Properties

Label 6039.2.a.j.1.11
Level 6039
Weight 2
Character 6039.1
Self dual Yes
Analytic conductor 48.222
Analytic rank 0
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6039.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2216577807\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(1.67203\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.67203 q^{2}\) \(+0.795679 q^{4}\) \(+1.45953 q^{5}\) \(-0.113904 q^{7}\) \(-2.01366 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.67203 q^{2}\) \(+0.795679 q^{4}\) \(+1.45953 q^{5}\) \(-0.113904 q^{7}\) \(-2.01366 q^{8}\) \(+2.44037 q^{10}\) \(+1.00000 q^{11}\) \(-2.41931 q^{13}\) \(-0.190451 q^{14}\) \(-4.95825 q^{16}\) \(-4.33956 q^{17}\) \(+5.52946 q^{19}\) \(+1.16132 q^{20}\) \(+1.67203 q^{22}\) \(+5.61639 q^{23}\) \(-2.86978 q^{25}\) \(-4.04515 q^{26}\) \(-0.0906313 q^{28}\) \(+2.97696 q^{29}\) \(+3.23872 q^{31}\) \(-4.26302 q^{32}\) \(-7.25587 q^{34}\) \(-0.166247 q^{35}\) \(+5.47586 q^{37}\) \(+9.24541 q^{38}\) \(-2.93899 q^{40}\) \(+3.54936 q^{41}\) \(+3.64080 q^{43}\) \(+0.795679 q^{44}\) \(+9.39076 q^{46}\) \(+6.81812 q^{47}\) \(-6.98703 q^{49}\) \(-4.79835 q^{50}\) \(-1.92499 q^{52}\) \(+0.123290 q^{53}\) \(+1.45953 q^{55}\) \(+0.229364 q^{56}\) \(+4.97756 q^{58}\) \(+14.8361 q^{59}\) \(+1.00000 q^{61}\) \(+5.41523 q^{62}\) \(+2.78861 q^{64}\) \(-3.53104 q^{65}\) \(+9.16048 q^{67}\) \(-3.45290 q^{68}\) \(-0.277969 q^{70}\) \(+9.69135 q^{71}\) \(-1.05277 q^{73}\) \(+9.15579 q^{74}\) \(+4.39968 q^{76}\) \(-0.113904 q^{77}\) \(+10.0943 q^{79}\) \(-7.23671 q^{80}\) \(+5.93464 q^{82}\) \(+2.01215 q^{83}\) \(-6.33371 q^{85}\) \(+6.08752 q^{86}\) \(-2.01366 q^{88}\) \(-16.8141 q^{89}\) \(+0.275569 q^{91}\) \(+4.46885 q^{92}\) \(+11.4001 q^{94}\) \(+8.07040 q^{95}\) \(-4.43143 q^{97}\) \(-11.6825 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.67203 1.18230 0.591151 0.806561i \(-0.298674\pi\)
0.591151 + 0.806561i \(0.298674\pi\)
\(3\) 0 0
\(4\) 0.795679 0.397840
\(5\) 1.45953 0.652721 0.326360 0.945245i \(-0.394178\pi\)
0.326360 + 0.945245i \(0.394178\pi\)
\(6\) 0 0
\(7\) −0.113904 −0.0430518 −0.0215259 0.999768i \(-0.506852\pi\)
−0.0215259 + 0.999768i \(0.506852\pi\)
\(8\) −2.01366 −0.711936
\(9\) 0 0
\(10\) 2.44037 0.771713
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −2.41931 −0.670995 −0.335497 0.942041i \(-0.608904\pi\)
−0.335497 + 0.942041i \(0.608904\pi\)
\(14\) −0.190451 −0.0509002
\(15\) 0 0
\(16\) −4.95825 −1.23956
\(17\) −4.33956 −1.05250 −0.526249 0.850330i \(-0.676402\pi\)
−0.526249 + 0.850330i \(0.676402\pi\)
\(18\) 0 0
\(19\) 5.52946 1.26855 0.634273 0.773110i \(-0.281300\pi\)
0.634273 + 0.773110i \(0.281300\pi\)
\(20\) 1.16132 0.259678
\(21\) 0 0
\(22\) 1.67203 0.356478
\(23\) 5.61639 1.17110 0.585549 0.810637i \(-0.300879\pi\)
0.585549 + 0.810637i \(0.300879\pi\)
\(24\) 0 0
\(25\) −2.86978 −0.573956
\(26\) −4.04515 −0.793319
\(27\) 0 0
\(28\) −0.0906313 −0.0171277
\(29\) 2.97696 0.552807 0.276404 0.961042i \(-0.410857\pi\)
0.276404 + 0.961042i \(0.410857\pi\)
\(30\) 0 0
\(31\) 3.23872 0.581691 0.290846 0.956770i \(-0.406063\pi\)
0.290846 + 0.956770i \(0.406063\pi\)
\(32\) −4.26302 −0.753603
\(33\) 0 0
\(34\) −7.25587 −1.24437
\(35\) −0.166247 −0.0281008
\(36\) 0 0
\(37\) 5.47586 0.900225 0.450113 0.892972i \(-0.351384\pi\)
0.450113 + 0.892972i \(0.351384\pi\)
\(38\) 9.24541 1.49980
\(39\) 0 0
\(40\) −2.93899 −0.464695
\(41\) 3.54936 0.554317 0.277159 0.960824i \(-0.410607\pi\)
0.277159 + 0.960824i \(0.410607\pi\)
\(42\) 0 0
\(43\) 3.64080 0.555217 0.277609 0.960694i \(-0.410458\pi\)
0.277609 + 0.960694i \(0.410458\pi\)
\(44\) 0.795679 0.119953
\(45\) 0 0
\(46\) 9.39076 1.38459
\(47\) 6.81812 0.994525 0.497263 0.867600i \(-0.334339\pi\)
0.497263 + 0.867600i \(0.334339\pi\)
\(48\) 0 0
\(49\) −6.98703 −0.998147
\(50\) −4.79835 −0.678589
\(51\) 0 0
\(52\) −1.92499 −0.266948
\(53\) 0.123290 0.0169352 0.00846758 0.999964i \(-0.497305\pi\)
0.00846758 + 0.999964i \(0.497305\pi\)
\(54\) 0 0
\(55\) 1.45953 0.196803
\(56\) 0.229364 0.0306501
\(57\) 0 0
\(58\) 4.97756 0.653585
\(59\) 14.8361 1.93149 0.965746 0.259488i \(-0.0835538\pi\)
0.965746 + 0.259488i \(0.0835538\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) 5.41523 0.687735
\(63\) 0 0
\(64\) 2.78861 0.348576
\(65\) −3.53104 −0.437972
\(66\) 0 0
\(67\) 9.16048 1.11913 0.559566 0.828786i \(-0.310968\pi\)
0.559566 + 0.828786i \(0.310968\pi\)
\(68\) −3.45290 −0.418726
\(69\) 0 0
\(70\) −0.277969 −0.0332236
