
\(715\) −34.0985 −1.27521
\(716\) 80.0014 2.98979
\(717\) −22.0092 −0.821947
\(718\) −39.2620 −1.46524
\(719\) 25.5237 0.951875 0.475938 0.879479i \(-0.342109\pi\)
0.475938 + 0.879479i \(0.342109\pi\)
\(720\) 77.1233 2.87422
\(721\) −0.0157465 −0.000586430 0
\(722\) −38.3775 −1.42826
\(723\) 47.4373 1.76421
\(724\) −85.5296 −3.17868
\(725\) −29.9457 −1.11216
\(726\) −73.1620 −2.71530
\(727\) 28.2944 1.04938 0.524691 0.851293i \(-0.324181\pi\)
0.524691 + 0.851293i \(0.324181\pi\)
\(728\) 1.42275 0.0527308
\(729\) 4.37541 0.162052
\(730\) 126.499 4.68193
\(731\) 14.1291 0.522584
\(732\) −88.2049 −3.26015
\(733\) 32.2757 1.19213 0.596066 0.802936i \(-0.296730\pi\)
0.596066 + 0.802936i \(0.296730\pi\)
\(734\) −23.7285 −0.875833
\(735\) −50.0360 −1.84560
\(736\) −159.750 −5.88846
\(737\) 66.1917 2.43820
\(738\) 29.8567 1.09904
\(739\) 36.0417 1.32581 0.662907 0.748701i \(-0.269322\pi\)
0.662907 + 0.748701i \(0.269322\pi\)
\(740\) 197.429 7.25762
\(741\) −25.0625 −0.920693
\(742\) 1.17805 0.0432476
\(743\) 25.9553 0.952208 0.476104 0.879389i \(-0.342049\pi\)
0.476104 + 0.879389i \(0.342049\pi\)
\(744\) −111.503 −4.08789
\(745\) −68.7318 −2.51814
\(746\) 39.7357 1.45483
\(747\) −7.54395 −0.276019
\(748\) 68.1388 2.49140
\(749\) −1.10652 −0.0404312
\(750\) −29.4198 −1.07426
\(751\) 25.0095 0.912610 0.456305 0.889823i \(-0.349173\pi\)
0.456305 + 0.889823i \(0.349173\pi\)
\(752\) −202.907 −7.39927
\(753\) 12.7793 0.465703
\(754\) 26.1998 0.954140
\(755\) 34.1930 1.24441
\(756\) 1.27947 0.0465340
\(757\) −49.1146 −1.78510 −0.892551 0.450947i \(-0.851086\pi\)
−0.892551 + 0.450947i \(0.851086\pi\)
\(758\) −66.0499 −2.39904
\(759\) −69.4362 −2.52038
\(760\) 189.762 6.88338
\(761\) −39.9875 −1.44955 −0.724774 0.688987i \(-0.758056\pi\)
−0.724774 + 0.688987i \(0.758056\pi\)
\(762\) −3.24647 −0.117607
\(763\) −0.224640 −0.00813252
\(764\) 92.1621 3.33431
\(765\) −12.4277 −0.449324
\(766\) 66.7859 2.41307
\(767\) −9.16162 −0.330807
\(768\) 117.981 4.25728
\(769\) −5.27196 −0.190112 −0.0950558 0.995472i \(-0.530303\pi\)
−0.0950558 + 0.995472i \(0.530303\pi\)
\(770\) −3.19427 −0.115113
\(771\) −32.5409 −1.17193
\(772\) 23.3494 0.840364
\(773\) −41.5028 −1.49275 −0.746377 0.665524i \(-0.768208\pi\)
−0.746377 + 0.665524i \(0.768208\pi\)
\(774\) 22.2796 0.800824
\(775\) 35.2322 1.26558
\(776\) −154.289 −5.53865
\(777\) −1.56206 −0.0560386
\(778\) −65.3326 −2.34229
\(779\) 43.0226 1.54144
\(780\) 82.1071 2.93991
\(781\) 4.86039 0.173919
\(782\) 47.0143 1.68123
\(783\) 15.0673 0.538461
\(784\) −109.696 −3.91772
\(785\) 12.7724 0.455866
\(786\) −84.1408 −3.00120
