Properties

Label 4014.2.a.l.1.1
Level 4014
Weight 2
Character 4014.1
Self dual Yes
Analytic conductor 32.052
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0519513713\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.30278\)
Character \(\chi\) = 4014.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -4.60555 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -4.60555 q^{7} +1.00000 q^{8} +2.69722 q^{11} +1.69722 q^{13} -4.60555 q^{14} +1.00000 q^{16} -2.60555 q^{17} +4.30278 q^{19} +2.69722 q^{22} -4.00000 q^{23} -5.00000 q^{25} +1.69722 q^{26} -4.60555 q^{28} +5.30278 q^{29} +6.60555 q^{31} +1.00000 q^{32} -2.60555 q^{34} +4.60555 q^{37} +4.30278 q^{38} -4.00000 q^{41} +3.90833 q^{43} +2.69722 q^{44} -4.00000 q^{46} +0.697224 q^{47} +14.2111 q^{49} -5.00000 q^{50} +1.69722 q^{52} +6.90833 q^{53} -4.60555 q^{56} +5.30278 q^{58} +0.302776 q^{59} -2.69722 q^{61} +6.60555 q^{62} +1.00000 q^{64} +4.60555 q^{67} -2.60555 q^{68} +11.2111 q^{71} -8.90833 q^{73} +4.60555 q^{74} +4.30278 q^{76} -12.4222 q^{77} +8.51388 q^{79} -4.00000 q^{82} -5.21110 q^{83} +3.90833 q^{86} +2.69722 q^{88} +17.2111 q^{89} -7.81665 q^{91} -4.00000 q^{92} +0.697224 q^{94} -0.788897 q^{97} +14.2111 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{4} - 2q^{7} + 2q^{8} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{4} - 2q^{7} + 2q^{8} + 9q^{11} + 7q^{13} - 2q^{14} + 2q^{16} + 2q^{17} + 5q^{19} + 9q^{22} - 8q^{23} - 10q^{25} + 7q^{26} - 2q^{28} + 7q^{29} + 6q^{31} + 2q^{32} + 2q^{34} + 2q^{37} + 5q^{38} - 8q^{41} - 3q^{43} + 9q^{44} - 8q^{46} + 5q^{47} + 14q^{49} - 10q^{50} + 7q^{52} + 3q^{53} - 2q^{56} + 7q^{58} - 3q^{59} - 9q^{61} + 6q^{62} + 2q^{64} + 2q^{67} + 2q^{68} + 8q^{71} - 7q^{73} + 2q^{74} + 5q^{76} + 4q^{77} - q^{79} - 8q^{82} + 4q^{83} - 3q^{86} + 9q^{88} + 20q^{89} + 6q^{91} - 8q^{92} + 5q^{94} - 16q^{97} + 14q^{98} + O(q^{100}) \)

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
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) −4.60555 −1.74073 −0.870367 0.492403i \(-0.836119\pi\)
−0.870367 + 0.492403i \(0.836119\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 2.69722 0.813244 0.406622 0.913597i \(-0.366707\pi\)
0.406622 + 0.913597i \(0.366707\pi\)
\(12\) 0 0
\(13\) 1.69722 0.470725 0.235363 0.971908i \(-0.424372\pi\)
0.235363 + 0.971908i \(0.424372\pi\)
\(14\) −4.60555 −1.23089
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.60555 −0.631939 −0.315970 0.948769i \(-0.602330\pi\)
−0.315970 + 0.948769i \(0.602330\pi\)
\(18\) 0 0
\(19\) 4.30278 0.987124 0.493562 0.869710i \(-0.335695\pi\)
0.493562 + 0.869710i \(0.335695\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.69722 0.575050
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 1.69722 0.332853
\(27\) 0 0
\(28\) −4.60555 −0.870367
\(29\) 5.30278 0.984701 0.492350 0.870397i \(-0.336138\pi\)
0.492350 + 0.870397i \(0.336138\pi\)
\(30\) 0 0
\(31\) 6.60555 1.18639 0.593196 0.805058i \(-0.297866\pi\)
0.593196 + 0.805058i \(0.297866\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −2.60555 −0.446848
\(35\) 0 0
\(36\) 0 0
\(37\) 4.60555 0.757148 0.378574 0.925571i \(-0.376415\pi\)
0.378574 + 0.925571i \(0.376415\pi\)
\(38\) 4.30278 0.698002
\(39\) 0 0
\(40\) 0 0
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) 0 0
\(43\) 3.90833 0.596014 0.298007 0.954564i \(-0.403678\pi\)
0.298007 + 0.954564i \(0.403678\pi\)
\(44\) 2.69722 0.406622
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) 0.697224 0.101701 0.0508503 0.998706i \(-0.483807\pi\)
0.0508503 + 0.998706i \(0.483807\pi\)
\(48\) 0 0
\(49\) 14.2111 2.03016
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) 1.69722 0.235363
\(53\) 6.90833 0.948932 0.474466 0.880274i \(-0.342641\pi\)
0.474466 + 0.880274i \(0.342641\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −4.60555 −0.615443
\(57\) 0 0
\(58\) 5.30278 0.696289
\(59\) 0.302776 0.0394180 0.0197090 0.999806i \(-0.493726\pi\)
0.0197090 + 0.999806i \(0.493726\pi\)
\(60\) 0 0
\(61\) −2.69722 −0.345344 −0.172672 0.984979i \(-0.555240\pi\)
−0.172672 + 0.984979i \(0.555240\pi\)
\(62\) 6.60555 0.838906
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.60555 0.562658 0.281329 0.959611i \(-0.409225\pi\)