\(71\) 9.69135 1.15015 0.575076 0.818100i \(-0.304973\pi\)
0.575076 + 0.818100i \(0.304973\pi\)
\(72\) 0 0
\(73\) −1.05277 −0.123217 −0.0616087 0.998100i \(-0.519623\pi\)
−0.0616087 + 0.998100i \(0.519623\pi\)
\(74\) 9.15579 1.06434
\(75\) 0 0
\(76\) 4.39968 0.504678
\(77\) −0.113904 −0.0129806
\(78\) 0 0
\(79\) 10.0943 1.13570 0.567850 0.823132i \(-0.307775\pi\)
0.567850 + 0.823132i \(0.307775\pi\)
\(80\) −7.23671 −0.809089
\(81\) 0 0
\(82\) 5.93464 0.655371
\(83\) 2.01215 0.220862 0.110431 0.993884i \(-0.464777\pi\)
0.110431 + 0.993884i \(0.464777\pi\)
\(84\) 0 0
\(85\) −6.33371 −0.686988
\(86\) 6.08752 0.656435
\(87\) 0 0
\(88\) −2.01366 −0.214657
\(89\) −16.8141 −1.78229 −0.891145 0.453719i \(-0.850097\pi\)
−0.891145 + 0.453719i \(0.850097\pi\)
\(90\) 0 0
\(91\) 0.275569 0.0288875
\(92\) 4.46885 0.465909
\(93\) 0 0
\(94\) 11.4001 1.17583
\(95\) 8.07040 0.828006
\(96\) 0 0
\(97\) −4.43143 −0.449944 −0.224972 0.974365i \(-0.572229\pi\)
−0.224972 + 0.974365i \(0.572229\pi\)
\(98\) −11.6825 −1.18011
\(99\) 0 0
\(100\) −2.28342 −0.228342
\(101\) 9.12365 0.907837 0.453918 0.891043i \(-0.350026\pi\)
0.453918 + 0.891043i \(0.350026\pi\)
\(102\) 0 0
\(103\) −4.46502 −0.439951 −0.219976 0.975505i \(-0.570598\pi\)
−0.219976 + 0.975505i \(0.570598\pi\)
\(104\) 4.87165 0.477705
\(105\) 0 0
\(106\) 0.206144 0.0200225
\(107\) −3.58525 −0.346599 −0.173300 0.984869i \(-0.555443\pi\)
−0.173300 + 0.984869i \(0.555443\pi\)
\(108\) 0 0
\(109\) 3.16796 0.303435 0.151718 0.988424i \(-0.451520\pi\)
0.151718 + 0.988424i \(0.451520\pi\)
\(110\) 2.44037 0.232680
\(111\) 0 0
\(112\) 0.564766 0.0533654
\(113\) −9.84126 −0.925788 −0.462894 0.886414i \(-0.653189\pi\)
−0.462894 + 0.886414i \(0.653189\pi\)
\(114\) 0 0
\(115\) 8.19728 0.764400
\(116\) 2.36870 0.219929
\(117\) 0 0
\(118\) 24.8063 2.28361
\(119\) 0.494295 0.0453119
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 1.67203 0.151378
\(123\) 0 0
\(124\) 2.57698 0.231420
\(125\) −11.4862 −1.02735
\(126\) 0 0
\(127\) 7.25474 0.643754 0.321877 0.946782i \(-0.395686\pi\)
0.321877 + 0.946782i \(0.395686\pi\)
\(128\) 13.1887 1.16573
\(129\) 0 0
\(130\) −5.90401 −0.517816
\(131\) −5.18052 −0.452624 −0.226312 0.974055i \(-0.572667\pi\)
−0.226312 + 0.974055i \(0.572667\pi\)
\(132\) 0 0
\(133\) −0.629829 −0.0546131
\(134\) 15.3166 1.32315
\(135\) 0 0
\(136\) 8.73840 0.749311
\(137\) −15.9087 −1.35918 −0.679588 0.733594i \(-0.737841\pi\)
−0.679588 + 0.733594i \(0.737841\pi\)
\(138\) 0 0
\(139\) 17.4182 1.47740 0.738698 0.674037i \(-0.235441\pi\)
0.738698 + 0.674037i \(0.235441\pi\)
\(140\) −0.132279 −0.0111796
\(141\) 0 0
\(142\) 16.2042 1.35983
\(143\) −2.41931 −0.202312
\(144\) 0 0
\(145\) 4.34495 0.360829
\(146\) −1.76026 −0.145680
\(147\) 0 0
\(148\) 4.35703 0.358145
\(149\) 20.0971 1.64642 0.823208 0.567740i \(-0.192182\pi\)
0.823208 + 0.567740i \(0.192182\pi\)
\(150\) 0 0
\(151\) 14.1784 1.15382 0.576910 0.816808i \(-0.304258\pi\)
0.576910 + 0.816808i \(0.304258\pi\)
\(152\) −11.1344 −0.903123
\(153\) 0 0
\(154\) −0.190451 −0.0153470
\(155\) 4.72700 0.379682
\(156\) 0 0
\(157\) 4.99242 0.398439 0.199219 0.979955i \(-0.436159\pi\)
0.199219 + 0.979955i \(0.436159\pi\)
\(158\) 16.8780 1.34274
\(159\) 0 0
\(160\) −6.22200 −0.491892
\(161\) −0.639731 −0.0504179
\(162\) 0 0
\(163\) −5.98250 −0.468586 −0.234293 0.972166i \(-0.575277\pi\)
−0.234293 + 0.972166i \(0.575277\pi\)
\(164\) 2.82416 0.220529
\(165\) 0 0
\(166\) 3.36438 0.261126
\(167\) −24.2227 −1.87441 −0.937203 0.348784i \(-0.886595\pi\)
−0.937203 + 0.348784i \(0.886595\pi\)
\(168\) 0 0
\(169\) −7.14696 −0.549766
\(170\) −10.5901 −0.812227
\(171\) 0 0
\(172\) 2.89691 0.220887
\(173\) −11.4724 −0.872227 −0.436114 0.899892i \(-0.643645\pi\)
−0.436114 + 0.899892i \(0.643645\pi\)
\(174\) 0 0
\(175\) 0.326880 0.0247098
\(176\) −4.95825 −0.373742
\(177\) 0 0
\(178\) −28.1136 −2.10721
\(179\) −16.7617 −1.25283 −0.626413 0.779492i \(-0.715477\pi\)
−0.626413 + 0.779492i \(0.715477\pi\)
\(180\) 0 0
\(181\) 23.4517 1.74315 0.871574 0.490264i \(-0.163100\pi\)
0.871574 + 0.490264i \(0.163100\pi\)
\(182\) 0.460760 0.0341538
\(183\) 0 0
\(184\) −11.3095 −0.833747
\(185\) 7.99217 0.587596
\(186\) 0 0
\(187\) −4.33956 −0.317340
\(188\) 5.42504 0.395662
\(189\) 0 0
\(190\) 13.4939 0.978953
\(191\) 8.77663 0.635054 0.317527 0.948249i \(-0.397148\pi\)
0.317527 + 0.948249i \(0.397148\pi\)
\(192\) 0 0
\(193\) 11.8741 0.854716 0.427358 0.904083i \(-0.359444\pi\)
