Properties

Label 8018.2.a.j.1.16
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.10999 q^{3}\) \(+1.00000 q^{4}\) \(+3.90024 q^{5}\) \(-1.10999 q^{6}\) \(-4.77719 q^{7}\) \(+1.00000 q^{8}\) \(-1.76791 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.10999 q^{3}\) \(+1.00000 q^{4}\) \(+3.90024 q^{5}\) \(-1.10999 q^{6}\) \(-4.77719 q^{7}\) \(+1.00000 q^{8}\) \(-1.76791 q^{9}\) \(+3.90024 q^{10}\) \(+5.69601 q^{11}\) \(-1.10999 q^{12}\) \(-4.09260 q^{13}\) \(-4.77719 q^{14}\) \(-4.32924 q^{15}\) \(+1.00000 q^{16}\) \(-0.265098 q^{17}\) \(-1.76791 q^{18}\) \(-1.00000 q^{19}\) \(+3.90024 q^{20}\) \(+5.30265 q^{21}\) \(+5.69601 q^{22}\) \(-3.37328 q^{23}\) \(-1.10999 q^{24}\) \(+10.2119 q^{25}\) \(-4.09260 q^{26}\) \(+5.29236 q^{27}\) \(-4.77719 q^{28}\) \(-8.30007 q^{29}\) \(-4.32924 q^{30}\) \(-6.89712 q^{31}\) \(+1.00000 q^{32}\) \(-6.32254 q^{33}\) \(-0.265098 q^{34}\) \(-18.6322 q^{35}\) \(-1.76791 q^{36}\) \(+10.1552 q^{37}\) \(-1.00000 q^{38}\) \(+4.54276 q^{39}\) \(+3.90024 q^{40}\) \(+10.0818 q^{41}\) \(+5.30265 q^{42}\) \(-2.35239 q^{43}\) \(+5.69601 q^{44}\) \(-6.89527 q^{45}\) \(-3.37328 q^{46}\) \(+0.906948 q^{47}\) \(-1.10999 q^{48}\) \(+15.8215 q^{49}\) \(+10.2119 q^{50}\) \(+0.294258 q^{51}\) \(-4.09260 q^{52}\) \(+11.1377 q^{53}\) \(+5.29236 q^{54}\) \(+22.2158 q^{55}\) \(-4.77719 q^{56}\) \(+1.10999 q^{57}\) \(-8.30007 q^{58}\) \(+14.5586 q^{59}\) \(-4.32924 q^{60}\) \(+3.09695 q^{61}\) \(-6.89712 q^{62}\) \(+8.44564 q^{63}\) \(+1.00000 q^{64}\) \(-15.9621 q^{65}\) \(-6.32254 q^{66}\) \(+14.6212 q^{67}\) \(-0.265098 q^{68}\) \(+3.74432 q^{69}\) \(-18.6322 q^{70}\) \(-12.7624 q^{71}\) \(-1.76791 q^{72}\) \(-4.58606 q^{73}\) \(+10.1552 q^{74}\) \(-11.3351 q^{75}\) \(-1.00000 q^{76}\) \(-27.2109 q^{77}\) \(+4.54276 q^{78}\) \(-5.66673 q^{79}\) \(+3.90024 q^{80}\) \(-0.570756 q^{81}\) \(+10.0818 q^{82}\) \(+9.13201 q^{83}\) \(+5.30265 q^{84}\) \(-1.03395 q^{85}\) \(-2.35239 q^{86}\) \(+9.21304 q^{87}\) \(+5.69601 q^{88}\) \(-6.19037 q^{89}\) \(-6.89527 q^{90}\) \(+19.5511 q^{91}\) \(-3.37328 q^{92}\) \(+7.65577 q^{93}\) \(+0.906948 q^{94}\) \(-3.90024 q^{95}\) \(-1.10999 q^{96}\) \(+8.89825 q^{97}\) \(+15.8215 q^{98}\) \(-10.0700 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.10999 −0.640856 −0.320428 0.947273i \(-0.603827\pi\)
−0.320428 + 0.947273i \(0.603827\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.90024 1.74424 0.872120 0.489293i \(-0.162745\pi\)
0.872120 + 0.489293i \(0.162745\pi\)
\(6\) −1.10999 −0.453154
\(7\) −4.77719 −1.80561 −0.902803 0.430054i \(-0.858494\pi\)
−0.902803 + 0.430054i \(0.858494\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.76791 −0.589304
\(10\) 3.90024 1.23336
\(11\) 5.69601 1.71741 0.858705 0.512470i \(-0.171269\pi\)
0.858705 + 0.512470i \(0.171269\pi\)
\(12\) −1.10999 −0.320428
\(13\) −4.09260 −1.13508 −0.567541 0.823345i \(-0.692105\pi\)
−0.567541 + 0.823345i \(0.692105\pi\)
\(14\) −4.77719 −1.27676
\(15\) −4.32924 −1.11781
\(16\) 1.00000 0.250000
\(17\) −0.265098 −0.0642958 −0.0321479 0.999483i \(-0.510235\pi\)
−0.0321479 + 0.999483i \(0.510235\pi\)
\(18\) −1.76791 −0.416701
\(19\) −1.00000 −0.229416
\(20\) 3.90024 0.872120
\(21\) 5.30265 1.15713
\(22\) 5.69601 1.21439
\(23\) −3.37328 −0.703378 −0.351689 0.936117i \(-0.614392\pi\)
−0.351689 + 0.936117i \(0.614392\pi\)
\(24\) −1.10999 −0.226577
\(25\) 10.2119 2.04237
\(26\) −4.09260 −0.802624
\(27\) 5.29236 1.01851
\(28\) −4.77719 −0.902803
\(29\) −8.30007 −1.54128 −0.770642 0.637268i \(-0.780065\pi\)
−0.770642 + 0.637268i \(0.780065\pi\)
\(30\) −4.32924 −0.790408
\(31\) −6.89712 −1.23876 −0.619380 0.785092i \(-0.712616\pi\)
−0.619380 + 0.785092i \(0.712616\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.32254 −1.10061
\(34\) −0.265098 −0.0454640
\(35\) −18.6322 −3.14941
\(36\) −1.76791 −0.294652
\(37\) 10.1552 1.66950 0.834752 0.550625i \(-0.185611\pi\)
0.834752 + 0.550625i \(0.185611\pi\)
\(38\) −1.00000 −0.162221
\(39\) 4.54276 0.727424
\(40\) 3.90024 0.616682
\(41\) 10.0818 1.57452 0.787260 0.616622i \(-0.211499\pi\)
0.787260 + 0.616622i \(0.211499\pi\)
\(42\) 5.30265 0.818217
\(43\) −2.35239 −0.358735 −0.179368 0.983782i \(-0.557405\pi\)
−0.179368 + 0.983782i \(0.557405\pi\)
\(44\) 5.69601 0.858705
\(45\) −6.89527 −1.02789
\(46\) −3.37328 −0.497363
\(47\) 0.906948 0.132292 0.0661460 0.997810i \(-0.478930\pi\)
0.0661460 + 0.997810i \(0.478930\pi\)
\(48\) −1.10999 −0.160214
\(49\) 15.8215 2.26021
\(50\) 10.2119 1.44417
\(51\) 0.294258 0.0412043
\(52\) −4.09260 −0.567541
\(53\) 11.1377 1.52989 0.764943 0.644098i \(-0.222767\pi\)
0.764943 + 0.644098i \(0.222767\pi\)
\(54\) 5.29236 0.720199
\(55\) 22.2158 2.99557
\(56\) −4.77719 −0.638378
\(57\) 1.10999 0.147022
\(58\) −8.30007 −1.08985
\(59\) 14.5586 1.89537 0.947685 0.319207i \(-0.103416\pi\)
0.947685 + 0.319207i \(0.103416\pi\)
\(60\) −4.32924 −0.558903
\(61\) 3.09695 0.396524 0.198262 0.980149i \(-0.436470\pi\)
0.198262 + 0.980149i \(0.436470\pi\)
\(62\) −6.89712 −0.875935
\(63\) 8.44564 1.06405
\(64\) 1.00000 0.125000
\(65\) −15.9621 −1.97985
\(66\) −6.32254 −0.778251
