Properties

Label 4028.2.a.d.1.12
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-0.365086\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.365086 q^{3} +1.83829 q^{5} +2.27559 q^{7} -2.86671 q^{9} +O(q^{10})\) \(q+0.365086 q^{3} +1.83829 q^{5} +2.27559 q^{7} -2.86671 q^{9} +2.41308 q^{11} -4.42773 q^{13} +0.671133 q^{15} -4.27528 q^{17} -1.00000 q^{19} +0.830786 q^{21} -3.42566 q^{23} -1.62070 q^{25} -2.14185 q^{27} -5.90044 q^{29} -0.273458 q^{31} +0.880982 q^{33} +4.18319 q^{35} -5.93087 q^{37} -1.61650 q^{39} -0.691610 q^{41} +5.57072 q^{43} -5.26984 q^{45} -10.2444 q^{47} -1.82169 q^{49} -1.56084 q^{51} +1.00000 q^{53} +4.43594 q^{55} -0.365086 q^{57} -4.01636 q^{59} -10.2050 q^{61} -6.52347 q^{63} -8.13944 q^{65} +2.97188 q^{67} -1.25066 q^{69} -0.559721 q^{71} -8.72913 q^{73} -0.591694 q^{75} +5.49119 q^{77} +0.654191 q^{79} +7.81818 q^{81} +3.92577 q^{83} -7.85920 q^{85} -2.15417 q^{87} +14.2283 q^{89} -10.0757 q^{91} -0.0998356 q^{93} -1.83829 q^{95} +1.00481 q^{97} -6.91762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.365086 0.210782 0.105391 0.994431i \(-0.466391\pi\)
0.105391 + 0.994431i \(0.466391\pi\)
\(4\) 0 0
\(5\) 1.83829 0.822107 0.411054 0.911611i \(-0.365161\pi\)
0.411054 + 0.911611i \(0.365161\pi\)
\(6\) 0 0
\(7\) 2.27559 0.860093 0.430046 0.902807i \(-0.358497\pi\)
0.430046 + 0.902807i \(0.358497\pi\)
\(8\) 0 0
\(9\) −2.86671 −0.955571
\(10\) 0 0
\(11\) 2.41308 0.727572 0.363786 0.931483i \(-0.381484\pi\)
0.363786 + 0.931483i \(0.381484\pi\)
\(12\) 0 0
\(13\) −4.42773 −1.22803 −0.614016 0.789294i \(-0.710447\pi\)
−0.614016 + 0.789294i \(0.710447\pi\)
\(14\) 0 0
\(15\) 0.671133 0.173286
\(16\) 0 0
\(17\) −4.27528 −1.03691 −0.518454 0.855105i \(-0.673492\pi\)
−0.518454 + 0.855105i \(0.673492\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0.830786 0.181292
\(22\) 0 0
\(23\) −3.42566 −0.714299 −0.357150 0.934047i \(-0.616251\pi\)
−0.357150 + 0.934047i \(0.616251\pi\)
\(24\) 0 0
\(25\) −1.62070 −0.324140
\(26\) 0 0
\(27\) −2.14185 −0.412200
\(28\) 0 0
\(29\) −5.90044 −1.09568 −0.547842 0.836582i \(-0.684551\pi\)
−0.547842 + 0.836582i \(0.684551\pi\)
\(30\) 0 0
\(31\) −0.273458 −0.0491145 −0.0245572 0.999698i \(-0.507818\pi\)
−0.0245572 + 0.999698i \(0.507818\pi\)
\(32\) 0 0
\(33\) 0.880982 0.153359
\(34\) 0 0
\(35\) 4.18319 0.707088
\(36\) 0 0
\(37\) −5.93087 −0.975028 −0.487514 0.873115i \(-0.662096\pi\)
−0.487514 + 0.873115i \(0.662096\pi\)
\(38\) 0 0
\(39\) −1.61650 −0.258847
\(40\) 0 0
\(41\) −0.691610 −0.108011 −0.0540057 0.998541i \(-0.517199\pi\)
−0.0540057 + 0.998541i \(0.517199\pi\)
\(42\) 0 0
\(43\) 5.57072 0.849527 0.424763 0.905304i \(-0.360357\pi\)
0.424763 + 0.905304i \(0.360357\pi\)
\(44\) 0 0
\(45\) −5.26984 −0.785582
\(46\) 0 0
\(47\) −10.2444 −1.49429 −0.747147 0.664659i \(-0.768577\pi\)
−0.747147 + 0.664659i \(0.768577\pi\)
\(48\) 0 0
\(49\) −1.82169 −0.260241
\(50\) 0 0
\(51\) −1.56084 −0.218562
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 4.43594 0.598142
\(56\) 0 0
\(57\) −0.365086 −0.0483568
\(58\) 0 0
\(59\) −4.01636 −0.522886 −0.261443 0.965219i \(-0.584198\pi\)
−0.261443 + 0.965219i \(0.584198\pi\)
\(60\) 0 0
\(61\) −10.2050 −1.30662 −0.653309 0.757091i \(-0.726620\pi\)
−0.653309 + 0.757091i \(0.726620\pi\)
\(62\) 0 0
\(63\) −6.52347 −0.821879
\(64\) 0 0
\(65\) −8.13944 −1.00957
\(66\) 0 0
\(67\) 2.97188 0.363073 0.181536 0.983384i \(-0.441893\pi\)
0.181536 + 0.983384i \(0.441893\pi\)
\(68\) 0 0
\(69\) −1.25066 −0.150562
\(70\) 0 0
\(71\) −0.559721 −0.0664266 −0.0332133 0.999448i \(-0.510574\pi\)
−0.0332133 + 0.999448i \(0.510574\pi\)
\(72\) 0 0
\(73\) −8.72913 −1.02167 −0.510834 0.859679i \(-0.670663\pi\)
−0.510834 + 0.859679i \(0.670663\pi\)
\(74\) 0 0
\(75\) −0.591694 −0.0683230
\(76\) 0 0
\(77\) 5.49119 0.625779
\(78\) 0 0
\(79\) 0.654191 0.0736022 0.0368011 0.999323i \(-0.488283\pi\)
0.0368011 + 0.999323i \(0.488283\pi\)
\(80\) 0 0
\(81\) 7.81818 0.868686
\(82\) 0 0
\(83\) 3.92577 0.430909 0.215455 0.976514i \(-0.430877\pi\)
0.215455 + 0.976514i \(0.430877\pi\)
\(84\) 0 0
