Properties

Label 6001.2.a.b.1.1
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.79736 q^{2}\) \(+1.48474 q^{3}\) \(+5.82522 q^{4}\) \(+0.639507 q^{5}\) \(-4.15334 q^{6}\) \(+0.101329 q^{7}\) \(-10.7005 q^{8}\) \(-0.795561 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.79736 q^{2}\) \(+1.48474 q^{3}\) \(+5.82522 q^{4}\) \(+0.639507 q^{5}\) \(-4.15334 q^{6}\) \(+0.101329 q^{7}\) \(-10.7005 q^{8}\) \(-0.795561 q^{9}\) \(-1.78893 q^{10}\) \(-3.15797 q^{11}\) \(+8.64890 q^{12}\) \(-1.87733 q^{13}\) \(-0.283453 q^{14}\) \(+0.949499 q^{15}\) \(+18.2827 q^{16}\) \(+1.00000 q^{17}\) \(+2.22547 q^{18}\) \(+3.76627 q^{19}\) \(+3.72527 q^{20}\) \(+0.150446 q^{21}\) \(+8.83396 q^{22}\) \(+4.51994 q^{23}\) \(-15.8874 q^{24}\) \(-4.59103 q^{25}\) \(+5.25155 q^{26}\) \(-5.63540 q^{27}\) \(+0.590261 q^{28}\) \(+3.83813 q^{29}\) \(-2.65609 q^{30}\) \(+2.57699 q^{31}\) \(-29.7423 q^{32}\) \(-4.68874 q^{33}\) \(-2.79736 q^{34}\) \(+0.0648004 q^{35}\) \(-4.63432 q^{36}\) \(-1.98047 q^{37}\) \(-10.5356 q^{38}\) \(-2.78733 q^{39}\) \(-6.84305 q^{40}\) \(-3.78408 q^{41}\) \(-0.420852 q^{42}\) \(+3.02029 q^{43}\) \(-18.3958 q^{44}\) \(-0.508767 q^{45}\) \(-12.6439 q^{46}\) \(+8.87393 q^{47}\) \(+27.1450 q^{48}\) \(-6.98973 q^{49}\) \(+12.8428 q^{50}\) \(+1.48474 q^{51}\) \(-10.9358 q^{52}\) \(-7.39587 q^{53}\) \(+15.7642 q^{54}\) \(-2.01954 q^{55}\) \(-1.08427 q^{56}\) \(+5.59191 q^{57}\) \(-10.7366 q^{58}\) \(-7.61184 q^{59}\) \(+5.53104 q^{60}\) \(-1.42549 q^{61}\) \(-7.20877 q^{62}\) \(-0.0806132 q^{63}\) \(+46.6344 q^{64}\) \(-1.20056 q^{65}\) \(+13.1161 q^{66}\) \(+6.79364 q^{67}\) \(+5.82522 q^{68}\) \(+6.71091 q^{69}\) \(-0.181270 q^{70}\) \(+3.66082 q^{71}\) \(+8.51291 q^{72}\) \(+4.12875 q^{73}\) \(+5.54010 q^{74}\) \(-6.81646 q^{75}\) \(+21.9393 q^{76}\) \(-0.319992 q^{77}\) \(+7.79717 q^{78}\) \(+15.2849 q^{79}\) \(+11.6919 q^{80}\) \(-5.98040 q^{81}\) \(+10.5854 q^{82}\) \(-4.12323 q^{83}\) \(+0.876382 q^{84}\) \(+0.639507 q^{85}\) \(-8.44885 q^{86}\) \(+5.69860 q^{87}\) \(+33.7918 q^{88}\) \(-17.2913 q^{89}\) \(+1.42320 q^{90}\) \(-0.190227 q^{91}\) \(+26.3296 q^{92}\) \(+3.82615 q^{93}\) \(-24.8236 q^{94}\) \(+2.40856 q^{95}\) \(-44.1594 q^{96}\) \(-6.63908 q^{97}\) \(+19.5528 q^{98}\) \(+2.51236 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79736 −1.97803 −0.989016 0.147811i \(-0.952777\pi\)
−0.989016 + 0.147811i \(0.952777\pi\)
\(3\) 1.48474 0.857212 0.428606 0.903491i \(-0.359005\pi\)
0.428606 + 0.903491i \(0.359005\pi\)
\(4\) 5.82522 2.91261
\(5\) 0.639507 0.285996 0.142998 0.989723i \(-0.454326\pi\)
0.142998 + 0.989723i \(0.454326\pi\)
\(6\) −4.15334 −1.69559
\(7\) 0.101329 0.0382986 0.0191493 0.999817i \(-0.493904\pi\)
0.0191493 + 0.999817i \(0.493904\pi\)
\(8\) −10.7005 −3.78320
\(9\) −0.795561 −0.265187
\(10\) −1.78893 −0.565710
\(11\) −3.15797 −0.952162 −0.476081 0.879401i \(-0.657943\pi\)
−0.476081 + 0.879401i \(0.657943\pi\)
\(12\) 8.64890 2.49672
\(13\) −1.87733 −0.520677 −0.260338 0.965517i \(-0.583834\pi\)
−0.260338 + 0.965517i \(0.583834\pi\)
\(14\) −0.283453 −0.0757559
\(15\) 0.949499 0.245160
\(16\) 18.2827 4.57068
\(17\) 1.00000 0.242536
\(18\) 2.22547 0.524549
\(19\) 3.76627 0.864041 0.432020 0.901864i \(-0.357801\pi\)
0.432020 + 0.901864i \(0.357801\pi\)
\(20\) 3.72527 0.832995
\(21\) 0.150446 0.0328301
\(22\) 8.83396 1.88341
\(23\) 4.51994 0.942472 0.471236 0.882007i \(-0.343808\pi\)
0.471236 + 0.882007i \(0.343808\pi\)
\(24\) −15.8874 −3.24300
\(25\) −4.59103 −0.918206
\(26\) 5.25155 1.02991
\(27\) −5.63540 −1.08453
\(28\) 0.590261 0.111549
\(29\) 3.83813 0.712722 0.356361 0.934348i \(-0.384017\pi\)
0.356361 + 0.934348i \(0.384017\pi\)
\(30\) −2.65609 −0.484933
\(31\) 2.57699 0.462841 0.231421 0.972854i \(-0.425663\pi\)
0.231421 + 0.972854i \(0.425663\pi\)
\(32\) −29.7423 −5.25774
\(33\) −4.68874 −0.816205
\(34\) −2.79736 −0.479743
\(35\) 0.0648004 0.0109533
\(36\) −4.63432 −0.772386
\(37\) −1.98047 −0.325588 −0.162794 0.986660i \(-0.552051\pi\)
−0.162794 + 0.986660i \(0.552051\pi\)
\(38\) −10.5356 −1.70910
\(39\) −2.78733 −0.446330
\(40\) −6.84305 −1.08198
\(41\) −3.78408 −0.590975 −0.295487 0.955347i \(-0.595482\pi\)
−0.295487 + 0.955347i \(0.595482\pi\)
\(42\) −0.420852 −0.0649389
\(43\) 3.02029 0.460591 0.230295 0.973121i \(-0.426031\pi\)
0.230295 + 0.973121i \(0.426031\pi\)
\(44\) −18.3958 −2.77328
\(45\) −0.508767 −0.0758426
\(46\) −12.6439 −1.86424
\(47\) 8.87393 1.29440 0.647198 0.762322i \(-0.275941\pi\)
0.647198 + 0.762322i \(0.275941\pi\)
\(48\) 27.1450 3.91804
\(49\) −6.98973 −0.998533
\(50\) 12.8428 1.81624
\(51\) 1.48474 0.207905
\(52\) −10.9358 −1.51653
\(53\) −7.39587 −1.01590 −0.507951 0.861386i \(-0.669597\pi\)
−0.507951 + 0.861386i \(0.669597\pi\)
\(54\) 15.7642 2.14524
\(55\) −2.01954 −0.272315
\(56\) −1.08427 −0.144891
\(57\) 5.59191 0.740666
\(58\) −10.7366 −1.40979
\(59\) −7.61184 −0.990977 −0.495488 0.868615i \(-0.665011\pi\)
−0.495488 + 0.868615i \(0.665011\pi\)
\(60\) 5.53104 0.714054
\(61\) −1.42549 −0.182515 −0.0912577 0.995827i \(-0.529089\pi\)
−0.0912577 + 0.995827i \(0.529089\pi\)
\(62\) −7.20877 −0.915514