\(67\) 14.6212 1.78626 0.893130 0.449799i \(-0.148504\pi\)
0.893130 + 0.449799i \(0.148504\pi\)
\(68\) −0.265098 −0.0321479
\(69\) 3.74432 0.450764
\(70\) −18.6322 −2.22697
\(71\) −12.7624 −1.51462 −0.757311 0.653055i \(-0.773487\pi\)
−0.757311 + 0.653055i \(0.773487\pi\)
\(72\) −1.76791 −0.208350
\(73\) −4.58606 −0.536758 −0.268379 0.963313i \(-0.586488\pi\)
−0.268379 + 0.963313i \(0.586488\pi\)
\(74\) 10.1552 1.18052
\(75\) −11.3351 −1.30886
\(76\) −1.00000 −0.114708
\(77\) −27.2109 −3.10097
\(78\) 4.54276 0.514367
\(79\) −5.66673 −0.637557 −0.318778 0.947829i \(-0.603273\pi\)
−0.318778 + 0.947829i \(0.603273\pi\)
\(80\) 3.90024 0.436060
\(81\) −0.570756 −0.0634174
\(82\) 10.0818 1.11335
\(83\) 9.13201 1.00237 0.501184 0.865341i \(-0.332898\pi\)
0.501184 + 0.865341i \(0.332898\pi\)
\(84\) 5.30265 0.578567
\(85\) −1.03395 −0.112147
\(86\) −2.35239 −0.253664
\(87\) 9.21304 0.987742
\(88\) 5.69601 0.607196
\(89\) −6.19037 −0.656178 −0.328089 0.944647i \(-0.606405\pi\)
−0.328089 + 0.944647i \(0.606405\pi\)
\(90\) −6.89527 −0.726826
\(91\) 19.5511 2.04951
\(92\) −3.37328 −0.351689
\(93\) 7.65577 0.793866
\(94\) 0.906948 0.0935446
\(95\) −3.90024 −0.400156
\(96\) −1.10999 −0.113288
\(97\) 8.89825 0.903481 0.451740 0.892149i \(-0.350803\pi\)
0.451740 + 0.892149i \(0.350803\pi\)
\(98\) 15.8215 1.59821
\(99\) −10.0700 −1.01208
\(100\) 10.2119 1.02119
\(101\) 8.26913 0.822809 0.411405 0.911453i \(-0.365038\pi\)
0.411405 + 0.911453i \(0.365038\pi\)
\(102\) 0.294258 0.0291359
\(103\) 17.0859 1.68352 0.841760 0.539852i \(-0.181520\pi\)
0.841760 + 0.539852i \(0.181520\pi\)
\(104\) −4.09260 −0.401312
\(105\) 20.6816 2.01832
\(106\) 11.1377 1.08179
\(107\) −6.12056 −0.591697 −0.295848 0.955235i \(-0.595602\pi\)
−0.295848 + 0.955235i \(0.595602\pi\)
\(108\) 5.29236 0.509257
\(109\) −2.99120 −0.286505 −0.143252 0.989686i \(-0.545756\pi\)
−0.143252 + 0.989686i \(0.545756\pi\)
\(110\) 22.2158 2.11819
\(111\) −11.2722 −1.06991
\(112\) −4.77719 −0.451402
\(113\) 8.75944 0.824019 0.412010 0.911180i \(-0.364827\pi\)
0.412010 + 0.911180i \(0.364827\pi\)
\(114\) 1.10999 0.103961
\(115\) −13.1566 −1.22686
\(116\) −8.30007 −0.770642
\(117\) 7.23535 0.668908
\(118\) 14.5586 1.34023
\(119\) 1.26642 0.116093
\(120\) −4.32924 −0.395204
\(121\) 21.4445 1.94950
\(122\) 3.09695 0.280385
\(123\) −11.1908 −1.00904
\(124\) −6.89712 −0.619380
\(125\) 20.3275 1.81814
\(126\) 8.44564 0.752397
\(127\) −8.60658 −0.763711 −0.381855 0.924222i \(-0.624715\pi\)
−0.381855 + 0.924222i \(0.624715\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.61114 0.229898
\(130\) −15.9621 −1.39997
\(131\) −8.06289 −0.704458 −0.352229 0.935914i \(-0.614576\pi\)
−0.352229 + 0.935914i \(0.614576\pi\)
\(132\) −6.32254 −0.550306
\(133\) 4.77719 0.414234
\(134\) 14.6212 1.26308
\(135\) 20.6414 1.77653
\(136\) −0.265098 −0.0227320
\(137\) 6.95245 0.593988 0.296994 0.954879i \(-0.404016\pi\)
0.296994 + 0.954879i \(0.404016\pi\)
\(138\) 3.74432 0.318738
\(139\) 17.1520 1.45481 0.727406 0.686208i \(-0.240726\pi\)
0.727406 + 0.686208i \(0.240726\pi\)
\(140\) −18.6322 −1.57470
\(141\) −1.00671 −0.0847801
\(142\) −12.7624 −1.07100
\(143\) −23.3115 −1.94940
\(144\) −1.76791 −0.147326
\(145\) −32.3723 −2.68837
\(146\) −4.58606 −0.379545
\(147\) −17.5618 −1.44847
\(148\) 10.1552 0.834752
\(149\) −16.3458 −1.33910 −0.669552 0.742765i \(-0.733514\pi\)
−0.669552 + 0.742765i \(0.733514\pi\)
\(150\) −11.3351 −0.925507
\(151\) −10.9227 −0.888880 −0.444440 0.895809i \(-0.646597\pi\)
−0.444440 + 0.895809i \(0.646597\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 0.468670 0.0378897
\(154\) −27.2109 −2.19271
\(155\) −26.9004 −2.16069
\(156\) 4.54276 0.363712
\(157\) −2.38660 −0.190472 −0.0952359 0.995455i \(-0.530361\pi\)
−0.0952359 + 0.995455i \(0.530361\pi\)
\(158\) −5.66673 −0.450821
\(159\) −12.3628 −0.980437
\(160\) 3.90024 0.308341
\(161\) 16.1148 1.27002
\(162\) −0.570756 −0.0448428
\(163\) 3.26419 0.255671 0.127836 0.991795i \(-0.459197\pi\)
0.127836 + 0.991795i \(0.459197\pi\)
\(164\) 10.0818 0.787260
\(165\) −24.6594 −1.91973
\(166\) 9.13201 0.708782
\(167\) 2.79406 0.216211 0.108105 0.994139i \(-0.465522\pi\)
0.108105 + 0.994139i \(0.465522\pi\)
\(168\) 5.30265 0.409108
\(169\) 3.74935 0.288412
\(170\) −1.03395 −0.0793001
\(171\) 1.76791 0.135196
\(172\) −2.35239 −0.179368
\(173\) 16.5663 1.25951 0.629756 0.776793i \(-0.283155\pi\)
0.629756 + 0.776793i \(0.283155\pi\)
\(174\) 9.21304 0.698439
\(175\) −48.7839 −3.68772
\(176\) 5.69601 0.429353
\(177\) −16.1600 −1.21466
\(178\) −6.19037 −0.463988
\(179\) 11.5835 0.865793 0.432897 0.901444i \(-0.357492\pi\)
0.432897 + 0.901444i \(0.357492\pi\)
\(180\) −6.89527 −0.513943
\(181\) −1.55513 −0.115592 −0.0577960 0.998328i \(-0.518407\pi\)
−0.0577960 + 0.998328i \(0.518407\pi\)
\(182\) 19.5511 1.44922
\(183\) −3.43760 −0.254115
\(184\) −3.37328 −0.248682
\(185\) 39.6077 2.91202
\(186\) 7.65577 0.561348
\(187\) −1.51000 −0.110422
\(188\) 0.906948 0.0661460
\(189\) −25.2826 −1.83904
\(190\) −3.90024 −0.282953
\(191\) 2.81445 0.203647 0.101823 0.994802i \(-0.467532\pi\)