\(85\) −7.85920 −0.852450
\(86\) 0 0
\(87\) −2.15417 −0.230951
\(88\) 0 0
\(89\) 14.2283 1.50819 0.754097 0.656763i \(-0.228075\pi\)
0.754097 + 0.656763i \(0.228075\pi\)
\(90\) 0 0
\(91\) −10.0757 −1.05622
\(92\) 0 0
\(93\) −0.0998356 −0.0103525
\(94\) 0 0
\(95\) −1.83829 −0.188604
\(96\) 0 0
\(97\) 1.00481 0.102023 0.0510117 0.998698i \(-0.483755\pi\)
0.0510117 + 0.998698i \(0.483755\pi\)
\(98\) 0 0
\(99\) −6.91762 −0.695247
\(100\) 0 0
\(101\) 12.3438 1.22826 0.614129 0.789205i \(-0.289507\pi\)
0.614129 + 0.789205i \(0.289507\pi\)
\(102\) 0 0
\(103\) 11.7699 1.15972 0.579859 0.814717i \(-0.303108\pi\)
0.579859 + 0.814717i \(0.303108\pi\)
\(104\) 0 0
\(105\) 1.52722 0.149042
\(106\) 0 0
\(107\) 5.20495 0.503181 0.251591 0.967834i \(-0.419046\pi\)
0.251591 + 0.967834i \(0.419046\pi\)
\(108\) 0 0
\(109\) −7.37331 −0.706235 −0.353117 0.935579i \(-0.614878\pi\)
−0.353117 + 0.935579i \(0.614878\pi\)
\(110\) 0 0
\(111\) −2.16527 −0.205519
\(112\) 0 0
\(113\) −0.159471 −0.0150018 −0.00750088 0.999972i \(-0.502388\pi\)
−0.00750088 + 0.999972i \(0.502388\pi\)
\(114\) 0 0
\(115\) −6.29735 −0.587230
\(116\) 0 0
\(117\) 12.6930 1.17347
\(118\) 0 0
\(119\) −9.72880 −0.891837
\(120\) 0 0
\(121\) −5.17703 −0.470639
\(122\) 0 0
\(123\) −0.252497 −0.0227669
\(124\) 0 0
\(125\) −12.1707 −1.08858
\(126\) 0 0
\(127\) 3.00101 0.266297 0.133148 0.991096i \(-0.457491\pi\)
0.133148 + 0.991096i \(0.457491\pi\)
\(128\) 0 0
\(129\) 2.03379 0.179065
\(130\) 0 0
\(131\) 17.8334 1.55811 0.779055 0.626955i \(-0.215699\pi\)
0.779055 + 0.626955i \(0.215699\pi\)
\(132\) 0 0
\(133\) −2.27559 −0.197319
\(134\) 0 0
\(135\) −3.93734 −0.338872
\(136\) 0 0
\(137\) −14.4180 −1.23181 −0.615906 0.787819i \(-0.711210\pi\)
−0.615906 + 0.787819i \(0.711210\pi\)
\(138\) 0 0
\(139\) −4.92369 −0.417622 −0.208811 0.977956i \(-0.566959\pi\)
−0.208811 + 0.977956i \(0.566959\pi\)
\(140\) 0 0
\(141\) −3.74007 −0.314971
\(142\) 0 0
\(143\) −10.6845 −0.893481
\(144\) 0 0
\(145\) −10.8467 −0.900770
\(146\) 0 0
\(147\) −0.665071 −0.0548542
\(148\) 0 0
\(149\) 0.916035 0.0750445 0.0375222 0.999296i \(-0.488053\pi\)
0.0375222 + 0.999296i \(0.488053\pi\)
\(150\) 0 0
\(151\) 22.1694 1.80412 0.902062 0.431607i \(-0.142053\pi\)
0.902062 + 0.431607i \(0.142053\pi\)
\(152\) 0 0
\(153\) 12.2560 0.990839
\(154\) 0 0
\(155\) −0.502694 −0.0403774
\(156\) 0 0
\(157\) 18.2162 1.45381 0.726904 0.686739i \(-0.240958\pi\)
0.726904 + 0.686739i \(0.240958\pi\)
\(158\) 0 0
\(159\) 0.365086 0.0289532
\(160\) 0 0
\(161\) −7.79540 −0.614363
\(162\) 0 0
\(163\) −2.36979 −0.185616 −0.0928080 0.995684i \(-0.529584\pi\)
−0.0928080 + 0.995684i \(0.529584\pi\)
\(164\) 0 0
\(165\) 1.61950 0.126078
\(166\) 0 0
\(167\) −16.2737 −1.25930 −0.629649 0.776880i \(-0.716801\pi\)
−0.629649 + 0.776880i \(0.716801\pi\)
\(168\) 0 0
\(169\) 6.60481 0.508062
\(170\) 0 0
\(171\) 2.86671 0.219223
\(172\) 0 0
\(173\) 4.09383 0.311248 0.155624 0.987816i \(-0.450261\pi\)
0.155624 + 0.987816i \(0.450261\pi\)
\(174\) 0 0
\(175\) −3.68805 −0.278790
\(176\) 0 0
\(177\) −1.46632 −0.110215
\(178\) 0 0
\(179\) 10.0618 0.752056 0.376028 0.926608i \(-0.377290\pi\)
0.376028 + 0.926608i \(0.377290\pi\)
\(180\) 0 0
\(181\) 7.04187 0.523418 0.261709 0.965147i \(-0.415714\pi\)
0.261709 + 0.965147i \(0.415714\pi\)
\(182\) 0 0
\(183\) −3.72571 −0.275412
\(184\) 0 0
\(185\) −10.9026 −0.801578
\(186\) 0 0
\(187\) −10.3166 −0.754425
\(188\) 0 0
\(189\) −4.87398 −0.354530
\(190\) 0 0
\(191\) −10.8187 −0.782815 −0.391408 0.920217i \(-0.628012\pi\)
−0.391408 + 0.920217i \(0.628012\pi\)
\(192\) 0 0
\(193\) 7.23220 0.520585 0.260293 0.965530i \(-0.416181\pi\)
0.260293 + 0.965530i \(0.416181\pi\)
\(194\) 0 0
\(195\) −2.97160 −0.212800
\(196\) 0 0
\(197\) −10.3616 −0.738231 −0.369116 0.929384i \(-0.620339\pi\)
−0.369116 + 0.929384i \(0.620339\pi\)
\(198\) 0 0
\(199\) 3.63058 0.257365 0.128683 0.991686i \(-0.458925\pi\)
0.128683 + 0.991686i \(0.458925\pi\)
\(200\) 0 0
\(201\) 1.08499 0.0765293
\(202\) 0 0
\(203\) −13.4270 −0.942390
\(204\) 0 0
\(205\) −1.27138 −0.0887969
\(206\) 0 0
\(207\) 9.82038 0.682563