\(63\) −0.0806132 −0.0101563
\(64\) 46.6344 5.82931
\(65\) −1.20056 −0.148912
\(66\) 13.1161 1.61448
\(67\) 6.79364 0.829975 0.414987 0.909827i \(-0.363786\pi\)
0.414987 + 0.909827i \(0.363786\pi\)
\(68\) 5.82522 0.706411
\(69\) 6.71091 0.807899
\(70\) −0.181270 −0.0216659
\(71\) 3.66082 0.434459 0.217230 0.976121i \(-0.430298\pi\)
0.217230 + 0.976121i \(0.430298\pi\)
\(72\) 8.51291 1.00326
\(73\) 4.12875 0.483234 0.241617 0.970372i \(-0.422322\pi\)
0.241617 + 0.970372i \(0.422322\pi\)
\(74\) 5.54010 0.644023
\(75\) −6.81646 −0.787097
\(76\) 21.9393 2.51661
\(77\) −0.319992 −0.0364665
\(78\) 7.79717 0.882855
\(79\) 15.2849 1.71968 0.859842 0.510561i \(-0.170562\pi\)
0.859842 + 0.510561i \(0.170562\pi\)
\(80\) 11.6919 1.30720
\(81\) −5.98040 −0.664489
\(82\) 10.5854 1.16897
\(83\) −4.12323 −0.452583 −0.226292 0.974060i \(-0.572660\pi\)
−0.226292 + 0.974060i \(0.572660\pi\)
\(84\) 0.876382 0.0956211
\(85\) 0.639507 0.0693643
\(86\) −8.44885 −0.911063
\(87\) 5.69860 0.610954
\(88\) 33.7918 3.60222
\(89\) −17.2913 −1.83287 −0.916437 0.400179i \(-0.868948\pi\)
−0.916437 + 0.400179i \(0.868948\pi\)
\(90\) 1.42320 0.150019
\(91\) −0.190227 −0.0199412
\(92\) 26.3296 2.74505
\(93\) 3.82615 0.396753
\(94\) −24.8236 −2.56036
\(95\) 2.40856 0.247113
\(96\) −44.1594 −4.50700
\(97\) −6.63908 −0.674096 −0.337048 0.941487i \(-0.609429\pi\)
−0.337048 + 0.941487i \(0.609429\pi\)
\(98\) 19.5528 1.97513
\(99\) 2.51236 0.252501
\(100\) −26.7437 −2.67437
\(101\) −14.8755 −1.48017 −0.740084 0.672515i \(-0.765214\pi\)
−0.740084 + 0.672515i \(0.765214\pi\)
\(102\) −4.15334 −0.411242
\(103\) 18.2938 1.80254 0.901270 0.433258i \(-0.142636\pi\)
0.901270 + 0.433258i \(0.142636\pi\)
\(104\) 20.0883 1.96982
\(105\) 0.0962115 0.00938928
\(106\) 20.6889 2.00948
\(107\) 4.22880 0.408814 0.204407 0.978886i \(-0.434473\pi\)
0.204407 + 0.978886i \(0.434473\pi\)
\(108\) −32.8274 −3.15882
\(109\) −1.26827 −0.121478 −0.0607389 0.998154i \(-0.519346\pi\)
−0.0607389 + 0.998154i \(0.519346\pi\)
\(110\) 5.64938 0.538648
\(111\) −2.94048 −0.279098
\(112\) 1.85256 0.175051
\(113\) −5.59199 −0.526050 −0.263025 0.964789i \(-0.584720\pi\)
−0.263025 + 0.964789i \(0.584720\pi\)
\(114\) −15.6426 −1.46506
\(115\) 2.89053 0.269544
\(116\) 22.3579 2.07588
\(117\) 1.49353 0.138077
\(118\) 21.2930 1.96018
\(119\) 0.101329 0.00928878
\(120\) −10.1601 −0.927487
\(121\) −1.02725 −0.0933866
\(122\) 3.98761 0.361021
\(123\) −5.61836 −0.506591
\(124\) 15.0115 1.34807
\(125\) −6.13353 −0.548600
\(126\) 0.225504 0.0200895
\(127\) 1.30542 0.115837 0.0579184 0.998321i \(-0.481554\pi\)
0.0579184 + 0.998321i \(0.481554\pi\)
\(128\) −70.9687 −6.27281
\(129\) 4.48434 0.394824
\(130\) 3.35841 0.294552
\(131\) −12.0900 −1.05631 −0.528155 0.849148i \(-0.677116\pi\)
−0.528155 + 0.849148i \(0.677116\pi\)
\(132\) −27.3129 −2.37729
\(133\) 0.381631 0.0330916
\(134\) −19.0042 −1.64172
\(135\) −3.60388 −0.310173
\(136\) −10.7005 −0.917560
\(137\) −13.1154 −1.12052 −0.560262 0.828315i \(-0.689300\pi\)
−0.560262 + 0.828315i \(0.689300\pi\)
\(138\) −18.7728 −1.59805
\(139\) 8.02261 0.680469 0.340234 0.940341i \(-0.389494\pi\)
0.340234 + 0.940341i \(0.389494\pi\)
\(140\) 0.377476 0.0319026
\(141\) 13.1754 1.10957
\(142\) −10.2406 −0.859374
\(143\) 5.92853 0.495769
\(144\) −14.5450 −1.21208
\(145\) 2.45451 0.203836
\(146\) −11.5496 −0.955852
\(147\) −10.3779 −0.855955
\(148\) −11.5367 −0.948310
\(149\) 6.49004 0.531685 0.265842 0.964017i \(-0.414350\pi\)
0.265842 + 0.964017i \(0.414350\pi\)
\(150\) 19.0681 1.55690
\(151\) −6.29066 −0.511926 −0.255963 0.966687i \(-0.582393\pi\)
−0.255963 + 0.966687i \(0.582393\pi\)
\(152\) −40.3009 −3.26884
\(153\) −0.795561 −0.0643173
\(154\) 0.895134 0.0721319
\(155\) 1.64800 0.132371
\(156\) −16.2368 −1.29999
\(157\) −4.61294 −0.368153 −0.184076 0.982912i \(-0.558929\pi\)
−0.184076 + 0.982912i \(0.558929\pi\)
\(158\) −42.7573 −3.40159
\(159\) −10.9809 −0.870843
\(160\) −19.0204 −1.50370
\(161\) 0.457999 0.0360954
\(162\) 16.7293 1.31438
\(163\) −14.3112 −1.12094 −0.560469 0.828175i \(-0.689379\pi\)
−0.560469 + 0.828175i \(0.689379\pi\)
\(164\) −22.0431 −1.72128
\(165\) −2.99849 −0.233432
\(166\) 11.5342 0.895224
\(167\) 13.7503 1.06403 0.532014 0.846735i \(-0.321435\pi\)
0.532014 + 0.846735i \(0.321435\pi\)
\(168\) −1.60985 −0.124203
\(169\) −9.47565 −0.728896
\(170\) −1.78893 −0.137205
\(171\) −2.99630 −0.229133
\(172\) 17.5939 1.34152
\(173\) −2.84904 −0.216608 −0.108304 0.994118i \(-0.534542\pi\)
−0.108304 + 0.994118i \(0.534542\pi\)
\(174\) −15.9410 −1.20849
\(175\) −0.465203 −0.0351660
\(176\) −57.7362 −4.35203
\(177\) −11.3016 −0.849478
\(178\) 48.3700 3.62548
\(179\) −16.7721 −1.25361 −0.626804 0.779177i \(-0.715637\pi\)
−0.626804 + 0.779177i \(0.715637\pi\)
\(180\) −2.96368 −0.220900
\(181\) 8.92632 0.663488 0.331744 0.943369i \(-0.392363\pi\)
0.331744 + 0.943369i \(0.392363\pi\)
\(182\) 0.532133 0.0394443
\(183\) −2.11648 −0.156454
\(184\) −48.3656 −3.56556
\(185\) −1.26653 −0.0931170
\(186\) −10.7031 −0.784790
\(187\) −3.15797 −0.230933
\(188\) 51.6926 3.77007
\(189\) −0.571028 −0.0415362
\(190\) −6.73759 −0.488796
