Properties

Label 6026.2.a.i.1.2
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.94469 q^{3}\) \(+1.00000 q^{4}\) \(-3.10338 q^{5}\) \(+2.94469 q^{6}\) \(+2.18728 q^{7}\) \(-1.00000 q^{8}\) \(+5.67118 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.94469 q^{3}\) \(+1.00000 q^{4}\) \(-3.10338 q^{5}\) \(+2.94469 q^{6}\) \(+2.18728 q^{7}\) \(-1.00000 q^{8}\) \(+5.67118 q^{9}\) \(+3.10338 q^{10}\) \(+3.62591 q^{11}\) \(-2.94469 q^{12}\) \(+2.36826 q^{13}\) \(-2.18728 q^{14}\) \(+9.13847 q^{15}\) \(+1.00000 q^{16}\) \(+2.10389 q^{17}\) \(-5.67118 q^{18}\) \(-7.83273 q^{19}\) \(-3.10338 q^{20}\) \(-6.44085 q^{21}\) \(-3.62591 q^{22}\) \(+1.00000 q^{23}\) \(+2.94469 q^{24}\) \(+4.63094 q^{25}\) \(-2.36826 q^{26}\) \(-7.86580 q^{27}\) \(+2.18728 q^{28}\) \(-6.98856 q^{29}\) \(-9.13847 q^{30}\) \(+8.62487 q^{31}\) \(-1.00000 q^{32}\) \(-10.6772 q^{33}\) \(-2.10389 q^{34}\) \(-6.78794 q^{35}\) \(+5.67118 q^{36}\) \(-3.55379 q^{37}\) \(+7.83273 q^{38}\) \(-6.97379 q^{39}\) \(+3.10338 q^{40}\) \(+8.94001 q^{41}\) \(+6.44085 q^{42}\) \(-6.48678 q^{43}\) \(+3.62591 q^{44}\) \(-17.5998 q^{45}\) \(-1.00000 q^{46}\) \(-5.16620 q^{47}\) \(-2.94469 q^{48}\) \(-2.21582 q^{49}\) \(-4.63094 q^{50}\) \(-6.19531 q^{51}\) \(+2.36826 q^{52}\) \(-0.484015 q^{53}\) \(+7.86580 q^{54}\) \(-11.2526 q^{55}\) \(-2.18728 q^{56}\) \(+23.0649 q^{57}\) \(+6.98856 q^{58}\) \(-2.97827 q^{59}\) \(+9.13847 q^{60}\) \(-12.4970 q^{61}\) \(-8.62487 q^{62}\) \(+12.4045 q^{63}\) \(+1.00000 q^{64}\) \(-7.34961 q^{65}\) \(+10.6772 q^{66}\) \(+2.65610 q^{67}\) \(+2.10389 q^{68}\) \(-2.94469 q^{69}\) \(+6.78794 q^{70}\) \(+11.1030 q^{71}\) \(-5.67118 q^{72}\) \(+3.40502 q^{73}\) \(+3.55379 q^{74}\) \(-13.6367 q^{75}\) \(-7.83273 q^{76}\) \(+7.93088 q^{77}\) \(+6.97379 q^{78}\) \(-17.7107 q^{79}\) \(-3.10338 q^{80}\) \(+6.14878 q^{81}\) \(-8.94001 q^{82}\) \(+12.1133 q^{83}\) \(-6.44085 q^{84}\) \(-6.52917 q^{85}\) \(+6.48678 q^{86}\) \(+20.5791 q^{87}\) \(-3.62591 q^{88}\) \(+10.4427 q^{89}\) \(+17.5998 q^{90}\) \(+5.18005 q^{91}\) \(+1.00000 q^{92}\) \(-25.3976 q^{93}\) \(+5.16620 q^{94}\) \(+24.3079 q^{95}\) \(+2.94469 q^{96}\) \(-10.9363 q^{97}\) \(+2.21582 q^{98}\) \(+20.5632 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.94469 −1.70012 −0.850058 0.526689i \(-0.823433\pi\)
−0.850058 + 0.526689i \(0.823433\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.10338 −1.38787 −0.693936 0.720037i \(-0.744125\pi\)
−0.693936 + 0.720037i \(0.744125\pi\)
\(6\) 2.94469 1.20216
\(7\) 2.18728 0.826713 0.413357 0.910569i \(-0.364356\pi\)
0.413357 + 0.910569i \(0.364356\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.67118 1.89039
\(10\) 3.10338 0.981373
\(11\) 3.62591 1.09325 0.546627 0.837376i \(-0.315912\pi\)
0.546627 + 0.837376i \(0.315912\pi\)
\(12\) −2.94469 −0.850058
\(13\) 2.36826 0.656838 0.328419 0.944532i \(-0.393484\pi\)
0.328419 + 0.944532i \(0.393484\pi\)
\(14\) −2.18728 −0.584575
\(15\) 9.13847 2.35954
\(16\) 1.00000 0.250000
\(17\) 2.10389 0.510269 0.255135 0.966906i \(-0.417880\pi\)
0.255135 + 0.966906i \(0.417880\pi\)
\(18\) −5.67118 −1.33671
\(19\) −7.83273 −1.79695 −0.898475 0.439024i \(-0.855324\pi\)
−0.898475 + 0.439024i \(0.855324\pi\)
\(20\) −3.10338 −0.693936
\(21\) −6.44085 −1.40551
\(22\) −3.62591 −0.773047
\(23\) 1.00000 0.208514
\(24\) 2.94469 0.601082
\(25\) 4.63094 0.926188
\(26\) −2.36826 −0.464454
\(27\) −7.86580 −1.51377
\(28\) 2.18728 0.413357
\(29\) −6.98856 −1.29774 −0.648871 0.760898i \(-0.724759\pi\)
−0.648871 + 0.760898i \(0.724759\pi\)
\(30\) −9.13847 −1.66845
\(31\) 8.62487 1.54907 0.774537 0.632529i \(-0.217983\pi\)
0.774537 + 0.632529i \(0.217983\pi\)
\(32\) −1.00000 −0.176777
\(33\) −10.6772 −1.85866
\(34\) −2.10389 −0.360815
\(35\) −6.78794 −1.14737
\(36\) 5.67118 0.945197
\(37\) −3.55379 −0.584240 −0.292120 0.956382i \(-0.594361\pi\)
−0.292120 + 0.956382i \(0.594361\pi\)
\(38\) 7.83273 1.27064
\(39\) −6.97379 −1.11670
\(40\) 3.10338 0.490687
\(41\) 8.94001 1.39620 0.698098 0.716003i \(-0.254030\pi\)
0.698098 + 0.716003i \(0.254030\pi\)
\(42\) 6.44085 0.993845
\(43\) −6.48678 −0.989225 −0.494612 0.869114i \(-0.664690\pi\)
−0.494612 + 0.869114i \(0.664690\pi\)
\(44\) 3.62591 0.546627
\(45\) −17.5998 −2.62363
\(46\) −1.00000 −0.147442
\(47\) −5.16620 −0.753567 −0.376784 0.926301i \(-0.622970\pi\)
−0.376784 + 0.926301i \(0.622970\pi\)
\(48\) −2.94469 −0.425029
\(49\) −2.21582 −0.316545
\(50\) −4.63094 −0.654913
\(51\) −6.19531 −0.867517
\(52\) 2.36826 0.328419
\(53\) −0.484015 −0.0664845 −0.0332423 0.999447i \(-0.510583\pi\)
−0.0332423 + 0.999447i \(0.510583\pi\)
\(54\) 7.86580 1.07040
\(55\) −11.2526 −1.51730
\(56\) −2.18728 −0.292287
\(57\) 23.0649 3.05502
\(58\) 6.98856 0.917643
\(59\) −2.97827 −0.387737 −0.193869 0.981027i \(-0.562104\pi\)
−0.193869 + 0.981027i \(0.562104\pi\)
\(60\) 9.13847 1.17977
\(61\) −12.4970 −1.60008 −0.800042 0.599945i \(-0.795189\pi\)
−0.800042 + 0.599945i \(0.795189\pi\)
\(62\) −8.62487 −1.09536
\(63\) 12.4045 1.56281
\(64\) 1.00000 0.125000
\(65\) −7.34961 −0.911607
\(66\) 10.6772 1.31427