0.101823 + 0.994802i \(0.467532\pi\)
\(192\) −1.10999 −0.0801070
\(193\) 12.1750 0.876378 0.438189 0.898883i \(-0.355620\pi\)
0.438189 + 0.898883i \(0.355620\pi\)
\(194\) 8.89825 0.638857
\(195\) 17.7179 1.26880
\(196\) 15.8215 1.13011
\(197\) 19.1442 1.36397 0.681983 0.731368i \(-0.261118\pi\)
0.681983 + 0.731368i \(0.261118\pi\)
\(198\) −10.0700 −0.715646
\(199\) 8.27226 0.586405 0.293203 0.956050i \(-0.405279\pi\)
0.293203 + 0.956050i \(0.405279\pi\)
\(200\) 10.2119 0.722087
\(201\) −16.2294 −1.14474
\(202\) 8.26913 0.581814
\(203\) 39.6510 2.78295
\(204\) 0.294258 0.0206022
\(205\) 39.3216 2.74634
\(206\) 17.0859 1.19043
\(207\) 5.96366 0.414503
\(208\) −4.09260 −0.283771
\(209\) −5.69601 −0.394001
\(210\) 20.6816 1.42717
\(211\) −1.00000 −0.0688428
\(212\) 11.1377 0.764943
\(213\) 14.1662 0.970654
\(214\) −6.12056 −0.418393
\(215\) −9.17486 −0.625720
\(216\) 5.29236 0.360099
\(217\) 32.9488 2.23671
\(218\) −2.99120 −0.202589
\(219\) 5.09051 0.343984
\(220\) 22.2158 1.49779
\(221\) 1.08494 0.0729810
\(222\) −11.2722 −0.756542
\(223\) −19.2777 −1.29093 −0.645465 0.763790i \(-0.723336\pi\)
−0.645465 + 0.763790i \(0.723336\pi\)
\(224\) −4.77719 −0.319189
\(225\) −18.0536 −1.20358
\(226\) 8.75944 0.582670
\(227\) 8.67176 0.575565 0.287782 0.957696i \(-0.407082\pi\)
0.287782 + 0.957696i \(0.407082\pi\)
\(228\) 1.10999 0.0735112
\(229\) 9.69642 0.640758 0.320379 0.947290i \(-0.396190\pi\)
0.320379 + 0.947290i \(0.396190\pi\)
\(230\) −13.1566 −0.867520
\(231\) 30.2039 1.98727
\(232\) −8.30007 −0.544927
\(233\) −7.18392 −0.470634 −0.235317 0.971919i \(-0.575613\pi\)
−0.235317 + 0.971919i \(0.575613\pi\)
\(234\) 7.23535 0.472990
\(235\) 3.53731 0.230749
\(236\) 14.5586 0.947685
\(237\) 6.29004 0.408582
\(238\) 1.26642 0.0820901
\(239\) 0.963091 0.0622972 0.0311486 0.999515i \(-0.490083\pi\)
0.0311486 + 0.999515i \(0.490083\pi\)
\(240\) −4.32924 −0.279451
\(241\) −11.6759 −0.752111 −0.376055 0.926597i \(-0.622720\pi\)
−0.376055 + 0.926597i \(0.622720\pi\)
\(242\) 21.4445 1.37850
\(243\) −15.2435 −0.977873
\(244\) 3.09695 0.198262
\(245\) 61.7076 3.94235
\(246\) −11.1908 −0.713499
\(247\) 4.09260 0.260406
\(248\) −6.89712 −0.437968
\(249\) −10.1365 −0.642374
\(250\) 20.3275 1.28562
\(251\) −18.5865 −1.17317 −0.586586 0.809887i \(-0.699529\pi\)
−0.586586 + 0.809887i \(0.699529\pi\)
\(252\) 8.44564 0.532025
\(253\) −19.2142 −1.20799
\(254\) −8.60658 −0.540025
\(255\) 1.14768 0.0718702
\(256\) 1.00000 0.0625000
\(257\) 17.1609 1.07047 0.535235 0.844703i \(-0.320223\pi\)
0.535235 + 0.844703i \(0.320223\pi\)
\(258\) 2.61114 0.162562
\(259\) −48.5133 −3.01447
\(260\) −15.9621 −0.989927
\(261\) 14.6738 0.908285
\(262\) −8.06289 −0.498127
\(263\) −8.25844 −0.509237 −0.254619 0.967042i \(-0.581950\pi\)
−0.254619 + 0.967042i \(0.581950\pi\)
\(264\) −6.32254 −0.389125
\(265\) 43.4398 2.66849
\(266\) 4.77719 0.292908
\(267\) 6.87128 0.420516
\(268\) 14.6212 0.893130
\(269\) 17.4591 1.06450 0.532249 0.846588i \(-0.321347\pi\)
0.532249 + 0.846588i \(0.321347\pi\)
\(270\) 20.6414 1.25620
\(271\) −8.67176 −0.526772 −0.263386 0.964691i \(-0.584839\pi\)
−0.263386 + 0.964691i \(0.584839\pi\)
\(272\) −0.265098 −0.0160739
\(273\) −21.7016 −1.31344
\(274\) 6.95245 0.420013
\(275\) 58.1668 3.50759
\(276\) 3.74432 0.225382
\(277\) 13.0111 0.781763 0.390881 0.920441i \(-0.372170\pi\)
0.390881 + 0.920441i \(0.372170\pi\)
\(278\) 17.1520 1.02871
\(279\) 12.1935 0.730005
\(280\) −18.6322 −1.11348
\(281\) −15.3504 −0.915730 −0.457865 0.889022i \(-0.651386\pi\)
−0.457865 + 0.889022i \(0.651386\pi\)
\(282\) −1.00671 −0.0599486
\(283\) −26.4750 −1.57377 −0.786887 0.617097i \(-0.788308\pi\)
−0.786887 + 0.617097i \(0.788308\pi\)
\(284\) −12.7624 −0.757311
\(285\) 4.32924 0.256442
\(286\) −23.3115 −1.37844
\(287\) −48.1628 −2.84296
\(288\) −1.76791 −0.104175
\(289\) −16.9297 −0.995866
\(290\) −32.3723 −1.90096
\(291\) −9.87702 −0.579001
\(292\) −4.58606 −0.268379
\(293\) −27.8945 −1.62961 −0.814806 0.579734i \(-0.803157\pi\)
−0.814806 + 0.579734i \(0.803157\pi\)
\(294\) −17.5618 −1.02422
\(295\) 56.7821 3.30598
\(296\) 10.1552 0.590259
\(297\) 30.1453 1.74921
\(298\) −16.3458 −0.946889
\(299\) 13.8055 0.798392
\(300\) −11.3351 −0.654432
\(301\) 11.2378 0.647735
\(302\) −10.9227 −0.628533
\(303\) −9.17869 −0.527302
\(304\) −1.00000 −0.0573539
\(305\) 12.0788 0.691632
\(306\) 0.468670 0.0267921
\(307\) 5.14591 0.293693 0.146846 0.989159i \(-0.453088\pi\)
0.146846 + 0.989159i \(0.453088\pi\)
\(308\) −27.2109 −1.55048
\(309\) −18.9652 −1.07889
\(310\) −26.9004 −1.52784
\(311\) −0.505072 −0.0286400 −0.0143200 0.999897i \(-0.504558\pi\)
−0.0143200 + 0.999897i \(0.504558\pi\)
\(312\) 4.54276 0.257183
\(313\) −13.1933 −0.745727 −0.372863 0.927886i \(-0.621624\pi\)
−0.372863 + 0.927886i \(0.621624\pi\)
\(314\) −2.38660 −0.134684
\(315\) 32.9400 1.85596
\(316\) −5.66673 −0.318778
\(317\) 30.1676 1.69438 0.847190 0.531290i \(-0.178292\pi\)
0.847190 + 0.531290i \(0.178292\pi\)
\(318\) −12.3628 −0.693273
\(319\) −47.2773 −2.64702
\(320\) 3.90024 0.218030
\(321\) 6.79379 0.379192
\(322\) 16.1148 0.898042