\(191\) −11.9926 −0.867754 −0.433877 0.900972i \(-0.642855\pi\)
−0.433877 + 0.900972i \(0.642855\pi\)
\(192\) 69.2398 4.99695
\(193\) −6.64884 −0.478594 −0.239297 0.970946i \(-0.576917\pi\)
−0.239297 + 0.970946i \(0.576917\pi\)
\(194\) 18.5719 1.33338
\(195\) −1.78252 −0.127649
\(196\) −40.7167 −2.90834
\(197\) 11.5746 0.824654 0.412327 0.911036i \(-0.364716\pi\)
0.412327 + 0.911036i \(0.364716\pi\)
\(198\) −7.02796 −0.499455
\(199\) −15.4792 −1.09729 −0.548644 0.836056i \(-0.684856\pi\)
−0.548644 + 0.836056i \(0.684856\pi\)
\(200\) 49.1263 3.47376
\(201\) 10.0868 0.711465
\(202\) 41.6121 2.92782
\(203\) 0.388912 0.0272963
\(204\) 8.64890 0.605544
\(205\) −2.41995 −0.169017
\(206\) −51.1743 −3.56548
\(207\) −3.59589 −0.249931
\(208\) −34.3226 −2.37984
\(209\) −11.8937 −0.822707
\(210\) −0.269138 −0.0185723
\(211\) 12.0398 0.828856 0.414428 0.910082i \(-0.363982\pi\)
0.414428 + 0.910082i \(0.363982\pi\)
\(212\) −43.0825 −2.95892
\(213\) 5.43535 0.372424
\(214\) −11.8295 −0.808646
\(215\) 1.93150 0.131727
\(216\) 60.3016 4.10301
\(217\) 0.261123 0.0177262
\(218\) 3.54779 0.240287
\(219\) 6.13011 0.414234
\(220\) −11.7643 −0.793147
\(221\) −1.87733 −0.126283
\(222\) 8.22558 0.552065
\(223\) −14.7568 −0.988185 −0.494093 0.869409i \(-0.664500\pi\)
−0.494093 + 0.869409i \(0.664500\pi\)
\(224\) −3.01375 −0.201364
\(225\) 3.65245 0.243496
\(226\) 15.6428 1.04054
\(227\) −22.6487 −1.50325 −0.751625 0.659591i \(-0.770730\pi\)
−0.751625 + 0.659591i \(0.770730\pi\)
\(228\) 32.5741 2.15727
\(229\) 8.72949 0.576861 0.288430 0.957501i \(-0.406867\pi\)
0.288430 + 0.957501i \(0.406867\pi\)
\(230\) −8.08586 −0.533166
\(231\) −0.475104 −0.0312596
\(232\) −41.0699 −2.69637
\(233\) −9.24232 −0.605485 −0.302742 0.953072i \(-0.597902\pi\)
−0.302742 + 0.953072i \(0.597902\pi\)
\(234\) −4.17793 −0.273120
\(235\) 5.67494 0.370192
\(236\) −44.3406 −2.88633
\(237\) 22.6940 1.47413
\(238\) −0.283453 −0.0183735
\(239\) −12.8169 −0.829056 −0.414528 0.910037i \(-0.636053\pi\)
−0.414528 + 0.910037i \(0.636053\pi\)
\(240\) 17.3594 1.12055
\(241\) −25.0976 −1.61668 −0.808340 0.588717i \(-0.799633\pi\)
−0.808340 + 0.588717i \(0.799633\pi\)
\(242\) 2.87360 0.184722
\(243\) 8.02690 0.514926
\(244\) −8.30379 −0.531596
\(245\) −4.46999 −0.285577
\(246\) 15.7166 1.00205
\(247\) −7.07051 −0.449886
\(248\) −27.5751 −1.75102
\(249\) −6.12191 −0.387960
\(250\) 17.1577 1.08515
\(251\) −15.4669 −0.976265 −0.488133 0.872769i \(-0.662322\pi\)
−0.488133 + 0.872769i \(0.662322\pi\)
\(252\) −0.469589 −0.0295813
\(253\) −14.2738 −0.897387
\(254\) −3.65172 −0.229129
\(255\) 0.949499 0.0594599
\(256\) 105.256 6.57850
\(257\) −7.82671 −0.488217 −0.244109 0.969748i \(-0.578495\pi\)
−0.244109 + 0.969748i \(0.578495\pi\)
\(258\) −12.5443 −0.780974
\(259\) −0.200679 −0.0124696
\(260\) −6.99354 −0.433721
\(261\) −3.05347 −0.189005
\(262\) 33.8201 2.08942
\(263\) −7.16826 −0.442014 −0.221007 0.975272i \(-0.570934\pi\)
−0.221007 + 0.975272i \(0.570934\pi\)
\(264\) 50.1719 3.08787
\(265\) −4.72971 −0.290544
\(266\) −1.06756 −0.0654562
\(267\) −25.6730 −1.57116
\(268\) 39.5744 2.41739
\(269\) −3.27187 −0.199490 −0.0997449 0.995013i \(-0.531803\pi\)
−0.0997449 + 0.995013i \(0.531803\pi\)
\(270\) 10.0814 0.613531
\(271\) 10.5903 0.643313 0.321656 0.946857i \(-0.395760\pi\)
0.321656 + 0.946857i \(0.395760\pi\)
\(272\) 18.2827 1.10855
\(273\) −0.282437 −0.0170938
\(274\) 36.6885 2.21643
\(275\) 14.4983 0.874281
\(276\) 39.0925 2.35309
\(277\) 24.1277 1.44969 0.724846 0.688911i \(-0.241911\pi\)
0.724846 + 0.688911i \(0.241911\pi\)
\(278\) −22.4421 −1.34599
\(279\) −2.05015 −0.122740
\(280\) −0.693397 −0.0414384
\(281\) 3.25958 0.194450 0.0972250 0.995262i \(-0.469003\pi\)
0.0972250 + 0.995262i \(0.469003\pi\)
\(282\) −36.8564 −2.19477
\(283\) 12.9396 0.769180 0.384590 0.923088i \(-0.374343\pi\)
0.384590 + 0.923088i \(0.374343\pi\)
\(284\) 21.3251 1.26541
\(285\) 3.57607 0.211828
\(286\) −16.5842 −0.980646
\(287\) −0.383436 −0.0226335
\(288\) 23.6618 1.39429
\(289\) 1.00000 0.0588235
\(290\) −6.86615 −0.403194
\(291\) −9.85728 −0.577844
\(292\) 24.0509 1.40747
\(293\) −12.5905 −0.735544 −0.367772 0.929916i \(-0.619879\pi\)
−0.367772 + 0.929916i \(0.619879\pi\)
\(294\) 29.0307 1.69311
\(295\) −4.86783 −0.283416
\(296\) 21.1921 1.23176
\(297\) 17.7964 1.03265
\(298\) −18.1550 −1.05169
\(299\) −8.48540 −0.490723
\(300\) −39.7074 −2.29251
\(301\) 0.306042 0.0176400
\(302\) 17.5972 1.01261
\(303\) −22.0862 −1.26882
\(304\) 68.8576 3.94925
\(305\) −0.911612 −0.0521987
\(306\) 2.22547 0.127222
\(307\) −14.4317 −0.823661 −0.411830 0.911261i \(-0.635110\pi\)
−0.411830 + 0.911261i \(0.635110\pi\)
\(308\) −1.86403 −0.106213
\(309\) 27.1614 1.54516
\(310\) −4.61006 −0.261834
\(311\) 5.18238 0.293866 0.146933 0.989146i \(-0.453060\pi\)
0.146933 + 0.989146i \(0.453060\pi\)
\(312\) 29.8259 1.68856
\(313\) −25.7190 −1.45372 −0.726861 0.686785i \(-0.759021\pi\)
−0.726861 + 0.686785i \(0.759021\pi\)
\(314\) 12.9041 0.728218
\(315\) −0.0515527 −0.00290467
\(316\) 89.0377 5.00876
\(317\) −23.5528 −1.32286 −0.661429 0.750007i \(-0.730050\pi\)