\(208\) 0 0
\(209\) −2.41308 −0.166916
\(210\) 0 0
\(211\) 18.3740 1.26492 0.632459 0.774593i \(-0.282045\pi\)
0.632459 + 0.774593i \(0.282045\pi\)
\(212\) 0 0
\(213\) −0.204346 −0.0140016
\(214\) 0 0
\(215\) 10.2406 0.698402
\(216\) 0 0
\(217\) −0.622278 −0.0422430
\(218\) 0 0
\(219\) −3.18688 −0.215350
\(220\) 0 0
\(221\) 18.9298 1.27336
\(222\) 0 0
\(223\) −4.42784 −0.296510 −0.148255 0.988949i \(-0.547366\pi\)
−0.148255 + 0.988949i \(0.547366\pi\)
\(224\) 0 0
\(225\) 4.64608 0.309739
\(226\) 0 0
\(227\) −16.5773 −1.10027 −0.550136 0.835075i \(-0.685424\pi\)
−0.550136 + 0.835075i \(0.685424\pi\)
\(228\) 0 0
\(229\) 3.81084 0.251828 0.125914 0.992041i \(-0.459814\pi\)
0.125914 + 0.992041i \(0.459814\pi\)
\(230\) 0 0
\(231\) 2.00476 0.131903
\(232\) 0 0
\(233\) 16.7584 1.09788 0.548938 0.835863i \(-0.315032\pi\)
0.548938 + 0.835863i \(0.315032\pi\)
\(234\) 0 0
\(235\) −18.8321 −1.22847
\(236\) 0 0
\(237\) 0.238836 0.0155141
\(238\) 0 0
\(239\) −19.2842 −1.24739 −0.623696 0.781667i \(-0.714370\pi\)
−0.623696 + 0.781667i \(0.714370\pi\)
\(240\) 0 0
\(241\) 1.26067 0.0812068 0.0406034 0.999175i \(-0.487072\pi\)
0.0406034 + 0.999175i \(0.487072\pi\)
\(242\) 0 0
\(243\) 9.27986 0.595304
\(244\) 0 0
\(245\) −3.34878 −0.213946
\(246\) 0 0
\(247\) 4.42773 0.281730
\(248\) 0 0
\(249\) 1.43324 0.0908281
\(250\) 0 0
\(251\) −22.5871 −1.42569 −0.712843 0.701324i \(-0.752593\pi\)
−0.712843 + 0.701324i \(0.752593\pi\)
\(252\) 0 0
\(253\) −8.26640 −0.519704
\(254\) 0 0
\(255\) −2.86928 −0.179681
\(256\) 0 0
\(257\) −14.5451 −0.907300 −0.453650 0.891180i \(-0.649878\pi\)
−0.453650 + 0.891180i \(0.649878\pi\)
\(258\) 0 0
\(259\) −13.4962 −0.838615
\(260\) 0 0
\(261\) 16.9149 1.04700
\(262\) 0 0
\(263\) −18.9001 −1.16543 −0.582717 0.812675i \(-0.698010\pi\)
−0.582717 + 0.812675i \(0.698010\pi\)
\(264\) 0 0
\(265\) 1.83829 0.112925
\(266\) 0 0
\(267\) 5.19454 0.317901
\(268\) 0 0
\(269\) 17.3478 1.05772 0.528858 0.848710i \(-0.322620\pi\)
0.528858 + 0.848710i \(0.322620\pi\)
\(270\) 0 0
\(271\) −2.20084 −0.133691 −0.0668456 0.997763i \(-0.521293\pi\)
−0.0668456 + 0.997763i \(0.521293\pi\)
\(272\) 0 0
\(273\) −3.67850 −0.222633
\(274\) 0 0
\(275\) −3.91088 −0.235835
\(276\) 0 0
\(277\) −5.93069 −0.356341 −0.178170 0.984000i \(-0.557018\pi\)
−0.178170 + 0.984000i \(0.557018\pi\)
\(278\) 0 0
\(279\) 0.783925 0.0469324
\(280\) 0 0
\(281\) 13.7347 0.819346 0.409673 0.912232i \(-0.365643\pi\)
0.409673 + 0.912232i \(0.365643\pi\)
\(282\) 0 0
\(283\) −17.7038 −1.05238 −0.526191 0.850367i \(-0.676380\pi\)
−0.526191 + 0.850367i \(0.676380\pi\)
\(284\) 0 0
\(285\) −0.671133 −0.0397545
\(286\) 0 0
\(287\) −1.57382 −0.0928998
\(288\) 0 0
\(289\) 1.27804 0.0751790
\(290\) 0 0
\(291\) 0.366843 0.0215047
\(292\) 0 0
\(293\) 7.75305 0.452938 0.226469 0.974018i \(-0.427282\pi\)
0.226469 + 0.974018i \(0.427282\pi\)
\(294\) 0 0
\(295\) −7.38323 −0.429868
\(296\) 0 0
\(297\) −5.16847 −0.299905
\(298\) 0 0
\(299\) 15.1679 0.877182
\(300\) 0 0
\(301\) 12.6767 0.730672
\(302\) 0 0
\(303\) 4.50656 0.258895
\(304\) 0 0
\(305\) −18.7598 −1.07418
\(306\) 0 0
\(307\) −17.1912 −0.981154 −0.490577 0.871398i \(-0.663214\pi\)
−0.490577 + 0.871398i \(0.663214\pi\)
\(308\) 0 0
\(309\) 4.29701 0.244448
\(310\) 0 0
\(311\) 3.14829 0.178523 0.0892615 0.996008i \(-0.471549\pi\)
0.0892615 + 0.996008i \(0.471549\pi\)
\(312\) 0 0
\(313\) 15.5784 0.880543 0.440271 0.897865i \(-0.354882\pi\)
0.440271 + 0.897865i \(0.354882\pi\)
\(314\) 0 0
\(315\) −11.9920 −0.675673
\(316\) 0 0
\(317\) 10.4030 0.584292 0.292146 0.956374i \(-0.405631\pi\)
0.292146 + 0.956374i \(0.405631\pi\)
\(318\) 0 0
\(319\) −14.2383 −0.797189
\(320\) 0 0
\(321\) 1.90025 0.106062
\(322\) 0 0
\(323\) 4.27528 0.237883
\(324\) 0 0
\(325\) 7.17602 0.398054
\(326\) 0 0
\(327\) −2.69189 −0.148862
\(328\) 0 0
\(329\) −23.3120 −1.28523
\(330\) 0 0
\(331\) −13.9480 −0.766653 −0.383326 0.923613i \(-0.625222\pi\)
−0.383326 + 0.923613i \(0.625222\pi\)
\(332\) 0 0
\(333\) 17.0021 0.931708
\(334\) 0 0
\(335\) 5.46317 0.298485
\(336\) 0 0