\(323\) 0.265098 0.0147505
\(324\) −0.570756 −0.0317087
\(325\) −41.7930 −2.31826
\(326\) 3.26419 0.180787
\(327\) 3.32021 0.183608
\(328\) 10.0818 0.556677
\(329\) −4.33266 −0.238867
\(330\) −24.6594 −1.35746
\(331\) 12.9868 0.713818 0.356909 0.934139i \(-0.383831\pi\)
0.356909 + 0.934139i \(0.383831\pi\)
\(332\) 9.13201 0.501184
\(333\) −17.9535 −0.983845
\(334\) 2.79406 0.152884
\(335\) 57.0260 3.11566
\(336\) 5.30265 0.289283
\(337\) 14.6345 0.797190 0.398595 0.917127i \(-0.369498\pi\)
0.398595 + 0.917127i \(0.369498\pi\)
\(338\) 3.74935 0.203938
\(339\) −9.72294 −0.528078
\(340\) −1.03395 −0.0560736
\(341\) −39.2860 −2.12746
\(342\) 1.76791 0.0955977
\(343\) −42.1419 −2.27545
\(344\) −2.35239 −0.126832
\(345\) 14.6038 0.786240
\(346\) 16.5663 0.890609
\(347\) 13.9248 0.747522 0.373761 0.927525i \(-0.378068\pi\)
0.373761 + 0.927525i \(0.378068\pi\)
\(348\) 9.21304 0.493871
\(349\) 12.9954 0.695628 0.347814 0.937564i \(-0.386924\pi\)
0.347814 + 0.937564i \(0.386924\pi\)
\(350\) −48.7839 −2.60761
\(351\) −21.6595 −1.15610
\(352\) 5.69601 0.303598
\(353\) −0.158909 −0.00845787 −0.00422893 0.999991i \(-0.501346\pi\)
−0.00422893 + 0.999991i \(0.501346\pi\)
\(354\) −16.1600 −0.858894
\(355\) −49.7765 −2.64186
\(356\) −6.19037 −0.328089
\(357\) −1.40572 −0.0743988
\(358\) 11.5835 0.612208
\(359\) −20.9540 −1.10591 −0.552955 0.833211i \(-0.686500\pi\)
−0.552955 + 0.833211i \(0.686500\pi\)
\(360\) −6.89527 −0.363413
\(361\) 1.00000 0.0526316
\(362\) −1.55513 −0.0817359
\(363\) −23.8033 −1.24935
\(364\) 19.5511 1.02476
\(365\) −17.8867 −0.936234
\(366\) −3.43760 −0.179686
\(367\) −17.7347 −0.925745 −0.462873 0.886425i \(-0.653181\pi\)
−0.462873 + 0.886425i \(0.653181\pi\)
\(368\) −3.37328 −0.175844
\(369\) −17.8238 −0.927870
\(370\) 39.6077 2.05911
\(371\) −53.2071 −2.76237
\(372\) 7.65577 0.396933
\(373\) −3.71068 −0.192131 −0.0960657 0.995375i \(-0.530626\pi\)
−0.0960657 + 0.995375i \(0.530626\pi\)
\(374\) −1.51000 −0.0780803
\(375\) −22.5634 −1.16517
\(376\) 0.906948 0.0467723
\(377\) 33.9689 1.74949
\(378\) −25.2826 −1.30040
\(379\) 30.0212 1.54209 0.771043 0.636783i \(-0.219735\pi\)
0.771043 + 0.636783i \(0.219735\pi\)
\(380\) −3.90024 −0.200078
\(381\) 9.55326 0.489428
\(382\) 2.81445 0.144000
\(383\) −14.3270 −0.732077 −0.366039 0.930600i \(-0.619286\pi\)
−0.366039 + 0.930600i \(0.619286\pi\)
\(384\) −1.10999 −0.0566442
\(385\) −106.129 −5.40883
\(386\) 12.1750 0.619693
\(387\) 4.15881 0.211404
\(388\) 8.89825 0.451740
\(389\) 2.66506 0.135124 0.0675619 0.997715i \(-0.478478\pi\)
0.0675619 + 0.997715i \(0.478478\pi\)
\(390\) 17.7179 0.897178
\(391\) 0.894251 0.0452242
\(392\) 15.8215 0.799106
\(393\) 8.94976 0.451456
\(394\) 19.1442 0.964469
\(395\) −22.1016 −1.11205
\(396\) −10.0700 −0.506038
\(397\) −8.22764 −0.412933 −0.206467 0.978454i \(-0.566197\pi\)
−0.206467 + 0.978454i \(0.566197\pi\)
\(398\) 8.27226 0.414651
\(399\) −5.30265 −0.265465
\(400\) 10.2119 0.510593
\(401\) 16.2754 0.812757 0.406378 0.913705i \(-0.366792\pi\)
0.406378 + 0.913705i \(0.366792\pi\)
\(402\) −16.2294 −0.809450
\(403\) 28.2271 1.40609
\(404\) 8.26913 0.411405
\(405\) −2.22608 −0.110615
\(406\) 39.6510 1.96785
\(407\) 57.8441 2.86722
\(408\) 0.294258 0.0145679
\(409\) −2.15867 −0.106740 −0.0533698 0.998575i \(-0.516996\pi\)
−0.0533698 + 0.998575i \(0.516996\pi\)
\(410\) 39.3216 1.94195
\(411\) −7.71718 −0.380661
\(412\) 17.0859 0.841760
\(413\) −69.5492 −3.42229
\(414\) 5.96366 0.293098
\(415\) 35.6170 1.74837
\(416\) −4.09260 −0.200656
\(417\) −19.0386 −0.932324
\(418\) −5.69601 −0.278601
\(419\) −12.5558 −0.613393 −0.306697 0.951807i \(-0.599224\pi\)
−0.306697 + 0.951807i \(0.599224\pi\)
\(420\) 20.6816 1.00916
\(421\) −16.4123 −0.799889 −0.399944 0.916539i \(-0.630971\pi\)
−0.399944 + 0.916539i \(0.630971\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −1.60340 −0.0779602
\(424\) 11.1377 0.540897
\(425\) −2.70714 −0.131316
\(426\) 14.1662 0.686356
\(427\) −14.7947 −0.715966
\(428\) −6.12056 −0.295848
\(429\) 25.8756 1.24929
\(430\) −9.17486 −0.442451
\(431\) 6.50015 0.313101 0.156551 0.987670i \(-0.449963\pi\)
0.156551 + 0.987670i \(0.449963\pi\)
\(432\) 5.29236 0.254629
\(433\) 11.9525 0.574399 0.287200 0.957871i \(-0.407276\pi\)
0.287200 + 0.957871i \(0.407276\pi\)
\(434\) 32.9488 1.58159
\(435\) 35.9330 1.72286
\(436\) −2.99120 −0.143252
\(437\) 3.37328 0.161366
\(438\) 5.09051 0.243234
\(439\) −12.3919 −0.591434 −0.295717 0.955276i \(-0.595559\pi\)
−0.295717 + 0.955276i \(0.595559\pi\)
\(440\) 22.2158 1.05910
\(441\) −27.9710 −1.33195
\(442\) 1.08494 0.0516054
\(443\) −13.0536 −0.620194 −0.310097 0.950705i \(-0.600362\pi\)
−0.310097 + 0.950705i \(0.600362\pi\)
\(444\) −11.2722 −0.534956
\(445\) −24.1439 −1.14453
\(446\) −19.2777 −0.912826
\(447\) 18.1438 0.858173
\(448\) −4.77719 −0.225701
\(449\) 29.4917 1.39180 0.695900 0.718139i \(-0.255006\pi\)
0.695900 + 0.718139i \(0.255006\pi\)
\(450\) −18.0536 −0.851057
\(451\) 57.4262 2.70410
\(452\) 8.75944 0.412010
\(453\) 12.1242 0.569644
\(454\) 8.67176 0.406986
\(455\) 76.2539 3.57484
\(456\) 1.10999 0.0519803