0.281329 + 0.959611i \(0.409225\pi\)
\(68\) −2.60555 −0.315970
\(69\) 0 0
\(70\) 0 0
\(71\) 11.2111 1.33051 0.665257 0.746615i \(-0.268322\pi\)
0.665257 + 0.746615i \(0.268322\pi\)
\(72\) 0 0
\(73\) −8.90833 −1.04264 −0.521320 0.853361i \(-0.674560\pi\)
−0.521320 + 0.853361i \(0.674560\pi\)
\(74\) 4.60555 0.535384
\(75\) 0 0
\(76\) 4.30278 0.493562
\(77\) −12.4222 −1.41564
\(78\) 0 0
\(79\) 8.51388 0.957886 0.478943 0.877846i \(-0.341020\pi\)
0.478943 + 0.877846i \(0.341020\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −4.00000 −0.441726
\(83\) −5.21110 −0.571993 −0.285996 0.958231i \(-0.592325\pi\)
−0.285996 + 0.958231i \(0.592325\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 3.90833 0.421446
\(87\) 0 0
\(88\) 2.69722 0.287525
\(89\) 17.2111 1.82437 0.912187 0.409775i \(-0.134393\pi\)
0.912187 + 0.409775i \(0.134393\pi\)
\(90\) 0 0
\(91\) −7.81665 −0.819408
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) 0.697224 0.0719132
\(95\) 0 0
\(96\) 0 0
\(97\) −0.788897 −0.0801004 −0.0400502 0.999198i \(-0.512752\pi\)
−0.0400502 + 0.999198i \(0.512752\pi\)
\(98\) 14.2111 1.43554
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 10.9083 1.08542 0.542710 0.839920i \(-0.317398\pi\)
0.542710 + 0.839920i \(0.317398\pi\)
\(102\) 0 0
\(103\) −2.90833 −0.286566 −0.143283 0.989682i \(-0.545766\pi\)
−0.143283 + 0.989682i \(0.545766\pi\)
\(104\) 1.69722 0.166427
\(105\) 0 0
\(106\) 6.90833 0.670996
\(107\) 0.908327 0.0878113 0.0439056 0.999036i \(-0.486020\pi\)
0.0439056 + 0.999036i \(0.486020\pi\)
\(108\) 0 0
\(109\) −5.39445 −0.516694 −0.258347 0.966052i \(-0.583178\pi\)
−0.258347 + 0.966052i \(0.583178\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −4.60555 −0.435184
\(113\) 15.6972 1.47667 0.738335 0.674434i \(-0.235612\pi\)
0.738335 + 0.674434i \(0.235612\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.30278 0.492350
\(117\) 0 0
\(118\) 0.302776 0.0278728
\(119\) 12.0000 1.10004
\(120\) 0 0
\(121\) −3.72498 −0.338635
\(122\) −2.69722 −0.244195
\(123\) 0 0
\(124\) 6.60555 0.593196
\(125\) 0 0
\(126\) 0 0
\(127\) 7.21110 0.639882 0.319941 0.947437i \(-0.396337\pi\)
0.319941 + 0.947437i \(0.396337\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 16.4222 1.43481 0.717407 0.696654i \(-0.245329\pi\)
0.717407 + 0.696654i \(0.245329\pi\)
\(132\) 0 0
\(133\) −19.8167 −1.71832
\(134\) 4.60555 0.397859
\(135\) 0 0
\(136\) −2.60555 −0.223424
\(137\) 7.30278 0.623918 0.311959 0.950096i \(-0.399015\pi\)
0.311959 + 0.950096i \(0.399015\pi\)
\(138\) 0 0
\(139\) −11.9083 −1.01005 −0.505026 0.863104i \(-0.668517\pi\)
−0.505026 + 0.863104i \(0.668517\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 11.2111 0.940815
\(143\) 4.57779 0.382814
\(144\) 0 0
\(145\) 0 0
\(146\) −8.90833 −0.737258
\(147\) 0 0
\(148\) 4.60555 0.378574
\(149\) 5.21110 0.426910 0.213455 0.976953i \(-0.431528\pi\)
0.213455 + 0.976953i \(0.431528\pi\)
\(150\) 0 0
\(151\) 0.486122 0.0395600 0.0197800 0.999804i \(-0.493703\pi\)
0.0197800 + 0.999804i \(0.493703\pi\)
\(152\) 4.30278 0.349001
\(153\) 0 0
\(154\) −12.4222 −1.00101
\(155\) 0 0
\(156\) 0 0
\(157\) 2.69722 0.215262 0.107631 0.994191i \(-0.465674\pi\)
0.107631 + 0.994191i \(0.465674\pi\)
\(158\) 8.51388 0.677328
\(159\) 0 0
\(160\) 0 0
\(161\) 18.4222 1.45187
\(162\) 0 0
\(163\) 8.60555 0.674039 0.337019 0.941498i \(-0.390581\pi\)
0.337019 + 0.941498i \(0.390581\pi\)
\(164\) −4.00000 −0.312348
\(165\) 0 0
\(166\) −5.21110 −0.404460
\(167\) 2.60555 0.201624 0.100812 0.994906i \(-0.467856\pi\)
0.100812 + 0.994906i \(0.467856\pi\)
\(168\) 0 0
\(169\) −10.1194 −0.778418
\(170\) 0 0
\(171\) 0 0
\(172\) 3.90833 0.298007
\(173\) −13.0278 −0.990482 −0.495241 0.868756i \(-0.664920\pi\)
−0.495241 + 0.868756i \(0.664920\pi\)
\(174\) 0 0
\(175\) 23.0278 1.74073
\(176\) 2.69722 0.203311
\(177\) 0 0
\(178\) 17.2111 1.29003
\(179\) 13.2111 0.987444 0.493722 0.869620i \(-0.335636\pi\)
0.493722 + 0.869620i \(0.335636\pi\)
\(180\) 0 0
\(181\) 1.39445 0.103649 0.0518243 0.998656i \(-0.483496\pi\)
0.0518243 + 0.998656i \(0.483496\pi\)
\(182\) −7.81665 −0.579409
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) 0 0
\(186\) 0 0
\(187\) −7.02776 −0.513920
\(188\) 0.697224 0.0508503
\(189\) 0 0
\(190\) 0 0