\(337\) −20.5402 −1.11890 −0.559449 0.828865i \(-0.688987\pi\)
−0.559449 + 0.828865i \(0.688987\pi\)
\(338\) 0 0
\(339\) −0.0582205 −0.00316211
\(340\) 0 0
\(341\) −0.659877 −0.0357343
\(342\) 0 0
\(343\) −20.0745 −1.08392
\(344\) 0 0
\(345\) −2.29907 −0.123778
\(346\) 0 0
\(347\) −7.07054 −0.379567 −0.189783 0.981826i \(-0.560779\pi\)
−0.189783 + 0.981826i \(0.560779\pi\)
\(348\) 0 0
\(349\) −12.8202 −0.686252 −0.343126 0.939289i \(-0.611486\pi\)
−0.343126 + 0.939289i \(0.611486\pi\)
\(350\) 0 0
\(351\) 9.48355 0.506195
\(352\) 0 0
\(353\) 4.87465 0.259451 0.129726 0.991550i \(-0.458590\pi\)
0.129726 + 0.991550i \(0.458590\pi\)
\(354\) 0 0
\(355\) −1.02893 −0.0546098
\(356\) 0 0
\(357\) −3.55184 −0.187984
\(358\) 0 0
\(359\) 3.96853 0.209451 0.104726 0.994501i \(-0.466604\pi\)
0.104726 + 0.994501i \(0.466604\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −1.89006 −0.0992024
\(364\) 0 0
\(365\) −16.0467 −0.839921
\(366\) 0 0
\(367\) −0.171291 −0.00894131 −0.00447066 0.999990i \(-0.501423\pi\)
−0.00447066 + 0.999990i \(0.501423\pi\)
\(368\) 0 0
\(369\) 1.98265 0.103212
\(370\) 0 0
\(371\) 2.27559 0.118143
\(372\) 0 0
\(373\) −17.7392 −0.918502 −0.459251 0.888307i \(-0.651882\pi\)
−0.459251 + 0.888307i \(0.651882\pi\)
\(374\) 0 0
\(375\) −4.44337 −0.229454
\(376\) 0 0
\(377\) 26.1256 1.34554
\(378\) 0 0
\(379\) −28.5638 −1.46722 −0.733612 0.679568i \(-0.762167\pi\)
−0.733612 + 0.679568i \(0.762167\pi\)
\(380\) 0 0
\(381\) 1.09563 0.0561307
\(382\) 0 0
\(383\) 9.44208 0.482468 0.241234 0.970467i \(-0.422448\pi\)
0.241234 + 0.970467i \(0.422448\pi\)
\(384\) 0 0
\(385\) 10.0944 0.514458
\(386\) 0 0
\(387\) −15.9697 −0.811783
\(388\) 0 0
\(389\) 6.93596 0.351667 0.175834 0.984420i \(-0.443738\pi\)
0.175834 + 0.984420i \(0.443738\pi\)
\(390\) 0 0
\(391\) 14.6457 0.740663
\(392\) 0 0
\(393\) 6.51072 0.328422
\(394\) 0 0
\(395\) 1.20259 0.0605089
\(396\) 0 0
\(397\) 9.30878 0.467194 0.233597 0.972333i \(-0.424950\pi\)
0.233597 + 0.972333i \(0.424950\pi\)
\(398\) 0 0
\(399\) −0.830786 −0.0415913
\(400\) 0 0
\(401\) −9.58048 −0.478427 −0.239213 0.970967i \(-0.576890\pi\)
−0.239213 + 0.970967i \(0.576890\pi\)
\(402\) 0 0
\(403\) 1.21080 0.0603141
\(404\) 0 0
\(405\) 14.3721 0.714153
\(406\) 0 0
\(407\) −14.3117 −0.709403
\(408\) 0 0
\(409\) −34.6263 −1.71216 −0.856081 0.516841i \(-0.827108\pi\)
−0.856081 + 0.516841i \(0.827108\pi\)
\(410\) 0 0
\(411\) −5.26381 −0.259644
\(412\) 0 0
\(413\) −9.13959 −0.449730
\(414\) 0 0
\(415\) 7.21670 0.354254
\(416\) 0 0
\(417\) −1.79757 −0.0880273
\(418\) 0 0
\(419\) 8.12708 0.397034 0.198517 0.980097i \(-0.436388\pi\)
0.198517 + 0.980097i \(0.436388\pi\)
\(420\) 0 0
\(421\) −18.8936 −0.920819 −0.460410 0.887707i \(-0.652297\pi\)
−0.460410 + 0.887707i \(0.652297\pi\)
\(422\) 0 0
\(423\) 29.3676 1.42790
\(424\) 0 0
\(425\) 6.92895 0.336103
\(426\) 0 0
\(427\) −23.2224 −1.12381
\(428\) 0 0
\(429\) −3.90075 −0.188330
\(430\) 0 0
\(431\) −2.09780 −0.101048 −0.0505238 0.998723i \(-0.516089\pi\)
−0.0505238 + 0.998723i \(0.516089\pi\)
\(432\) 0 0
\(433\) 36.9969 1.77796 0.888980 0.457947i \(-0.151415\pi\)
0.888980 + 0.457947i \(0.151415\pi\)
\(434\) 0 0
\(435\) −3.95998 −0.189866
\(436\) 0 0
\(437\) 3.42566 0.163871
\(438\) 0 0
\(439\) −4.05435 −0.193504 −0.0967519 0.995309i \(-0.530845\pi\)
−0.0967519 + 0.995309i \(0.530845\pi\)
\(440\) 0 0
\(441\) 5.22225 0.248678
\(442\) 0 0
\(443\) 27.0595 1.28563 0.642817 0.766020i \(-0.277765\pi\)
0.642817 + 0.766020i \(0.277765\pi\)
\(444\) 0 0
\(445\) 26.1557 1.23990
\(446\) 0 0
\(447\) 0.334431 0.0158181
\(448\) 0 0
\(449\) 28.5046 1.34521 0.672607 0.740000i \(-0.265175\pi\)
0.672607 + 0.740000i \(0.265175\pi\)
\(450\) 0 0
\(451\) −1.66891 −0.0785860
\(452\) 0 0
\(453\) 8.09375 0.380277
\(454\) 0 0
\(455\) −18.5220 −0.868327
\(456\) 0 0
\(457\) −12.9074 −0.603782 −0.301891 0.953342i \(-0.597618\pi\)
−0.301891 + 0.953342i \(0.597618\pi\)
\(458\) 0 0
\(459\) 9.15703 0.427413
\(460\) 0 0
\(461\) 14.8318 0.690787 0.345393 0.938458i \(-0.387746\pi\)
0.345393 + 0.938458i \(0.387746\pi\)
\(462\) 0 0