0.427358 + 0.904083i \(0.359444\pi\)
\(194\) −7.40948 −0.531970
\(195\) 0 0
\(196\) −5.55943 −0.397102
\(197\) 6.68035 0.475956 0.237978 0.971271i \(-0.423515\pi\)
0.237978 + 0.971271i \(0.423515\pi\)
\(198\) 0 0
\(199\) −12.2108 −0.865602 −0.432801 0.901490i \(-0.642475\pi\)
−0.432801 + 0.901490i \(0.642475\pi\)
\(200\) 5.77875 0.408620
\(201\) 0 0
\(202\) 15.2550 1.07334
\(203\) −0.339088 −0.0237993
\(204\) 0 0
\(205\) 5.18039 0.361814
\(206\) −7.46564 −0.520156
\(207\) 0 0
\(208\) 11.9955 0.831740
\(209\) 5.52946 0.382481
\(210\) 0 0
\(211\) 2.24877 0.154812 0.0774058 0.997000i \(-0.475336\pi\)
0.0774058 + 0.997000i \(0.475336\pi\)
\(212\) 0.0980991 0.00673748
\(213\) 0 0
\(214\) −5.99464 −0.409785
\(215\) 5.31385 0.362402
\(216\) 0 0
\(217\) −0.368904 −0.0250428
\(218\) 5.29692 0.358753
\(219\) 0 0
\(220\) 1.16132 0.0782959
\(221\) 10.4987 0.706221
\(222\) 0 0
\(223\) 25.2425 1.69036 0.845181 0.534480i \(-0.179493\pi\)
0.845181 + 0.534480i \(0.179493\pi\)
\(224\) 0.485577 0.0324440
\(225\) 0 0
\(226\) −16.4549 −1.09456
\(227\) 15.9227 1.05682 0.528412 0.848988i \(-0.322788\pi\)
0.528412 + 0.848988i \(0.322788\pi\)
\(228\) 0 0
\(229\) 4.84415 0.320111 0.160055 0.987108i \(-0.448833\pi\)
0.160055 + 0.987108i \(0.448833\pi\)
\(230\) 13.7061 0.903752
\(231\) 0 0
\(232\) −5.99457 −0.393563
\(233\) 6.87950 0.450691 0.225346 0.974279i \(-0.427649\pi\)
0.225346 + 0.974279i \(0.427649\pi\)
\(234\) 0 0
\(235\) 9.95124 0.649147
\(236\) 11.8048 0.768425
\(237\) 0 0
\(238\) 0.826475 0.0535724
\(239\) −26.2207 −1.69607 −0.848037 0.529938i \(-0.822215\pi\)
−0.848037 + 0.529938i \(0.822215\pi\)
\(240\) 0 0
\(241\) −21.9334 −1.41286 −0.706428 0.707785i \(-0.749694\pi\)
−0.706428 + 0.707785i \(0.749694\pi\)
\(242\) 1.67203 0.107482
\(243\) 0 0
\(244\) 0.795679 0.0509382
\(245\) −10.1978 −0.651511
\(246\) 0 0
\(247\) −13.3775 −0.851187
\(248\) −6.52167 −0.414127
\(249\) 0 0
\(250\) −19.2052 −1.21464
\(251\) −24.9091 −1.57225 −0.786125 0.618068i \(-0.787916\pi\)
−0.786125 + 0.618068i \(0.787916\pi\)
\(252\) 0 0
\(253\) 5.61639 0.353099
\(254\) 12.1301 0.761112
\(255\) 0 0
\(256\) 16.4746 1.02966
\(257\) −0.438875 −0.0273763 −0.0136881 0.999906i \(-0.504357\pi\)
−0.0136881 + 0.999906i \(0.504357\pi\)
\(258\) 0 0
\(259\) −0.623724 −0.0387563
\(260\) −2.80958 −0.174243
\(261\) 0 0
\(262\) −8.66198 −0.535139
\(263\) −21.5826 −1.33084 −0.665421 0.746469i \(-0.731748\pi\)
−0.665421 + 0.746469i \(0.731748\pi\)
\(264\) 0 0
\(265\) 0.179945 0.0110539
\(266\) −1.05309 −0.0645692
\(267\) 0 0
\(268\) 7.28881 0.445235
\(269\) 24.6911 1.50544 0.752720 0.658341i \(-0.228741\pi\)
0.752720 + 0.658341i \(0.228741\pi\)
\(270\) 0 0
\(271\) −18.7879 −1.14128 −0.570641 0.821200i \(-0.693305\pi\)
−0.570641 + 0.821200i \(0.693305\pi\)
\(272\) 21.5167 1.30464
\(273\) 0 0
\(274\) −26.5999 −1.60696
\(275\) −2.86978 −0.173054
\(276\) 0 0
\(277\) −1.86162 −0.111854 −0.0559270 0.998435i \(-0.517811\pi\)
−0.0559270 + 0.998435i \(0.517811\pi\)
\(278\) 29.1238 1.74673
\(279\) 0 0
\(280\) 0.334764 0.0200060
\(281\) −12.0550 −0.719140 −0.359570 0.933118i \(-0.617077\pi\)
−0.359570 + 0.933118i \(0.617077\pi\)
\(282\) 0 0
\(283\) 17.4984 1.04017 0.520084 0.854115i \(-0.325900\pi\)
0.520084 + 0.854115i \(0.325900\pi\)
\(284\) 7.71121 0.457576
\(285\) 0 0
\(286\) −4.04515 −0.239195
\(287\) −0.404288 −0.0238644
\(288\) 0 0
\(289\) 1.83181 0.107754
\(290\) 7.26488 0.426609
\(291\) 0 0
\(292\) −0.837667 −0.0490208
\(293\) 4.01414 0.234509 0.117254 0.993102i \(-0.462591\pi\)
0.117254 + 0.993102i \(0.462591\pi\)
\(294\) 0 0
\(295\) 21.6537 1.26073
\(296\) −11.0265 −0.640903
\(297\) 0 0
\(298\) 33.6029 1.94656
\(299\) −13.5878 −0.785801
\(300\) 0 0
\(301\) −0.414703 −0.0239031
\(302\) 23.7066 1.36416
\(303\) 0 0
\(304\) −27.4165 −1.57244
\(305\) 1.45953 0.0835723
\(306\) 0 0
\(307\) 15.3443 0.875746 0.437873 0.899037i \(-0.355732\pi\)
0.437873 + 0.899037i \(0.355732\pi\)
\(308\) −0.0906313 −0.00516420
\(309\) 0 0
\(310\) 7.90368 0.448899
\(311\) −28.3138 −1.60553 −0.802764 0.596297i \(-0.796638\pi\)
−0.802764 + 0.596297i \(0.796638\pi\)
\(312\) 0 0
\(313\) 26.2747 1.48513 0.742567 0.669771i \(-0.233608\pi\)
0.742567 + 0.669771i \(0.233608\pi\)
\(314\) 8.34748 0.471075
\(315\) 0 0
\(316\) 8.03185 0.451827
\(317\) −31.0474 −1.74379 −0.871897 0.489689i \(-0.837110\pi\)
−0.871897 + 0.489689i \(0.837110\pi\)
\(318\) 0 0
\(319\) 2.97696 0.166678
\(320\) 4.07005 0.227523
\(321\) 0 0
\(322\) −1.06965 −0.0596092
\(323\) −23.9954 −1.33514
