Properties

Label 8008.2.a.n.1.5
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.10969\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.10969 q^{3} -2.48203 q^{5} -1.00000 q^{7} -1.76859 q^{9} +O(q^{10})\) \(q-1.10969 q^{3} -2.48203 q^{5} -1.00000 q^{7} -1.76859 q^{9} +1.00000 q^{11} -1.00000 q^{13} +2.75428 q^{15} -6.03031 q^{17} +0.989367 q^{19} +1.10969 q^{21} +8.81617 q^{23} +1.16047 q^{25} +5.29165 q^{27} -4.44880 q^{29} +2.66711 q^{31} -1.10969 q^{33} +2.48203 q^{35} -10.0381 q^{37} +1.10969 q^{39} -1.71649 q^{41} -12.1359 q^{43} +4.38969 q^{45} -2.96869 q^{47} +1.00000 q^{49} +6.69178 q^{51} -7.19148 q^{53} -2.48203 q^{55} -1.09789 q^{57} -7.72532 q^{59} -0.918973 q^{61} +1.76859 q^{63} +2.48203 q^{65} +4.50502 q^{67} -9.78321 q^{69} -12.7548 q^{71} -5.38509 q^{73} -1.28776 q^{75} -1.00000 q^{77} -5.36852 q^{79} -0.566329 q^{81} -2.96934 q^{83} +14.9674 q^{85} +4.93679 q^{87} +3.26674 q^{89} +1.00000 q^{91} -2.95966 q^{93} -2.45564 q^{95} -15.0794 q^{97} -1.76859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + O(q^{10}) \) \( 9q - 3q^{3} + q^{5} - 9q^{7} + 12q^{9} + 9q^{11} - 9q^{13} + 11q^{15} + 7q^{17} - 17q^{19} + 3q^{21} + 11q^{23} + 18q^{25} - 9q^{27} + 9q^{29} - 8q^{31} - 3q^{33} - q^{35} + 2q^{37} + 3q^{39} + 18q^{41} + 7q^{43} + 5q^{45} + 15q^{47} + 9q^{49} - 7q^{51} - 4q^{53} + q^{55} + 22q^{57} - 23q^{59} + 12q^{61} - 12q^{63} - q^{65} - 16q^{67} - 32q^{69} - 6q^{71} + 4q^{73} - 14q^{75} - 9q^{77} + 21q^{79} + 5q^{81} - 16q^{83} + 53q^{85} + 41q^{87} + 5q^{89} + 9q^{91} + 29q^{93} + 19q^{95} + 18q^{97} + 12q^{99} + O(q^{100}) \)

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
\(3\) −1.10969 −0.640680 −0.320340 0.947303i \(-0.603797\pi\)
−0.320340 + 0.947303i \(0.603797\pi\)
\(4\) 0 0
\(5\) −2.48203 −1.11000 −0.554998 0.831851i \(-0.687281\pi\)
−0.554998 + 0.831851i \(0.687281\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −1.76859 −0.589530
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 2.75428 0.711152
\(16\) 0 0
\(17\) −6.03031 −1.46257 −0.731283 0.682075i \(-0.761078\pi\)
−0.731283 + 0.682075i \(0.761078\pi\)
\(18\) 0 0
\(19\) 0.989367 0.226976 0.113488 0.993539i \(-0.463798\pi\)
0.113488 + 0.993539i \(0.463798\pi\)
\(20\) 0 0
\(21\) 1.10969 0.242154
\(22\) 0 0
\(23\) 8.81617 1.83830 0.919149 0.393909i \(-0.128878\pi\)
0.919149 + 0.393909i \(0.128878\pi\)
\(24\) 0 0
\(25\) 1.16047 0.232093
\(26\) 0 0
\(27\) 5.29165 1.01838
\(28\) 0 0
\(29\) −4.44880 −0.826122 −0.413061 0.910703i \(-0.635540\pi\)
−0.413061 + 0.910703i \(0.635540\pi\)
\(30\) 0 0
\(31\) 2.66711 0.479027 0.239514 0.970893i \(-0.423012\pi\)
0.239514 + 0.970893i \(0.423012\pi\)
\(32\) 0 0
\(33\) −1.10969 −0.193172
\(34\) 0 0
\(35\) 2.48203 0.419539
\(36\) 0 0
\(37\) −10.0381 −1.65026 −0.825129 0.564945i \(-0.808897\pi\)