\(463\) −19.7785 −0.919187 −0.459593 0.888129i \(-0.652005\pi\)
−0.459593 + 0.888129i \(0.652005\pi\)
\(464\) 0 0
\(465\) −0.183526 −0.00851084
\(466\) 0 0
\(467\) −32.3974 −1.49917 −0.749586 0.661907i \(-0.769747\pi\)
−0.749586 + 0.661907i \(0.769747\pi\)
\(468\) 0 0
\(469\) 6.76278 0.312276
\(470\) 0 0
\(471\) 6.65047 0.306437
\(472\) 0 0
\(473\) 13.4426 0.618092
\(474\) 0 0
\(475\) 1.62070 0.0743628
\(476\) 0 0
\(477\) −2.86671 −0.131258
\(478\) 0 0
\(479\) −0.910503 −0.0416019 −0.0208010 0.999784i \(-0.506622\pi\)
−0.0208010 + 0.999784i \(0.506622\pi\)
\(480\) 0 0
\(481\) 26.2603 1.19737
\(482\) 0 0
\(483\) −2.84599 −0.129497
\(484\) 0 0
\(485\) 1.84714 0.0838741
\(486\) 0 0
\(487\) 12.7737 0.578830 0.289415 0.957204i \(-0.406539\pi\)
0.289415 + 0.957204i \(0.406539\pi\)
\(488\) 0 0
\(489\) −0.865175 −0.0391246
\(490\) 0 0
\(491\) −14.7255 −0.664554 −0.332277 0.943182i \(-0.607817\pi\)
−0.332277 + 0.943182i \(0.607817\pi\)
\(492\) 0 0
\(493\) 25.2261 1.13612
\(494\) 0 0
\(495\) −12.7166 −0.571567
\(496\) 0 0
\(497\) −1.27370 −0.0571331
\(498\) 0 0
\(499\) −18.7657 −0.840066 −0.420033 0.907509i \(-0.637982\pi\)
−0.420033 + 0.907509i \(0.637982\pi\)
\(500\) 0 0
\(501\) −5.94130 −0.265438
\(502\) 0 0
\(503\) −7.27932 −0.324569 −0.162284 0.986744i \(-0.551886\pi\)
−0.162284 + 0.986744i \(0.551886\pi\)
\(504\) 0 0
\(505\) 22.6915 1.00976
\(506\) 0 0
\(507\) 2.41132 0.107091
\(508\) 0 0
\(509\) 15.2015 0.673795 0.336898 0.941541i \(-0.390622\pi\)
0.336898 + 0.941541i \(0.390622\pi\)
\(510\) 0 0
\(511\) −19.8639 −0.878729
\(512\) 0 0
\(513\) 2.14185 0.0945651
\(514\) 0 0
\(515\) 21.6364 0.953413
\(516\) 0 0
\(517\) −24.7205 −1.08721
\(518\) 0 0
\(519\) 1.49460 0.0656057
\(520\) 0 0
\(521\) −33.0490 −1.44790 −0.723952 0.689850i \(-0.757676\pi\)
−0.723952 + 0.689850i \(0.757676\pi\)
\(522\) 0 0
\(523\) 5.66824 0.247855 0.123927 0.992291i \(-0.460451\pi\)
0.123927 + 0.992291i \(0.460451\pi\)
\(524\) 0 0
\(525\) −1.34645 −0.0587641
\(526\) 0 0
\(527\) 1.16911 0.0509272
\(528\) 0 0
\(529\) −11.2649 −0.489777
\(530\) 0 0
\(531\) 11.5138 0.499654
\(532\) 0 0
\(533\) 3.06226 0.132641
\(534\) 0 0
\(535\) 9.56819 0.413669
\(536\) 0 0
\(537\) 3.67343 0.158520
\(538\) 0 0
\(539\) −4.39588 −0.189344
\(540\) 0 0
\(541\) −25.9925 −1.11750 −0.558752 0.829335i \(-0.688720\pi\)
−0.558752 + 0.829335i \(0.688720\pi\)
\(542\) 0 0
\(543\) 2.57089 0.110327
\(544\) 0 0
\(545\) −13.5543 −0.580601
\(546\) 0 0
\(547\) −9.23811 −0.394993 −0.197496 0.980304i \(-0.563281\pi\)
−0.197496 + 0.980304i \(0.563281\pi\)
\(548\) 0 0
\(549\) 29.2548 1.24857
\(550\) 0 0
\(551\) 5.90044 0.251367
\(552\) 0 0
\(553\) 1.48867 0.0633047
\(554\) 0 0
\(555\) −3.98040 −0.168958
\(556\) 0 0
\(557\) −15.5011 −0.656801 −0.328401 0.944539i \(-0.606510\pi\)
−0.328401 + 0.944539i \(0.606510\pi\)
\(558\) 0 0
\(559\) −24.6657 −1.04325
\(560\) 0 0
\(561\) −3.76645 −0.159020
\(562\) 0 0
\(563\) −15.1780 −0.639678 −0.319839 0.947472i \(-0.603629\pi\)
−0.319839 + 0.947472i \(0.603629\pi\)
\(564\) 0 0
\(565\) −0.293153 −0.0123331
\(566\) 0 0
\(567\) 17.7910 0.747151
\(568\) 0 0
\(569\) −22.3694 −0.937773 −0.468887 0.883258i \(-0.655345\pi\)
−0.468887 + 0.883258i \(0.655345\pi\)
\(570\) 0 0
\(571\) 29.8261 1.24818 0.624091 0.781351i \(-0.285469\pi\)
0.624091 + 0.781351i \(0.285469\pi\)
\(572\) 0 0
\(573\) −3.94976 −0.165004
\(574\) 0 0
\(575\) 5.55196 0.231533
\(576\) 0 0
\(577\) −19.8886 −0.827974 −0.413987 0.910283i \(-0.635864\pi\)
−0.413987 + 0.910283i \(0.635864\pi\)
\(578\) 0 0
\(579\) 2.64037 0.109730
\(580\) 0 0
\(581\) 8.93345 0.370622
\(582\) 0 0
\(583\) 2.41308 0.0999397
\(584\) 0 0
\(585\) 23.3334 0.964719
\(586\) 0 0
\(587\) −1.00191 −0.0413533 −0.0206766 0.999786i \(-0.506582\pi\)
−0.0206766 + 0.999786i \(0.506582\pi\)
\(588\) 0 0
\(589\) 0.273458 0.0112676
\(590\) 0 0
\(591\) −3.78286 −0.155606
\(592\) 0 0
\(593\) −0.251773 −0.0103391 −0.00516954 0.999987i \(-0.501646\pi\)
−0.00516954 + 0.999987i \(0.501646\pi\)
\(594\) 0 0
\(595\) −17.8843 −0.733186
\(596\) 0 0
\(597\) 1.32547 0.0542480
\(598\) 0 0
\(599\) 18.1401 0.741186 0.370593 0.928795i \(-0.379154\pi\)