\(324\) 0 0
\(325\) 6.94287 0.385121
\(326\) −10.0029 −0.554010
\(327\) 0 0
\(328\) −7.14720 −0.394638
\(329\) −0.776614 −0.0428161
\(330\) 0 0
\(331\) −20.5558 −1.12985 −0.564924 0.825143i \(-0.691094\pi\)
−0.564924 + 0.825143i \(0.691094\pi\)
\(332\) 1.60103 0.0878679
\(333\) 0 0
\(334\) −40.5010 −2.21612
\(335\) 13.3700 0.730480
\(336\) 0 0
\(337\) −0.489461 −0.0266626 −0.0133313 0.999911i \(-0.504244\pi\)
−0.0133313 + 0.999911i \(0.504244\pi\)
\(338\) −11.9499 −0.649990
\(339\) 0 0
\(340\) −5.03961 −0.273311
\(341\) 3.23872 0.175386
\(342\) 0 0
\(343\) 1.59318 0.0860238
\(344\) −7.33133 −0.395279
\(345\) 0 0
\(346\) −19.1821 −1.03124
\(347\) 8.54263 0.458593 0.229296 0.973357i \(-0.426358\pi\)
0.229296 + 0.973357i \(0.426358\pi\)
\(348\) 0 0
\(349\) 28.5046 1.52582 0.762909 0.646506i \(-0.223770\pi\)
0.762909 + 0.646506i \(0.223770\pi\)
\(350\) 0.546553 0.0292145
\(351\) 0 0
\(352\) −4.26302 −0.227220
\(353\) −15.4235 −0.820912 −0.410456 0.911880i \(-0.634630\pi\)
−0.410456 + 0.911880i \(0.634630\pi\)
\(354\) 0 0
\(355\) 14.1448 0.750728
\(356\) −13.3786 −0.709066
\(357\) 0 0
\(358\) −28.0260 −1.48122
\(359\) 30.6063 1.61534 0.807669 0.589637i \(-0.200729\pi\)
0.807669 + 0.589637i \(0.200729\pi\)
\(360\) 0 0
\(361\) 11.5749 0.609206
\(362\) 39.2118 2.06093
\(363\) 0 0
\(364\) 0.219265 0.0114926
\(365\) −1.53655 −0.0804265
\(366\) 0 0
\(367\) 2.65622 0.138654 0.0693268 0.997594i \(-0.477915\pi\)
0.0693268 + 0.997594i \(0.477915\pi\)
\(368\) −27.8475 −1.45165
\(369\) 0 0
\(370\) 13.3631 0.694716
\(371\) −0.0140432 −0.000729089 0
\(372\) 0 0
\(373\) −0.426449 −0.0220807 −0.0110404 0.999939i \(-0.503514\pi\)
−0.0110404 + 0.999939i \(0.503514\pi\)
\(374\) −7.25587 −0.375192
\(375\) 0 0
\(376\) −13.7294 −0.708038
\(377\) −7.20217 −0.370931
\(378\) 0 0
\(379\) 28.8875 1.48385 0.741925 0.670483i \(-0.233913\pi\)
0.741925 + 0.670483i \(0.233913\pi\)
\(380\) 6.42145 0.329414
\(381\) 0 0
\(382\) 14.6748 0.750827
\(383\) 29.4474 1.50469 0.752346 0.658768i \(-0.228922\pi\)
0.752346 + 0.658768i \(0.228922\pi\)
\(384\) 0 0
\(385\) −0.166247 −0.00847271
\(386\) 19.8538 1.01053
\(387\) 0 0
\(388\) −3.52600 −0.179006
\(389\) 11.6234 0.589329 0.294665 0.955601i \(-0.404792\pi\)
0.294665 + 0.955601i \(0.404792\pi\)
\(390\) 0 0
\(391\) −24.3727 −1.23258
\(392\) 14.0695 0.710616
\(393\) 0 0
\(394\) 11.1697 0.562724
\(395\) 14.7330 0.741295
\(396\) 0 0
\(397\) −25.8143 −1.29558 −0.647791 0.761818i \(-0.724307\pi\)
−0.647791 + 0.761818i \(0.724307\pi\)
\(398\) −20.4168 −1.02340
\(399\) 0 0
\(400\) 14.2291 0.711454
\(401\) 6.33074 0.316142 0.158071 0.987428i \(-0.449472\pi\)
0.158071 + 0.987428i \(0.449472\pi\)
\(402\) 0 0
\(403\) −7.83545 −0.390312
\(404\) 7.25950 0.361174
\(405\) 0 0
\(406\) −0.566965 −0.0281380
\(407\) 5.47586 0.271428
\(408\) 0 0
\(409\) −17.4823 −0.864446 −0.432223 0.901767i \(-0.642271\pi\)
−0.432223 + 0.901767i \(0.642271\pi\)
\(410\) 8.66177 0.427774
\(411\) 0 0
\(412\) −3.55272 −0.175030
\(413\) −1.68989 −0.0831542
\(414\) 0 0
\(415\) 2.93679 0.144161
\(416\) 10.3136 0.505664
\(417\) 0 0
\(418\) 9.24541 0.452208
\(419\) −16.0311 −0.783171 −0.391585 0.920142i \(-0.628073\pi\)
−0.391585 + 0.920142i \(0.628073\pi\)
\(420\) 0 0
\(421\) 2.65713 0.129500 0.0647502 0.997902i \(-0.479375\pi\)
0.0647502 + 0.997902i \(0.479375\pi\)
\(422\) 3.76001 0.183034
\(423\) 0 0
\(424\) −0.248263 −0.0120567
\(425\) 12.4536 0.604088
\(426\) 0 0
\(427\) −0.113904 −0.00551222
\(428\) −2.85271 −0.137891
\(429\) 0 0
\(430\) 8.88491 0.428468
\(431\) 16.3460 0.787358 0.393679 0.919248i \(-0.371202\pi\)
0.393679 + 0.919248i \(0.371202\pi\)
\(432\) 0 0
\(433\) −19.2280 −0.924038 −0.462019 0.886870i \(-0.652875\pi\)
−0.462019 + 0.886870i \(0.652875\pi\)
\(434\) −0.616818 −0.0296082
\(435\) 0 0
\(436\) 2.52068 0.120719
\(437\) 31.0556 1.48559
\(438\) 0 0
\(439\) −1.73219 −0.0826728 −0.0413364 0.999145i \(-0.513162\pi\)
−0.0413364 + 0.999145i \(0.513162\pi\)
\(440\) −2.93899 −0.140111
\(441\) 0 0
\(442\) 17.5542 0.834967
\(443\) −12.1970 −0.579497 −0.289749 0.957103i \(-0.593572\pi\)
−0.289749 + 0.957103i \(0.593572\pi\)
\(444\) 0 0
\(445\) −24.5406 −1.16334
\(446\) 42.2062 1.99852
\(447\) 0 0
\(448\) −0.317635 −0.0150068
\(449\) 17.4644 0.824195 0.412098 0.911140i \(-0.364796\pi\)
0.412098 + 0.911140i \(0.364796\pi\)
\(450\) 0 0
\(451\) 3.54936 0.167133
\(452\) −7.83049 −0.368315
\(453\) 0 0
\(454\) 26.6232 1.24949
\(455\) 0.402201 0.0188555
\(456\) 0 0