\(191\) −7.81665 −0.565593 −0.282797 0.959180i \(-0.591262\pi\)
−0.282797 + 0.959180i \(0.591262\pi\)
\(192\) 0 0
\(193\) 8.42221 0.606244 0.303122 0.952952i \(-0.401971\pi\)
0.303122 + 0.952952i \(0.401971\pi\)
\(194\) −0.788897 −0.0566395
\(195\) 0 0
\(196\) 14.2111 1.01508
\(197\) −5.30278 −0.377807 −0.188904 0.981996i \(-0.560493\pi\)
−0.188904 + 0.981996i \(0.560493\pi\)
\(198\) 0 0
\(199\) 10.4222 0.738811 0.369405 0.929268i \(-0.379561\pi\)
0.369405 + 0.929268i \(0.379561\pi\)
\(200\) −5.00000 −0.353553
\(201\) 0 0
\(202\) 10.9083 0.767507
\(203\) −24.4222 −1.71410
\(204\) 0 0
\(205\) 0 0
\(206\) −2.90833 −0.202633
\(207\) 0 0
\(208\) 1.69722 0.117681
\(209\) 11.6056 0.802773
\(210\) 0 0
\(211\) 5.30278 0.365058 0.182529 0.983200i \(-0.441572\pi\)
0.182529 + 0.983200i \(0.441572\pi\)
\(212\) 6.90833 0.474466
\(213\) 0 0
\(214\) 0.908327 0.0620919
\(215\) 0 0
\(216\) 0 0
\(217\) −30.4222 −2.06519
\(218\) −5.39445 −0.365358
\(219\) 0 0
\(220\) 0 0
\(221\) −4.42221 −0.297470
\(222\) 0 0
\(223\) −1.00000 −0.0669650
\(224\) −4.60555 −0.307721
\(225\) 0 0
\(226\) 15.6972 1.04416
\(227\) 19.0278 1.26292 0.631458 0.775410i \(-0.282457\pi\)
0.631458 + 0.775410i \(0.282457\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 5.30278 0.348144
\(233\) −4.69722 −0.307725 −0.153863 0.988092i \(-0.549171\pi\)
−0.153863 + 0.988092i \(0.549171\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.302776 0.0197090
\(237\) 0 0
\(238\) 12.0000 0.777844
\(239\) −8.72498 −0.564372 −0.282186 0.959360i \(-0.591060\pi\)
−0.282186 + 0.959360i \(0.591060\pi\)
\(240\) 0 0
\(241\) −4.51388 −0.290764 −0.145382 0.989376i \(-0.546441\pi\)
−0.145382 + 0.989376i \(0.546441\pi\)
\(242\) −3.72498 −0.239451
\(243\) 0 0
\(244\) −2.69722 −0.172672
\(245\) 0 0
\(246\) 0 0
\(247\) 7.30278 0.464664
\(248\) 6.60555 0.419453
\(249\) 0 0
\(250\) 0 0
\(251\) −22.4222 −1.41528 −0.707639 0.706575i \(-0.750239\pi\)
−0.707639 + 0.706575i \(0.750239\pi\)
\(252\) 0 0
\(253\) −10.7889 −0.678292
\(254\) 7.21110 0.452465
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) −21.2111 −1.31799
\(260\) 0 0
\(261\) 0 0
\(262\) 16.4222 1.01457
\(263\) −7.39445 −0.455961 −0.227981 0.973666i \(-0.573212\pi\)
−0.227981 + 0.973666i \(0.573212\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −19.8167 −1.21504
\(267\) 0 0
\(268\) 4.60555 0.281329
\(269\) 15.0278 0.916258 0.458129 0.888886i \(-0.348520\pi\)
0.458129 + 0.888886i \(0.348520\pi\)
\(270\) 0 0
\(271\) 15.1194 0.918440 0.459220 0.888323i \(-0.348129\pi\)
0.459220 + 0.888323i \(0.348129\pi\)
\(272\) −2.60555 −0.157985
\(273\) 0 0
\(274\) 7.30278 0.441177
\(275\) −13.4861 −0.813244
\(276\) 0 0
\(277\) −32.4222 −1.94806 −0.974031 0.226416i \(-0.927299\pi\)
−0.974031 + 0.226416i \(0.927299\pi\)
\(278\) −11.9083 −0.714214
\(279\) 0 0
\(280\) 0 0
\(281\) 14.6056 0.871294 0.435647 0.900118i \(-0.356520\pi\)
0.435647 + 0.900118i \(0.356520\pi\)
\(282\) 0 0
\(283\) −15.6972 −0.933103 −0.466552 0.884494i \(-0.654504\pi\)
−0.466552 + 0.884494i \(0.654504\pi\)
\(284\) 11.2111 0.665257
\(285\) 0 0
\(286\) 4.57779 0.270691
\(287\) 18.4222 1.08743
\(288\) 0 0
\(289\) −10.2111 −0.600653
\(290\) 0 0
\(291\) 0 0
\(292\) −8.90833 −0.521320
\(293\) −20.2389 −1.18237 −0.591183 0.806537i \(-0.701339\pi\)
−0.591183 + 0.806537i \(0.701339\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.60555 0.267692
\(297\) 0 0
\(298\) 5.21110 0.301871
\(299\) −6.78890 −0.392612
\(300\) 0 0
\(301\) −18.0000 −1.03750
\(302\) 0.486122 0.0279732
\(303\) 0 0
\(304\) 4.30278 0.246781
\(305\) 0 0
\(306\) 0 0
\(307\) 33.0278 1.88499 0.942497 0.334215i \(-0.108471\pi\)
0.942497 + 0.334215i \(0.108471\pi\)
\(308\) −12.4222 −0.707821
\(309\) 0 0
\(310\) 0 0
\(311\) 10.6056 0.601386 0.300693 0.953721i \(-0.402782\pi\)
0.300693 + 0.953721i \(0.402782\pi\)
\(312\) 0 0
\(313\) −20.0000 −1.13047 −0.565233 0.824931i \(-0.691214\pi\)
−0.565233 + 0.824931i \(0.691214\pi\)
\(314\) 2.69722 0.152213
\(315\) 0 0
\(316\) 8.51388 0.478943
\(317\) −9.69722 −0.544650 −0.272325 0.962205i \(-0.587793\pi\)
−0.272325 + 0.962205i \(0.587793\pi\)
\(318\) 0 0
\(319\) 14.3028 0.800802
\(320\) 0 0
\(321\) 0 0
\(322\) 18.4222 1.02663
\(323\) −11.2111 −0.623802
\(324\) 0 0