0.370593 + 0.928795i \(0.379154\pi\)
\(600\) 0 0
\(601\) 28.5244 1.16354 0.581768 0.813355i \(-0.302361\pi\)
0.581768 + 0.813355i \(0.302361\pi\)
\(602\) 0 0
\(603\) −8.51952 −0.346942
\(604\) 0 0
\(605\) −9.51687 −0.386916
\(606\) 0 0
\(607\) −0.241729 −0.00981147 −0.00490574 0.999988i \(-0.501562\pi\)
−0.00490574 + 0.999988i \(0.501562\pi\)
\(608\) 0 0
\(609\) −4.90200 −0.198639
\(610\) 0 0
\(611\) 45.3593 1.83504
\(612\) 0 0
\(613\) 8.05012 0.325141 0.162571 0.986697i \(-0.448021\pi\)
0.162571 + 0.986697i \(0.448021\pi\)
\(614\) 0 0
\(615\) −0.464162 −0.0187168
\(616\) 0 0
\(617\) −28.9280 −1.16460 −0.582299 0.812975i \(-0.697847\pi\)
−0.582299 + 0.812975i \(0.697847\pi\)
\(618\) 0 0
\(619\) 32.7646 1.31692 0.658460 0.752615i \(-0.271208\pi\)
0.658460 + 0.752615i \(0.271208\pi\)
\(620\) 0 0
\(621\) 7.33726 0.294434
\(622\) 0 0
\(623\) 32.3777 1.29719
\(624\) 0 0
\(625\) −14.2698 −0.570794
\(626\) 0 0
\(627\) −0.880982 −0.0351830
\(628\) 0 0
\(629\) 25.3561 1.01101
\(630\) 0 0
\(631\) −36.8516 −1.46704 −0.733519 0.679669i \(-0.762124\pi\)
−0.733519 + 0.679669i \(0.762124\pi\)
\(632\) 0 0
\(633\) 6.70809 0.266623
\(634\) 0 0
\(635\) 5.51673 0.218925
\(636\) 0 0
\(637\) 8.06593 0.319584
\(638\) 0 0
\(639\) 1.60456 0.0634754
\(640\) 0 0
\(641\) −6.60568 −0.260909 −0.130454 0.991454i \(-0.541644\pi\)
−0.130454 + 0.991454i \(0.541644\pi\)
\(642\) 0 0
\(643\) 42.7741 1.68685 0.843424 0.537249i \(-0.180536\pi\)
0.843424 + 0.537249i \(0.180536\pi\)
\(644\) 0 0
\(645\) 3.73869 0.147211
\(646\) 0 0
\(647\) 8.15034 0.320423 0.160211 0.987083i \(-0.448782\pi\)
0.160211 + 0.987083i \(0.448782\pi\)
\(648\) 0 0
\(649\) −9.69181 −0.380437
\(650\) 0 0
\(651\) −0.227185 −0.00890408
\(652\) 0 0
\(653\) −4.60838 −0.180340 −0.0901700 0.995926i \(-0.528741\pi\)
−0.0901700 + 0.995926i \(0.528741\pi\)
\(654\) 0 0
\(655\) 32.7829 1.28093
\(656\) 0 0
\(657\) 25.0239 0.976276
\(658\) 0 0
\(659\) 44.4681 1.73223 0.866116 0.499843i \(-0.166609\pi\)
0.866116 + 0.499843i \(0.166609\pi\)
\(660\) 0 0
\(661\) 12.0881 0.470173 0.235087 0.971974i \(-0.424463\pi\)
0.235087 + 0.971974i \(0.424463\pi\)
\(662\) 0 0
\(663\) 6.91100 0.268401
\(664\) 0 0
\(665\) −4.18319 −0.162217
\(666\) 0 0
\(667\) 20.2129 0.782647
\(668\) 0 0
\(669\) −1.61654 −0.0624991
\(670\) 0 0
\(671\) −24.6256 −0.950659
\(672\) 0 0
\(673\) 19.5988 0.755476 0.377738 0.925912i \(-0.376702\pi\)
0.377738 + 0.925912i \(0.376702\pi\)
\(674\) 0 0
\(675\) 3.47130 0.133610
\(676\) 0 0
\(677\) 12.8702 0.494643 0.247322 0.968933i \(-0.420450\pi\)
0.247322 + 0.968933i \(0.420450\pi\)
\(678\) 0 0
\(679\) 2.28654 0.0877495
\(680\) 0 0
\(681\) −6.05213 −0.231918
\(682\) 0 0
\(683\) −1.10598 −0.0423193 −0.0211596 0.999776i \(-0.506736\pi\)
−0.0211596 + 0.999776i \(0.506736\pi\)
\(684\) 0 0
\(685\) −26.5044 −1.01268
\(686\) 0 0
\(687\) 1.39129 0.0530808
\(688\) 0 0
\(689\) −4.42773 −0.168683
\(690\) 0 0
\(691\) −19.1982 −0.730336 −0.365168 0.930942i \(-0.618988\pi\)
−0.365168 + 0.930942i \(0.618988\pi\)
\(692\) 0 0
\(693\) −15.7417 −0.597976
\(694\) 0 0
\(695\) −9.05116 −0.343330
\(696\) 0 0
\(697\) 2.95683 0.111998
\(698\) 0 0
\(699\) 6.11824 0.231413
\(700\) 0 0
\(701\) 13.4882 0.509442 0.254721 0.967015i \(-0.418016\pi\)
0.254721 + 0.967015i \(0.418016\pi\)
\(702\) 0 0
\(703\) 5.93087 0.223687
\(704\) 0 0
\(705\) −6.87532 −0.258940
\(706\) 0 0
\(707\) 28.0895 1.05642
\(708\) 0 0
\(709\) −32.4390 −1.21827 −0.609136 0.793066i \(-0.708484\pi\)
−0.609136 + 0.793066i \(0.708484\pi\)
\(710\) 0 0
\(711\) −1.87538 −0.0703322
\(712\) 0 0
\(713\) 0.936773 0.0350824
\(714\) 0 0
\(715\) −19.6412 −0.734538
\(716\) 0 0
\(717\) −7.04040 −0.262928
\(718\) 0 0
\(719\) 12.3977 0.462358 0.231179 0.972911i \(-0.425742\pi\)
0.231179 + 0.972911i \(0.425742\pi\)
\(720\) 0 0
\(721\) 26.7834 0.997465
\(722\) 0 0
\(723\) 0.460252 0.0171170
\(724\) 0 0
\(725\) 9.56284 0.355155
\(726\) 0 0
\(727\) −4.21713 −0.156405 −0.0782024 0.996938i \(-0.524918\pi\)
−0.0782024 + 0.996938i \(0.524918\pi\)
\(728\) 0 0
\(729\) −20.0666 −0.743207
\(730\) 0 0