\(457\) −0.324966 −0.0152013 −0.00760063 0.999971i \(-0.502419\pi\)
−0.00760063 + 0.999971i \(0.502419\pi\)
\(458\) 9.69642 0.453084
\(459\) −1.40300 −0.0654862
\(460\) −13.1566 −0.613429
\(461\) 38.2872 1.78321 0.891607 0.452811i \(-0.149579\pi\)
0.891607 + 0.452811i \(0.149579\pi\)
\(462\) 30.2039 1.40521
\(463\) 34.0027 1.58024 0.790119 0.612953i \(-0.210019\pi\)
0.790119 + 0.612953i \(0.210019\pi\)
\(464\) −8.30007 −0.385321
\(465\) 29.8593 1.38469
\(466\) −7.18392 −0.332788
\(467\) −21.4709 −0.993556 −0.496778 0.867878i \(-0.665484\pi\)
−0.496778 + 0.867878i \(0.665484\pi\)
\(468\) 7.23535 0.334454
\(469\) −69.8480 −3.22528
\(470\) 3.53731 0.163164
\(471\) 2.64912 0.122065
\(472\) 14.5586 0.670115
\(473\) −13.3992 −0.616096
\(474\) 6.29004 0.288911
\(475\) −10.2119 −0.468552
\(476\) 1.26642 0.0580464
\(477\) −19.6905 −0.901568
\(478\) 0.963091 0.0440508
\(479\) 5.37891 0.245769 0.122884 0.992421i \(-0.460786\pi\)
0.122884 + 0.992421i \(0.460786\pi\)
\(480\) −4.32924 −0.197602
\(481\) −41.5612 −1.89503
\(482\) −11.6759 −0.531823
\(483\) −17.8873 −0.813902
\(484\) 21.4445 0.974749
\(485\) 34.7053 1.57589
\(486\) −15.2435 −0.691461
\(487\) −14.1416 −0.640815 −0.320407 0.947280i \(-0.603820\pi\)
−0.320407 + 0.947280i \(0.603820\pi\)
\(488\) 3.09695 0.140192
\(489\) −3.62324 −0.163848
\(490\) 61.7076 2.78767
\(491\) 19.7165 0.889791 0.444895 0.895582i \(-0.353241\pi\)
0.444895 + 0.895582i \(0.353241\pi\)
\(492\) −11.1908 −0.504520
\(493\) 2.20034 0.0990981
\(494\) 4.09260 0.184135
\(495\) −39.2755 −1.76530
\(496\) −6.89712 −0.309690
\(497\) 60.9685 2.73481
\(498\) −10.1365 −0.454227
\(499\) −38.5801 −1.72708 −0.863541 0.504278i \(-0.831759\pi\)
−0.863541 + 0.504278i \(0.831759\pi\)
\(500\) 20.3275 0.909071
\(501\) −3.10139 −0.138560
\(502\) −18.5865 −0.829558
\(503\) 33.1204 1.47677 0.738383 0.674381i \(-0.235590\pi\)
0.738383 + 0.674381i \(0.235590\pi\)
\(504\) 8.44564 0.376199
\(505\) 32.2516 1.43518
\(506\) −19.2142 −0.854177
\(507\) −4.16176 −0.184830
\(508\) −8.60658 −0.381855
\(509\) −35.2099 −1.56065 −0.780326 0.625373i \(-0.784947\pi\)
−0.780326 + 0.625373i \(0.784947\pi\)
\(510\) 1.14768 0.0508199
\(511\) 21.9085 0.969173
\(512\) 1.00000 0.0441942
\(513\) −5.29236 −0.233663
\(514\) 17.1609 0.756937
\(515\) 66.6389 2.93646
\(516\) 2.61114 0.114949
\(517\) 5.16598 0.227200
\(518\) −48.5133 −2.13155
\(519\) −18.3885 −0.807165
\(520\) −15.9621 −0.699984
\(521\) 1.90798 0.0835903 0.0417952 0.999126i \(-0.486692\pi\)
0.0417952 + 0.999126i \(0.486692\pi\)
\(522\) 14.6738 0.642254
\(523\) −15.5924 −0.681808 −0.340904 0.940098i \(-0.610733\pi\)
−0.340904 + 0.940098i \(0.610733\pi\)
\(524\) −8.06289 −0.352229
\(525\) 54.1499 2.36329
\(526\) −8.25844 −0.360085
\(527\) 1.82841 0.0796470
\(528\) −6.32254 −0.275153
\(529\) −11.6210 −0.505260
\(530\) 43.4398 1.88691
\(531\) −25.7383 −1.11695
\(532\) 4.77719 0.207117
\(533\) −41.2609 −1.78721
\(534\) 6.87128 0.297349
\(535\) −23.8716 −1.03206
\(536\) 14.6212 0.631538
\(537\) −12.8577 −0.554849
\(538\) 17.4591 0.752713
\(539\) 90.1193 3.88171
\(540\) 20.6414 0.888267
\(541\) −15.8687 −0.682249 −0.341125 0.940018i \(-0.610808\pi\)
−0.341125 + 0.940018i \(0.610808\pi\)
\(542\) −8.67176 −0.372484
\(543\) 1.72619 0.0740778
\(544\) −0.265098 −0.0113660
\(545\) −11.6664 −0.499733
\(546\) −21.7016 −0.928744
\(547\) 43.4619 1.85830 0.929149 0.369706i \(-0.120542\pi\)
0.929149 + 0.369706i \(0.120542\pi\)
\(548\) 6.95245 0.296994
\(549\) −5.47513 −0.233673
\(550\) 58.1668 2.48024
\(551\) 8.30007 0.353595
\(552\) 3.74432 0.159369
\(553\) 27.0710 1.15118
\(554\) 13.0111 0.552790
\(555\) −43.9643 −1.86618
\(556\) 17.1520 0.727406
\(557\) −3.97633 −0.168483 −0.0842413 0.996445i \(-0.526847\pi\)
−0.0842413 + 0.996445i \(0.526847\pi\)
\(558\) 12.1935 0.516192
\(559\) 9.62737 0.407194
\(560\) −18.6322 −0.787352
\(561\) 1.67609 0.0707647
\(562\) −15.3504 −0.647519
\(563\) −15.0266 −0.633298 −0.316649 0.948543i \(-0.602558\pi\)
−0.316649 + 0.948543i \(0.602558\pi\)
\(564\) −1.00671 −0.0423901
\(565\) 34.1639 1.43729
\(566\) −26.4750 −1.11283
\(567\) 2.72661 0.114507
\(568\) −12.7624 −0.535499
\(569\) 42.1744 1.76804 0.884022 0.467446i \(-0.154826\pi\)
0.884022 + 0.467446i \(0.154826\pi\)
\(570\) 4.32924 0.181332
\(571\) −23.6897 −0.991384 −0.495692 0.868498i \(-0.665086\pi\)
−0.495692 + 0.868498i \(0.665086\pi\)
\(572\) −23.3115 −0.974701
\(573\) −3.12403 −0.130508
\(574\) −48.1628 −2.01028
\(575\) −34.4474 −1.43656
\(576\) −1.76791 −0.0736630
\(577\) −20.6733 −0.860639 −0.430320 0.902677i \(-0.641599\pi\)
−0.430320 + 0.902677i \(0.641599\pi\)
\(578\) −16.9297 −0.704184
\(579\) −13.5142 −0.561632
\(580\) −32.3723 −1.34418
\(581\) −43.6253 −1.80988
\(582\) −9.87702 −0.409416
\(583\) 63.4406 2.62744
\(584\) −4.58606 −0.189773
\(585\) 28.2196 1.16674
\(586\) −27.8945 −1.15231
\(587\) 41.0597 1.69472 0.847358 0.531022i \(-0.178192\pi\)
0.847358 + 0.531022i \(0.178192\pi\)
\(588\) −17.5618 −0.724236
\(589\) 6.89712 0.284191
\(590\) 56.7821 2.33768
\(591\) −21.2499 −0.874106
\(592\) 10.1552 0.417376