\(67\) 2.65610 0.324494 0.162247 0.986750i \(-0.448126\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(68\) 2.10389 0.255135
\(69\) −2.94469 −0.354499
\(70\) 6.78794 0.811314
\(71\) 11.1030 1.31769 0.658845 0.752279i \(-0.271045\pi\)
0.658845 + 0.752279i \(0.271045\pi\)
\(72\) −5.67118 −0.668356
\(73\) 3.40502 0.398527 0.199264 0.979946i \(-0.436145\pi\)
0.199264 + 0.979946i \(0.436145\pi\)
\(74\) 3.55379 0.413120
\(75\) −13.6367 −1.57463
\(76\) −7.83273 −0.898475
\(77\) 7.93088 0.903808
\(78\) 6.97379 0.789627
\(79\) −17.7107 −1.99261 −0.996303 0.0859104i \(-0.972620\pi\)
−0.996303 + 0.0859104i \(0.972620\pi\)
\(80\) −3.10338 −0.346968
\(81\) 6.14878 0.683198
\(82\) −8.94001 −0.987259
\(83\) 12.1133 1.32961 0.664805 0.747017i \(-0.268515\pi\)
0.664805 + 0.747017i \(0.268515\pi\)
\(84\) −6.44085 −0.702754
\(85\) −6.52917 −0.708188
\(86\) 6.48678 0.699487
\(87\) 20.5791 2.20631
\(88\) −3.62591 −0.386524
\(89\) 10.4427 1.10692 0.553461 0.832875i \(-0.313307\pi\)
0.553461 + 0.832875i \(0.313307\pi\)
\(90\) 17.5998 1.85518
\(91\) 5.18005 0.543017
\(92\) 1.00000 0.104257
\(93\) −25.3976 −2.63360
\(94\) 5.16620 0.532853
\(95\) 24.3079 2.49394
\(96\) 2.94469 0.300541
\(97\) −10.9363 −1.11042 −0.555208 0.831712i \(-0.687361\pi\)
−0.555208 + 0.831712i \(0.687361\pi\)
\(98\) 2.21582 0.223831
\(99\) 20.5632 2.06668
\(100\) 4.63094 0.463094
\(101\) 2.37124 0.235947 0.117973 0.993017i \(-0.462360\pi\)
0.117973 + 0.993017i \(0.462360\pi\)
\(102\) 6.19531 0.613427
\(103\) 5.46826 0.538803 0.269402 0.963028i \(-0.413174\pi\)
0.269402 + 0.963028i \(0.413174\pi\)
\(104\) −2.36826 −0.232227
\(105\) 19.9884 1.95067
\(106\) 0.484015 0.0470117
\(107\) −10.6025 −1.02498 −0.512490 0.858693i \(-0.671277\pi\)
−0.512490 + 0.858693i \(0.671277\pi\)
\(108\) −7.86580 −0.756887
\(109\) −8.89287 −0.851783 −0.425891 0.904774i \(-0.640039\pi\)
−0.425891 + 0.904774i \(0.640039\pi\)
\(110\) 11.2526 1.07289
\(111\) 10.4648 0.993276
\(112\) 2.18728 0.206678
\(113\) 17.5993 1.65560 0.827800 0.561024i \(-0.189592\pi\)
0.827800 + 0.561024i \(0.189592\pi\)
\(114\) −23.0649 −2.16023
\(115\) −3.10338 −0.289391
\(116\) −6.98856 −0.648871
\(117\) 13.4309 1.24168
\(118\) 2.97827 0.274172
\(119\) 4.60180 0.421846
\(120\) −9.13847 −0.834224
\(121\) 2.14725 0.195204
\(122\) 12.4970 1.13143
\(123\) −26.3255 −2.37369
\(124\) 8.62487 0.774537
\(125\) 1.14534 0.102442
\(126\) −12.4045 −1.10508
\(127\) 6.05866 0.537619 0.268809 0.963193i \(-0.413370\pi\)
0.268809 + 0.963193i \(0.413370\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 19.1015 1.68180
\(130\) 7.34961 0.644603
\(131\) 1.00000 0.0873704
\(132\) −10.6772 −0.929329
\(133\) −17.1323 −1.48556
\(134\) −2.65610 −0.229452
\(135\) 24.4105 2.10092
\(136\) −2.10389 −0.180407
\(137\) 4.99231 0.426522 0.213261 0.976995i \(-0.431592\pi\)
0.213261 + 0.976995i \(0.431592\pi\)
\(138\) 2.94469 0.250668
\(139\) 17.5415 1.48785 0.743925 0.668263i \(-0.232962\pi\)
0.743925 + 0.668263i \(0.232962\pi\)
\(140\) −6.78794 −0.573686
\(141\) 15.2128 1.28115
\(142\) −11.1030 −0.931747
\(143\) 8.58711 0.718091
\(144\) 5.67118 0.472599
\(145\) 21.6881 1.80110
\(146\) −3.40502 −0.281801
\(147\) 6.52489 0.538164
\(148\) −3.55379 −0.292120
\(149\) 15.8629 1.29954 0.649768 0.760132i \(-0.274866\pi\)
0.649768 + 0.760132i \(0.274866\pi\)
\(150\) 13.6367 1.11343
\(151\) −14.8429 −1.20790 −0.603949 0.797023i \(-0.706407\pi\)
−0.603949 + 0.797023i \(0.706407\pi\)
\(152\) 7.83273 0.635318
\(153\) 11.9316 0.964610
\(154\) −7.93088 −0.639088
\(155\) −26.7662 −2.14991
\(156\) −6.97379 −0.558350
\(157\) 20.9546 1.67236 0.836179 0.548457i \(-0.184785\pi\)
0.836179 + 0.548457i \(0.184785\pi\)
\(158\) 17.7107 1.40899
\(159\) 1.42527 0.113031
\(160\) 3.10338 0.245343
\(161\) 2.18728 0.172382
\(162\) −6.14878 −0.483094
\(163\) −15.9931 −1.25268 −0.626339 0.779551i \(-0.715447\pi\)
−0.626339 + 0.779551i \(0.715447\pi\)
\(164\) 8.94001 0.698098
\(165\) 33.1353 2.57958
\(166\) −12.1133 −0.940176
\(167\) 17.4060 1.34692 0.673460 0.739224i \(-0.264807\pi\)
0.673460 + 0.739224i \(0.264807\pi\)
\(168\) 6.44085 0.496922
\(169\) −7.39133 −0.568564
\(170\) 6.52917 0.500765
\(171\) −44.4208 −3.39695
\(172\) −6.48678 −0.494612
\(173\) −6.34656 −0.482520 −0.241260 0.970461i \(-0.577561\pi\)
−0.241260 + 0.970461i \(0.577561\pi\)
\(174\) −20.5791 −1.56010
\(175\) 10.1291 0.765692
\(176\) 3.62591 0.273313
\(177\) 8.77007 0.659199
\(178\) −10.4427 −0.782711
\(179\) −19.4219 −1.45166 −0.725832 0.687872i \(-0.758545\pi\)
−0.725832 + 0.687872i \(0.758545\pi\)
\(180\) −17.5998 −1.31181
\(181\) 1.49109 0.110832 0.0554160 0.998463i \(-0.482351\pi\)
0.0554160 + 0.998463i \(0.482351\pi\)
\(182\) −5.18005 −0.383971
\(183\) 36.7999 2.72033
\(184\) −1.00000 −0.0737210
\(185\) 11.0288 0.810850
\(186\) 25.3976 1.86224
\(187\) 7.62854 0.557854
\(188\) −5.16620 −0.376784
\(189\) −17.2047 −1.25146
\(190\) −24.3079 −1.76348
\(191\) 10.1041 0.731110 0.365555 0.930790i \(-0.380879\pi\)
0.365555 + 0.930790i \(0.380879\pi\)
\(192\) −2.94469 −0.212515
\(193\) 5.66583 0.407835 0.203918 0.978988i \(-0.434632\pi\)