\(731\) −23.8164 −0.880882
\(732\) 0 0
\(733\) 31.9424 1.17982 0.589910 0.807469i \(-0.299163\pi\)
0.589910 + 0.807469i \(0.299163\pi\)
\(734\) 0 0
\(735\) −1.22259 −0.0450960
\(736\) 0 0
\(737\) 7.17139 0.264162
\(738\) 0 0
\(739\) 32.4801 1.19480 0.597399 0.801944i \(-0.296201\pi\)
0.597399 + 0.801944i \(0.296201\pi\)
\(740\) 0 0
\(741\) 1.61650 0.0593837
\(742\) 0 0
\(743\) 22.5413 0.826959 0.413479 0.910514i \(-0.364313\pi\)
0.413479 + 0.910514i \(0.364313\pi\)
\(744\) 0 0
\(745\) 1.68393 0.0616946
\(746\) 0 0
\(747\) −11.2541 −0.411764
\(748\) 0 0
\(749\) 11.8443 0.432783
\(750\) 0 0
\(751\) −39.7138 −1.44918 −0.724589 0.689181i \(-0.757971\pi\)
−0.724589 + 0.689181i \(0.757971\pi\)
\(752\) 0 0
\(753\) −8.24623 −0.300509
\(754\) 0 0
\(755\) 40.7538 1.48318
\(756\) 0 0
\(757\) 5.77538 0.209910 0.104955 0.994477i \(-0.466530\pi\)
0.104955 + 0.994477i \(0.466530\pi\)
\(758\) 0 0
\(759\) −3.01794 −0.109544
\(760\) 0 0
\(761\) 45.3770 1.64492 0.822458 0.568826i \(-0.192602\pi\)
0.822458 + 0.568826i \(0.192602\pi\)
\(762\) 0 0
\(763\) −16.7786 −0.607427
\(764\) 0 0
\(765\) 22.5301 0.814576
\(766\) 0 0
\(767\) 17.7834 0.642120
\(768\) 0 0
\(769\) −31.1945 −1.12490 −0.562450 0.826831i \(-0.690141\pi\)
−0.562450 + 0.826831i \(0.690141\pi\)
\(770\) 0 0
\(771\) −5.31022 −0.191243
\(772\) 0 0
\(773\) −20.9001 −0.751724 −0.375862 0.926676i \(-0.622653\pi\)
−0.375862 + 0.926676i \(0.622653\pi\)
\(774\) 0 0
\(775\) 0.443193 0.0159200
\(776\) 0 0
\(777\) −4.92728 −0.176765
\(778\) 0 0
\(779\) 0.691610 0.0247795
\(780\) 0 0
\(781\) −1.35065 −0.0483302
\(782\) 0 0
\(783\) 12.6379 0.451641
\(784\) 0 0
\(785\) 33.4866 1.19519
\(786\) 0 0
\(787\) 8.58949 0.306182 0.153091 0.988212i \(-0.451077\pi\)
0.153091 + 0.988212i \(0.451077\pi\)
\(788\) 0 0
\(789\) −6.90018 −0.245653
\(790\) 0 0
\(791\) −0.362890 −0.0129029
\(792\) 0 0
\(793\) 45.1851 1.60457
\(794\) 0 0
\(795\) 0.671133 0.0238026
\(796\) 0 0
\(797\) −1.70559 −0.0604149 −0.0302075 0.999544i \(-0.509617\pi\)
−0.0302075 + 0.999544i \(0.509617\pi\)
\(798\) 0 0
\(799\) 43.7975 1.54945
\(800\) 0 0
\(801\) −40.7884 −1.44119
\(802\) 0 0
\(803\) −21.0641 −0.743337
\(804\) 0 0
\(805\) −14.3302 −0.505073
\(806\) 0 0
\(807\) 6.33345 0.222948
\(808\) 0 0
\(809\) 49.2670 1.73214 0.866068 0.499926i \(-0.166639\pi\)
0.866068 + 0.499926i \(0.166639\pi\)
\(810\) 0 0
\(811\) 43.8455 1.53962 0.769812 0.638270i \(-0.220350\pi\)
0.769812 + 0.638270i \(0.220350\pi\)
\(812\) 0 0
\(813\) −0.803494 −0.0281798
\(814\) 0 0
\(815\) −4.35635 −0.152596
\(816\) 0 0
\(817\) −5.57072 −0.194895
\(818\) 0 0
\(819\) 28.8842 1.00929
\(820\) 0 0
\(821\) −8.27610 −0.288838 −0.144419 0.989517i \(-0.546131\pi\)
−0.144419 + 0.989517i \(0.546131\pi\)
\(822\) 0 0
\(823\) 31.7299 1.10603 0.553017 0.833170i \(-0.313477\pi\)
0.553017 + 0.833170i \(0.313477\pi\)
\(824\) 0 0
\(825\) −1.42781 −0.0497099
\(826\) 0 0
\(827\) −3.99508 −0.138923 −0.0694613 0.997585i \(-0.522128\pi\)
−0.0694613 + 0.997585i \(0.522128\pi\)
\(828\) 0 0
\(829\) −32.9878 −1.14571 −0.572857 0.819655i \(-0.694165\pi\)
−0.572857 + 0.819655i \(0.694165\pi\)
\(830\) 0 0
\(831\) −2.16521 −0.0751103
\(832\) 0 0
\(833\) 7.78822 0.269846
\(834\) 0 0
\(835\) −29.9158 −1.03528
\(836\) 0 0
\(837\) 0.585707 0.0202450
\(838\) 0 0
\(839\) 0.191877 0.00662434 0.00331217 0.999995i \(-0.498946\pi\)
0.00331217 + 0.999995i \(0.498946\pi\)
\(840\) 0 0
\(841\) 5.81522 0.200525
\(842\) 0 0
\(843\) 5.01436 0.172704
\(844\) 0 0
\(845\) 12.1415 0.417681
\(846\) 0 0
\(847\) −11.7808 −0.404793
\(848\) 0 0
\(849\) −6.46340 −0.221823
\(850\) 0 0
\(851\) 20.3171 0.696462
\(852\) 0 0
\(853\) −53.2103 −1.82189 −0.910943 0.412532i \(-0.864644\pi\)
−0.910943 + 0.412532i \(0.864644\pi\)
\(854\) 0 0
\(855\) 5.26984 0.180225
\(856\) 0 0
\(857\) −11.5394 −0.394179 −0.197090 0.980385i \(-0.563149\pi\)
−0.197090 + 0.980385i \(0.563149\pi\)
\(858\) 0 0
\(859\) −48.1549 −1.64303 −0.821513 0.570190i \(-0.806870\pi\)
−0.821513 + 0.570190i \(0.806870\pi\)
\(860\) 0 0
\(861\) −0.574580 −0.0195816
\(862\) 0 0