\(325\) −8.48612 −0.470725
\(326\) 8.60555 0.476617
\(327\) 0 0
\(328\) −4.00000 −0.220863
\(329\) −3.21110 −0.177034
\(330\) 0 0
\(331\) −19.2111 −1.05594 −0.527969 0.849264i \(-0.677046\pi\)
−0.527969 + 0.849264i \(0.677046\pi\)
\(332\) −5.21110 −0.285996
\(333\) 0 0
\(334\) 2.60555 0.142569
\(335\) 0 0
\(336\) 0 0
\(337\) 5.21110 0.283867 0.141933 0.989876i \(-0.454668\pi\)
0.141933 + 0.989876i \(0.454668\pi\)
\(338\) −10.1194 −0.550424
\(339\) 0 0
\(340\) 0 0
\(341\) 17.8167 0.964826
\(342\) 0 0
\(343\) −33.2111 −1.79323
\(344\) 3.90833 0.210723
\(345\) 0 0
\(346\) −13.0278 −0.700377
\(347\) −10.4222 −0.559493 −0.279747 0.960074i \(-0.590250\pi\)
−0.279747 + 0.960074i \(0.590250\pi\)
\(348\) 0 0
\(349\) −25.3944 −1.35933 −0.679667 0.733521i \(-0.737876\pi\)
−0.679667 + 0.733521i \(0.737876\pi\)
\(350\) 23.0278 1.23089
\(351\) 0 0
\(352\) 2.69722 0.143763
\(353\) 15.3944 0.819364 0.409682 0.912228i \(-0.365640\pi\)
0.409682 + 0.912228i \(0.365640\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 17.2111 0.912187
\(357\) 0 0
\(358\) 13.2111 0.698228
\(359\) 23.5139 1.24102 0.620508 0.784201i \(-0.286927\pi\)
0.620508 + 0.784201i \(0.286927\pi\)
\(360\) 0 0
\(361\) −0.486122 −0.0255854
\(362\) 1.39445 0.0732906
\(363\) 0 0
\(364\) −7.81665 −0.409704
\(365\) 0 0
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) 0 0
\(371\) −31.8167 −1.65184
\(372\) 0 0
\(373\) −26.8444 −1.38995 −0.694975 0.719033i \(-0.744585\pi\)
−0.694975 + 0.719033i \(0.744585\pi\)
\(374\) −7.02776 −0.363397
\(375\) 0 0
\(376\) 0.697224 0.0359566
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) −3.33053 −0.171078 −0.0855390 0.996335i \(-0.527261\pi\)
−0.0855390 + 0.996335i \(0.527261\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −7.81665 −0.399935
\(383\) 9.81665 0.501608 0.250804 0.968038i \(-0.419305\pi\)
0.250804 + 0.968038i \(0.419305\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 8.42221 0.428679
\(387\) 0 0
\(388\) −0.788897 −0.0400502
\(389\) −24.9361 −1.26431 −0.632155 0.774842i \(-0.717829\pi\)
−0.632155 + 0.774842i \(0.717829\pi\)
\(390\) 0 0
\(391\) 10.4222 0.527074
\(392\) 14.2111 0.717769
\(393\) 0 0
\(394\) −5.30278 −0.267150
\(395\) 0 0
\(396\) 0 0
\(397\) −1.48612 −0.0745863 −0.0372932 0.999304i \(-0.511874\pi\)
−0.0372932 + 0.999304i \(0.511874\pi\)
\(398\) 10.4222 0.522418
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −39.0278 −1.94895 −0.974477 0.224489i \(-0.927929\pi\)
−0.974477 + 0.224489i \(0.927929\pi\)
\(402\) 0 0
\(403\) 11.2111 0.558465
\(404\) 10.9083 0.542710
\(405\) 0 0
\(406\) −24.4222 −1.21205
\(407\) 12.4222 0.615746
\(408\) 0 0
\(409\) −26.2389 −1.29743 −0.648714 0.761032i \(-0.724693\pi\)
−0.648714 + 0.761032i \(0.724693\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.90833 −0.143283
\(413\) −1.39445 −0.0686163
\(414\) 0 0
\(415\) 0 0
\(416\) 1.69722 0.0832133
\(417\) 0 0
\(418\) 11.6056 0.567646
\(419\) 10.6056 0.518115 0.259058 0.965862i \(-0.416588\pi\)
0.259058 + 0.965862i \(0.416588\pi\)
\(420\) 0 0
\(421\) 12.7250 0.620178 0.310089 0.950708i \(-0.399641\pi\)
0.310089 + 0.950708i \(0.399641\pi\)
\(422\) 5.30278 0.258135
\(423\) 0 0
\(424\) 6.90833 0.335498
\(425\) 13.0278 0.631939
\(426\) 0 0
\(427\) 12.4222 0.601153
\(428\) 0.908327 0.0439056
\(429\) 0 0
\(430\) 0 0
\(431\) 4.18335 0.201505 0.100752 0.994912i \(-0.467875\pi\)
0.100752 + 0.994912i \(0.467875\pi\)
\(432\) 0 0
\(433\) −32.5416 −1.56385 −0.781926 0.623372i \(-0.785762\pi\)
−0.781926 + 0.623372i \(0.785762\pi\)
\(434\) −30.4222 −1.46031
\(435\) 0 0
\(436\) −5.39445 −0.258347
\(437\) −17.2111 −0.823319
\(438\) 0 0
\(439\) 27.6333 1.31887 0.659433 0.751763i \(-0.270796\pi\)
0.659433 + 0.751763i \(0.270796\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −4.42221 −0.210343
\(443\) −1.39445 −0.0662523 −0.0331261 0.999451i \(-0.510546\pi\)
−0.0331261 + 0.999451i \(0.510546\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.00000 −0.0473514
\(447\) 0 0
\(448\) −4.60555 −0.217592
\(449\) −15.2111 −0.717856 −0.358928 0.933365i \(-0.616858\pi\)
−0.358928 + 0.933365i \(0.616858\pi\)
\(450\) 0 0
\(451\) −10.7889 −0.508029
\(452\) 15.6972 0.738335
\(453\) 0 0
\(454\) 19.0278 0.893017
\(455\) 0 0
\(456\) 0 0