0.203918 + 0.978988i \(0.434632\pi\)
\(194\) 10.9363 0.785182
\(195\) 21.6423 1.54984
\(196\) −2.21582 −0.158273
\(197\) 16.5679 1.18042 0.590208 0.807251i \(-0.299046\pi\)
0.590208 + 0.807251i \(0.299046\pi\)
\(198\) −20.5632 −1.46136
\(199\) −18.5510 −1.31505 −0.657523 0.753435i \(-0.728396\pi\)
−0.657523 + 0.753435i \(0.728396\pi\)
\(200\) −4.63094 −0.327457
\(201\) −7.82137 −0.551677
\(202\) −2.37124 −0.166840
\(203\) −15.2859 −1.07286
\(204\) −6.19531 −0.433759
\(205\) −27.7442 −1.93774
\(206\) −5.46826 −0.380992
\(207\) 5.67118 0.394175
\(208\) 2.36826 0.164209
\(209\) −28.4008 −1.96452
\(210\) −19.9884 −1.37933
\(211\) −11.4540 −0.788527 −0.394264 0.918997i \(-0.629000\pi\)
−0.394264 + 0.918997i \(0.629000\pi\)
\(212\) −0.484015 −0.0332423
\(213\) −32.6950 −2.24023
\(214\) 10.6025 0.724770
\(215\) 20.1309 1.37292
\(216\) 7.86580 0.535200
\(217\) 18.8650 1.28064
\(218\) 8.89287 0.602301
\(219\) −10.0267 −0.677543
\(220\) −11.2526 −0.758648
\(221\) 4.98257 0.335164
\(222\) −10.4648 −0.702352
\(223\) 12.2575 0.820825 0.410412 0.911900i \(-0.365385\pi\)
0.410412 + 0.911900i \(0.365385\pi\)
\(224\) −2.18728 −0.146144
\(225\) 26.2629 1.75086
\(226\) −17.5993 −1.17069
\(227\) 19.0016 1.26118 0.630589 0.776117i \(-0.282813\pi\)
0.630589 + 0.776117i \(0.282813\pi\)
\(228\) 23.0649 1.52751
\(229\) 11.8474 0.782895 0.391448 0.920200i \(-0.371974\pi\)
0.391448 + 0.920200i \(0.371974\pi\)
\(230\) 3.10338 0.204631
\(231\) −23.3540 −1.53658
\(232\) 6.98856 0.458821
\(233\) −16.5439 −1.08383 −0.541914 0.840434i \(-0.682300\pi\)
−0.541914 + 0.840434i \(0.682300\pi\)
\(234\) −13.4309 −0.878002
\(235\) 16.0326 1.04585
\(236\) −2.97827 −0.193869
\(237\) 52.1524 3.38766
\(238\) −4.60180 −0.298290
\(239\) 4.23998 0.274261 0.137131 0.990553i \(-0.456212\pi\)
0.137131 + 0.990553i \(0.456212\pi\)
\(240\) 9.13847 0.589886
\(241\) −12.1426 −0.782176 −0.391088 0.920353i \(-0.627901\pi\)
−0.391088 + 0.920353i \(0.627901\pi\)
\(242\) −2.14725 −0.138030
\(243\) 5.49117 0.352259
\(244\) −12.4970 −0.800042
\(245\) 6.87651 0.439324
\(246\) 26.3255 1.67846
\(247\) −18.5500 −1.18031
\(248\) −8.62487 −0.547680
\(249\) −35.6700 −2.26049
\(250\) −1.14534 −0.0724376
\(251\) −16.9133 −1.06756 −0.533778 0.845625i \(-0.679228\pi\)
−0.533778 + 0.845625i \(0.679228\pi\)
\(252\) 12.4045 0.781407
\(253\) 3.62591 0.227959
\(254\) −6.05866 −0.380154
\(255\) 19.2264 1.20400
\(256\) 1.00000 0.0625000
\(257\) −24.8346 −1.54914 −0.774569 0.632489i \(-0.782033\pi\)
−0.774569 + 0.632489i \(0.782033\pi\)
\(258\) −19.1015 −1.18921
\(259\) −7.77313 −0.482999
\(260\) −7.34961 −0.455803
\(261\) −39.6334 −2.45325
\(262\) −1.00000 −0.0617802
\(263\) −27.7018 −1.70817 −0.854084 0.520135i \(-0.825882\pi\)
−0.854084 + 0.520135i \(0.825882\pi\)
\(264\) 10.6772 0.657135
\(265\) 1.50208 0.0922720
\(266\) 17.1323 1.05045
\(267\) −30.7504 −1.88189
\(268\) 2.65610 0.162247
\(269\) −8.55168 −0.521405 −0.260703 0.965419i \(-0.583954\pi\)
−0.260703 + 0.965419i \(0.583954\pi\)
\(270\) −24.4105 −1.48558
\(271\) 5.58610 0.339331 0.169666 0.985502i \(-0.445731\pi\)
0.169666 + 0.985502i \(0.445731\pi\)
\(272\) 2.10389 0.127567
\(273\) −15.2536 −0.923191
\(274\) −4.99231 −0.301596
\(275\) 16.7914 1.01256
\(276\) −2.94469 −0.177249
\(277\) −24.9240 −1.49754 −0.748768 0.662832i \(-0.769354\pi\)
−0.748768 + 0.662832i \(0.769354\pi\)
\(278\) −17.5415 −1.05207
\(279\) 48.9133 2.92836
\(280\) 6.78794 0.405657
\(281\) −30.8789 −1.84208 −0.921041 0.389466i \(-0.872660\pi\)
−0.921041 + 0.389466i \(0.872660\pi\)
\(282\) −15.2128 −0.905911
\(283\) 11.5982 0.689442 0.344721 0.938705i \(-0.387974\pi\)
0.344721 + 0.938705i \(0.387974\pi\)
\(284\) 11.1030 0.658845
\(285\) −71.5791 −4.23998
\(286\) −8.58711 −0.507767
\(287\) 19.5543 1.15425
\(288\) −5.67118 −0.334178
\(289\) −12.5736 −0.739625
\(290\) −21.6881 −1.27357
\(291\) 32.2040 1.88783
\(292\) 3.40502 0.199264
\(293\) 27.0359 1.57945 0.789726 0.613460i \(-0.210223\pi\)
0.789726 + 0.613460i \(0.210223\pi\)
\(294\) −6.52489 −0.380539
\(295\) 9.24268 0.538130
\(296\) 3.55379 0.206560
\(297\) −28.5207 −1.65494
\(298\) −15.8629 −0.918911
\(299\) 2.36826 0.136960
\(300\) −13.6367 −0.787313
\(301\) −14.1884 −0.817805
\(302\) 14.8429 0.854113
\(303\) −6.98255 −0.401137
\(304\) −7.83273 −0.449238
\(305\) 38.7830 2.22071
\(306\) −11.9316 −0.682083
\(307\) −8.64534 −0.493416 −0.246708 0.969090i \(-0.579349\pi\)
−0.246708 + 0.969090i \(0.579349\pi\)
\(308\) 7.93088 0.451904
\(309\) −16.1023 −0.916028
\(310\) 26.7662 1.52022
\(311\) −20.8347 −1.18142 −0.590712 0.806882i \(-0.701153\pi\)
−0.590712 + 0.806882i \(0.701153\pi\)
\(312\) 6.97379 0.394813
\(313\) −26.6602 −1.50692 −0.753461 0.657493i \(-0.771617\pi\)
−0.753461 + 0.657493i \(0.771617\pi\)
\(314\) −20.9546 −1.18254
\(315\) −38.4957 −2.16899
\(316\) −17.7107 −0.996303
\(317\) −28.7093 −1.61248 −0.806238 0.591592i \(-0.798500\pi\)
−0.806238 + 0.591592i \(0.798500\pi\)
\(318\) −1.42527 −0.0799253
\(319\) −25.3399 −1.41876
\(320\) −3.10338 −0.173484
\(321\) 31.2210 1.74258