\(457\) 15.5179 0.725897 0.362949 0.931809i \(-0.381770\pi\)
0.362949 + 0.931809i \(0.381770\pi\)
\(458\) 8.09956 0.378468
\(459\) 0 0
\(460\) 6.52241 0.304109
\(461\) 12.5703 0.585458 0.292729 0.956195i \(-0.405437\pi\)
0.292729 + 0.956195i \(0.405437\pi\)
\(462\) 0 0
\(463\) 12.0019 0.557778 0.278889 0.960323i \(-0.410034\pi\)
0.278889 + 0.960323i \(0.410034\pi\)
\(464\) −14.7605 −0.685239
\(465\) 0 0
\(466\) 11.5027 0.532853
\(467\) −37.4089 −1.73108 −0.865539 0.500842i \(-0.833024\pi\)
−0.865539 + 0.500842i \(0.833024\pi\)
\(468\) 0 0
\(469\) −1.04342 −0.0481806
\(470\) 16.6388 0.767489
\(471\) 0 0
\(472\) −29.8748 −1.37510
\(473\) 3.64080 0.167404
\(474\) 0 0
\(475\) −15.8683 −0.728089
\(476\) 0.393300 0.0180269
\(477\) 0 0
\(478\) −43.8417 −2.00527
\(479\) 17.7608 0.811514 0.405757 0.913981i \(-0.367008\pi\)
0.405757 + 0.913981i \(0.367008\pi\)
\(480\) 0 0
\(481\) −13.2478 −0.604046
\(482\) −36.6733 −1.67042
\(483\) 0 0
\(484\) 0.795679 0.0361672
\(485\) −6.46780 −0.293688
\(486\) 0 0
\(487\) −13.1113 −0.594129 −0.297064 0.954857i \(-0.596008\pi\)
−0.297064 + 0.954857i \(0.596008\pi\)
\(488\) −2.01366 −0.0911540
\(489\) 0 0
\(490\) −17.0509 −0.770283
\(491\) 22.4438 1.01287 0.506437 0.862277i \(-0.330962\pi\)
0.506437 + 0.862277i \(0.330962\pi\)
\(492\) 0 0
\(493\) −12.9187 −0.581829
\(494\) −22.3675 −1.00636
\(495\) 0 0
\(496\) −16.0584 −0.721043
\(497\) −1.10389 −0.0495161
\(498\) 0 0
\(499\) 17.9269 0.802517 0.401259 0.915965i \(-0.368573\pi\)
0.401259 + 0.915965i \(0.368573\pi\)
\(500\) −9.13930 −0.408722
\(501\) 0 0
\(502\) −41.6487 −1.85887
\(503\) 43.4638 1.93796 0.968978 0.247148i \(-0.0794932\pi\)
0.968978 + 0.247148i \(0.0794932\pi\)
\(504\) 0 0
\(505\) 13.3162 0.592564
\(506\) 9.39076 0.417470
\(507\) 0 0
\(508\) 5.77245 0.256111
\(509\) −3.04838 −0.135117 −0.0675585 0.997715i \(-0.521521\pi\)
−0.0675585 + 0.997715i \(0.521521\pi\)
\(510\) 0 0
\(511\) 0.119915 0.00530473
\(512\) 1.16870 0.0516496
\(513\) 0 0
\(514\) −0.733812 −0.0323670
\(515\) −6.51682 −0.287165
\(516\) 0 0
\(517\) 6.81812 0.299861
\(518\) −1.04288 −0.0458217
\(519\) 0 0
\(520\) 7.11032 0.311808
\(521\) 4.92667 0.215841 0.107921 0.994160i \(-0.465581\pi\)
0.107921 + 0.994160i \(0.465581\pi\)
\(522\) 0 0
\(523\) 1.37122 0.0599595 0.0299797 0.999551i \(-0.490456\pi\)
0.0299797 + 0.999551i \(0.490456\pi\)
\(524\) −4.12203 −0.180072
\(525\) 0 0
\(526\) −36.0867 −1.57346
\(527\) −14.0546 −0.612229
\(528\) 0 0
\(529\) 8.54384 0.371471
\(530\) 0.300873 0.0130691
\(531\) 0 0
\(532\) −0.501142 −0.0217273
\(533\) −8.58699 −0.371944
\(534\) 0 0
\(535\) −5.23277 −0.226232
\(536\) −18.4461 −0.796750
\(537\) 0 0
\(538\) 41.2842 1.77989
\(539\) −6.98703 −0.300953
\(540\) 0 0
\(541\) −37.0801 −1.59420 −0.797099 0.603848i \(-0.793633\pi\)
−0.797099 + 0.603848i \(0.793633\pi\)
\(542\) −31.4139 −1.34934
\(543\) 0 0
\(544\) 18.4997 0.793167
\(545\) 4.62372 0.198059
\(546\) 0 0
\(547\) 11.1746 0.477790 0.238895 0.971045i \(-0.423215\pi\)
0.238895 + 0.971045i \(0.423215\pi\)
\(548\) −12.6583 −0.540734
\(549\) 0 0
\(550\) −4.79835 −0.204602
\(551\) 16.4610 0.701261
\(552\) 0 0
\(553\) −1.14979 −0.0488939
\(554\) −3.11268 −0.132245
\(555\) 0 0
\(556\) 13.8593 0.587766
\(557\) 15.3427 0.650092 0.325046 0.945698i \(-0.394620\pi\)
0.325046 + 0.945698i \(0.394620\pi\)
\(558\) 0 0
\(559\) −8.80821 −0.372548
\(560\) 0.824292 0.0348327
\(561\) 0 0
\(562\) −20.1563 −0.850241
\(563\) −43.3954 −1.82890 −0.914449 0.404701i \(-0.867376\pi\)
−0.914449 + 0.404701i \(0.867376\pi\)
\(564\) 0 0
\(565\) −14.3636 −0.604281
\(566\) 29.2577 1.22979
\(567\) 0 0
\(568\) −19.5151 −0.818834
\(569\) −1.47086 −0.0616615 −0.0308308 0.999525i \(-0.509815\pi\)
−0.0308308 + 0.999525i \(0.509815\pi\)
\(570\) 0 0
\(571\) −7.09968 −0.297112 −0.148556 0.988904i \(-0.547463\pi\)
−0.148556 + 0.988904i \(0.547463\pi\)
\(572\) −1.92499 −0.0804879
\(573\) 0 0
\(574\) −0.675981 −0.0282149
\(575\) −16.1178 −0.672159
\(576\) 0 0
\(577\) −20.6477 −0.859575 −0.429788 0.902930i \(-0.641412\pi\)
−0.429788 + 0.902930i \(0.641412\pi\)
\(578\) 3.06284 0.127397
\(579\) 0 0
\(580\) 3.45719 0.143552
\(581\) −0.229193 −0.00950852
\(582\) 0 0
\(583\) 0.123290 0.00510614
\(584\) 2.11992 0.0877229
\(585\) 0 0
\(586\) 6.71176 0.277260
\(587\) 3.56601 0.147185 0.0735925 0.997288i \(-0.476554\pi\)
0.0735925 + 0.997288i \(0.476554\pi\)
\(588\) 0 0
\(589\) 17.9084 0.737901
\(590\) 36.2056 1.49056
\(591\) 0 0
\(592\) −27.1507 −1.11589
\(593\) −23.6716 −0.972077 −0.486038 0.873937i \(-0.661558\pi\)