\(457\) 31.8167 1.48832 0.744160 0.668001i \(-0.232850\pi\)
0.744160 + 0.668001i \(0.232850\pi\)
\(458\) −10.0000 −0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) −4.72498 −0.220064 −0.110032 0.993928i \(-0.535095\pi\)
−0.110032 + 0.993928i \(0.535095\pi\)
\(462\) 0 0
\(463\) −11.2111 −0.521024 −0.260512 0.965471i \(-0.583891\pi\)
−0.260512 + 0.965471i \(0.583891\pi\)
\(464\) 5.30278 0.246175
\(465\) 0 0
\(466\) −4.69722 −0.217595
\(467\) −12.9083 −0.597326 −0.298663 0.954359i \(-0.596541\pi\)
−0.298663 + 0.954359i \(0.596541\pi\)
\(468\) 0 0
\(469\) −21.2111 −0.979438
\(470\) 0 0
\(471\) 0 0
\(472\) 0.302776 0.0139364
\(473\) 10.5416 0.484705
\(474\) 0 0
\(475\) −21.5139 −0.987124
\(476\) 12.0000 0.550019
\(477\) 0 0
\(478\) −8.72498 −0.399071
\(479\) 26.0917 1.19216 0.596079 0.802925i \(-0.296724\pi\)
0.596079 + 0.802925i \(0.296724\pi\)
\(480\) 0 0
\(481\) 7.81665 0.356409
\(482\) −4.51388 −0.205602
\(483\) 0 0
\(484\) −3.72498 −0.169317
\(485\) 0 0
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) −2.69722 −0.122098
\(489\) 0 0
\(490\) 0 0
\(491\) 32.9361 1.48638 0.743192 0.669078i \(-0.233311\pi\)
0.743192 + 0.669078i \(0.233311\pi\)
\(492\) 0 0
\(493\) −13.8167 −0.622271
\(494\) 7.30278 0.328567
\(495\) 0 0
\(496\) 6.60555 0.296598
\(497\) −51.6333 −2.31607
\(498\) 0 0
\(499\) −2.69722 −0.120744 −0.0603722 0.998176i \(-0.519229\pi\)
−0.0603722 + 0.998176i \(0.519229\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −22.4222 −1.00075
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −10.7889 −0.479625
\(507\) 0 0
\(508\) 7.21110 0.319941
\(509\) 40.7527 1.80633 0.903167 0.429290i \(-0.141236\pi\)
0.903167 + 0.429290i \(0.141236\pi\)
\(510\) 0 0
\(511\) 41.0278 1.81496
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) 0 0
\(516\) 0 0
\(517\) 1.88057 0.0827074
\(518\) −21.2111 −0.931962
\(519\) 0 0
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −34.4222 −1.50518 −0.752589 0.658491i \(-0.771195\pi\)
−0.752589 + 0.658491i \(0.771195\pi\)
\(524\) 16.4222 0.717407
\(525\) 0 0
\(526\) −7.39445 −0.322413
\(527\) −17.2111 −0.749727
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0 0
\(532\) −19.8167 −0.859161
\(533\) −6.78890 −0.294060
\(534\) 0 0
\(535\) 0 0
\(536\) 4.60555 0.198930
\(537\) 0 0
\(538\) 15.0278 0.647893
\(539\) 38.3305 1.65101
\(540\) 0 0
\(541\) 40.7250 1.75090 0.875452 0.483305i \(-0.160564\pi\)
0.875452 + 0.483305i \(0.160564\pi\)
\(542\) 15.1194 0.649435
\(543\) 0 0
\(544\) −2.60555 −0.111712
\(545\) 0 0
\(546\) 0 0
\(547\) −22.7250 −0.971650 −0.485825 0.874056i \(-0.661481\pi\)
−0.485825 + 0.874056i \(0.661481\pi\)
\(548\) 7.30278 0.311959
\(549\) 0 0
\(550\) −13.4861 −0.575050
\(551\) 22.8167 0.972022
\(552\) 0 0
\(553\) −39.2111 −1.66743
\(554\) −32.4222 −1.37749
\(555\) 0 0
\(556\) −11.9083 −0.505026
\(557\) 9.57779 0.405824 0.202912 0.979197i \(-0.434959\pi\)
0.202912 + 0.979197i \(0.434959\pi\)
\(558\) 0 0
\(559\) 6.63331 0.280559
\(560\) 0 0
\(561\) 0 0
\(562\) 14.6056 0.616098
\(563\) −11.5416 −0.486422 −0.243211 0.969973i \(-0.578201\pi\)
−0.243211 + 0.969973i \(0.578201\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −15.6972 −0.659804
\(567\) 0 0
\(568\) 11.2111 0.470407
\(569\) 20.5416 0.861150 0.430575 0.902555i \(-0.358311\pi\)
0.430575 + 0.902555i \(0.358311\pi\)
\(570\) 0 0
\(571\) 8.00000 0.334790 0.167395 0.985890i \(-0.446465\pi\)
0.167395 + 0.985890i \(0.446465\pi\)
\(572\) 4.57779 0.191407
\(573\) 0 0
\(574\) 18.4222 0.768928
\(575\) 20.0000 0.834058
\(576\) 0 0
\(577\) 39.9638 1.66372 0.831858 0.554988i \(-0.187277\pi\)
0.831858 + 0.554988i \(0.187277\pi\)
\(578\) −10.2111 −0.424726
\(579\) 0 0
\(580\) 0 0
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) 18.6333 0.771713
\(584\) −8.90833 −0.368629
\(585\) 0 0
\(586\) −20.2389 −0.836060
\(587\) 31.9361 1.31814 0.659072 0.752080i \(-0.270949\pi\)
0.659072 + 0.752080i \(0.270949\pi\)
\(588\) 0 0
\(589\) 28.4222 1.17112
\(590\) 0 0
\(591\) 0 0
\(592\) 4.60555 0.189287
\(593\) −3.57779 −0.146922 −0.0734612 0.997298i \(-0.523405\pi\)
−0.0734612 + 0.997298i \(0.523405\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5.21110 0.213455
\(597\) 0 0
\(598\) −6.78890 −0.277619