\(322\) −2.18728 −0.121892
\(323\) −16.4792 −0.916929
\(324\) 6.14878 0.341599
\(325\) 10.9673 0.608355
\(326\) 15.9931 0.885777
\(327\) 26.1867 1.44813
\(328\) −8.94001 −0.493630
\(329\) −11.2999 −0.622984
\(330\) −33.1353 −1.82404
\(331\) 27.2290 1.49664 0.748322 0.663336i \(-0.230860\pi\)
0.748322 + 0.663336i \(0.230860\pi\)
\(332\) 12.1133 0.664805
\(333\) −20.1542 −1.10444
\(334\) −17.4060 −0.952416
\(335\) −8.24286 −0.450356
\(336\) −6.44085 −0.351377
\(337\) 32.8194 1.78779 0.893893 0.448280i \(-0.147963\pi\)
0.893893 + 0.448280i \(0.147963\pi\)
\(338\) 7.39133 0.402035
\(339\) −51.8243 −2.81471
\(340\) −6.52917 −0.354094
\(341\) 31.2730 1.69353
\(342\) 44.4208 2.40200
\(343\) −20.1575 −1.08841
\(344\) 6.48678 0.349744
\(345\) 9.13847 0.491999
\(346\) 6.34656 0.341193
\(347\) −8.08355 −0.433948 −0.216974 0.976177i \(-0.569619\pi\)
−0.216974 + 0.976177i \(0.569619\pi\)
\(348\) 20.5791 1.10316
\(349\) 11.8759 0.635703 0.317852 0.948140i \(-0.397039\pi\)
0.317852 + 0.948140i \(0.397039\pi\)
\(350\) −10.1291 −0.541426
\(351\) −18.6283 −0.994304
\(352\) −3.62591 −0.193262
\(353\) 8.38985 0.446547 0.223273 0.974756i \(-0.428326\pi\)
0.223273 + 0.974756i \(0.428326\pi\)
\(354\) −8.77007 −0.466124
\(355\) −34.4569 −1.82878
\(356\) 10.4427 0.553461
\(357\) −13.5509 −0.717188
\(358\) 19.4219 1.02648
\(359\) −35.4681 −1.87193 −0.935967 0.352087i \(-0.885472\pi\)
−0.935967 + 0.352087i \(0.885472\pi\)
\(360\) 17.5998 0.927592
\(361\) 42.3516 2.22903
\(362\) −1.49109 −0.0783701
\(363\) −6.32297 −0.331870
\(364\) 5.18005 0.271508
\(365\) −10.5671 −0.553105
\(366\) −36.7999 −1.92356
\(367\) 0.676424 0.0353091 0.0176545 0.999844i \(-0.494380\pi\)
0.0176545 + 0.999844i \(0.494380\pi\)
\(368\) 1.00000 0.0521286
\(369\) 50.7005 2.63936
\(370\) −11.0288 −0.573357
\(371\) −1.05867 −0.0549637
\(372\) −25.3976 −1.31680
\(373\) 6.07299 0.314447 0.157224 0.987563i \(-0.449746\pi\)
0.157224 + 0.987563i \(0.449746\pi\)
\(374\) −7.62854 −0.394462
\(375\) −3.37266 −0.174164
\(376\) 5.16620 0.266426
\(377\) −16.5507 −0.852406
\(378\) 17.2047 0.884914
\(379\) 36.2852 1.86384 0.931922 0.362659i \(-0.118131\pi\)
0.931922 + 0.362659i \(0.118131\pi\)
\(380\) 24.3079 1.24697
\(381\) −17.8409 −0.914015
\(382\) −10.1041 −0.516973
\(383\) 0.322645 0.0164864 0.00824320 0.999966i \(-0.497376\pi\)
0.00824320 + 0.999966i \(0.497376\pi\)
\(384\) 2.94469 0.150270
\(385\) −24.6125 −1.25437
\(386\) −5.66583 −0.288383
\(387\) −36.7877 −1.87003
\(388\) −10.9363 −0.555208
\(389\) 26.8223 1.35995 0.679973 0.733237i \(-0.261992\pi\)
0.679973 + 0.733237i \(0.261992\pi\)
\(390\) −21.6423 −1.09590
\(391\) 2.10389 0.106399
\(392\) 2.21582 0.111916
\(393\) −2.94469 −0.148540
\(394\) −16.5679 −0.834680
\(395\) 54.9628 2.76548
\(396\) 20.5632 1.03334
\(397\) 9.55849 0.479727 0.239863 0.970807i \(-0.422897\pi\)
0.239863 + 0.970807i \(0.422897\pi\)
\(398\) 18.5510 0.929877
\(399\) 50.4494 2.52563
\(400\) 4.63094 0.231547
\(401\) −5.91647 −0.295455 −0.147727 0.989028i \(-0.547196\pi\)
−0.147727 + 0.989028i \(0.547196\pi\)
\(402\) 7.82137 0.390095
\(403\) 20.4260 1.01749
\(404\) 2.37124 0.117973
\(405\) −19.0820 −0.948191
\(406\) 15.2859 0.758627
\(407\) −12.8857 −0.638722
\(408\) 6.19531 0.306714
\(409\) −32.3124 −1.59775 −0.798873 0.601499i \(-0.794570\pi\)
−0.798873 + 0.601499i \(0.794570\pi\)
\(410\) 27.7442 1.37019
\(411\) −14.7008 −0.725136
\(412\) 5.46826 0.269402
\(413\) −6.51430 −0.320548
\(414\) −5.67118 −0.278724
\(415\) −37.5922 −1.84533
\(416\) −2.36826 −0.116114
\(417\) −51.6542 −2.52952
\(418\) 28.4008 1.38913
\(419\) 21.7720 1.06363 0.531817 0.846859i \(-0.321510\pi\)
0.531817 + 0.846859i \(0.321510\pi\)
\(420\) 19.9884 0.975333
\(421\) 36.4888 1.77836 0.889179 0.457560i \(-0.151276\pi\)
0.889179 + 0.457560i \(0.151276\pi\)
\(422\) 11.4540 0.557573
\(423\) −29.2985 −1.42454
\(424\) 0.484015 0.0235058
\(425\) 9.74300 0.472605
\(426\) 32.6950 1.58408
\(427\) −27.3345 −1.32281
\(428\) −10.6025 −0.512490
\(429\) −25.2864 −1.22084
\(430\) −20.1309 −0.970799
\(431\) 4.27848 0.206087 0.103044 0.994677i \(-0.467142\pi\)
0.103044 + 0.994677i \(0.467142\pi\)
\(432\) −7.86580 −0.378444
\(433\) 33.7058 1.61980 0.809900 0.586569i \(-0.199522\pi\)
0.809900 + 0.586569i \(0.199522\pi\)
\(434\) −18.8650 −0.905549
\(435\) −63.8647 −3.06208
\(436\) −8.89287 −0.425891
\(437\) −7.83273 −0.374690
\(438\) 10.0267 0.479095
\(439\) −20.8215 −0.993757 −0.496879 0.867820i \(-0.665521\pi\)
−0.496879 + 0.867820i \(0.665521\pi\)
\(440\) 11.2526 0.536445
\(441\) −12.5663 −0.598395
\(442\) −4.98257 −0.236997
\(443\) −14.9194 −0.708842 −0.354421 0.935086i \(-0.615322\pi\)
−0.354421 + 0.935086i \(0.615322\pi\)
\(444\) 10.4648 0.496638
\(445\) −32.4075 −1.53626
\(446\) −12.2575 −0.580411
\(447\) −46.7112 −2.20936
\(448\) 2.18728 0.103339
\(449\) −26.4598 −1.24871 −0.624357 0.781139i \(-0.714639\pi\)
−0.624357 + 0.781139i \(0.714639\pi\)
\(450\) −26.2629 −1.23805
\(451\) 32.4157 1.52640
\(452\) 17.5993 0.827800
\(453\) 43.7077 2.05357
\(454\) −19.0016 −0.891788
\(455\) −16.0756 −0.753637
\(456\) −23.0649 −1.08011