−0.486038 + 0.873937i \(0.661558\pi\)
\(594\) 0 0
\(595\) 0.721437 0.0295760
\(596\) 15.9908 0.655010
\(597\) 0 0
\(598\) −22.7191 −0.929054
\(599\) −34.3309 −1.40272 −0.701360 0.712807i \(-0.747424\pi\)
−0.701360 + 0.712807i \(0.747424\pi\)
\(600\) 0 0
\(601\) 2.29548 0.0936346 0.0468173 0.998903i \(-0.485092\pi\)
0.0468173 + 0.998903i \(0.485092\pi\)
\(602\) −0.693395 −0.0282607
\(603\) 0 0
\(604\) 11.2814 0.459035
\(605\) 1.45953 0.0593382
\(606\) 0 0
\(607\) −47.1071 −1.91202 −0.956010 0.293335i \(-0.905235\pi\)
−0.956010 + 0.293335i \(0.905235\pi\)
\(608\) −23.5722 −0.955980
\(609\) 0 0
\(610\) 2.44037 0.0988078
\(611\) −16.4951 −0.667321
\(612\) 0 0
\(613\) 19.9949 0.807586 0.403793 0.914850i \(-0.367692\pi\)
0.403793 + 0.914850i \(0.367692\pi\)
\(614\) 25.6561 1.03540
\(615\) 0 0
\(616\) 0.229364 0.00924135
\(617\) −28.3395 −1.14090 −0.570452 0.821331i \(-0.693232\pi\)
−0.570452 + 0.821331i \(0.693232\pi\)
\(618\) 0 0
\(619\) −18.4108 −0.739994 −0.369997 0.929033i \(-0.620641\pi\)
−0.369997 + 0.929033i \(0.620641\pi\)
\(620\) 3.76118 0.151053
\(621\) 0 0
\(622\) −47.3415 −1.89822
\(623\) 1.91520 0.0767308
\(624\) 0 0
\(625\) −2.41548 −0.0966192
\(626\) 43.9321 1.75588
\(627\) 0 0
\(628\) 3.97237 0.158515
\(629\) −23.7628 −0.947486
\(630\) 0 0
\(631\) 7.42123 0.295435 0.147717 0.989030i \(-0.452807\pi\)
0.147717 + 0.989030i \(0.452807\pi\)
\(632\) −20.3265 −0.808546
\(633\) 0 0
\(634\) −51.9121 −2.06169
\(635\) 10.5885 0.420191
\(636\) 0 0
\(637\) 16.9038 0.669751
\(638\) 4.97756 0.197063
\(639\) 0 0
\(640\) 19.2492 0.760893
\(641\) −6.86699 −0.271230 −0.135615 0.990762i \(-0.543301\pi\)
−0.135615 + 0.990762i \(0.543301\pi\)
\(642\) 0 0
\(643\) 45.7495 1.80418 0.902092 0.431544i \(-0.142031\pi\)
0.902092 + 0.431544i \(0.142031\pi\)
\(644\) −0.509021 −0.0200582
\(645\) 0 0
\(646\) −40.1211 −1.57854
\(647\) 17.7282 0.696968 0.348484 0.937315i \(-0.386697\pi\)
0.348484 + 0.937315i \(0.386697\pi\)
\(648\) 0 0
\(649\) 14.8361 0.582367
\(650\) 11.6087 0.455330
\(651\) 0 0
\(652\) −4.76015 −0.186422
\(653\) −25.1767 −0.985239 −0.492619 0.870245i \(-0.663960\pi\)
−0.492619 + 0.870245i \(0.663960\pi\)
\(654\) 0 0
\(655\) −7.56112 −0.295437
\(656\) −17.5986 −0.687111
\(657\) 0 0
\(658\) −1.29852 −0.0506216
\(659\) −47.2222 −1.83951 −0.919757 0.392487i \(-0.871615\pi\)
−0.919757 + 0.392487i \(0.871615\pi\)
\(660\) 0 0
\(661\) −10.8885 −0.423512 −0.211756 0.977323i \(-0.567918\pi\)
−0.211756 + 0.977323i \(0.567918\pi\)
\(662\) −34.3698 −1.33582
\(663\) 0 0
\(664\) −4.05179 −0.157240
\(665\) −0.919253 −0.0356471
\(666\) 0 0
\(667\) 16.7198 0.647391
\(668\) −19.2735 −0.745713
\(669\) 0 0
\(670\) 22.3550 0.863649
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −3.19833 −0.123287 −0.0616433 0.998098i \(-0.519634\pi\)
−0.0616433 + 0.998098i \(0.519634\pi\)
\(674\) −0.818392 −0.0315233
\(675\) 0 0
\(676\) −5.68669 −0.218719
\(677\) 20.9309 0.804439 0.402219 0.915543i \(-0.368239\pi\)
0.402219 + 0.915543i \(0.368239\pi\)
\(678\) 0 0
\(679\) 0.504759 0.0193709
\(680\) 12.7539 0.489091
\(681\) 0 0
\(682\) 5.41523 0.207360
\(683\) −9.41323 −0.360187 −0.180094 0.983649i \(-0.557640\pi\)
−0.180094 + 0.983649i \(0.557640\pi\)
\(684\) 0 0
\(685\) −23.2193 −0.887162
\(686\) 2.66385 0.101706
\(687\) 0 0
\(688\) −18.0520 −0.688227
\(689\) −0.298276 −0.0113634
\(690\) 0 0
\(691\) 34.9093 1.32801 0.664006 0.747727i \(-0.268855\pi\)
0.664006 + 0.747727i \(0.268855\pi\)
\(692\) −9.12832 −0.347007
\(693\) 0 0
\(694\) 14.2835 0.542195
\(695\) 25.4224 0.964326
\(696\) 0 0
\(697\) −15.4027 −0.583418
\(698\) 47.6606 1.80398
\(699\) 0 0
\(700\) 0.260092 0.00983055
\(701\) 21.4585 0.810478 0.405239 0.914211i \(-0.367188\pi\)
0.405239 + 0.914211i \(0.367188\pi\)
\(702\) 0 0
\(703\) 30.2785 1.14198
\(704\) 2.78861 0.105100
\(705\) 0 0
\(706\) −25.7886 −0.970566
\(707\) −1.03922 −0.0390840
\(708\) 0 0
\(709\) 14.7920 0.555527 0.277764 0.960649i \(-0.410407\pi\)
0.277764 + 0.960649i \(0.410407\pi\)
\(710\) 23.6505 0.887588
\(711\) 0 0
\(712\) 33.8578 1.26888
\(713\) 18.1899 0.681217
\(714\) 0 0
\(715\) −3.53104 −0.132054
\(716\) −13.3369 −0.498424
\(717\) 0 0
\(718\) 51.1746 1.90982
\(719\) −3.91313 −0.145935 −0.0729676 0.997334i \(-0.523247\pi\)
−0.0729676 + 0.997334i \(0.523247\pi\)
\(720\) 0 0
\(721\) 0.508585 0.0189407
\(722\) 19.3536 0.720266
\(723\) 0 0
\(724\) 18.6600 0.693494
\(725\) −8.54321 −0.317287
\(726\) 0 0