\(787\) −34.8188 −1.24116 −0.620578 0.784145i \(-0.713102\pi\)
−0.620578 + 0.784145i \(0.713102\pi\)
\(788\) −56.4639 −2.01144
\(789\) 40.8768 1.45525
\(790\) −86.4106 −3.07435
\(791\) 0.0705501 0.00250847
\(792\) 68.7106 2.44152
\(793\) −15.5936 −0.553745
\(794\) 18.0801 0.641638
\(795\) 43.4761 1.54194
\(796\) −19.9999 −0.708879
\(797\) −35.7960 −1.26796 −0.633980 0.773349i \(-0.718580\pi\)
−0.633980 + 0.773349i \(0.718580\pi\)
\(798\) −2.34779 −0.0831110
\(799\) 32.6966 1.15672
\(800\) −153.265 −5.41873
\(801\) −23.1887 −0.819331
\(802\) 41.9180 1.48018
\(803\) 66.0018 2.32915
\(804\) −159.386 −5.62109
\(805\) −1.61997 −0.0570963
\(806\) −30.8250 −1.08576
\(807\) −20.2653 −0.713371
\(808\) 127.353 4.48027
\(809\) −2.93962 −0.103351 −0.0516757 0.998664i \(-0.516456\pi\)
−0.0516757 + 0.998664i \(0.516456\pi\)
\(810\) 104.775 3.68143
\(811\) −26.0315 −0.914091 −0.457045 0.889443i \(-0.651092\pi\)
−0.457045 + 0.889443i \(0.651092\pi\)
\(812\) 1.80398 0.0633075
\(813\) 52.4265 1.83868
\(814\) 140.146 4.91211
\(815\) −9.18601 −0.321772
\(816\) −83.6003 −2.92660
\(817\) 32.1042 1.12318
\(818\) −10.9567 −0.383094
\(819\) −0.211718 −0.00739804
\(820\) −140.946 −4.92205
\(821\) 20.9181 0.730048 0.365024 0.930998i \(-0.381061\pi\)
0.365024 + 0.930998i \(0.381061\pi\)
\(822\) −15.8599 −0.553176
\(823\) −29.2742 −1.02043 −0.510217 0.860046i \(-0.670435\pi\)
−0.510217 + 0.860046i \(0.670435\pi\)
\(824\) −2.17544 −0.0757851
\(825\) −66.6174 −2.31932
\(826\) −0.858239 −0.0298619
\(827\) 23.2797 0.809516 0.404758 0.914424i \(-0.367356\pi\)
0.404758 + 0.914424i \(0.367356\pi\)
\(828\) 54.4907 1.89368
\(829\) 35.9960 1.25019 0.625096 0.780548i \(-0.285060\pi\)
0.625096 + 0.780548i \(0.285060\pi\)
\(830\) 48.4518 1.68179
\(831\) 19.6127 0.680357
\(832\) 69.1990 2.39905
\(833\) 17.6765 0.612453
\(834\) 18.9030 0.654557
\(835\) −26.9276 −0.931867
\(836\) 154.825 5.35474
\(837\) −17.7272 −0.612743
\(838\) 68.5643 2.36851
\(839\) 21.5665 0.744558 0.372279 0.928121i \(-0.378576\pi\)
0.372279 + 0.928121i \(0.378576\pi\)
\(840\) 4.91872 0.169712
\(841\) −7.75597 −0.267447
\(842\) 71.0496 2.44853
\(843\) 15.1695 0.522465
\(844\) 16.1386 0.555515
\(845\) −29.5639 −1.01703
\(846\) 51.5579 1.77260
\(847\) −0.890583 −0.0306008
\(848\) 95.3146 3.27312
\(849\) 60.9528 2.09189
\(850\) 45.1057 1.54711
\(851\) 71.0747 2.43641
\(852\) −11.7035 −0.400956
\(853\) 6.56556 0.224800 0.112400 0.993663i \(-0.464146\pi\)
0.112400 + 0.993663i \(0.464146\pi\)
\(854\) −1.46077 −0.0499866
\(855\) −28.2382 −0.965727
\(856\) −152.870 −5.22498
\(857\) −25.9975 −0.888057 −0.444029 0.896013i \(-0.646451\pi\)
−0.444029 + 0.896013i \(0.646451\pi\)