\(599\) 35.1194 1.43494 0.717470 0.696589i \(-0.245300\pi\)
0.717470 + 0.696589i \(0.245300\pi\)
\(600\) 0 0
\(601\) 0.183346 0.00747885 0.00373942 0.999993i \(-0.498810\pi\)
0.00373942 + 0.999993i \(0.498810\pi\)
\(602\) −18.0000 −0.733625
\(603\) 0 0
\(604\) 0.486122 0.0197800
\(605\) 0 0
\(606\) 0 0
\(607\) −24.8444 −1.00840 −0.504202 0.863586i \(-0.668213\pi\)
−0.504202 + 0.863586i \(0.668213\pi\)
\(608\) 4.30278 0.174501
\(609\) 0 0
\(610\) 0 0
\(611\) 1.18335 0.0478731
\(612\) 0 0
\(613\) 18.5139 0.747768 0.373884 0.927475i \(-0.378026\pi\)
0.373884 + 0.927475i \(0.378026\pi\)
\(614\) 33.0278 1.33289
\(615\) 0 0
\(616\) −12.4222 −0.500505
\(617\) −10.4222 −0.419582 −0.209791 0.977746i \(-0.567278\pi\)
−0.209791 + 0.977746i \(0.567278\pi\)
\(618\) 0 0
\(619\) −18.4222 −0.740451 −0.370225 0.928942i \(-0.620720\pi\)
−0.370225 + 0.928942i \(0.620720\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 10.6056 0.425244
\(623\) −79.2666 −3.17575
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) −20.0000 −0.799361
\(627\) 0 0
\(628\) 2.69722 0.107631
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 8.88057 0.353530 0.176765 0.984253i \(-0.443437\pi\)
0.176765 + 0.984253i \(0.443437\pi\)
\(632\) 8.51388 0.338664
\(633\) 0 0
\(634\) −9.69722 −0.385126
\(635\) 0 0
\(636\) 0 0
\(637\) 24.1194 0.955647
\(638\) 14.3028 0.566252
\(639\) 0 0
\(640\) 0 0
\(641\) −22.4861 −0.888148 −0.444074 0.895990i \(-0.646467\pi\)
−0.444074 + 0.895990i \(0.646467\pi\)
\(642\) 0 0
\(643\) 26.6972 1.05284 0.526418 0.850226i \(-0.323535\pi\)
0.526418 + 0.850226i \(0.323535\pi\)
\(644\) 18.4222 0.725937
\(645\) 0 0
\(646\) −11.2111 −0.441095
\(647\) 34.9083 1.37239 0.686194 0.727419i \(-0.259280\pi\)
0.686194 + 0.727419i \(0.259280\pi\)
\(648\) 0 0
\(649\) 0.816654 0.0320565
\(650\) −8.48612 −0.332853
\(651\) 0 0
\(652\) 8.60555 0.337019
\(653\) 35.6333 1.39444 0.697220 0.716858i \(-0.254420\pi\)
0.697220 + 0.716858i \(0.254420\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −4.00000 −0.156174
\(657\) 0 0
\(658\) −3.21110 −0.125182
\(659\) 21.6333 0.842714 0.421357 0.906895i \(-0.361554\pi\)
0.421357 + 0.906895i \(0.361554\pi\)
\(660\) 0 0
\(661\) 8.93608 0.347573 0.173787 0.984783i \(-0.444400\pi\)
0.173787 + 0.984783i \(0.444400\pi\)
\(662\) −19.2111 −0.746661
\(663\) 0 0
\(664\) −5.21110 −0.202230
\(665\) 0 0
\(666\) 0 0
\(667\) −21.2111 −0.821297
\(668\) 2.60555 0.100812
\(669\) 0 0
\(670\) 0 0
\(671\) −7.27502 −0.280849
\(672\) 0 0
\(673\) −14.1194 −0.544264 −0.272132 0.962260i \(-0.587729\pi\)
−0.272132 + 0.962260i \(0.587729\pi\)
\(674\) 5.21110 0.200724
\(675\) 0 0
\(676\) −10.1194 −0.389209
\(677\) −35.2111 −1.35327 −0.676636 0.736317i \(-0.736563\pi\)
−0.676636 + 0.736317i \(0.736563\pi\)
\(678\) 0 0
\(679\) 3.63331 0.139434
\(680\) 0 0
\(681\) 0 0
\(682\) 17.8167 0.682235
\(683\) −24.1833 −0.925350 −0.462675 0.886528i \(-0.653110\pi\)
−0.462675 + 0.886528i \(0.653110\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −33.2111 −1.26801
\(687\) 0 0
\(688\) 3.90833 0.149004
\(689\) 11.7250 0.446686
\(690\) 0 0
\(691\) −21.8167 −0.829945 −0.414972 0.909834i \(-0.636209\pi\)
−0.414972 + 0.909834i \(0.636209\pi\)
\(692\) −13.0278 −0.495241
\(693\) 0 0
\(694\) −10.4222 −0.395621
\(695\) 0 0
\(696\) 0 0
\(697\) 10.4222 0.394769
\(698\) −25.3944 −0.961194
\(699\) 0 0
\(700\) 23.0278 0.870367
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) 19.8167 0.747399
\(704\) 2.69722 0.101655
\(705\) 0 0
\(706\) 15.3944 0.579378
\(707\) −50.2389 −1.88943
\(708\) 0 0
\(709\) −32.4222 −1.21764 −0.608821 0.793308i \(-0.708357\pi\)
−0.608821 + 0.793308i \(0.708357\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 17.2111 0.645013
\(713\) −26.4222 −0.989519
\(714\) 0 0
\(715\) 0 0
\(716\) 13.2111 0.493722
\(717\) 0 0
\(718\) 23.5139 0.877530
\(719\) 6.78890 0.253183 0.126592 0.991955i \(-0.459596\pi\)
0.126592 + 0.991955i \(0.459596\pi\)
\(720\) 0 0
\(721\) 13.3944 0.498835
\(722\) −0.486122 −0.0180916
\(723\) 0 0
\(724\) 1.39445 0.0518243
\(725\) −26.5139 −0.984701
\(726\) 0 0
\(727\) −35.8167 −1.32837 −0.664183 0.747570i \(-0.731220\pi\)
−0.664183 + 0.747570i \(0.731220\pi\)
\(728\) −7.81665 −0.289704
\(729\) 0 0
\(730\) 0 0
\(731\) −10.1833 −0.376645