−0.661429 + 0.750007i \(0.730050\pi\)
\(318\) 30.7175 1.72255
\(319\) −12.1207 −0.678627
\(320\) 29.8231 1.66716
\(321\) 6.27865 0.350440
\(322\) −1.28119 −0.0713978
\(323\) 3.76627 0.209561
\(324\) −34.8371 −1.93539
\(325\) 8.61886 0.478088
\(326\) 40.0335 2.21725
\(327\) −1.88304 −0.104132
\(328\) 40.4916 2.23577
\(329\) 0.899183 0.0495736
\(330\) 8.38784 0.461735
\(331\) −17.8657 −0.981987 −0.490994 0.871163i \(-0.663366\pi\)
−0.490994 + 0.871163i \(0.663366\pi\)
\(332\) −24.0187 −1.31820
\(333\) 1.57559 0.0863418
\(334\) −38.4645 −2.10468
\(335\) 4.34458 0.237370
\(336\) 2.75056 0.150056
\(337\) 17.7767 0.968356 0.484178 0.874969i \(-0.339119\pi\)
0.484178 + 0.874969i \(0.339119\pi\)
\(338\) 26.5068 1.44178
\(339\) −8.30263 −0.450937
\(340\) 3.72527 0.202031
\(341\) −8.13805 −0.440700
\(342\) 8.38172 0.453231
\(343\) −1.41756 −0.0765411
\(344\) −32.3187 −1.74251
\(345\) 4.29168 0.231056
\(346\) 7.96977 0.428458
\(347\) 20.7279 1.11273 0.556365 0.830938i \(-0.312196\pi\)
0.556365 + 0.830938i \(0.312196\pi\)
\(348\) 33.1956 1.77947
\(349\) −15.1982 −0.813540 −0.406770 0.913531i \(-0.633345\pi\)
−0.406770 + 0.913531i \(0.633345\pi\)
\(350\) 1.30134 0.0695595
\(351\) 10.5795 0.564691
\(352\) 93.9251 5.00623
\(353\) 1.00000 0.0532246
\(354\) 31.6145 1.68029
\(355\) 2.34112 0.124254
\(356\) −100.726 −5.33844
\(357\) 0.150446 0.00796246
\(358\) 46.9176 2.47967
\(359\) 11.5498 0.609575 0.304787 0.952420i \(-0.401415\pi\)
0.304787 + 0.952420i \(0.401415\pi\)
\(360\) 5.44407 0.286927
\(361\) −4.81523 −0.253433
\(362\) −24.9701 −1.31240
\(363\) −1.52520 −0.0800522
\(364\) −1.10811 −0.0580809
\(365\) 2.64037 0.138203
\(366\) 5.92054 0.309472
\(367\) 28.3479 1.47975 0.739873 0.672746i \(-0.234885\pi\)
0.739873 + 0.672746i \(0.234885\pi\)
\(368\) 82.6367 4.30774
\(369\) 3.01047 0.156719
\(370\) 3.54293 0.184188
\(371\) −0.749414 −0.0389076
\(372\) 22.2881 1.15559
\(373\) 2.18780 0.113280 0.0566400 0.998395i \(-0.481961\pi\)
0.0566400 + 0.998395i \(0.481961\pi\)
\(374\) 8.83396 0.456793
\(375\) −9.10667 −0.470267
\(376\) −94.9555 −4.89696
\(377\) −7.20542 −0.371098
\(378\) 1.59737 0.0821598
\(379\) 8.06008 0.414019 0.207009 0.978339i \(-0.433627\pi\)
0.207009 + 0.978339i \(0.433627\pi\)
\(380\) 14.0304 0.719742
\(381\) 1.93820 0.0992968
\(382\) 33.5476 1.71644
\(383\) −6.57773 −0.336106 −0.168053 0.985778i \(-0.553748\pi\)
−0.168053 + 0.985778i \(0.553748\pi\)
\(384\) −105.370 −5.37713
\(385\) −0.204638 −0.0104293
\(386\) 18.5992 0.946673
\(387\) −2.40283 −0.122143
\(388\) −38.6741 −1.96338
\(389\) −20.5918 −1.04404 −0.522022 0.852932i \(-0.674822\pi\)
−0.522022 + 0.852932i \(0.674822\pi\)
\(390\) 4.98635 0.252493
\(391\) 4.51994 0.228583
\(392\) 74.7936 3.77765
\(393\) −17.9505 −0.905482
\(394\) −32.3782 −1.63119
\(395\) 9.77479 0.491823
\(396\) 14.6350 0.735437
\(397\) −9.16305 −0.459880 −0.229940 0.973205i \(-0.573853\pi\)
−0.229940 + 0.973205i \(0.573853\pi\)
\(398\) 43.3008 2.17047
\(399\) 0.566621 0.0283665
\(400\) −83.9365 −4.19682
\(401\) −8.25806 −0.412388 −0.206194 0.978511i \(-0.566108\pi\)
−0.206194 + 0.978511i \(0.566108\pi\)
\(402\) −28.2163 −1.40730
\(403\) −4.83785 −0.240991
\(404\) −86.6530 −4.31115
\(405\) −3.82451 −0.190041
\(406\) −1.08793 −0.0539929
\(407\) 6.25427 0.310013
\(408\) −15.8874 −0.786544
\(409\) −25.9679 −1.28403 −0.642015 0.766692i \(-0.721901\pi\)
−0.642015 + 0.766692i \(0.721901\pi\)
\(410\) 6.76947 0.334320
\(411\) −19.4729 −0.960527
\(412\) 106.565 5.25009
\(413\) −0.771297 −0.0379531
\(414\) 10.0590 0.494372
\(415\) −2.63684 −0.129437
\(416\) 55.8360 2.73758
\(417\) 11.9115 0.583306
\(418\) 33.2711 1.62734
\(419\) −23.0324 −1.12521 −0.562603 0.826727i \(-0.690200\pi\)
−0.562603 + 0.826727i \(0.690200\pi\)
\(420\) 0.560453 0.0273473
\(421\) 0.885951 0.0431786 0.0215893 0.999767i \(-0.493127\pi\)
0.0215893 + 0.999767i \(0.493127\pi\)
\(422\) −33.6797 −1.63950
\(423\) −7.05976 −0.343257
\(424\) 79.1395 3.84336
\(425\) −4.59103 −0.222698
\(426\) −15.2046 −0.736666
\(427\) −0.144443 −0.00699009
\(428\) 24.6337 1.19071
\(429\) 8.80230 0.424979
\(430\) −5.40310 −0.260561
\(431\) 31.6398 1.52404 0.762018 0.647556i \(-0.224209\pi\)
0.762018 + 0.647556i \(0.224209\pi\)
\(432\) −103.030 −4.95705
\(433\) 29.4846 1.41694 0.708469 0.705742i \(-0.249386\pi\)
0.708469 + 0.705742i \(0.249386\pi\)
\(434\) −0.730455 −0.0350629
\(435\) 3.64430 0.174731
\(436\) −7.38792 −0.353817
\(437\) 17.0233 0.814334
\(438\) −17.1481 −0.819368
\(439\) −19.6191 −0.936368 −0.468184 0.883631i \(-0.655091\pi\)
−0.468184 + 0.883631i \(0.655091\pi\)
\(440\) 21.6101 1.03022
\(441\) 5.56076 0.264798
\(442\) 5.25155 0.249791
\(443\) 34.6408 1.64583 0.822917 0.568162i \(-0.192345\pi\)
0.822917 + 0.568162i \(0.192345\pi\)
\(444\) −17.1289 −0.812903
\(445\) −11.0579 −0.524195
\(446\) 41.2799 1.95466
\(447\) 9.63599 0.455767
\(448\) 4.72541 0.223254
\(449\) −17.0222 −0.803329 −0.401665 0.915787i \(-0.631568\pi\)
−0.401665 + 0.915787i \(0.631568\pi\)
\(450\) −10.2172 −0.481644
\(451\) 11.9500 0.562704
\(452\) −32.5746 −1.53218
\(453\) −9.33996 −0.438829
\(454\) 63.3567 2.97348
\(455\) −0.121652 −0.00570311