\(727\) −22.4942 −0.834263 −0.417131 0.908846i \(-0.636964\pi\)
−0.417131 + 0.908846i \(0.636964\pi\)
\(728\) −0.554903 −0.0205661
\(729\) 0 0
\(730\) −2.56915 −0.0950885
\(731\) −15.7995 −0.584365
\(732\) 0 0
\(733\) 19.0644 0.704161 0.352080 0.935970i \(-0.385474\pi\)
0.352080 + 0.935970i \(0.385474\pi\)
\(734\) 4.44128 0.163931
\(735\) 0 0
\(736\) −23.9428 −0.882544
\(737\) 9.16048 0.337431
\(738\) 0 0
\(739\) 28.1238 1.03455 0.517275 0.855819i \(-0.326946\pi\)
0.517275 + 0.855819i \(0.326946\pi\)
\(740\) 6.35920 0.233769
\(741\) 0 0
\(742\) −0.0234807 −0.000862003 0
\(743\) −26.7820 −0.982535 −0.491268 0.871009i \(-0.663466\pi\)
−0.491268 + 0.871009i \(0.663466\pi\)
\(744\) 0 0
\(745\) 29.3322 1.07465
\(746\) −0.713036 −0.0261061
\(747\) 0 0
\(748\) −3.45290 −0.126251
\(749\) 0.408375 0.0149217
\(750\) 0 0
\(751\) −48.7584 −1.77922 −0.889609 0.456722i \(-0.849023\pi\)
−0.889609 + 0.456722i \(0.849023\pi\)
\(752\) −33.8060 −1.23278
\(753\) 0 0
\(754\) −12.0422 −0.438552
\(755\) 20.6937 0.753122
\(756\) 0 0
\(757\) 19.1838 0.697246 0.348623 0.937263i \(-0.386649\pi\)
0.348623 + 0.937263i \(0.386649\pi\)
\(758\) 48.3007 1.75436
\(759\) 0 0
\(760\) −16.2510 −0.589487
\(761\) 26.2237 0.950608 0.475304 0.879822i \(-0.342338\pi\)
0.475304 + 0.879822i \(0.342338\pi\)
\(762\) 0 0
\(763\) −0.360844 −0.0130634
\(764\) 6.98338 0.252650
\(765\) 0 0
\(766\) 49.2369 1.77900
\(767\) −35.8930 −1.29602
\(768\) 0 0
\(769\) −34.4961 −1.24396 −0.621981 0.783032i \(-0.713672\pi\)
−0.621981 + 0.783032i \(0.713672\pi\)
\(770\) −0.277969 −0.0100173
\(771\) 0 0
\(772\) 9.44797 0.340040
\(773\) −36.7533 −1.32192 −0.660961 0.750420i \(-0.729851\pi\)
−0.660961 + 0.750420i \(0.729851\pi\)
\(774\) 0 0
\(775\) −9.29441 −0.333865
\(776\) 8.92339 0.320331
\(777\) 0 0
\(778\) 19.4346 0.696766
\(779\) 19.6261 0.703177
\(780\) 0 0
\(781\) 9.69135 0.346784
\(782\) −40.7518 −1.45728
\(783\) 0 0
\(784\) 34.6434 1.23727
\(785\) 7.28658 0.260069
\(786\) 0 0
\(787\) −5.85918 −0.208857 −0.104429 0.994532i \(-0.533301\pi\)
−0.104429 + 0.994532i \(0.533301\pi\)
\(788\) 5.31542 0.189354
\(789\) 0 0
\(790\) 24.6339 0.876435
\(791\) 1.12096 0.0398568
\(792\) 0 0
\(793\) −2.41931 −0.0859121
\(794\) −43.1622 −1.53177
\(795\) 0 0
\(796\) −9.71589 −0.344371
\(797\) −19.2286 −0.681112 −0.340556 0.940224i \(-0.610615\pi\)
−0.340556 + 0.940224i \(0.610615\pi\)
\(798\) 0 0
\(799\) −29.5877 −1.04674
\(800\) 12.2339 0.432535
\(801\) 0 0
\(802\) 10.5852 0.373776
\(803\) −1.05277 −0.0371514
\(804\) 0 0
\(805\) −0.933705 −0.0329088
\(806\) −13.1011 −0.461466
\(807\) 0 0
\(808\) −18.3719 −0.646321
\(809\) −8.57652 −0.301535 −0.150767 0.988569i \(-0.548174\pi\)
−0.150767 + 0.988569i \(0.548174\pi\)
\(810\) 0 0
\(811\) 51.6913 1.81513 0.907564 0.419914i \(-0.137940\pi\)
0.907564 + 0.419914i \(0.137940\pi\)
\(812\) −0.269806 −0.00946832
\(813\) 0 0
\(814\) 9.15579 0.320910
\(815\) −8.73163 −0.305856
\(816\) 0 0
\(817\) 20.1317 0.704318
\(818\) −29.2310 −1.02204
\(819\) 0 0
\(820\) 4.12193 0.143944
\(821\) 37.9548 1.32463 0.662316 0.749224i \(-0.269573\pi\)
0.662316 + 0.749224i \(0.269573\pi\)
\(822\) 0 0
\(823\) 23.9123 0.833531 0.416766 0.909014i \(-0.363164\pi\)
0.416766 + 0.909014i \(0.363164\pi\)
\(824\) 8.99102 0.313217
\(825\) 0 0
\(826\) −2.82555 −0.0983134
\(827\) −20.6669 −0.718658 −0.359329 0.933211i \(-0.616994\pi\)
−0.359329 + 0.933211i \(0.616994\pi\)
\(828\) 0 0
\(829\) 9.30470 0.323166 0.161583 0.986859i \(-0.448340\pi\)
0.161583 + 0.986859i \(0.448340\pi\)
\(830\) 4.91040 0.170443
\(831\) 0 0
\(832\) −6.74650 −0.233893
\(833\) 30.3206 1.05055
\(834\) 0 0
\(835\) −35.3537 −1.22346
\(836\) 4.39968 0.152166
\(837\) 0 0
\(838\) −26.8045 −0.925945
\(839\) −28.4780 −0.983170 −0.491585 0.870830i \(-0.663582\pi\)
−0.491585 + 0.870830i \(0.663582\pi\)
\(840\) 0 0
\(841\) −20.1377 −0.694404
\(842\) 4.44279 0.153109
\(843\) 0 0
\(844\) 1.78930 0.0615902
\(845\) −10.4312 −0.358844
\(846\) 0 0
\(847\) −0.113904 −0.00391380
\(848\) −0.611302 −0.0209922
\(849\) 0 0
\(850\) 20.8228 0.714214
\(851\) 30.7545 1.05425
\(852\) 0 0
\(853\) −16.0864 −0.550789 −0.275395 0.961331i \(-0.588808\pi\)
−0.275395 + 0.961331i \(0.588808\pi\)
\(854\) −0.190451 −0.00651711
\(855\) 0 0
\(856\) 7.21947 0.246756
\(857\) −32.5019 −1.11024 −0.555122 0.831769i \(-0.687328\pi\)
−0.555122 + 0.831769i \(0.687328\pi\)
\(858\) 0 0
\(859\) 53.0060 1.80854 0.904270 0.426961i \(-0.140416\pi\)
0.904270 + 0.426961i \(0.140416\pi\)
\(860\) 4.22812 0.144178
\(861\) 0 0