\(593\) −12.9632 −0.532334 −0.266167 0.963927i \(-0.585757\pi\)
−0.266167 + 0.963927i \(0.585757\pi\)
\(594\) 30.1453 1.23688
\(595\) 4.93935 0.202494
\(596\) −16.3458 −0.669552
\(597\) −9.18217 −0.375801
\(598\) 13.8055 0.564548
\(599\) 15.9737 0.652669 0.326334 0.945254i \(-0.394186\pi\)
0.326334 + 0.945254i \(0.394186\pi\)
\(600\) −11.3351 −0.462754
\(601\) 24.8221 1.01251 0.506257 0.862383i \(-0.331029\pi\)
0.506257 + 0.862383i \(0.331029\pi\)
\(602\) 11.2378 0.458018
\(603\) −25.8489 −1.05265
\(604\) −10.9227 −0.444440
\(605\) 83.6386 3.40039
\(606\) −9.17869 −0.372859
\(607\) −7.47649 −0.303462 −0.151731 0.988422i \(-0.548485\pi\)
−0.151731 + 0.988422i \(0.548485\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −44.0124 −1.78347
\(610\) 12.0788 0.489058
\(611\) −3.71178 −0.150162
\(612\) 0.468670 0.0189449
\(613\) −17.7196 −0.715689 −0.357844 0.933781i \(-0.616488\pi\)
−0.357844 + 0.933781i \(0.616488\pi\)
\(614\) 5.14591 0.207672
\(615\) −43.6468 −1.76001
\(616\) −27.2109 −1.09636
\(617\) 43.5877 1.75477 0.877387 0.479784i \(-0.159285\pi\)
0.877387 + 0.479784i \(0.159285\pi\)
\(618\) −18.9652 −0.762893
\(619\) −16.3139 −0.655712 −0.327856 0.944728i \(-0.606326\pi\)
−0.327856 + 0.944728i \(0.606326\pi\)
\(620\) −26.9004 −1.08035
\(621\) −17.8526 −0.716400
\(622\) −0.505072 −0.0202516
\(623\) 29.5726 1.18480
\(624\) 4.54276 0.181856
\(625\) 28.2226 1.12891
\(626\) −13.1933 −0.527308
\(627\) 6.32254 0.252498
\(628\) −2.38660 −0.0952359
\(629\) −2.69213 −0.107342
\(630\) 32.9400 1.31236
\(631\) −7.93271 −0.315796 −0.157898 0.987455i \(-0.550472\pi\)
−0.157898 + 0.987455i \(0.550472\pi\)
\(632\) −5.66673 −0.225410
\(633\) 1.10999 0.0441183
\(634\) 30.1676 1.19811
\(635\) −33.5677 −1.33209
\(636\) −12.3628 −0.490218
\(637\) −64.7510 −2.56553
\(638\) −47.2773 −1.87172
\(639\) 22.5628 0.892572
\(640\) 3.90024 0.154170
\(641\) 44.2457 1.74760 0.873799 0.486287i \(-0.161649\pi\)
0.873799 + 0.486287i \(0.161649\pi\)
\(642\) 6.79379 0.268129
\(643\) 20.3317 0.801805 0.400903 0.916121i \(-0.368697\pi\)
0.400903 + 0.916121i \(0.368697\pi\)
\(644\) 16.1148 0.635012
\(645\) 10.1840 0.400997
\(646\) 0.265098 0.0104302
\(647\) 38.4286 1.51078 0.755391 0.655274i \(-0.227447\pi\)
0.755391 + 0.655274i \(0.227447\pi\)
\(648\) −0.570756 −0.0224214
\(649\) 82.9260 3.25513
\(650\) −41.7930 −1.63926
\(651\) −36.5730 −1.43341
\(652\) 3.26419 0.127836
\(653\) −15.8840 −0.621587 −0.310794 0.950477i \(-0.600595\pi\)
−0.310794 + 0.950477i \(0.600595\pi\)
\(654\) 3.32021 0.129831
\(655\) −31.4472 −1.22874
\(656\) 10.0818 0.393630
\(657\) 8.10775 0.316313
\(658\) −4.33266 −0.168905
\(659\) −17.8974 −0.697185 −0.348592 0.937274i \(-0.613340\pi\)
−0.348592 + 0.937274i \(0.613340\pi\)
\(660\) −24.6594 −0.959866
\(661\) −46.5929 −1.81225 −0.906127 0.423005i \(-0.860975\pi\)
−0.906127 + 0.423005i \(0.860975\pi\)
\(662\) 12.9868 0.504745
\(663\) −1.20428 −0.0467703
\(664\) 9.13201 0.354391
\(665\) 18.6322 0.722524
\(666\) −17.9535 −0.695684
\(667\) 27.9985 1.08411
\(668\) 2.79406 0.108105
\(669\) 21.3982 0.827300
\(670\) 57.0260 2.20311
\(671\) 17.6402 0.680994
\(672\) 5.30265 0.204554
\(673\) 11.6224 0.448012 0.224006 0.974588i \(-0.428086\pi\)
0.224006 + 0.974588i \(0.428086\pi\)
\(674\) 14.6345 0.563699
\(675\) 54.0448 2.08018
\(676\) 3.74935 0.144206
\(677\) 24.5098 0.941988 0.470994 0.882137i \(-0.343895\pi\)
0.470994 + 0.882137i \(0.343895\pi\)
\(678\) −9.72294 −0.373407
\(679\) −42.5086 −1.63133
\(680\) −1.03395 −0.0396500
\(681\) −9.62561 −0.368854
\(682\) −39.2860 −1.50434
\(683\) 43.1677 1.65176 0.825882 0.563843i \(-0.190678\pi\)
0.825882 + 0.563843i \(0.190678\pi\)
\(684\) 1.76791 0.0675978
\(685\) 27.1162 1.03606
\(686\) −42.1419 −1.60899
\(687\) −10.7630 −0.410633
\(688\) −2.35239 −0.0896839
\(689\) −45.5823 −1.73655
\(690\) 14.6038 0.555955
\(691\) −35.8995 −1.36568 −0.682841 0.730567i \(-0.739256\pi\)
−0.682841 + 0.730567i \(0.739256\pi\)
\(692\) 16.5663 0.629756
\(693\) 48.1064 1.82741
\(694\) 13.9248 0.528578
\(695\) 66.8968 2.53754
\(696\) 9.21304 0.349219
\(697\) −2.67268 −0.101235
\(698\) 12.9954 0.491883
\(699\) 7.97411 0.301609
\(700\) −48.7839 −1.84386
\(701\) 49.3097 1.86240 0.931201 0.364506i \(-0.118762\pi\)
0.931201 + 0.364506i \(0.118762\pi\)
\(702\) −21.6595 −0.817485
\(703\) −10.1552 −0.383011
\(704\) 5.69601 0.214676
\(705\) −3.92640 −0.147877
\(706\) −0.158909 −0.00598061
\(707\) −39.5032 −1.48567
\(708\) −16.1600 −0.607330
\(709\) −20.2346 −0.759925 −0.379962 0.925002i \(-0.624063\pi\)
−0.379962 + 0.925002i \(0.624063\pi\)
\(710\) −49.7765 −1.86808
\(711\) 10.0183 0.375714
\(712\) −6.19037 −0.231994
\(713\) 23.2659 0.871316
\(714\) −1.40572 −0.0526079
\(715\) −90.9202 −3.40022
\(716\) 11.5835 0.432897
\(717\) −1.06903 −0.0399235
\(718\) −20.9540 −0.781997
\(719\) −0.478346 −0.0178393 −0.00891966 0.999960i \(-0.502839\pi\)
−0.00891966 + 0.999960i \(0.502839\pi\)
\(720\) −6.89527 −0.256972
\(721\) −81.6223 −3.03977
\(722\) 1.00000 0.0372161
\(723\) 12.9602 0.481995
\(724\) −1.55513 −0.0577960
\(725\) −84.7591 −3.14787
\(726\) −23.8033 −0.883422