\(457\) 7.95332 0.372041 0.186020 0.982546i \(-0.440441\pi\)
0.186020 + 0.982546i \(0.440441\pi\)
\(458\) −11.8474 −0.553591
\(459\) −16.5488 −0.772433
\(460\) −3.10338 −0.144696
\(461\) −2.10206 −0.0979027 −0.0489514 0.998801i \(-0.515588\pi\)
−0.0489514 + 0.998801i \(0.515588\pi\)
\(462\) 23.3540 1.08652
\(463\) −16.4349 −0.763796 −0.381898 0.924204i \(-0.624729\pi\)
−0.381898 + 0.924204i \(0.624729\pi\)
\(464\) −6.98856 −0.324436
\(465\) 78.8182 3.65510
\(466\) 16.5439 0.766382
\(467\) 1.76742 0.0817864 0.0408932 0.999164i \(-0.486980\pi\)
0.0408932 + 0.999164i \(0.486980\pi\)
\(468\) 13.4309 0.620841
\(469\) 5.80962 0.268263
\(470\) −16.0326 −0.739531
\(471\) −61.7047 −2.84320
\(472\) 2.97827 0.137086
\(473\) −23.5205 −1.08147
\(474\) −52.1524 −2.39544
\(475\) −36.2729 −1.66431
\(476\) 4.60180 0.210923
\(477\) −2.74494 −0.125682
\(478\) −4.23998 −0.193932
\(479\) 0.341661 0.0156109 0.00780544 0.999970i \(-0.497515\pi\)
0.00780544 + 0.999970i \(0.497515\pi\)
\(480\) −9.13847 −0.417112
\(481\) −8.41631 −0.383751
\(482\) 12.1426 0.553082
\(483\) −6.44085 −0.293069
\(484\) 2.14725 0.0976021
\(485\) 33.9395 1.54111
\(486\) −5.49117 −0.249085
\(487\) 3.60667 0.163434 0.0817169 0.996656i \(-0.473960\pi\)
0.0817169 + 0.996656i \(0.473960\pi\)
\(488\) 12.4970 0.565715
\(489\) 47.0947 2.12970
\(490\) −6.87651 −0.310649
\(491\) −37.2123 −1.67937 −0.839684 0.543075i \(-0.817260\pi\)
−0.839684 + 0.543075i \(0.817260\pi\)
\(492\) −26.3255 −1.18685
\(493\) −14.7032 −0.662198
\(494\) 18.5500 0.834602
\(495\) −63.8154 −2.86829
\(496\) 8.62487 0.387268
\(497\) 24.2855 1.08935
\(498\) 35.6700 1.59841
\(499\) 19.3933 0.868163 0.434082 0.900874i \(-0.357073\pi\)
0.434082 + 0.900874i \(0.357073\pi\)
\(500\) 1.14534 0.0512211
\(501\) −51.2554 −2.28992
\(502\) 16.9133 0.754876
\(503\) 1.57219 0.0701003 0.0350502 0.999386i \(-0.488841\pi\)
0.0350502 + 0.999386i \(0.488841\pi\)
\(504\) −12.4045 −0.552538
\(505\) −7.35883 −0.327464
\(506\) −3.62591 −0.161191
\(507\) 21.7652 0.966625
\(508\) 6.05866 0.268809
\(509\) −1.78489 −0.0791139 −0.0395569 0.999217i \(-0.512595\pi\)
−0.0395569 + 0.999217i \(0.512595\pi\)
\(510\) −19.2264 −0.851358
\(511\) 7.44772 0.329468
\(512\) −1.00000 −0.0441942
\(513\) 61.6107 2.72018
\(514\) 24.8346 1.09541
\(515\) −16.9701 −0.747790
\(516\) 19.1015 0.840898
\(517\) −18.7322 −0.823840
\(518\) 7.77313 0.341532
\(519\) 18.6886 0.820340
\(520\) 7.34961 0.322302
\(521\) −8.37462 −0.366899 −0.183449 0.983029i \(-0.558726\pi\)
−0.183449 + 0.983029i \(0.558726\pi\)
\(522\) 39.6334 1.73471
\(523\) −9.43547 −0.412584 −0.206292 0.978490i \(-0.566140\pi\)
−0.206292 + 0.978490i \(0.566140\pi\)
\(524\) 1.00000 0.0436852
\(525\) −29.8272 −1.30176
\(526\) 27.7018 1.20786
\(527\) 18.1458 0.790444
\(528\) −10.6772 −0.464665
\(529\) 1.00000 0.0434783
\(530\) −1.50208 −0.0652462
\(531\) −16.8903 −0.732977
\(532\) −17.1323 −0.742781
\(533\) 21.1723 0.917074
\(534\) 30.7504 1.33070
\(535\) 32.9035 1.42254
\(536\) −2.65610 −0.114726
\(537\) 57.1915 2.46800
\(538\) 8.55168 0.368689
\(539\) −8.03436 −0.346064
\(540\) 24.4105 1.05046
\(541\) −26.4989 −1.13927 −0.569637 0.821896i \(-0.692916\pi\)
−0.569637 + 0.821896i \(0.692916\pi\)
\(542\) −5.58610 −0.239944
\(543\) −4.39080 −0.188427
\(544\) −2.10389 −0.0902037
\(545\) 27.5979 1.18217
\(546\) 15.2536 0.652795
\(547\) −19.0525 −0.814627 −0.407314 0.913288i \(-0.633534\pi\)
−0.407314 + 0.913288i \(0.633534\pi\)
\(548\) 4.99231 0.213261
\(549\) −70.8731 −3.02479
\(550\) −16.7914 −0.715987
\(551\) 54.7395 2.33198
\(552\) 2.94469 0.125334
\(553\) −38.7381 −1.64731
\(554\) 24.9240 1.05892
\(555\) −32.4762 −1.37854
\(556\) 17.5415 0.743925
\(557\) 31.4974 1.33459 0.667294 0.744794i \(-0.267452\pi\)
0.667294 + 0.744794i \(0.267452\pi\)
\(558\) −48.9133 −2.07066
\(559\) −15.3624 −0.649760
\(560\) −6.78794 −0.286843
\(561\) −22.4637 −0.948416
\(562\) 30.8789 1.30255
\(563\) 38.8046 1.63542 0.817710 0.575630i \(-0.195243\pi\)
0.817710 + 0.575630i \(0.195243\pi\)
\(564\) 15.2128 0.640576
\(565\) −54.6171 −2.29776
\(566\) −11.5982 −0.487509
\(567\) 13.4491 0.564809
\(568\) −11.1030 −0.465874
\(569\) −5.13364 −0.215213 −0.107607 0.994194i \(-0.534319\pi\)
−0.107607 + 0.994194i \(0.534319\pi\)
\(570\) 71.5791 2.99812
\(571\) −43.9866 −1.84078 −0.920390 0.391001i \(-0.872129\pi\)
−0.920390 + 0.391001i \(0.872129\pi\)
\(572\) 8.58711 0.359045
\(573\) −29.7535 −1.24297
\(574\) −19.5543 −0.816180
\(575\) 4.63094 0.193123
\(576\) 5.67118 0.236299
\(577\) 28.4783 1.18557 0.592783 0.805362i \(-0.298029\pi\)
0.592783 + 0.805362i \(0.298029\pi\)
\(578\) 12.5736 0.522994
\(579\) −16.6841 −0.693368
\(580\) 21.6881 0.900550
\(581\) 26.4952 1.09921
\(582\) −32.2040 −1.33490
\(583\) −1.75500 −0.0726845
\(584\) −3.40502 −0.140901
\(585\) −41.6810 −1.72330
\(586\) −27.0359 −1.11684
\(587\) −39.5940 −1.63422 −0.817110 0.576482i \(-0.804425\pi\)
−0.817110 + 0.576482i \(0.804425\pi\)
\(588\) 6.52489 0.269082
\(589\) −67.5563 −2.78361
\(590\) −9.24268 −0.380515
\(591\) −48.7874 −2.00684
\(592\) −3.55379 −0.146060