\(456\) −59.8362 −2.80209
\(457\) 0.0164250 0.000768328 0 0.000384164 1.00000i \(-0.499878\pi\)
0.000384164 1.00000i \(0.499878\pi\)
\(458\) −24.4195 −1.14105
\(459\) −5.63540 −0.263038
\(460\) 16.8380 0.785075
\(461\) 4.13999 0.192818 0.0964092 0.995342i \(-0.469264\pi\)
0.0964092 + 0.995342i \(0.469264\pi\)
\(462\) 1.32904 0.0618324
\(463\) −40.9287 −1.90212 −0.951059 0.309009i \(-0.900003\pi\)
−0.951059 + 0.309009i \(0.900003\pi\)
\(464\) 70.1714 3.25762
\(465\) 2.44685 0.113470
\(466\) 25.8541 1.19767
\(467\) 24.6218 1.13936 0.569679 0.821867i \(-0.307067\pi\)
0.569679 + 0.821867i \(0.307067\pi\)
\(468\) 8.70013 0.402163
\(469\) 0.688390 0.0317869
\(470\) −15.8749 −0.732252
\(471\) −6.84900 −0.315585
\(472\) 81.4505 3.74906
\(473\) −9.53799 −0.438557
\(474\) −63.4832 −2.91588
\(475\) −17.2910 −0.793368
\(476\) 0.590261 0.0270546
\(477\) 5.88387 0.269404
\(478\) 35.8534 1.63990
\(479\) −21.3914 −0.977397 −0.488698 0.872453i \(-0.662528\pi\)
−0.488698 + 0.872453i \(0.662528\pi\)
\(480\) −28.2403 −1.28899
\(481\) 3.71800 0.169526
\(482\) 70.2070 3.19784
\(483\) 0.680008 0.0309414
\(484\) −5.98397 −0.271999
\(485\) −4.24574 −0.192789
\(486\) −22.4541 −1.01854
\(487\) −8.73761 −0.395939 −0.197970 0.980208i \(-0.563435\pi\)
−0.197970 + 0.980208i \(0.563435\pi\)
\(488\) 15.2535 0.690492
\(489\) −21.2483 −0.960882
\(490\) 12.5042 0.564880
\(491\) 18.8899 0.852491 0.426246 0.904607i \(-0.359836\pi\)
0.426246 + 0.904607i \(0.359836\pi\)
\(492\) −32.7282 −1.47550
\(493\) 3.83813 0.172861
\(494\) 19.7788 0.889888
\(495\) 1.60667 0.0722144
\(496\) 47.1144 2.11550
\(497\) 0.370946 0.0166392
\(498\) 17.1252 0.767397
\(499\) 0.776616 0.0347661 0.0173830 0.999849i \(-0.494467\pi\)
0.0173830 + 0.999849i \(0.494467\pi\)
\(500\) −35.7292 −1.59786
\(501\) 20.4155 0.912099
\(502\) 43.2666 1.93108
\(503\) −16.2869 −0.726196 −0.363098 0.931751i \(-0.618281\pi\)
−0.363098 + 0.931751i \(0.618281\pi\)
\(504\) 0.862601 0.0384233
\(505\) −9.51299 −0.423323
\(506\) 39.9290 1.77506
\(507\) −14.0688 −0.624818
\(508\) 7.60433 0.337387
\(509\) −7.79334 −0.345434 −0.172717 0.984972i \(-0.555255\pi\)
−0.172717 + 0.984972i \(0.555255\pi\)
\(510\) −2.65609 −0.117614
\(511\) 0.418361 0.0185072
\(512\) −152.501 −6.73967
\(513\) −21.2244 −0.937082
\(514\) 21.8941 0.965709
\(515\) 11.6990 0.515520
\(516\) 26.1222 1.14997
\(517\) −28.0236 −1.23247
\(518\) 0.561371 0.0246652
\(519\) −4.23006 −0.185679
\(520\) 12.8466 0.563362
\(521\) 29.3623 1.28639 0.643194 0.765703i \(-0.277609\pi\)
0.643194 + 0.765703i \(0.277609\pi\)
\(522\) 8.54164 0.373857
\(523\) −26.8371 −1.17351 −0.586753 0.809766i \(-0.699594\pi\)
−0.586753 + 0.809766i \(0.699594\pi\)
\(524\) −70.4270 −3.07662
\(525\) −0.690703 −0.0301448
\(526\) 20.0522 0.874317
\(527\) 2.57699 0.112255
\(528\) −85.7229 −3.73061
\(529\) −2.57017 −0.111746
\(530\) 13.2307 0.574705
\(531\) 6.05568 0.262794
\(532\) 2.22308 0.0963828
\(533\) 7.10396 0.307707
\(534\) 71.8166 3.10781
\(535\) 2.70435 0.116919
\(536\) −72.6953 −3.13996
\(537\) −24.9022 −1.07461
\(538\) 9.15261 0.394597
\(539\) 22.0733 0.950766
\(540\) −20.9934 −0.903412
\(541\) 40.8138 1.75472 0.877360 0.479833i \(-0.159303\pi\)
0.877360 + 0.479833i \(0.159303\pi\)
\(542\) −29.6248 −1.27249
\(543\) 13.2532 0.568750
\(544\) −29.7423 −1.27519
\(545\) −0.811065 −0.0347422
\(546\) 0.790077 0.0338122
\(547\) 1.53872 0.0657909 0.0328955 0.999459i \(-0.489527\pi\)
0.0328955 + 0.999459i \(0.489527\pi\)
\(548\) −76.4000 −3.26365
\(549\) 1.13407 0.0484007
\(550\) −40.5570 −1.72936
\(551\) 14.4554 0.615821
\(552\) −71.8101 −3.05644
\(553\) 1.54880 0.0658615
\(554\) −67.4938 −2.86754
\(555\) −1.88046 −0.0798210
\(556\) 46.7334 1.98194
\(557\) −22.3893 −0.948666 −0.474333 0.880345i \(-0.657311\pi\)
−0.474333 + 0.880345i \(0.657311\pi\)
\(558\) 5.73502 0.242783
\(559\) −5.67008 −0.239819
\(560\) 1.18473 0.0500639
\(561\) −4.68874 −0.197959
\(562\) −9.11821 −0.384628
\(563\) 10.4811 0.441724 0.220862 0.975305i \(-0.429113\pi\)
0.220862 + 0.975305i \(0.429113\pi\)
\(564\) 76.7498 3.23175
\(565\) −3.57612 −0.150448
\(566\) −36.1967 −1.52146
\(567\) −0.605986 −0.0254490
\(568\) −39.1726 −1.64365
\(569\) 9.04933 0.379368 0.189684 0.981845i \(-0.439254\pi\)
0.189684 + 0.981845i \(0.439254\pi\)
\(570\) −10.0035 −0.419002
\(571\) −18.9933 −0.794844 −0.397422 0.917636i \(-0.630095\pi\)
−0.397422 + 0.917636i \(0.630095\pi\)
\(572\) 34.5350 1.44398
\(573\) −17.8058 −0.743849
\(574\) 1.07261 0.0447698
\(575\) −20.7512 −0.865384
\(576\) −37.1006 −1.54586
\(577\) −16.8541 −0.701646 −0.350823 0.936442i \(-0.614098\pi\)
−0.350823 + 0.936442i \(0.614098\pi\)
\(578\) −2.79736 −0.116355
\(579\) −9.87176 −0.410256
\(580\) 14.2981 0.593694
\(581\) −0.417801 −0.0173333
\(582\) 27.5743 1.14299
\(583\) 23.3559 0.967303
\(584\) −44.1797 −1.82817
\(585\) 0.955122 0.0394894
\(586\) 35.2201 1.45493
\(587\) −17.3538 −0.716269 −0.358135 0.933670i \(-0.616587\pi\)
−0.358135 + 0.933670i \(0.616587\pi\)
\(588\) −60.4535 −2.49306
\(589\) 9.70563 0.399914
\(590\) 13.6171 0.560605
\(591\) 17.1852 0.706904
\(592\) −36.2084 −1.48816