\(858\) 58.2842 1.98979
\(859\) 27.9677 0.954246 0.477123 0.878837i \(-0.341680\pi\)
0.477123 + 0.878837i \(0.341680\pi\)
\(860\) −105.176 −3.58649
\(861\) 1.11517 0.0380048
\(862\) −13.9565 −0.475359
\(863\) −19.9730 −0.679889 −0.339944 0.940446i \(-0.610408\pi\)
−0.339944 + 0.940446i \(0.610408\pi\)
\(864\) 77.1157 2.62353
\(865\) 48.5566 1.65097
\(866\) 17.6428 0.599528
\(867\) −22.3918 −0.760466
\(868\) −2.12245 −0.0720408
\(869\) −45.0855 −1.52942
\(870\) 90.5775 3.07087
\(871\) −28.1775 −0.954759
\(872\) −31.0350 −1.05098
\(873\) 22.9596 0.777064
\(874\) 106.826 3.61344
\(875\) −0.358120 −0.0121067
\(876\) −158.928 −5.36969
\(877\) 6.70562 0.226433 0.113216 0.993570i \(-0.463885\pi\)
0.113216 + 0.993570i \(0.463885\pi\)
\(878\) 28.9585 0.977302
\(879\) −20.8149 −0.702070
\(880\) −258.444 −8.71215
\(881\) −9.70235 −0.326880 −0.163440 0.986553i \(-0.552259\pi\)
−0.163440 + 0.986553i \(0.552259\pi\)
\(882\) 27.8733 0.938543
\(883\) 39.7784 1.33865 0.669325 0.742970i \(-0.266583\pi\)
0.669325 + 0.742970i \(0.266583\pi\)
\(884\) −29.0064 −0.975590
\(885\) −31.6734 −1.06469
\(886\) 90.9156 3.05437
\(887\) 2.06359 0.0692885 0.0346442 0.999400i \(-0.488970\pi\)
0.0346442 + 0.999400i \(0.488970\pi\)
\(888\) −215.805 −7.24194
\(889\) −0.0395185 −0.00132541
\(890\) 148.932 4.99220
\(891\) 54.6675 1.83143
\(892\) −33.0071 −1.10516
\(893\) 74.2933 2.48613
\(894\) 117.482 3.92920
\(895\) 48.8961 1.63442
\(896\) 3.15386 0.105363
\(897\) 29.5587 0.986936
\(898\) −92.7543 −3.09525
\(899\) −24.9944 −0.833609
\(900\) 52.2786 1.74262
\(901\) −15.3590 −0.511683
\(902\) −100.051 −3.33135
\(903\) 0.832159 0.0276925
\(904\) 9.74679 0.324173
\(905\) −52.2749 −1.73768
\(906\) −58.4457 −1.94173
\(907\) −17.4025 −0.577841 −0.288921 0.957353i \(-0.593296\pi\)
−0.288921 + 0.957353i \(0.593296\pi\)
\(908\) 39.2108 1.30126
\(909\) −18.9513 −0.628574
\(910\) 1.35979 0.0450764
\(911\) −30.5724 −1.01291 −0.506455 0.862267i \(-0.669044\pi\)
−0.506455 + 0.862267i \(0.669044\pi\)
\(912\) −189.957 −6.29011
\(913\) 25.2801 0.836650
\(914\) 23.7597 0.785900
\(915\) −53.9100 −1.78221
\(916\) −122.590 −4.05049
\(917\) −1.02423 −0.0338229
\(918\) −22.6951 −0.749049
\(919\) 50.4772 1.66509 0.832544 0.553958i \(-0.186883\pi\)
0.832544 + 0.553958i \(0.186883\pi\)
\(920\) −223.805 −7.37863
\(921\) −12.7643 −0.420599
\(922\) 27.0926 0.892246
\(923\) −2.06905 −0.0681035
\(924\) 4.01315 0.132023
\(925\) 68.1894 2.24205
\(926\) −27.2767 −0.896368
\(927\) 0.323725 0.0106325
\(928\) 108.729 3.56920
\(929\) −23.5744 −0.773452 −0.386726 0.922195i \(-0.626394\pi\)
−0.386726 + 0.922195i \(0.626394\pi\)