\(593\) −20.2218 −0.830411 −0.415205 0.909728i \(-0.636290\pi\)
−0.415205 + 0.909728i \(0.636290\pi\)
\(594\) 28.5207 1.17022
\(595\) −14.2811 −0.585469
\(596\) 15.8629 0.649768
\(597\) 54.6269 2.23573
\(598\) −2.36826 −0.0968455
\(599\) −17.6542 −0.721331 −0.360665 0.932695i \(-0.617450\pi\)
−0.360665 + 0.932695i \(0.617450\pi\)
\(600\) 13.6367 0.556714
\(601\) 36.2954 1.48052 0.740259 0.672321i \(-0.234703\pi\)
0.740259 + 0.672321i \(0.234703\pi\)
\(602\) 14.1884 0.578276
\(603\) 15.0632 0.613422
\(604\) −14.8429 −0.603949
\(605\) −6.66371 −0.270918
\(606\) 6.98255 0.283647
\(607\) −8.46238 −0.343478 −0.171739 0.985143i \(-0.554938\pi\)
−0.171739 + 0.985143i \(0.554938\pi\)
\(608\) 7.83273 0.317659
\(609\) 45.0122 1.82399
\(610\) −38.7830 −1.57028
\(611\) −12.2349 −0.494972
\(612\) 11.9316 0.482305
\(613\) −3.71525 −0.150057 −0.0750287 0.997181i \(-0.523905\pi\)
−0.0750287 + 0.997181i \(0.523905\pi\)
\(614\) 8.64534 0.348898
\(615\) 81.6980 3.29438
\(616\) −7.93088 −0.319544
\(617\) −17.5091 −0.704890 −0.352445 0.935832i \(-0.614650\pi\)
−0.352445 + 0.935832i \(0.614650\pi\)
\(618\) 16.1023 0.647730
\(619\) 19.0680 0.766408 0.383204 0.923664i \(-0.374821\pi\)
0.383204 + 0.923664i \(0.374821\pi\)
\(620\) −26.7662 −1.07496
\(621\) −7.86580 −0.315644
\(622\) 20.8347 0.835393
\(623\) 22.8410 0.915106
\(624\) −6.97379 −0.279175
\(625\) −26.7091 −1.06836
\(626\) 26.6602 1.06555
\(627\) 83.6314 3.33992
\(628\) 20.9546 0.836179
\(629\) −7.47680 −0.298120
\(630\) 38.4957 1.53370
\(631\) −11.5181 −0.458529 −0.229264 0.973364i \(-0.573632\pi\)
−0.229264 + 0.973364i \(0.573632\pi\)
\(632\) 17.7107 0.704493
\(633\) 33.7285 1.34059
\(634\) 28.7093 1.14019
\(635\) −18.8023 −0.746146
\(636\) 1.42527 0.0565157
\(637\) −5.24763 −0.207919
\(638\) 25.3399 1.00322
\(639\) 62.9674 2.49095
\(640\) 3.10338 0.122672
\(641\) 32.2720 1.27467 0.637334 0.770588i \(-0.280037\pi\)
0.637334 + 0.770588i \(0.280037\pi\)
\(642\) −31.2210 −1.23219
\(643\) −21.8448 −0.861477 −0.430738 0.902477i \(-0.641747\pi\)
−0.430738 + 0.902477i \(0.641747\pi\)
\(644\) 2.18728 0.0861908
\(645\) −59.2792 −2.33412
\(646\) 16.4792 0.648367
\(647\) −5.56417 −0.218750 −0.109375 0.994001i \(-0.534885\pi\)
−0.109375 + 0.994001i \(0.534885\pi\)
\(648\) −6.14878 −0.241547
\(649\) −10.7989 −0.423895
\(650\) −10.9673 −0.430172
\(651\) −55.5515 −2.17724
\(652\) −15.9931 −0.626339
\(653\) 26.7343 1.04619 0.523097 0.852273i \(-0.324777\pi\)
0.523097 + 0.852273i \(0.324777\pi\)
\(654\) −26.1867 −1.02398
\(655\) −3.10338 −0.121259
\(656\) 8.94001 0.349049
\(657\) 19.3105 0.753374
\(658\) 11.2999 0.440516
\(659\) −29.7182 −1.15766 −0.578828 0.815449i \(-0.696490\pi\)
−0.578828 + 0.815449i \(0.696490\pi\)
\(660\) 33.1353 1.28979
\(661\) −32.1926 −1.25215 −0.626074 0.779764i \(-0.715339\pi\)
−0.626074 + 0.779764i \(0.715339\pi\)
\(662\) −27.2290 −1.05829
\(663\) −14.6721 −0.569818
\(664\) −12.1133 −0.470088
\(665\) 53.1681 2.06177
\(666\) 20.1542 0.780960
\(667\) −6.98856 −0.270598
\(668\) 17.4060 0.673460
\(669\) −36.0946 −1.39550
\(670\) 8.24286 0.318450
\(671\) −45.3132 −1.74930
\(672\) 6.44085 0.248461
\(673\) −24.7289 −0.953229 −0.476614 0.879112i \(-0.658136\pi\)
−0.476614 + 0.879112i \(0.658136\pi\)
\(674\) −32.8194 −1.26416
\(675\) −36.4260 −1.40204
\(676\) −7.39133 −0.284282
\(677\) 19.8487 0.762846 0.381423 0.924401i \(-0.375434\pi\)
0.381423 + 0.924401i \(0.375434\pi\)
\(678\) 51.8243 1.99030
\(679\) −23.9208 −0.917995
\(680\) 6.52917 0.250382
\(681\) −55.9537 −2.14415
\(682\) −31.2730 −1.19751
\(683\) 49.5924 1.89760 0.948801 0.315875i \(-0.102298\pi\)
0.948801 + 0.315875i \(0.102298\pi\)
\(684\) −44.4208 −1.69847
\(685\) −15.4930 −0.591957
\(686\) 20.1575 0.769619
\(687\) −34.8868 −1.33101
\(688\) −6.48678 −0.247306
\(689\) −1.14627 −0.0436696
\(690\) −9.13847 −0.347896
\(691\) 4.18250 0.159110 0.0795550 0.996830i \(-0.474650\pi\)
0.0795550 + 0.996830i \(0.474650\pi\)
\(692\) −6.34656 −0.241260
\(693\) 44.9775 1.70855
\(694\) 8.08355 0.306847
\(695\) −54.4378 −2.06494
\(696\) −20.5791 −0.780049
\(697\) 18.8088 0.712436
\(698\) −11.8759 −0.449510
\(699\) 48.7166 1.84263
\(700\) 10.1291 0.382846
\(701\) 20.5458 0.776004 0.388002 0.921659i \(-0.373165\pi\)
0.388002 + 0.921659i \(0.373165\pi\)
\(702\) 18.6283 0.703079
\(703\) 27.8359 1.04985
\(704\) 3.62591 0.136657
\(705\) −47.2111 −1.77807
\(706\) −8.38985 −0.315756
\(707\) 5.18655 0.195060
\(708\) 8.77007 0.329599
\(709\) 7.59865 0.285373 0.142687 0.989768i \(-0.454426\pi\)
0.142687 + 0.989768i \(0.454426\pi\)
\(710\) 34.4569 1.29315
\(711\) −100.440 −3.76681
\(712\) −10.4427 −0.391356
\(713\) 8.62487 0.323004
\(714\) 13.5509 0.507128
\(715\) −26.6490 −0.996617
\(716\) −19.4219 −0.725832
\(717\) −12.4854 −0.466276
\(718\) 35.4681 1.32366
\(719\) −33.4537 −1.24761 −0.623806 0.781579i \(-0.714415\pi\)
−0.623806 + 0.781579i \(0.714415\pi\)
\(720\) −17.5998 −0.655906
\(721\) 11.9606 0.445436
\(722\) −42.3516 −1.57616
\(723\) 35.7563 1.32979
\(724\) 1.49109 0.0554160
\(725\) −32.3636 −1.20195
\(726\) 6.32297 0.234667