\(593\) 30.2476 1.24212 0.621059 0.783763i \(-0.286703\pi\)
0.621059 + 0.783763i \(0.286703\pi\)
\(594\) −49.7829 −2.04262
\(595\) 0.0648004 0.00265656
\(596\) 37.8059 1.54859
\(597\) −22.9825 −0.940609
\(598\) 23.7367 0.970666
\(599\) −14.7850 −0.604097 −0.302048 0.953293i \(-0.597670\pi\)
−0.302048 + 0.953293i \(0.597670\pi\)
\(600\) 72.9396 2.97775
\(601\) −31.8594 −1.29957 −0.649786 0.760117i \(-0.725142\pi\)
−0.649786 + 0.760117i \(0.725142\pi\)
\(602\) −0.856110 −0.0348925
\(603\) −5.40476 −0.220099
\(604\) −36.6444 −1.49104
\(605\) −0.656936 −0.0267082
\(606\) 61.7830 2.50976
\(607\) −32.7173 −1.32795 −0.663977 0.747753i \(-0.731133\pi\)
−0.663977 + 0.747753i \(0.731133\pi\)
\(608\) −112.017 −4.54291
\(609\) 0.577432 0.0233987
\(610\) 2.55011 0.103251
\(611\) −16.6593 −0.673961
\(612\) −4.63432 −0.187331
\(613\) 27.3628 1.10517 0.552587 0.833455i \(-0.313641\pi\)
0.552587 + 0.833455i \(0.313641\pi\)
\(614\) 40.3707 1.62923
\(615\) −3.59298 −0.144883
\(616\) 3.42408 0.137960
\(617\) 14.0799 0.566836 0.283418 0.958996i \(-0.408532\pi\)
0.283418 + 0.958996i \(0.408532\pi\)
\(618\) −75.9802 −3.05637
\(619\) −38.8920 −1.56320 −0.781601 0.623778i \(-0.785597\pi\)
−0.781601 + 0.623778i \(0.785597\pi\)
\(620\) 9.59998 0.385545
\(621\) −25.4717 −1.02214
\(622\) −14.4970 −0.581276
\(623\) −1.75210 −0.0701966
\(624\) −50.9600 −2.04003
\(625\) 19.0327 0.761308
\(626\) 71.9452 2.87551
\(627\) −17.6591 −0.705235
\(628\) −26.8714 −1.07228
\(629\) −1.98047 −0.0789667
\(630\) 0.144211 0.00574552
\(631\) 20.0506 0.798202 0.399101 0.916907i \(-0.369322\pi\)
0.399101 + 0.916907i \(0.369322\pi\)
\(632\) −163.556 −6.50590
\(633\) 17.8760 0.710506
\(634\) 65.8857 2.61666
\(635\) 0.834823 0.0331289
\(636\) −63.9662 −2.53642
\(637\) 13.1220 0.519913
\(638\) 33.9059 1.34235
\(639\) −2.91241 −0.115213
\(640\) −45.3850 −1.79400
\(641\) −4.91583 −0.194164 −0.0970819 0.995276i \(-0.530951\pi\)
−0.0970819 + 0.995276i \(0.530951\pi\)
\(642\) −17.5636 −0.693182
\(643\) 10.8734 0.428807 0.214403 0.976745i \(-0.431219\pi\)
0.214403 + 0.976745i \(0.431219\pi\)
\(644\) 2.66794 0.105132
\(645\) 2.86777 0.112918
\(646\) −10.5356 −0.414518
\(647\) 0.0316748 0.00124527 0.000622633 1.00000i \(-0.499802\pi\)
0.000622633 1.00000i \(0.499802\pi\)
\(648\) 63.9933 2.51389
\(649\) 24.0379 0.943571
\(650\) −24.1100 −0.945674
\(651\) 0.387698 0.0151951
\(652\) −83.3657 −3.26485
\(653\) 27.6432 1.08176 0.540881 0.841099i \(-0.318091\pi\)
0.540881 + 0.841099i \(0.318091\pi\)
\(654\) 5.26753 0.205977
\(655\) −7.73166 −0.302101
\(656\) −69.1833 −2.70115
\(657\) −3.28468 −0.128147
\(658\) −2.51534 −0.0980581
\(659\) 21.9828 0.856330 0.428165 0.903701i \(-0.359160\pi\)
0.428165 + 0.903701i \(0.359160\pi\)
\(660\) −17.4668 −0.679895
\(661\) −1.79999 −0.0700114 −0.0350057 0.999387i \(-0.511145\pi\)
−0.0350057 + 0.999387i \(0.511145\pi\)
\(662\) 49.9767 1.94240
\(663\) −2.78733 −0.108251
\(664\) 44.1206 1.71221
\(665\) 0.244056 0.00946407
\(666\) −4.40749 −0.170787
\(667\) 17.3481 0.671721
\(668\) 80.0984 3.09910
\(669\) −21.9099 −0.847084
\(670\) −12.1533 −0.469525
\(671\) 4.50165 0.173784
\(672\) −4.47462 −0.172612
\(673\) −37.8346 −1.45842 −0.729208 0.684292i \(-0.760111\pi\)
−0.729208 + 0.684292i \(0.760111\pi\)
\(674\) −49.7277 −1.91544
\(675\) 25.8723 0.995826
\(676\) −55.1977 −2.12299
\(677\) −15.4724 −0.594654 −0.297327 0.954776i \(-0.596095\pi\)
−0.297327 + 0.954776i \(0.596095\pi\)
\(678\) 23.2254 0.891967
\(679\) −0.672729 −0.0258170
\(680\) −6.84305 −0.262419
\(681\) −33.6274 −1.28860
\(682\) 22.7650 0.871718
\(683\) 31.2040 1.19399 0.596994 0.802246i \(-0.296362\pi\)
0.596994 + 0.802246i \(0.296362\pi\)
\(684\) −17.4541 −0.667373
\(685\) −8.38739 −0.320466
\(686\) 3.96543 0.151401
\(687\) 12.9610 0.494492
\(688\) 55.2192 2.10521
\(689\) 13.8845 0.528956
\(690\) −12.0054 −0.457036
\(691\) 33.7403 1.28354 0.641770 0.766897i \(-0.278200\pi\)
0.641770 + 0.766897i \(0.278200\pi\)
\(692\) −16.5962 −0.630895
\(693\) 0.254574 0.00967045
\(694\) −57.9833 −2.20101
\(695\) 5.13052 0.194612
\(696\) −60.9779 −2.31136
\(697\) −3.78408 −0.143332
\(698\) 42.5147 1.60921
\(699\) −13.7224 −0.519029
\(700\) −2.70991 −0.102425
\(701\) 33.8760 1.27948 0.639740 0.768591i \(-0.279042\pi\)
0.639740 + 0.768591i \(0.279042\pi\)
\(702\) −29.5946 −1.11698
\(703\) −7.45900 −0.281321
\(704\) −147.270 −5.55045
\(705\) 8.42579 0.317334
\(706\) −2.79736 −0.105280
\(707\) −1.50731 −0.0566884
\(708\) −65.8340 −2.47420
\(709\) −12.6587 −0.475407 −0.237704 0.971338i \(-0.576395\pi\)
−0.237704 + 0.971338i \(0.576395\pi\)
\(710\) −6.54895 −0.245778
\(711\) −12.1601 −0.456038
\(712\) 185.026 6.93413
\(713\) 11.6478 0.436215
\(714\) −0.420852 −0.0157500
\(715\) 3.79134 0.141788
\(716\) −97.7012 −3.65127
\(717\) −19.0297 −0.710677
\(718\) −32.3089 −1.20576
\(719\) 43.3953 1.61837 0.809185 0.587553i \(-0.199909\pi\)
0.809185 + 0.587553i \(0.199909\pi\)
\(720\) −9.30165 −0.346652
\(721\) 1.85368 0.0690348
\(722\) 13.4699 0.501299
\(723\) −37.2633 −1.38584
\(724\) 51.9977 1.93248
\(725\) −17.6210 −0.654426
\(726\) 4.26653 0.158346