\(732\) 0 0
\(733\) −8.42221 −0.311081 −0.155541 0.987829i \(-0.549712\pi\)
−0.155541 + 0.987829i \(0.549712\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) 12.4222 0.457578
\(738\) 0 0
\(739\) −21.4500 −0.789050 −0.394525 0.918885i \(-0.629091\pi\)
−0.394525 + 0.918885i \(0.629091\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −31.8167 −1.16803
\(743\) −29.9361 −1.09825 −0.549124 0.835741i \(-0.685039\pi\)
−0.549124 + 0.835741i \(0.685039\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −26.8444 −0.982844
\(747\) 0 0
\(748\) −7.02776 −0.256960
\(749\) −4.18335 −0.152856
\(750\) 0 0
\(751\) −21.4500 −0.782720 −0.391360 0.920238i \(-0.627995\pi\)
−0.391360 + 0.920238i \(0.627995\pi\)
\(752\) 0.697224 0.0254252
\(753\) 0 0
\(754\) 9.00000 0.327761
\(755\) 0 0
\(756\) 0 0
\(757\) 33.3305 1.21142 0.605709 0.795686i \(-0.292889\pi\)
0.605709 + 0.795686i \(0.292889\pi\)
\(758\) −3.33053 −0.120970
\(759\) 0 0
\(760\) 0 0
\(761\) −36.9083 −1.33793 −0.668963 0.743296i \(-0.733262\pi\)
−0.668963 + 0.743296i \(0.733262\pi\)
\(762\) 0 0
\(763\) 24.8444 0.899428
\(764\) −7.81665 −0.282797
\(765\) 0 0
\(766\) 9.81665 0.354690
\(767\) 0.513878 0.0185551
\(768\) 0 0
\(769\) −8.88057 −0.320242 −0.160121 0.987097i \(-0.551188\pi\)
−0.160121 + 0.987097i \(0.551188\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.42221 0.303122
\(773\) 22.2389 0.799876 0.399938 0.916542i \(-0.369032\pi\)
0.399938 + 0.916542i \(0.369032\pi\)
\(774\) 0 0
\(775\) −33.0278 −1.18639
\(776\) −0.788897 −0.0283198
\(777\) 0 0
\(778\) −24.9361 −0.894002
\(779\) −17.2111 −0.616652
\(780\) 0 0
\(781\) 30.2389 1.08203
\(782\) 10.4222 0.372697
\(783\) 0 0
\(784\) 14.2111 0.507539
\(785\) 0 0
\(786\) 0 0
\(787\) 14.7889 0.527167 0.263584 0.964637i \(-0.415096\pi\)
0.263584 + 0.964637i \(0.415096\pi\)
\(788\) −5.30278 −0.188904
\(789\) 0 0
\(790\) 0 0
\(791\) −72.2944 −2.57049
\(792\) 0 0
\(793\) −4.57779 −0.162562
\(794\) −1.48612 −0.0527405
\(795\) 0 0
\(796\) 10.4222 0.369405
\(797\) 16.4222 0.581704 0.290852 0.956768i \(-0.406061\pi\)
0.290852 + 0.956768i \(0.406061\pi\)
\(798\) 0 0
\(799\) −1.81665 −0.0642686
\(800\) −5.00000 −0.176777
\(801\) 0 0
\(802\) −39.0278 −1.37812
\(803\) −24.0278 −0.847921
\(804\) 0 0
\(805\) 0 0
\(806\) 11.2111 0.394894
\(807\) 0 0
\(808\) 10.9083 0.383754
\(809\) −42.8444 −1.50633 −0.753165 0.657832i \(-0.771474\pi\)
−0.753165 + 0.657832i \(0.771474\pi\)
\(810\) 0 0
\(811\) −46.2389 −1.62367 −0.811833 0.583890i \(-0.801530\pi\)
−0.811833 + 0.583890i \(0.801530\pi\)
\(812\) −24.4222 −0.857051
\(813\) 0 0
\(814\) 12.4222 0.435398
\(815\) 0 0
\(816\) 0 0
\(817\) 16.8167 0.588340
\(818\) −26.2389 −0.917420
\(819\) 0 0
\(820\) 0 0
\(821\) −55.5416 −1.93842 −0.969208 0.246243i \(-0.920804\pi\)
−0.969208 + 0.246243i \(0.920804\pi\)
\(822\) 0 0
\(823\) 35.2666 1.22932 0.614658 0.788793i \(-0.289294\pi\)
0.614658 + 0.788793i \(0.289294\pi\)
\(824\) −2.90833 −0.101316
\(825\) 0 0
\(826\) −1.39445 −0.0485191
\(827\) 0.0639167 0.00222260 0.00111130 0.999999i \(-0.499646\pi\)
0.00111130 + 0.999999i \(0.499646\pi\)
\(828\) 0 0
\(829\) −33.4861 −1.16302 −0.581511 0.813539i \(-0.697538\pi\)
−0.581511 + 0.813539i \(0.697538\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.69722 0.0588407
\(833\) −37.0278 −1.28294
\(834\) 0 0
\(835\) 0 0
\(836\) 11.6056 0.401386
\(837\) 0 0
\(838\) 10.6056 0.366363
\(839\) −9.39445 −0.324332 −0.162166 0.986763i \(-0.551848\pi\)
−0.162166 + 0.986763i \(0.551848\pi\)
\(840\) 0 0
\(841\) −0.880571 −0.0303645
\(842\) 12.7250 0.438532
\(843\) 0 0
\(844\) 5.30278 0.182529
\(845\) 0 0
\(846\) 0 0
\(847\) 17.1556 0.589473
\(848\) 6.90833 0.237233
\(849\) 0 0
\(850\) 13.0278 0.446848
\(851\) −18.4222 −0.631505
\(852\) 0 0
\(853\) 2.88057 0.0986289 0.0493144 0.998783i \(-0.484296\pi\)
0.0493144 + 0.998783i \(0.484296\pi\)
\(854\) 12.4222 0.425079
\(855\) 0 0
\(856\) 0.908327 0.0310460
\(857\) −14.6056 −0.498916 −0.249458 0.968386i \(-0.580252\pi\)
−0.249458 + 0.968386i \(0.580252\pi\)
\(858\) 0 0
\(859\) −18.9722 −0.647325 −0.323662 0.946173i \(-0.604914\pi\)
−0.323662 + 0.946173i \(0.604914\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 4.18335 0.142485
\(863\) 20.7889 0.707662 0.353831 0.935309i \(-0.384879\pi\)