\(862\) 27.3309 0.930895
\(863\) −18.4211 −0.627061 −0.313530 0.949578i \(-0.601512\pi\)
−0.313530 + 0.949578i \(0.601512\pi\)
\(864\) 0 0
\(865\) −16.7442 −0.569321
\(866\) −32.1497 −1.09249
\(867\) 0 0
\(868\) −0.293529 −0.00996304
\(869\) 10.0943 0.342427
\(870\) 0 0
\(871\) −22.1620 −0.750931
\(872\) −6.37919 −0.216027
\(873\) 0 0
\(874\) 51.9259 1.75642
\(875\) 1.30832 0.0442294
\(876\) 0 0
\(877\) 14.6497 0.494684 0.247342 0.968928i \(-0.420443\pi\)
0.247342 + 0.968928i \(0.420443\pi\)
\(878\) −2.89627 −0.0977443
\(879\) 0 0
\(880\) −7.23671 −0.243949
\(881\) 47.0593 1.58547 0.792733 0.609569i \(-0.208657\pi\)
0.792733 + 0.609569i \(0.208657\pi\)
\(882\) 0 0
\(883\) 16.8945 0.568544 0.284272 0.958744i \(-0.408248\pi\)
0.284272 + 0.958744i \(0.408248\pi\)
\(884\) 8.35362 0.280963
\(885\) 0 0
\(886\) −20.3938 −0.685141
\(887\) −38.0179 −1.27651 −0.638257 0.769823i \(-0.720344\pi\)
−0.638257 + 0.769823i \(0.720344\pi\)
\(888\) 0 0
\(889\) −0.826346 −0.0277147
\(890\) −41.0326 −1.37542
\(891\) 0 0
\(892\) 20.0849 0.672493
\(893\) 37.7005 1.26160
\(894\) 0 0
\(895\) −24.4641 −0.817745
\(896\) −1.50225 −0.0501866
\(897\) 0 0
\(898\) 29.2010 0.974448
\(899\) 9.64153 0.321563
\(900\) 0 0
\(901\) −0.535024 −0.0178242
\(902\) 5.93464 0.197602
\(903\) 0 0
\(904\) 19.8169 0.659101
\(905\) 34.2283 1.13779
\(906\) 0 0
\(907\) −3.40956 −0.113213 −0.0566063 0.998397i \(-0.518028\pi\)
−0.0566063 + 0.998397i \(0.518028\pi\)
\(908\) 12.6693 0.420447
\(909\) 0 0
\(910\) 0.672492 0.0222929
\(911\) 35.6182 1.18009 0.590043 0.807372i \(-0.299111\pi\)
0.590043 + 0.807372i \(0.299111\pi\)
\(912\) 0 0
\(913\) 2.01215 0.0665925
\(914\) 25.9464 0.858230
\(915\) 0 0
\(916\) 3.85439 0.127353
\(917\) 0.590084 0.0194863
\(918\) 0 0
\(919\) −23.5214 −0.775899 −0.387950 0.921681i \(-0.626817\pi\)
−0.387950 + 0.921681i \(0.626817\pi\)
\(920\) −16.5065 −0.544204
\(921\) 0 0
\(922\) 21.0179 0.692188
\(923\) −23.4463 −0.771746
\(924\) 0 0
\(925\) −15.7145 −0.516689
\(926\) 20.0676 0.659462
\(927\) 0 0
\(928\) −12.6908 −0.416597
\(929\) −17.9960 −0.590430 −0.295215 0.955431i \(-0.595391\pi\)
−0.295215 + 0.955431i \(0.595391\pi\)
\(930\) 0 0
\(931\) −38.6345 −1.26619
\(932\) 5.47388 0.179303
\(933\) 0 0
\(934\) −62.5487 −2.04666
\(935\) −6.33371 −0.207135
\(936\) 0 0
\(937\) −6.46056 −0.211057 −0.105529 0.994416i \(-0.533653\pi\)
−0.105529 + 0.994416i \(0.533653\pi\)
\(938\) −1.74463 −0.0569640
\(939\) 0 0
\(940\) 7.91800 0.258257
\(941\) −19.8660 −0.647614 −0.323807 0.946123i \(-0.604963\pi\)
−0.323807 + 0.946123i \(0.604963\pi\)
\(942\) 0 0
\(943\) 19.9346 0.649160
\(944\) −73.5610 −2.39421
\(945\) 0 0
\(946\) 6.08752 0.197922
\(947\) −53.8245 −1.74906 −0.874531 0.484970i \(-0.838831\pi\)
−0.874531 + 0.484970i \(0.838831\pi\)
\(948\) 0 0
\(949\) 2.54697 0.0826782
\(950\) −26.5323 −0.860821
\(951\) 0 0
\(952\) −0.995341 −0.0322592
\(953\) −37.5503 −1.21637 −0.608186 0.793794i \(-0.708103\pi\)
−0.608186 + 0.793794i \(0.708103\pi\)
\(954\) 0 0
\(955\) 12.8097 0.414513
\(956\) −20.8632 −0.674765
\(957\) 0 0
\(958\) 29.6966 0.959455
\(959\) 1.81207 0.0585149
\(960\) 0 0
\(961\) −20.5107 −0.661636
\(962\) −22.1507 −0.714166
\(963\) 0 0
\(964\) −17.4520 −0.562090
\(965\) 17.3306 0.557891
\(966\) 0 0
\(967\) 29.7039 0.955211 0.477606 0.878574i \(-0.341505\pi\)
0.477606 + 0.878574i \(0.341505\pi\)
\(968\) −2.01366 −0.0647214
\(969\) 0 0
\(970\) −10.8143 −0.347228
\(971\) −20.9546 −0.672464 −0.336232 0.941779i \(-0.609153\pi\)
−0.336232 + 0.941779i \(0.609153\pi\)
\(972\) 0 0
\(973\) −1.98401 −0.0636045
\(974\) −21.9224 −0.702440
\(975\) 0 0
\(976\) −4.95825 −0.158710
\(977\) 29.9552 0.958353 0.479177 0.877718i \(-0.340935\pi\)
0.479177 + 0.877718i \(0.340935\pi\)
\(978\) 0 0
\(979\) −16.8141 −0.537381
\(980\) −8.11415 −0.259197
\(981\) 0 0
\(982\) 37.5266 1.19752
\(983\) −52.2964 −1.66800 −0.833998 0.551767i \(-0.813954\pi\)
−0.833998 + 0.551767i \(0.813954\pi\)
\(984\) 0 0
\(985\) 9.75016 0.310666
\(986\) −21.6004 −0.687898
\(987\) 0 0
\(988\) −10.6442 −0.338636
\(989\) 20.4482 0.650214
\(990\) 0 0
\(991\) 23.5537 0.748209 0.374105 0.927387i \(-0.377950\pi\)
0.374105 + 0.927387i \(0.377950\pi\)
\(992\) −13.8067 −0.438364
\(993\) 0 0
\(994\) −1.84573 −0.0585430
\(995\) −17.8220 −0.564996
\(996\) 0 0
\(997\) 38.4376 1.21733 0.608665 0.793427i \(-0.291705\pi\)
0.608665 + 0.793427i \(0.291705\pi\)
\(998\) 29.9743 0.948818
\(999\) 0 0
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 \(a_p\))