\(863\) −1.82690 −0.0621885 −0.0310942 0.999516i \(-0.509899\pi\)
−0.0310942 + 0.999516i \(0.509899\pi\)
\(864\) 0 0
\(865\) 7.52564 0.255880
\(866\) 0 0
\(867\) 0.466595 0.0158464
\(868\) 0 0
\(869\) 1.57862 0.0535509
\(870\) 0 0
\(871\) −13.1587 −0.445865
\(872\) 0 0
\(873\) −2.88051 −0.0974905
\(874\) 0 0
\(875\) −27.6956 −0.936284
\(876\) 0 0
\(877\) −11.5880 −0.391300 −0.195650 0.980674i \(-0.562682\pi\)
−0.195650 + 0.980674i \(0.562682\pi\)
\(878\) 0 0
\(879\) 2.83053 0.0954714
\(880\) 0 0
\(881\) 54.2666 1.82829 0.914145 0.405388i \(-0.132864\pi\)
0.914145 + 0.405388i \(0.132864\pi\)
\(882\) 0 0
\(883\) −28.4020 −0.955803 −0.477902 0.878413i \(-0.658602\pi\)
−0.477902 + 0.878413i \(0.658602\pi\)
\(884\) 0 0
\(885\) −2.69551 −0.0906086
\(886\) 0 0
\(887\) −47.4924 −1.59464 −0.797319 0.603559i \(-0.793749\pi\)
−0.797319 + 0.603559i \(0.793749\pi\)
\(888\) 0 0
\(889\) 6.82908 0.229040
\(890\) 0 0
\(891\) 18.8659 0.632032
\(892\) 0 0
\(893\) 10.2444 0.342814
\(894\) 0 0
\(895\) 18.4965 0.618271
\(896\) 0 0
\(897\) 5.53758 0.184895
\(898\) 0 0
\(899\) 1.61352 0.0538140
\(900\) 0 0
\(901\) −4.27528 −0.142430
\(902\) 0 0
\(903\) 4.62808 0.154013
\(904\) 0 0
\(905\) 12.9450 0.430306
\(906\) 0 0
\(907\) 22.2406 0.738487 0.369243 0.929333i \(-0.379617\pi\)
0.369243 + 0.929333i \(0.379617\pi\)
\(908\) 0 0
\(909\) −35.3863 −1.17369
\(910\) 0 0
\(911\) 40.4905 1.34151 0.670755 0.741679i \(-0.265970\pi\)
0.670755 + 0.741679i \(0.265970\pi\)
\(912\) 0 0
\(913\) 9.47321 0.313518
\(914\) 0 0
\(915\) −6.84892 −0.226418
\(916\) 0 0
\(917\) 40.5815 1.34012
\(918\) 0 0
\(919\) 32.8769 1.08451 0.542254 0.840215i \(-0.317571\pi\)
0.542254 + 0.840215i \(0.317571\pi\)
\(920\) 0 0
\(921\) −6.27627 −0.206810
\(922\) 0 0
\(923\) 2.47829 0.0815740
\(924\) 0 0
\(925\) 9.61215 0.316045
\(926\) 0 0
\(927\) −33.7408 −1.10819
\(928\) 0 0
\(929\) 8.85144 0.290406 0.145203 0.989402i \(-0.453616\pi\)
0.145203 + 0.989402i \(0.453616\pi\)
\(930\) 0 0
\(931\) 1.82169 0.0597033
\(932\) 0 0
\(933\) 1.14940 0.0376295
\(934\) 0 0
\(935\) −18.9649 −0.620219
\(936\) 0 0
\(937\) 43.5859 1.42389 0.711944 0.702236i \(-0.247815\pi\)
0.711944 + 0.702236i \(0.247815\pi\)
\(938\) 0 0
\(939\) 5.68745 0.185603
\(940\) 0 0
\(941\) 34.7750 1.13363 0.566816 0.823844i \(-0.308175\pi\)
0.566816 + 0.823844i \(0.308175\pi\)
\(942\) 0 0
\(943\) 2.36922 0.0771524
\(944\) 0 0
\(945\) −8.95978 −0.291462
\(946\) 0 0
\(947\) 8.61235 0.279864 0.139932 0.990161i \(-0.455312\pi\)
0.139932 + 0.990161i \(0.455312\pi\)
\(948\) 0 0
\(949\) 38.6503 1.25464
\(950\) 0 0
\(951\) 3.79799 0.123158
\(952\) 0 0
\(953\) 32.9224 1.06646 0.533231 0.845970i \(-0.320978\pi\)
0.533231 + 0.845970i \(0.320978\pi\)
\(954\) 0 0
\(955\) −19.8879 −0.643558
\(956\) 0 0
\(957\) −5.19819 −0.168033
\(958\) 0 0
\(959\) −32.8095 −1.05947
\(960\) 0 0
\(961\) −30.9252 −0.997588
\(962\) 0 0
\(963\) −14.9211 −0.480825
\(964\) 0 0
\(965\) 13.2949 0.427977
\(966\) 0 0
\(967\) −29.4130 −0.945857 −0.472929 0.881101i \(-0.656803\pi\)
−0.472929 + 0.881101i \(0.656803\pi\)
\(968\) 0 0
\(969\) 1.56084 0.0501416
\(970\) 0 0
\(971\) −55.8139 −1.79115 −0.895576 0.444908i \(-0.853236\pi\)
−0.895576 + 0.444908i \(0.853236\pi\)
\(972\) 0 0
\(973\) −11.2043 −0.359193
\(974\) 0 0
\(975\) 2.61986 0.0839028
\(976\) 0 0
\(977\) 52.6188 1.68342 0.841712 0.539927i \(-0.181548\pi\)
0.841712 + 0.539927i \(0.181548\pi\)
\(978\) 0 0
\(979\) 34.3340 1.09732
\(980\) 0 0
\(981\) 21.1372 0.674857
\(982\) 0 0
\(983\) 23.0219 0.734284 0.367142 0.930165i \(-0.380336\pi\)
0.367142 + 0.930165i \(0.380336\pi\)
\(984\) 0 0
\(985\) −19.0475 −0.606905
\(986\) 0 0
\(987\) −8.51087 −0.270904
\(988\) 0 0
\(989\) −19.0834 −0.606816
\(990\) 0 0
\(991\) −44.8664 −1.42523 −0.712614 0.701557i \(-0.752489\pi\)
−0.712614 + 0.701557i \(0.752489\pi\)
\(992\) 0 0
\(993\) −5.09223 −0.161597
\(994\) 0 0
\(995\) 6.67405 0.211582
\(996\) 0 0
\(997\) −57.3091 −1.81500 −0.907498 0.420056i \(-0.862011\pi\)
−0.907498 + 0.420056i \(0.862011\pi\)
\(998\) 0 0
\(999\) 12.7030 0.401906
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 \(a_p\))