0.353831 + 0.935309i \(0.384879\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −32.5416 −1.10581
\(867\) 0 0
\(868\) −30.4222 −1.03260
\(869\) 22.9638 0.778995
\(870\) 0 0
\(871\) 7.81665 0.264857
\(872\) −5.39445 −0.182679
\(873\) 0 0
\(874\) −17.2111 −0.582174
\(875\) 0 0
\(876\) 0 0
\(877\) 14.8806 0.502481 0.251241 0.967925i \(-0.419161\pi\)
0.251241 + 0.967925i \(0.419161\pi\)
\(878\) 27.6333 0.932579
\(879\) 0 0
\(880\) 0 0
\(881\) 33.2111 1.11891 0.559455 0.828861i \(-0.311010\pi\)
0.559455 + 0.828861i \(0.311010\pi\)
\(882\) 0 0
\(883\) −40.0555 −1.34798 −0.673988 0.738743i \(-0.735420\pi\)
−0.673988 + 0.738743i \(0.735420\pi\)
\(884\) −4.42221 −0.148735
\(885\) 0 0
\(886\) −1.39445 −0.0468474
\(887\) −32.7250 −1.09880 −0.549399 0.835560i \(-0.685143\pi\)
−0.549399 + 0.835560i \(0.685143\pi\)
\(888\) 0 0
\(889\) −33.2111 −1.11386
\(890\) 0 0
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) 3.00000 0.100391
\(894\) 0 0
\(895\) 0 0
\(896\) −4.60555 −0.153861
\(897\) 0 0
\(898\) −15.2111 −0.507601
\(899\) 35.0278 1.16824
\(900\) 0 0
\(901\) −18.0000 −0.599667
\(902\) −10.7889 −0.359231
\(903\) 0 0
\(904\) 15.6972 0.522082
\(905\) 0 0
\(906\) 0 0
\(907\) −11.3305 −0.376224 −0.188112 0.982148i \(-0.560237\pi\)
−0.188112 + 0.982148i \(0.560237\pi\)
\(908\) 19.0278 0.631458
\(909\) 0 0
\(910\) 0 0
\(911\) 38.4222 1.27298 0.636492 0.771283i \(-0.280385\pi\)
0.636492 + 0.771283i \(0.280385\pi\)
\(912\) 0 0
\(913\) −14.0555 −0.465170
\(914\) 31.8167 1.05240
\(915\) 0 0
\(916\) −10.0000 −0.330409
\(917\) −75.6333 −2.49763
\(918\) 0 0
\(919\) 46.5416 1.53527 0.767633 0.640889i \(-0.221434\pi\)
0.767633 + 0.640889i \(0.221434\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −4.72498 −0.155609
\(923\) 19.0278 0.626306
\(924\) 0 0
\(925\) −23.0278 −0.757148
\(926\) −11.2111 −0.368420
\(927\) 0 0
\(928\) 5.30278 0.174072
\(929\) −59.0278 −1.93664 −0.968319 0.249717i \(-0.919662\pi\)
−0.968319 + 0.249717i \(0.919662\pi\)
\(930\) 0 0
\(931\) 61.1472 2.00402
\(932\) −4.69722 −0.153863
\(933\) 0 0
\(934\) −12.9083 −0.422373
\(935\) 0 0
\(936\) 0 0
\(937\) −39.2111 −1.28097 −0.640485 0.767970i \(-0.721267\pi\)
−0.640485 + 0.767970i \(0.721267\pi\)
\(938\) −21.2111 −0.692567
\(939\) 0 0
\(940\) 0 0
\(941\) 23.8806 0.778484 0.389242 0.921135i \(-0.372737\pi\)
0.389242 + 0.921135i \(0.372737\pi\)
\(942\) 0 0
\(943\) 16.0000 0.521032
\(944\) 0.302776 0.00985451
\(945\) 0 0
\(946\) 10.5416 0.342738
\(947\) −4.18335 −0.135940 −0.0679702 0.997687i \(-0.521652\pi\)
−0.0679702 + 0.997687i \(0.521652\pi\)
\(948\) 0 0
\(949\) −15.1194 −0.490797
\(950\) −21.5139 −0.698002
\(951\) 0 0
\(952\) 12.0000 0.388922
\(953\) −28.0555 −0.908807 −0.454404 0.890796i \(-0.650148\pi\)
−0.454404 + 0.890796i \(0.650148\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −8.72498 −0.282186
\(957\) 0 0
\(958\) 26.0917 0.842984
\(959\) −33.6333 −1.08608
\(960\) 0 0
\(961\) 12.6333 0.407526
\(962\) 7.81665 0.252019
\(963\) 0 0
\(964\) −4.51388 −0.145382
\(965\) 0 0
\(966\) 0 0
\(967\) 22.9083 0.736682 0.368341 0.929691i \(-0.379926\pi\)
0.368341 + 0.929691i \(0.379926\pi\)
\(968\) −3.72498 −0.119725
\(969\) 0 0
\(970\) 0 0
\(971\) −4.27502 −0.137192 −0.0685959 0.997645i \(-0.521852\pi\)
−0.0685959 + 0.997645i \(0.521852\pi\)
\(972\) 0 0
\(973\) 54.8444 1.75823
\(974\) −4.00000 −0.128168
\(975\) 0 0
\(976\) −2.69722 −0.0863360
\(977\) 1.72498 0.0551870 0.0275935 0.999619i \(-0.491216\pi\)
0.0275935 + 0.999619i \(0.491216\pi\)
\(978\) 0 0
\(979\) 46.4222 1.48366
\(980\) 0 0
\(981\) 0 0
\(982\) 32.9361 1.05103
\(983\) −51.2111 −1.63338 −0.816690 0.577076i \(-0.804194\pi\)
−0.816690 + 0.577076i \(0.804194\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −13.8167 −0.440012
\(987\) 0 0
\(988\) 7.30278 0.232332
\(989\) −15.6333 −0.497110
\(990\) 0 0
\(991\) 56.1194 1.78269 0.891346 0.453323i \(-0.149762\pi\)
0.891346 + 0.453323i \(0.149762\pi\)
\(992\) 6.60555 0.209726
\(993\) 0 0
\(994\) −51.6333 −1.63771
\(995\) 0 0
\(996\) 0 0
\(997\) −9.81665 −0.310897 −0.155448 0.987844i \(-0.549682\pi\)
−0.155448 + 0.987844i \(0.549682\pi\)
\(998\) −2.69722 −0.0853791
\(999\) 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 \(a_p\))