\(930\) −106.568 −3.49449
\(931\) 40.1645 1.31634
\(932\) −128.929 −4.22322
\(933\) −66.8218 −2.18765
\(934\) 85.5436 2.79907
\(935\) 41.6458 1.36196
\(936\) −29.2498 −0.956059
\(937\) 11.9325 0.389819 0.194909 0.980821i \(-0.437559\pi\)
0.194909 + 0.980821i \(0.437559\pi\)
\(938\) −2.63960 −0.0861861
\(939\) 3.86799 0.126227
\(940\) −243.392 −7.93857
\(941\) 7.70366 0.251132 0.125566 0.992085i \(-0.459925\pi\)
0.125566 + 0.992085i \(0.459925\pi\)
\(942\) −21.8317 −0.711316
\(943\) −50.7409 −1.65235
\(944\) −69.4390 −2.26005
\(945\) 0.782002 0.0254385
\(946\) −74.6601 −2.42741
\(947\) −28.5590 −0.928043 −0.464022 0.885824i \(-0.653594\pi\)
−0.464022 + 0.885824i \(0.653594\pi\)
\(948\) 108.563 3.52596
\(949\) −28.0967 −0.912057
\(950\) 102.489 3.32519
\(951\) 1.45046 0.0470342
\(952\) −1.73766 −0.0563180
\(953\) −30.7035 −0.994584 −0.497292 0.867583i \(-0.665672\pi\)
−0.497292 + 0.867583i \(0.665672\pi\)
\(954\) −24.2190 −0.784120
\(955\) 56.3286 1.82275
\(956\) −57.8789 −1.87194
\(957\) 47.2596 1.52768
\(958\) −8.81935 −0.284940
\(959\) −0.193058 −0.00623417
\(960\) 239.234 7.72124
\(961\) −1.59320 −0.0513935
\(962\) −59.6595 −1.92350
\(963\) 22.7484 0.733056
\(964\) 124.749 4.01789
\(965\) 14.2709 0.459398
\(966\) 2.76899 0.0890908
\(967\) −56.8044 −1.82671 −0.913353 0.407169i \(-0.866516\pi\)
−0.913353 + 0.407169i \(0.866516\pi\)
\(968\) −123.038 −3.95458
\(969\) 30.6097 0.983326
\(970\) −147.460 −4.73467
\(971\) 28.8651 0.926326 0.463163 0.886273i \(-0.346714\pi\)
0.463163 + 0.886273i \(0.346714\pi\)
\(972\) −77.2289 −2.47712
\(973\) 0.230102 0.00737672
\(974\) −97.9978 −3.14005
\(975\) 28.3587 0.908207
\(976\) −118.189 −3.78315
\(977\) −38.7301 −1.23909 −0.619543 0.784962i \(-0.712682\pi\)
−0.619543 + 0.784962i \(0.712682\pi\)
\(978\) 15.7015 0.502080
\(979\) 77.7064 2.48351
\(980\) −131.583 −4.20326
\(981\) 4.61828 0.147450
\(982\) −41.9959 −1.34014
\(983\) −26.2927 −0.838608 −0.419304 0.907846i \(-0.637726\pi\)
−0.419304 + 0.907846i \(0.637726\pi\)
\(984\) 154.065 4.91142
\(985\) −34.5102 −1.09959
\(986\) −31.9988 −1.01905
\(987\) 1.92572 0.0612964
\(988\) −65.9084 −2.09683
\(989\) −37.8637 −1.20400
\(990\) 65.6695 2.08711
\(991\) 35.5457 1.12915 0.564573 0.825383i \(-0.309041\pi\)
0.564573 + 0.825383i \(0.309041\pi\)
\(992\) −127.923 −4.06157
\(993\) −35.4213 −1.12406
\(994\) −0.193823 −0.00614771
\(995\) −12.2238 −0.387519
\(996\) −60.8730 −1.92884
\(997\) 31.8339 1.00819 0.504095 0.863648i \(-0.331826\pi\)
0.504095 + 0.863648i \(0.331826\pi\)
\(998\) −75.3497 −2.38515
\(999\) −34.3097 −1.08551
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 \(a_p\))