\(727\) 1.60528 0.0595366 0.0297683 0.999557i \(-0.490523\pi\)
0.0297683 + 0.999557i \(0.490523\pi\)
\(728\) 19.5511 0.724612
\(729\) 18.6325 0.690093
\(730\) −17.8867 −0.662018
\(731\) 0.623613 0.0230652
\(732\) −3.43760 −0.127057
\(733\) 0.287647 0.0106245 0.00531224 0.999986i \(-0.498309\pi\)
0.00531224 + 0.999986i \(0.498309\pi\)
\(734\) −17.7347 −0.654601
\(735\) −68.4951 −2.52648
\(736\) −3.37328 −0.124341
\(737\) 83.2822 3.06774
\(738\) −17.8238 −0.656103
\(739\) −25.5231 −0.938882 −0.469441 0.882964i \(-0.655544\pi\)
−0.469441 + 0.882964i \(0.655544\pi\)
\(740\) 39.6077 1.45601
\(741\) −4.54276 −0.166883
\(742\) −53.2071 −1.95329
\(743\) −50.6257 −1.85728 −0.928638 0.370987i \(-0.879020\pi\)
−0.928638 + 0.370987i \(0.879020\pi\)
\(744\) 7.65577 0.280674
\(745\) −63.7527 −2.33572
\(746\) −3.71068 −0.135857
\(747\) −16.1446 −0.590700
\(748\) −1.51000 −0.0552111
\(749\) 29.2390 1.06837
\(750\) −22.5634 −0.823898
\(751\) 43.1146 1.57327 0.786637 0.617416i \(-0.211820\pi\)
0.786637 + 0.617416i \(0.211820\pi\)
\(752\) 0.906948 0.0330730
\(753\) 20.6310 0.751835
\(754\) 33.9689 1.23707
\(755\) −42.6013 −1.55042
\(756\) −25.2826 −0.919518
\(757\) −20.1770 −0.733345 −0.366672 0.930350i \(-0.619503\pi\)
−0.366672 + 0.930350i \(0.619503\pi\)
\(758\) 30.0212 1.09042
\(759\) 21.3277 0.774146
\(760\) −3.90024 −0.141476
\(761\) 52.9210 1.91838 0.959192 0.282757i \(-0.0912488\pi\)
0.959192 + 0.282757i \(0.0912488\pi\)
\(762\) 9.55326 0.346078
\(763\) 14.2895 0.517315
\(764\) 2.81445 0.101823
\(765\) 1.82793 0.0660888
\(766\) −14.3270 −0.517657
\(767\) −59.5826 −2.15140
\(768\) −1.10999 −0.0400535
\(769\) 0.842653 0.0303869 0.0151934 0.999885i \(-0.495164\pi\)
0.0151934 + 0.999885i \(0.495164\pi\)
\(770\) −106.129 −3.82462
\(771\) −19.0486 −0.686017
\(772\) 12.1750 0.438189
\(773\) −4.54848 −0.163598 −0.0817988 0.996649i \(-0.526066\pi\)
−0.0817988 + 0.996649i \(0.526066\pi\)
\(774\) 4.15881 0.149485
\(775\) −70.4324 −2.53000
\(776\) 8.89825 0.319429
\(777\) 53.8495 1.93184
\(778\) 2.66506 0.0955470
\(779\) −10.0818 −0.361220
\(780\) 17.7179 0.634401
\(781\) −72.6948 −2.60123
\(782\) 0.894251 0.0319784
\(783\) −43.9270 −1.56982
\(784\) 15.8215 0.565054
\(785\) −9.30832 −0.332228
\(786\) 8.94976 0.319228
\(787\) 40.8477 1.45606 0.728032 0.685544i \(-0.240435\pi\)
0.728032 + 0.685544i \(0.240435\pi\)
\(788\) 19.1442 0.681983
\(789\) 9.16683 0.326348
\(790\) −22.1016 −0.786339
\(791\) −41.8455 −1.48785
\(792\) −10.0700 −0.357823
\(793\) −12.6746 −0.450087
\(794\) −8.22764 −0.291988
\(795\) −48.2180 −1.71012
\(796\) 8.27226 0.293203
\(797\) 39.1845 1.38798 0.693992 0.719982i \(-0.255850\pi\)
0.693992 + 0.719982i \(0.255850\pi\)
\(798\) −5.30265 −0.187712
\(799\) −0.240431 −0.00850582
\(800\) 10.2119 0.361043
\(801\) 10.9440 0.386688
\(802\) 16.2754 0.574706
\(803\) −26.1222 −0.921834
\(804\) −16.2294 −0.572368
\(805\) 62.8515 2.21522
\(806\) 28.2271 0.994258
\(807\) −19.3795 −0.682189
\(808\) 8.26913 0.290907
\(809\) 10.3248 0.363000 0.181500 0.983391i \(-0.441905\pi\)
0.181500 + 0.983391i \(0.441905\pi\)
\(810\) −2.22608 −0.0782166
\(811\) −39.6352 −1.39178 −0.695890 0.718149i \(-0.744990\pi\)
−0.695890 + 0.718149i \(0.744990\pi\)
\(812\) 39.6510 1.39148
\(813\) 9.62561 0.337585
\(814\) 57.8441 2.02743
\(815\) 12.7311 0.445952
\(816\) 0.294258 0.0103011
\(817\) 2.35239 0.0822996
\(818\) −2.15867 −0.0754763
\(819\) −34.5646 −1.20778
\(820\) 39.3216 1.37317
\(821\) 11.2275 0.391844 0.195922 0.980620i \(-0.437230\pi\)
0.195922 + 0.980620i \(0.437230\pi\)
\(822\) −7.71718 −0.269168
\(823\) 35.1955 1.22684 0.613420 0.789757i \(-0.289793\pi\)
0.613420 + 0.789757i \(0.289793\pi\)
\(824\) 17.0859 0.595214
\(825\) −64.5648 −2.24786
\(826\) −69.5492 −2.41993
\(827\) −42.5451 −1.47944 −0.739719 0.672916i \(-0.765041\pi\)
−0.739719 + 0.672916i \(0.765041\pi\)
\(828\) 5.96366 0.207252
\(829\) 4.57321 0.158834 0.0794171 0.996841i \(-0.474694\pi\)
0.0794171 + 0.996841i \(0.474694\pi\)
\(830\) 35.6170 1.23628
\(831\) −14.4423 −0.500997
\(832\) −4.09260 −0.141885
\(833\) −4.19425 −0.145322
\(834\) −19.0386 −0.659253
\(835\) 10.8975 0.377123
\(836\) −5.69601 −0.197000
\(837\) −36.5020 −1.26169
\(838\) −12.5558 −0.433734
\(839\) −42.4314 −1.46489 −0.732447 0.680824i \(-0.761622\pi\)
−0.732447 + 0.680824i \(0.761622\pi\)
\(840\) 20.6816 0.713583
\(841\) 39.8912 1.37556
\(842\) −16.4123 −0.565607
\(843\) 17.0389 0.586851
\(844\) −1.00000 −0.0344214
\(845\) 14.6234 0.503059
\(846\) −1.60340 −0.0551262
\(847\) −102.444 −3.52003
\(848\) 11.1377 0.382472
\(849\) 29.3871 1.00856
\(850\) −2.70714 −0.0928543
\(851\) −34.2563 −1.17429
\(852\) 14.1662 0.485327
\(853\) −27.7354 −0.949641 −0.474820 0.880083i \(-0.657487\pi\)
−0.474820 + 0.880083i \(0.657487\pi\)
\(854\) −14.7947 −0.506264
\(855\) 6.89527 0.235813
\(856\) −6.12056 −0.209196
\(857\) −29.3738 −1.00339 −0.501695 0.865045i \(-0.667290\pi\)
−0.501695 + 0.865045i \(0.667290\pi\)
\(858\) 25.8756 0.883378
\(859\) 36.3973 1.24186 0.620930 0.783866i \(-0.286755\pi\)
0.620930 + 0.783866i \(0.286755\pi\)
\(860\) −9.17486 −0.312860
\(861\) 53.4605 1.82193