\(727\) −29.4651 −1.09280 −0.546399 0.837525i \(-0.684002\pi\)
−0.546399 + 0.837525i \(0.684002\pi\)
\(728\) 2.03552 0.0754415
\(729\) 29.8590 1.10589
\(730\) −7.38606 −0.273370
\(731\) 3.02029 0.111710
\(732\) −12.3289 −0.455690
\(733\) −11.1971 −0.413574 −0.206787 0.978386i \(-0.566301\pi\)
−0.206787 + 0.978386i \(0.566301\pi\)
\(734\) −79.2992 −2.92699
\(735\) −6.63674 −0.244800
\(736\) −134.433 −4.95528
\(737\) −21.4541 −0.790271
\(738\) −8.42137 −0.309995
\(739\) −40.5346 −1.49109 −0.745544 0.666456i \(-0.767810\pi\)
−0.745544 + 0.666456i \(0.767810\pi\)
\(740\) −7.37780 −0.271213
\(741\) −10.4978 −0.385648
\(742\) 2.09638 0.0769605
\(743\) 39.3921 1.44515 0.722577 0.691290i \(-0.242957\pi\)
0.722577 + 0.691290i \(0.242957\pi\)
\(744\) −40.9417 −1.50100
\(745\) 4.15043 0.152060
\(746\) −6.12007 −0.224072
\(747\) 3.28028 0.120019
\(748\) −18.3958 −0.672618
\(749\) 0.428499 0.0156570
\(750\) 25.4746 0.930202
\(751\) −38.6038 −1.40867 −0.704337 0.709866i \(-0.748756\pi\)
−0.704337 + 0.709866i \(0.748756\pi\)
\(752\) 162.239 5.91626
\(753\) −22.9643 −0.836866
\(754\) 20.1561 0.734043
\(755\) −4.02292 −0.146409
\(756\) −3.32636 −0.120979
\(757\) −21.6946 −0.788502 −0.394251 0.919003i \(-0.628996\pi\)
−0.394251 + 0.919003i \(0.628996\pi\)
\(758\) −22.5469 −0.818942
\(759\) −21.1928 −0.769251
\(760\) −25.7728 −0.934876
\(761\) −35.2702 −1.27854 −0.639272 0.768980i \(-0.720764\pi\)
−0.639272 + 0.768980i \(0.720764\pi\)
\(762\) −5.42183 −0.196412
\(763\) −0.128512 −0.00465243
\(764\) −69.8595 −2.52743
\(765\) −0.508767 −0.0183945
\(766\) 18.4003 0.664829
\(767\) 14.2899 0.515978
\(768\) 156.277 5.63917
\(769\) −16.7477 −0.603939 −0.301969 0.953318i \(-0.597644\pi\)
−0.301969 + 0.953318i \(0.597644\pi\)
\(770\) 0.572445 0.0206295
\(771\) −11.6206 −0.418506
\(772\) −38.7309 −1.39396
\(773\) 5.05437 0.181793 0.0908965 0.995860i \(-0.471027\pi\)
0.0908965 + 0.995860i \(0.471027\pi\)
\(774\) 6.72158 0.241602
\(775\) −11.8310 −0.424984
\(776\) 71.0415 2.55024
\(777\) −0.297955 −0.0106891
\(778\) 57.6026 2.06515
\(779\) −14.2519 −0.510626
\(780\) −10.3836 −0.371791
\(781\) −11.5607 −0.413676
\(782\) −12.6439 −0.452144
\(783\) −21.6294 −0.772971
\(784\) −127.791 −4.56397
\(785\) −2.95001 −0.105290
\(786\) 50.2140 1.79107
\(787\) −6.73811 −0.240188 −0.120094 0.992763i \(-0.538320\pi\)
−0.120094 + 0.992763i \(0.538320\pi\)
\(788\) 67.4244 2.40189
\(789\) −10.6430 −0.378900
\(790\) −27.3436 −0.972842
\(791\) −0.566629 −0.0201470
\(792\) −26.8835 −0.955262
\(793\) 2.67611 0.0950315
\(794\) 25.6323 0.909658
\(795\) −7.02237 −0.249058
\(796\) −90.1695 −3.19597
\(797\) 35.9824 1.27456 0.637281 0.770631i \(-0.280059\pi\)
0.637281 + 0.770631i \(0.280059\pi\)
\(798\) −1.58504 −0.0561099
\(799\) 8.87393 0.313937
\(800\) 136.548 4.82769
\(801\) 13.7563 0.486055
\(802\) 23.1008 0.815716
\(803\) −13.0385 −0.460117
\(804\) 58.7575 2.07222
\(805\) 0.292894 0.0103232
\(806\) 13.5332 0.476687
\(807\) −4.85787 −0.171005
\(808\) 159.175 5.59977
\(809\) 47.8332 1.68173 0.840863 0.541248i \(-0.182048\pi\)
0.840863 + 0.541248i \(0.182048\pi\)
\(810\) 10.6985 0.375908
\(811\) 0.650276 0.0228343 0.0114171 0.999935i \(-0.496366\pi\)
0.0114171 + 0.999935i \(0.496366\pi\)
\(812\) 2.26550 0.0795034
\(813\) 15.7237 0.551455
\(814\) −17.4954 −0.613215
\(815\) −9.15211 −0.320584
\(816\) 27.1450 0.950264
\(817\) 11.3752 0.397969
\(818\) 72.6415 2.53985
\(819\) 0.151337 0.00528815
\(820\) −14.0967 −0.492279
\(821\) 12.3551 0.431197 0.215598 0.976482i \(-0.430830\pi\)
0.215598 + 0.976482i \(0.430830\pi\)
\(822\) 54.4727 1.89995
\(823\) 15.1516 0.528152 0.264076 0.964502i \(-0.414933\pi\)
0.264076 + 0.964502i \(0.414933\pi\)
\(824\) −195.753 −6.81937
\(825\) 21.5262 0.749445
\(826\) 2.15760 0.0750723
\(827\) −57.4000 −1.99599 −0.997997 0.0632634i \(-0.979849\pi\)
−0.997997 + 0.0632634i \(0.979849\pi\)
\(828\) −20.9468 −0.727952
\(829\) 41.3553 1.43633 0.718164 0.695874i \(-0.244983\pi\)
0.718164 + 0.695874i \(0.244983\pi\)
\(830\) 7.37618 0.256031
\(831\) 35.8232 1.24269
\(832\) −87.5481 −3.03518
\(833\) −6.98973 −0.242180
\(834\) −33.3206 −1.15380
\(835\) 8.79341 0.304308
\(836\) −69.2836 −2.39622
\(837\) −14.5224 −0.501967
\(838\) 64.4299 2.22569
\(839\) −54.2565 −1.87314 −0.936572 0.350476i \(-0.886020\pi\)
−0.936572 + 0.350476i \(0.886020\pi\)
\(840\) −1.02951 −0.0355215
\(841\) −14.2688 −0.492027
\(842\) −2.47832 −0.0854087
\(843\) 4.83961 0.166685
\(844\) 70.1346 2.41413
\(845\) −6.05975 −0.208462
\(846\) 19.7487 0.678973
\(847\) −0.104090 −0.00357658
\(848\) −135.217 −4.64336
\(849\) 19.2119 0.659350
\(850\) 12.8428 0.440503
\(851\) −8.95162 −0.306858
\(852\) 31.6621 1.08472
\(853\) −0.841557 −0.0288144 −0.0144072 0.999896i \(-0.504586\pi\)
−0.0144072 + 0.999896i \(0.504586\pi\)
\(854\) 0.404059 0.0138266
\(855\) −1.91615 −0.0655311
\(856\) −45.2503 −1.54662
\(857\) 27.3452 0.934094 0.467047 0.884232i \(-0.345318\pi\)
0.467047 + 0.884232i \(0.345318\pi\)
\(858\) −24.6232 −0.840622
\(859\) −32.1697 −1.09762 −0.548808 0.835948i \(-0.684918\pi\)
−0.548808 + 0.835948i \(0.684918\pi\)
\(860\) 11.2514 0.383670
\(861\) −0.569301 −0.0194017