\(727\) 5.83441 0.216386 0.108193 0.994130i \(-0.465494\pi\)
0.108193 + 0.994130i \(0.465494\pi\)
\(728\) −5.18005 −0.191985
\(729\) −34.6161 −1.28208
\(730\) 10.5671 0.391104
\(731\) −13.6475 −0.504771
\(732\) 36.7999 1.36016
\(733\) −29.1527 −1.07678 −0.538389 0.842696i \(-0.680967\pi\)
−0.538389 + 0.842696i \(0.680967\pi\)
\(734\) −0.676424 −0.0249673
\(735\) −20.2492 −0.746902
\(736\) −1.00000 −0.0368605
\(737\) 9.63078 0.354754
\(738\) −50.7005 −1.86631
\(739\) −27.7366 −1.02031 −0.510153 0.860084i \(-0.670411\pi\)
−0.510153 + 0.860084i \(0.670411\pi\)
\(740\) 11.0288 0.405425
\(741\) 54.6238 2.00666
\(742\) 1.05867 0.0388652
\(743\) −27.0473 −0.992271 −0.496135 0.868245i \(-0.665248\pi\)
−0.496135 + 0.868245i \(0.665248\pi\)
\(744\) 25.3976 0.931120
\(745\) −49.2284 −1.80359
\(746\) −6.07299 −0.222348
\(747\) 68.6969 2.51349
\(748\) 7.62854 0.278927
\(749\) −23.1906 −0.847365
\(750\) 3.37266 0.123152
\(751\) −12.9927 −0.474112 −0.237056 0.971496i \(-0.576182\pi\)
−0.237056 + 0.971496i \(0.576182\pi\)
\(752\) −5.16620 −0.188392
\(753\) 49.8043 1.81497
\(754\) 16.5507 0.602742
\(755\) 46.0631 1.67641
\(756\) −17.2047 −0.625729
\(757\) −6.19153 −0.225035 −0.112517 0.993650i \(-0.535891\pi\)
−0.112517 + 0.993650i \(0.535891\pi\)
\(758\) −36.2852 −1.31794
\(759\) −10.6772 −0.387557
\(760\) −24.3079 −0.881740
\(761\) 44.2892 1.60548 0.802741 0.596327i \(-0.203374\pi\)
0.802741 + 0.596327i \(0.203374\pi\)
\(762\) 17.8409 0.646306
\(763\) −19.4512 −0.704180
\(764\) 10.1041 0.365555
\(765\) −37.0281 −1.33876
\(766\) −0.322645 −0.0116576
\(767\) −7.05332 −0.254681
\(768\) −2.94469 −0.106257
\(769\) −12.2490 −0.441711 −0.220855 0.975307i \(-0.570885\pi\)
−0.220855 + 0.975307i \(0.570885\pi\)
\(770\) 24.6125 0.886973
\(771\) 73.1301 2.63372
\(772\) 5.66583 0.203918
\(773\) 9.67856 0.348114 0.174057 0.984736i \(-0.444312\pi\)
0.174057 + 0.984736i \(0.444312\pi\)
\(774\) 36.7877 1.32231
\(775\) 39.9413 1.43473
\(776\) 10.9363 0.392591
\(777\) 22.8894 0.821154
\(778\) −26.8223 −0.961627
\(779\) −70.0247 −2.50889
\(780\) 21.6423 0.774919
\(781\) 40.2587 1.44057
\(782\) −2.10389 −0.0752351
\(783\) 54.9706 1.96449
\(784\) −2.21582 −0.0791363
\(785\) −65.0299 −2.32102
\(786\) 2.94469 0.105034
\(787\) −36.5828 −1.30404 −0.652018 0.758203i \(-0.726077\pi\)
−0.652018 + 0.758203i \(0.726077\pi\)
\(788\) 16.5679 0.590208
\(789\) 81.5732 2.90408
\(790\) −54.9628 −1.95549
\(791\) 38.4945 1.36871
\(792\) −20.5632 −0.730682
\(793\) −29.5963 −1.05100
\(794\) −9.55849 −0.339218
\(795\) −4.42315 −0.156873
\(796\) −18.5510 −0.657523
\(797\) 14.2359 0.504262 0.252131 0.967693i \(-0.418869\pi\)
0.252131 + 0.967693i \(0.418869\pi\)
\(798\) −50.4494 −1.78589
\(799\) −10.8691 −0.384522
\(800\) −4.63094 −0.163728
\(801\) 59.2223 2.09252
\(802\) 5.91647 0.208918
\(803\) 12.3463 0.435692
\(804\) −7.82137 −0.275839
\(805\) −6.78794 −0.239244
\(806\) −20.4260 −0.719474
\(807\) 25.1820 0.886449
\(808\) −2.37124 −0.0834198
\(809\) −28.0023 −0.984508 −0.492254 0.870452i \(-0.663827\pi\)
−0.492254 + 0.870452i \(0.663827\pi\)
\(810\) 19.0820 0.670472
\(811\) −36.6956 −1.28856 −0.644278 0.764791i \(-0.722842\pi\)
−0.644278 + 0.764791i \(0.722842\pi\)
\(812\) −15.2859 −0.536431
\(813\) −16.4493 −0.576903
\(814\) 12.8857 0.451645
\(815\) 49.6326 1.73856
\(816\) −6.19531 −0.216879
\(817\) 50.8092 1.77759
\(818\) 32.3124 1.12978
\(819\) 29.3770 1.02652
\(820\) −27.7442 −0.968870
\(821\) 45.2201 1.57819 0.789096 0.614270i \(-0.210550\pi\)
0.789096 + 0.614270i \(0.210550\pi\)
\(822\) 14.7008 0.512749
\(823\) 35.2499 1.22873 0.614367 0.789020i \(-0.289411\pi\)
0.614367 + 0.789020i \(0.289411\pi\)
\(824\) −5.46826 −0.190496
\(825\) −49.4454 −1.72147
\(826\) 6.51430 0.226661
\(827\) −32.6500 −1.13535 −0.567676 0.823252i \(-0.692157\pi\)
−0.567676 + 0.823252i \(0.692157\pi\)
\(828\) 5.67118 0.197087
\(829\) −44.1424 −1.53313 −0.766565 0.642166i \(-0.778036\pi\)
−0.766565 + 0.642166i \(0.778036\pi\)
\(830\) 37.5922 1.30484
\(831\) 73.3933 2.54599
\(832\) 2.36826 0.0821047
\(833\) −4.66184 −0.161523
\(834\) 51.6542 1.78864
\(835\) −54.0175 −1.86935
\(836\) −28.4008 −0.982262
\(837\) −67.8416 −2.34495
\(838\) −21.7720 −0.752102
\(839\) −3.42614 −0.118283 −0.0591417 0.998250i \(-0.518836\pi\)
−0.0591417 + 0.998250i \(0.518836\pi\)
\(840\) −19.9884 −0.689664
\(841\) 19.8399 0.684136
\(842\) −36.4888 −1.25749
\(843\) 90.9288 3.13175
\(844\) −11.4540 −0.394264
\(845\) 22.9381 0.789094
\(846\) 29.2985 1.00730
\(847\) 4.69662 0.161378
\(848\) −0.484015 −0.0166211
\(849\) −34.1531 −1.17213
\(850\) −9.74300 −0.334182
\(851\) −3.55379 −0.121822
\(852\) −32.6950 −1.12011
\(853\) 30.7936 1.05435 0.527176 0.849756i \(-0.323251\pi\)
0.527176 + 0.849756i \(0.323251\pi\)
\(854\) 27.3345 0.935368
\(855\) 137.855 4.71453
\(856\) 10.6025 0.362385
\(857\) −5.53233 −0.188981 −0.0944904 0.995526i \(-0.530122\pi\)
−0.0944904 + 0.995526i \(0.530122\pi\)
\(858\) 25.2864 0.863262
\(859\) 23.4669 0.800680 0.400340 0.916367i \(-0.368892\pi\)
0.400340 + 0.916367i \(0.368892\pi\)
\(860\) 20.1309 0.686458
\(861\) −57.5813 −1.96236