−0.825129 + 0.564945i \(0.808897\pi\)
\(38\) 0 0
\(39\) 1.10969 0.177693
\(40\) 0 0
\(41\) −1.71649 −0.268070 −0.134035 0.990977i \(-0.542793\pi\)
−0.134035 + 0.990977i \(0.542793\pi\)
\(42\) 0 0
\(43\) −12.1359 −1.85070 −0.925350 0.379113i \(-0.876229\pi\)
−0.925350 + 0.379113i \(0.876229\pi\)
\(44\) 0 0
\(45\) 4.38969 0.654376
\(46\) 0 0
\(47\) −2.96869 −0.433028 −0.216514 0.976279i \(-0.569469\pi\)
−0.216514 + 0.976279i \(0.569469\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 6.69178 0.937036
\(52\) 0 0
\(53\) −7.19148 −0.987825 −0.493913 0.869512i \(-0.664434\pi\)
−0.493913 + 0.869512i \(0.664434\pi\)
\(54\) 0 0
\(55\) −2.48203 −0.334677
\(56\) 0 0
\(57\) −1.09789 −0.145419
\(58\) 0 0
\(59\) −7.72532 −1.00575 −0.502876 0.864359i \(-0.667725\pi\)
−0.502876 + 0.864359i \(0.667725\pi\)
\(60\) 0 0
\(61\) −0.918973 −0.117662 −0.0588312 0.998268i \(-0.518737\pi\)
−0.0588312 + 0.998268i \(0.518737\pi\)
\(62\) 0 0
\(63\) 1.76859 0.222821
\(64\) 0 0
\(65\) 2.48203 0.307858
\(66\) 0 0
\(67\) 4.50502 0.550376 0.275188 0.961390i \(-0.411260\pi\)
0.275188 + 0.961390i \(0.411260\pi\)
\(68\) 0 0
\(69\) −9.78321 −1.17776
\(70\) 0 0
\(71\) −12.7548 −1.51371 −0.756856 0.653582i \(-0.773266\pi\)
−0.756856 + 0.653582i \(0.773266\pi\)
\(72\) 0 0
\(73\) −5.38509 −0.630277 −0.315139 0.949046i \(-0.602051\pi\)
−0.315139 + 0.949046i \(0.602051\pi\)
\(74\) 0 0
\(75\) −1.28776 −0.148697
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −5.36852 −0.604005 −0.302003 0.953307i \(-0.597655\pi\)
−0.302003 + 0.953307i \(0.597655\pi\)
\(80\) 0 0
\(81\) −0.566329 −0.0629255
\(82\) 0 0
\(83\) −2.96934 −0.325928 −0.162964 0.986632i \(-0.552105\pi\)
−0.162964 + 0.986632i \(0.552105\pi\)
\(84\) 0 0
\(85\) 14.9674 1.62344
\(86\) 0 0
\(87\) 4.93679 0.529280
\(88\) 0 0
\(89\) 3.26674 0.346274 0.173137 0.984898i \(-0.444610\pi\)
0.173137 + 0.984898i \(0.444610\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −2.95966 −0.306903
\(94\) 0 0
\(95\) −2.45564 −0.251943
\(96\) 0 0
\(97\) −15.0794 −1.53108 −0.765542 0.643386i \(-0.777529\pi\)
−0.765542 + 0.643386i \(0.777529\pi\)
\(98\) 0 0
\(99\) −1.76859 −0.177750
\(100\) 0 0
\(101\) −6.98437 −0.694971 −0.347486 0.937685i \(-0.612964\pi\)
−0.347486 + 0.937685i \(0.612964\pi\)
\(102\) 0 0
\(103\) −8.84018 −0.871048 −0.435524 0.900177i \(-0.643437\pi\)
−0.435524 + 0.900177i \(0.643437\pi\)
\(104\) 0 0
\(105\) −2.75428 −0.268790
\(106\) 0 0
\(107\) 14.6040 1.41182 0.705909 0.708303i \(-0.250539\pi\)
0.705909 + 0.708303i \(0.250539\pi\)
\(108\) 0 0
\(109\) 8.61938 0.825587 0.412794 0.910825i \(-0.364553\pi\)
0.412794 + 0.910825i \(0.364553\pi\)
\(110\) 0 0
\(111\) 11.1392 1.05729
\(112\) 0 0
\(113\) 4.38285 0.412304 0.206152 0.978520i \(-0.433906\pi\)
0.206152 + 0.978520i \(0.433906\pi\)