\(862\) −88.5079 −3.01459
\(863\) −23.4200 −0.797227 −0.398614 0.917119i \(-0.630509\pi\)
−0.398614 + 0.917119i \(0.630509\pi\)
\(864\) 167.610 5.70220
\(865\) −1.82198 −0.0619491
\(866\) −82.4789 −2.80275
\(867\) 1.48474 0.0504242
\(868\) 1.52110 0.0516294
\(869\) −48.2691 −1.63742
\(870\) −10.1944 −0.345623
\(871\) −12.7539 −0.432148
\(872\) 13.5711 0.459575
\(873\) 5.28180 0.178762
\(874\) −47.6203 −1.61078
\(875\) −0.621503 −0.0210106
\(876\) 35.7092 1.20650
\(877\) −3.77327 −0.127414 −0.0637072 0.997969i \(-0.520292\pi\)
−0.0637072 + 0.997969i \(0.520292\pi\)
\(878\) 54.8816 1.85216
\(879\) −18.6935 −0.630517
\(880\) −36.9227 −1.24466
\(881\) −15.7213 −0.529665 −0.264833 0.964294i \(-0.585317\pi\)
−0.264833 + 0.964294i \(0.585317\pi\)
\(882\) −15.5554 −0.523779
\(883\) −31.1139 −1.04707 −0.523533 0.852005i \(-0.675386\pi\)
−0.523533 + 0.852005i \(0.675386\pi\)
\(884\) −10.9358 −0.367812
\(885\) −7.22743 −0.242947
\(886\) −96.9027 −3.25551
\(887\) 1.90150 0.0638461 0.0319230 0.999490i \(-0.489837\pi\)
0.0319230 + 0.999490i \(0.489837\pi\)
\(888\) 31.4646 1.05588
\(889\) 0.132276 0.00443639
\(890\) 30.9329 1.03687
\(891\) 18.8859 0.632701
\(892\) −85.9613 −2.87820
\(893\) 33.4216 1.11841
\(894\) −26.9553 −0.901520
\(895\) −10.7259 −0.358527
\(896\) −7.19116 −0.240240
\(897\) −12.5986 −0.420654
\(898\) 47.6173 1.58901
\(899\) 9.89082 0.329877
\(900\) 21.2763 0.709210
\(901\) −7.39587 −0.246392
\(902\) −33.4285 −1.11305
\(903\) 0.454392 0.0151212
\(904\) 59.8371 1.99015
\(905\) 5.70845 0.189755
\(906\) 26.1272 0.868018
\(907\) 35.8434 1.19016 0.595080 0.803667i \(-0.297120\pi\)
0.595080 + 0.803667i \(0.297120\pi\)
\(908\) −131.934 −4.37838
\(909\) 11.8344 0.392521
\(910\) 0.340303 0.0112809
\(911\) −8.28538 −0.274507 −0.137253 0.990536i \(-0.543827\pi\)
−0.137253 + 0.990536i \(0.543827\pi\)
\(912\) 102.235 3.38535
\(913\) 13.0210 0.430933
\(914\) −0.0459465 −0.00151978
\(915\) −1.35350 −0.0447454
\(916\) 50.8511 1.68017
\(917\) −1.22507 −0.0404553
\(918\) 15.7642 0.520298
\(919\) 38.7336 1.27770 0.638852 0.769329i \(-0.279410\pi\)
0.638852 + 0.769329i \(0.279410\pi\)
\(920\) −30.9302 −1.01974
\(921\) −21.4273 −0.706052
\(922\) −11.5810 −0.381401
\(923\) −6.87255 −0.226213
\(924\) −2.76758 −0.0910468
\(925\) 9.09242 0.298957
\(926\) 114.492 3.76245
\(927\) −14.5538 −0.478010
\(928\) −114.155 −3.74731
\(929\) 40.3157 1.32272 0.661358 0.750070i \(-0.269980\pi\)
0.661358 + 0.750070i \(0.269980\pi\)
\(930\) −6.84472 −0.224447
\(931\) −26.3252 −0.862774
\(932\) −53.8385 −1.76354
\(933\) 7.69447 0.251906
\(934\) −68.8759 −2.25369
\(935\) −2.01954 −0.0660461
\(936\) −15.9815 −0.522372
\(937\) −28.0304 −0.915714 −0.457857 0.889026i \(-0.651383\pi\)
−0.457857 + 0.889026i \(0.651383\pi\)
\(938\) −1.92567 −0.0628755
\(939\) −38.1858 −1.24615
\(940\) 33.0578 1.07823
\(941\) −25.3400 −0.826061 −0.413031 0.910717i \(-0.635530\pi\)
−0.413031 + 0.910717i \(0.635530\pi\)
\(942\) 19.1591 0.624237
\(943\) −17.1038 −0.556977
\(944\) −139.165 −4.52944
\(945\) −0.365177 −0.0118792
\(946\) 26.6812 0.867480
\(947\) 26.5795 0.863718 0.431859 0.901941i \(-0.357858\pi\)
0.431859 + 0.901941i \(0.357858\pi\)
\(948\) 132.197 4.29357
\(949\) −7.75102 −0.251609
\(950\) 48.3693 1.56931
\(951\) −34.9697 −1.13397
\(952\) −1.08427 −0.0351413
\(953\) 2.22132 0.0719557 0.0359778 0.999353i \(-0.488545\pi\)
0.0359778 + 0.999353i \(0.488545\pi\)
\(954\) −16.4593 −0.532889
\(955\) −7.66935 −0.248174
\(956\) −74.6611 −2.41471
\(957\) −17.9960 −0.581728
\(958\) 59.8393 1.93332
\(959\) −1.32897 −0.0429145
\(960\) 44.2794 1.42911
\(961\) −24.3591 −0.785778
\(962\) −10.4006 −0.335328
\(963\) −3.36427 −0.108412
\(964\) −146.199 −4.70875
\(965\) −4.25198 −0.136876
\(966\) −1.90223 −0.0612031
\(967\) 39.8654 1.28198 0.640992 0.767548i \(-0.278523\pi\)
0.640992 + 0.767548i \(0.278523\pi\)
\(968\) 10.9921 0.353300
\(969\) 5.59191 0.179638
\(970\) 11.8769 0.381343
\(971\) −32.3206 −1.03722 −0.518608 0.855012i \(-0.673550\pi\)
−0.518608 + 0.855012i \(0.673550\pi\)
\(972\) 46.7585 1.49978
\(973\) 0.812920 0.0260610
\(974\) 24.4422 0.783180
\(975\) 12.7967 0.409823
\(976\) −26.0618 −0.834219
\(977\) 28.1171 0.899547 0.449773 0.893143i \(-0.351505\pi\)
0.449773 + 0.893143i \(0.351505\pi\)
\(978\) 59.4392 1.90066
\(979\) 54.6053 1.74519
\(980\) −26.0386 −0.831774
\(981\) 1.00898 0.0322144
\(982\) −52.8420 −1.68625
\(983\) 38.9016 1.24077 0.620385 0.784298i \(-0.286977\pi\)
0.620385 + 0.784298i \(0.286977\pi\)
\(984\) 60.1193 1.91653
\(985\) 7.40202 0.235848
\(986\) −10.7366 −0.341924
\(987\) 1.33505 0.0424951
\(988\) −41.1873 −1.31034
\(989\) 13.6515 0.434094
\(990\) −4.49443 −0.142842
\(991\) −46.4117 −1.47431 −0.737157 0.675721i \(-0.763832\pi\)
−0.737157 + 0.675721i \(0.763832\pi\)
\(992\) −76.6456 −2.43350
\(993\) −26.5258 −0.841771
\(994\) −1.03767 −0.0329128
\(995\) −9.89904 −0.313821
\(996\) −35.6614 −1.12998
\(997\) −1.56609 −0.0495985 −0.0247993 0.999692i \(-0.507895\pi\)
−0.0247993 + 0.999692i \(0.507895\pi\)
\(998\) −2.17247 −0.0687684
\(999\) 11.1608 0.353111
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 \(a_p\))