\(862\) −4.27848 −0.145726
\(863\) −20.3034 −0.691136 −0.345568 0.938394i \(-0.612314\pi\)
−0.345568 + 0.938394i \(0.612314\pi\)
\(864\) 7.86580 0.267600
\(865\) 19.6957 0.669675
\(866\) −33.7058 −1.14537
\(867\) 37.0254 1.25745
\(868\) 18.8650 0.640320
\(869\) −64.2173 −2.17842
\(870\) 63.8647 2.16522
\(871\) 6.29033 0.213140
\(872\) 8.89287 0.301151
\(873\) −62.0219 −2.09912
\(874\) 7.83273 0.264946
\(875\) 2.50517 0.0846903
\(876\) −10.0267 −0.338772
\(877\) 18.6966 0.631340 0.315670 0.948869i \(-0.397771\pi\)
0.315670 + 0.948869i \(0.397771\pi\)
\(878\) 20.8215 0.702692
\(879\) −79.6121 −2.68525
\(880\) −11.2526 −0.379324
\(881\) 22.7740 0.767276 0.383638 0.923484i \(-0.374671\pi\)
0.383638 + 0.923484i \(0.374671\pi\)
\(882\) 12.5663 0.423129
\(883\) −38.1457 −1.28371 −0.641853 0.766828i \(-0.721834\pi\)
−0.641853 + 0.766828i \(0.721834\pi\)
\(884\) 4.98257 0.167582
\(885\) −27.2168 −0.914883
\(886\) 14.9194 0.501227
\(887\) −8.21436 −0.275811 −0.137906 0.990445i \(-0.544037\pi\)
−0.137906 + 0.990445i \(0.544037\pi\)
\(888\) −10.4648 −0.351176
\(889\) 13.2520 0.444457
\(890\) 32.4075 1.08630
\(891\) 22.2949 0.746909
\(892\) 12.2575 0.410412
\(893\) 40.4654 1.35412
\(894\) 46.7112 1.56226
\(895\) 60.2735 2.01472
\(896\) −2.18728 −0.0730718
\(897\) −6.97379 −0.232848
\(898\) 26.4598 0.882975
\(899\) −60.2754 −2.01030
\(900\) 26.2629 0.875430
\(901\) −1.01832 −0.0339250
\(902\) −32.4157 −1.07932
\(903\) 41.7804 1.39036
\(904\) −17.5993 −0.585343
\(905\) −4.62742 −0.153821
\(906\) −43.7077 −1.45209
\(907\) 24.1789 0.802847 0.401423 0.915893i \(-0.368516\pi\)
0.401423 + 0.915893i \(0.368516\pi\)
\(908\) 19.0016 0.630589
\(909\) 13.4477 0.446032
\(910\) 16.0756 0.532902
\(911\) −16.7466 −0.554840 −0.277420 0.960749i \(-0.589479\pi\)
−0.277420 + 0.960749i \(0.589479\pi\)
\(912\) 23.0649 0.763756
\(913\) 43.9219 1.45360
\(914\) −7.95332 −0.263072
\(915\) −114.204 −3.77546
\(916\) 11.8474 0.391448
\(917\) 2.18728 0.0722303
\(918\) 16.5488 0.546192
\(919\) −36.3207 −1.19811 −0.599054 0.800708i \(-0.704457\pi\)
−0.599054 + 0.800708i \(0.704457\pi\)
\(920\) 3.10338 0.102315
\(921\) 25.4578 0.838864
\(922\) 2.10206 0.0692277
\(923\) 26.2949 0.865508
\(924\) −23.3540 −0.768289
\(925\) −16.4574 −0.541116
\(926\) 16.4349 0.540086
\(927\) 31.0115 1.01855
\(928\) 6.98856 0.229411
\(929\) 49.7041 1.63074 0.815369 0.578941i \(-0.196534\pi\)
0.815369 + 0.578941i \(0.196534\pi\)
\(930\) −78.8182 −2.58455
\(931\) 17.3559 0.568816
\(932\) −16.5439 −0.541914
\(933\) 61.3515 2.00856
\(934\) −1.76742 −0.0578317
\(935\) −23.6742 −0.774230
\(936\) −13.4309 −0.439001
\(937\) −5.30193 −0.173207 −0.0866033 0.996243i \(-0.527601\pi\)
−0.0866033 + 0.996243i \(0.527601\pi\)
\(938\) −5.80962 −0.189691
\(939\) 78.5058 2.56194
\(940\) 16.0326 0.522927
\(941\) −11.9137 −0.388375 −0.194188 0.980964i \(-0.562207\pi\)
−0.194188 + 0.980964i \(0.562207\pi\)
\(942\) 61.7047 2.01045
\(943\) 8.94001 0.291127
\(944\) −2.97827 −0.0969344
\(945\) 53.3926 1.73686
\(946\) 23.5205 0.764717
\(947\) −22.9230 −0.744897 −0.372449 0.928053i \(-0.621482\pi\)
−0.372449 + 0.928053i \(0.621482\pi\)
\(948\) 52.1524 1.69383
\(949\) 8.06398 0.261768
\(950\) 36.2729 1.17685
\(951\) 84.5399 2.74140
\(952\) −4.60180 −0.149145
\(953\) 36.4016 1.17916 0.589582 0.807708i \(-0.299292\pi\)
0.589582 + 0.807708i \(0.299292\pi\)
\(954\) 2.74494 0.0888706
\(955\) −31.3569 −1.01469
\(956\) 4.23998 0.137131
\(957\) 74.6181 2.41206
\(958\) −0.341661 −0.0110386
\(959\) 10.9196 0.352611
\(960\) 9.13847 0.294943
\(961\) 43.3884 1.39963
\(962\) 8.41631 0.271353
\(963\) −60.1286 −1.93762
\(964\) −12.1426 −0.391088
\(965\) −17.5832 −0.566023
\(966\) 6.44085 0.207231
\(967\) 17.6323 0.567017 0.283508 0.958970i \(-0.408502\pi\)
0.283508 + 0.958970i \(0.408502\pi\)
\(968\) −2.14725 −0.0690151
\(969\) 48.5262 1.55889
\(970\) −33.9395 −1.08973
\(971\) −29.8520 −0.957997 −0.478999 0.877816i \(-0.659000\pi\)
−0.478999 + 0.877816i \(0.659000\pi\)
\(972\) 5.49117 0.176129
\(973\) 38.3681 1.23002
\(974\) −3.60667 −0.115565
\(975\) −32.2952 −1.03427
\(976\) −12.4970 −0.400021
\(977\) 26.6042 0.851142 0.425571 0.904925i \(-0.360073\pi\)
0.425571 + 0.904925i \(0.360073\pi\)
\(978\) −47.0947 −1.50592
\(979\) 37.8642 1.21015
\(980\) 6.87651 0.219662
\(981\) −50.4331 −1.61021
\(982\) 37.2123 1.18749
\(983\) −40.9438 −1.30590 −0.652952 0.757399i \(-0.726470\pi\)
−0.652952 + 0.757399i \(0.726470\pi\)
\(984\) 26.3255 0.839228
\(985\) −51.4165 −1.63827
\(986\) 14.7032 0.468245
\(987\) 33.2747 1.05915
\(988\) −18.5500 −0.590153
\(989\) −6.48678 −0.206268
\(990\) 63.8154 2.02819
\(991\) −20.5602 −0.653116 −0.326558 0.945177i \(-0.605889\pi\)
−0.326558 + 0.945177i \(0.605889\pi\)
\(992\) −8.62487 −0.273840
\(993\) −80.1810 −2.54447
\(994\) −24.2855 −0.770288
\(995\) 57.5707 1.82511
\(996\) −35.6700 −1.13025
\(997\) 7.19606 0.227902 0.113951 0.993486i \(-0.463649\pi\)
0.113951 + 0.993486i \(0.463649\pi\)
\(998\) −19.3933 −0.613884
\(999\) 27.9534 0.884407
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 \(a_p\))