\(862\) 6.50015 0.221396
\(863\) 41.5384 1.41398 0.706992 0.707221i \(-0.250052\pi\)
0.706992 + 0.707221i \(0.250052\pi\)
\(864\) 5.29236 0.180050
\(865\) 64.6124 2.19689
\(866\) 11.9525 0.406161
\(867\) 18.7919 0.638207
\(868\) 32.9488 1.11836
\(869\) −32.2777 −1.09495
\(870\) 35.9330 1.21824
\(871\) −59.8386 −2.02755
\(872\) −2.99120 −0.101295
\(873\) −15.7313 −0.532425
\(874\) 3.37328 0.114103
\(875\) −97.1080 −3.28285
\(876\) 5.09051 0.171992
\(877\) −19.7182 −0.665837 −0.332918 0.942956i \(-0.608033\pi\)
−0.332918 + 0.942956i \(0.608033\pi\)
\(878\) −12.3919 −0.418207
\(879\) 30.9627 1.04435
\(880\) 22.2158 0.748894
\(881\) 30.6119 1.03134 0.515670 0.856787i \(-0.327543\pi\)
0.515670 + 0.856787i \(0.327543\pi\)
\(882\) −27.9710 −0.941833
\(883\) −44.0343 −1.48187 −0.740937 0.671575i \(-0.765618\pi\)
−0.740937 + 0.671575i \(0.765618\pi\)
\(884\) 1.08494 0.0364905
\(885\) −63.0278 −2.11866
\(886\) −13.0536 −0.438544
\(887\) 14.0781 0.472696 0.236348 0.971668i \(-0.424049\pi\)
0.236348 + 0.971668i \(0.424049\pi\)
\(888\) −11.2722 −0.378271
\(889\) 41.1152 1.37896
\(890\) −24.1439 −0.809306
\(891\) −3.25103 −0.108914
\(892\) −19.2777 −0.645465
\(893\) −0.906948 −0.0303499
\(894\) 18.1438 0.606820
\(895\) 45.1785 1.51015
\(896\) −4.77719 −0.159595
\(897\) −15.3240 −0.511654
\(898\) 29.4917 0.984151
\(899\) 57.2466 1.90928
\(900\) −18.0536 −0.601788
\(901\) −2.95260 −0.0983653
\(902\) 57.4262 1.91208
\(903\) −12.4739 −0.415105
\(904\) 8.75944 0.291335
\(905\) −6.06538 −0.201620
\(906\) 12.1242 0.402799
\(907\) −22.2892 −0.740101 −0.370050 0.929012i \(-0.620660\pi\)
−0.370050 + 0.929012i \(0.620660\pi\)
\(908\) 8.67176 0.287782
\(909\) −14.6191 −0.484885
\(910\) 76.2539 2.52779
\(911\) −35.2058 −1.16642 −0.583210 0.812321i \(-0.698204\pi\)
−0.583210 + 0.812321i \(0.698204\pi\)
\(912\) 1.10999 0.0367556
\(913\) 52.0160 1.72148
\(914\) −0.324966 −0.0107489
\(915\) −13.4075 −0.443237
\(916\) 9.69642 0.320379
\(917\) 38.5179 1.27197
\(918\) −1.40300 −0.0463057
\(919\) −33.0931 −1.09164 −0.545820 0.837902i \(-0.683782\pi\)
−0.545820 + 0.837902i \(0.683782\pi\)
\(920\) −13.1566 −0.433760
\(921\) −5.71194 −0.188215
\(922\) 38.2872 1.26092
\(923\) 52.2315 1.71922
\(924\) 30.2039 0.993636
\(925\) 103.703 3.40975
\(926\) 34.0027 1.11740
\(927\) −30.2063 −0.992105
\(928\) −8.30007 −0.272463
\(929\) −15.3128 −0.502396 −0.251198 0.967936i \(-0.580825\pi\)
−0.251198 + 0.967936i \(0.580825\pi\)
\(930\) 29.8593 0.979125
\(931\) −15.8215 −0.518529
\(932\) −7.18392 −0.235317
\(933\) 0.560628 0.0183541
\(934\) −21.4709 −0.702550
\(935\) −5.88936 −0.192603
\(936\) 7.23535 0.236495
\(937\) 22.5877 0.737909 0.368955 0.929447i \(-0.379716\pi\)
0.368955 + 0.929447i \(0.379716\pi\)
\(938\) −69.8480 −2.28062
\(939\) 14.6444 0.477903
\(940\) 3.53731 0.115374
\(941\) 4.08923 0.133305 0.0666525 0.997776i \(-0.478768\pi\)
0.0666525 + 0.997776i \(0.478768\pi\)
\(942\) 2.64912 0.0863130
\(943\) −34.0089 −1.10748
\(944\) 14.5586 0.473843
\(945\) −98.6080 −3.20772
\(946\) −13.3992 −0.435646
\(947\) −17.9025 −0.581752 −0.290876 0.956761i \(-0.593947\pi\)
−0.290876 + 0.956761i \(0.593947\pi\)
\(948\) 6.29004 0.204291
\(949\) 18.7689 0.609264
\(950\) −10.2119 −0.331316
\(951\) −33.4859 −1.08585
\(952\) 1.26642 0.0410450
\(953\) −7.02237 −0.227477 −0.113738 0.993511i \(-0.536283\pi\)
−0.113738 + 0.993511i \(0.536283\pi\)
\(954\) −19.6905 −0.637505
\(955\) 10.9770 0.355209
\(956\) 0.963091 0.0311486
\(957\) 52.4775 1.69636
\(958\) 5.37891 0.173785
\(959\) −33.2131 −1.07251
\(960\) −4.32924 −0.139726
\(961\) 16.5703 0.534525
\(962\) −41.5612 −1.33999
\(963\) 10.8206 0.348689
\(964\) −11.6759 −0.376055
\(965\) 47.4855 1.52861
\(966\) −17.8873 −0.575515
\(967\) −22.6933 −0.729768 −0.364884 0.931053i \(-0.618891\pi\)
−0.364884 + 0.931053i \(0.618891\pi\)
\(968\) 21.4445 0.689252
\(969\) −0.294258 −0.00945292
\(970\) 34.7053 1.11432
\(971\) −39.1564 −1.25659 −0.628294 0.777976i \(-0.716247\pi\)
−0.628294 + 0.777976i \(0.716247\pi\)
\(972\) −15.2435 −0.488937
\(973\) −81.9381 −2.62682
\(974\) −14.1416 −0.453124
\(975\) 46.3900 1.48567
\(976\) 3.09695 0.0991310
\(977\) 54.7113 1.75037 0.875184 0.483790i \(-0.160740\pi\)
0.875184 + 0.483790i \(0.160740\pi\)
\(978\) −3.62324 −0.115858
\(979\) −35.2604 −1.12693
\(980\) 61.7076 1.97118
\(981\) 5.28817 0.168838
\(982\) 19.7165 0.629177
\(983\) −35.1469 −1.12101 −0.560506 0.828150i \(-0.689393\pi\)
−0.560506 + 0.828150i \(0.689393\pi\)
\(984\) −11.1908 −0.356750
\(985\) 74.6668 2.37908
\(986\) 2.20034 0.0700730
\(987\) 4.80923 0.153080
\(988\) 4.09260 0.130203
\(989\) 7.93526 0.252326
\(990\) −39.2755 −1.24826
\(991\) −26.9873 −0.857279 −0.428640 0.903476i \(-0.641007\pi\)
−0.428640 + 0.903476i \(0.641007\pi\)
\(992\) −6.89712 −0.218984
\(993\) −14.4153 −0.457454
\(994\) 60.9685 1.93380
\(995\) 32.2638 1.02283
\(996\) −10.1365 −0.321187
\(997\) −6.27963 −0.198878 −0.0994389 0.995044i \(-0.531705\pi\)
−0.0994389 + 0.995044i \(0.531705\pi\)
\(998\) −38.5801 −1.22123
\(999\) 53.7450 1.70042
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 \(a_p\))