\(114\) 0 0
\(115\) −21.8820 −2.04051
\(116\) 0 0
\(117\) 1.76859 0.163506
\(118\) 0 0
\(119\) 6.03031 0.552798
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 1.90477 0.171747
\(124\) 0 0
\(125\) 9.52983 0.852374
\(126\) 0 0
\(127\) 6.11501 0.542619 0.271310 0.962492i \(-0.412543\pi\)
0.271310 + 0.962492i \(0.412543\pi\)
\(128\) 0 0
\(129\) 13.4670 1.18571
\(130\) 0 0
\(131\) −17.9037 −1.56425 −0.782125 0.623121i \(-0.785864\pi\)
−0.782125 + 0.623121i \(0.785864\pi\)
\(132\) 0 0
\(133\) −0.989367 −0.0857890
\(134\) 0 0
\(135\) −13.1340 −1.13040
\(136\) 0 0
\(137\) 19.1604 1.63698 0.818492 0.574517i \(-0.194810\pi\)
0.818492 + 0.574517i \(0.194810\pi\)
\(138\) 0 0
\(139\) 5.32781 0.451899 0.225949 0.974139i \(-0.427452\pi\)
0.225949 + 0.974139i \(0.427452\pi\)
\(140\) 0 0
\(141\) 3.29433 0.277432
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 11.0421 0.916993
\(146\) 0 0
\(147\) −1.10969 −0.0915257
\(148\) 0 0
\(149\) −9.39378 −0.769568 −0.384784 0.923007i \(-0.625724\pi\)
−0.384784 + 0.923007i \(0.625724\pi\)
\(150\) 0 0
\(151\) −9.99856 −0.813671 −0.406836 0.913501i \(-0.633368\pi\)
−0.406836 + 0.913501i \(0.633368\pi\)
\(152\) 0 0
\(153\) 10.6651 0.862225
\(154\) 0 0
\(155\) −6.61984 −0.531719
\(156\) 0 0
\(157\) 15.9963 1.27664 0.638320 0.769771i \(-0.279630\pi\)
0.638320 + 0.769771i \(0.279630\pi\)
\(158\) 0 0
\(159\) 7.98031 0.632880
\(160\) 0 0
\(161\) −8.81617 −0.694812
\(162\) 0 0
\(163\) 5.21793 0.408700 0.204350 0.978898i \(-0.434492\pi\)
0.204350 + 0.978898i \(0.434492\pi\)
\(164\) 0 0
\(165\) 2.75428 0.214421
\(166\) 0 0
\(167\) 19.2181 1.48714 0.743571 0.668657i \(-0.233130\pi\)
0.743571 + 0.668657i \(0.233130\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −1.74978 −0.133809
\(172\) 0 0
\(173\) −11.7424 −0.892755 −0.446378 0.894845i \(-0.647286\pi\)
−0.446378 + 0.894845i \(0.647286\pi\)
\(174\) 0 0
\(175\) −1.16047 −0.0877229
\(176\) 0 0
\(177\) 8.57271 0.644365
\(178\) 0 0
\(179\) 2.27123 0.169760 0.0848800 0.996391i \(-0.472949\pi\)
0.0848800 + 0.996391i \(0.472949\pi\)
\(180\) 0 0
\(181\) 10.6236 0.789644 0.394822 0.918758i \(-0.370806\pi\)
0.394822 + 0.918758i \(0.370806\pi\)
\(182\) 0 0
\(183\) 1.01978 0.0753839
\(184\) 0 0
\(185\) 24.9149 1.83178
\(186\) 0 0
\(187\) −6.03031 −0.440980
\(188\) 0 0
\(189\) −5.29165 −0.384911
\(190\) 0 0
\(191\) −13.9117 −1.00662 −0.503309 0.864106i \(-0.667884\pi\)
−0.503309 + 0.864106i \(0.667884\pi\)
\(192\) 0 0
\(193\) 21.9918 1.58301 0.791504 0.611164i \(-0.209299\pi\)
0.791504 + 0.611164i \(0.209299\pi\)
\(194\) 0 0
\(195\) −2.75428 −0.197238
\(196\) 0 0
\(197\) 9.25748 0.659568 0.329784 0.944056i \(-0.393024\pi\)
0.329784 + 0.944056i \(0.393024\pi\)
\(198\) 0 0
\(199\) 1.45245 0.102961 0.0514806 0.998674i \(-0.483606\pi\)
0.0514806 + 0.998674i \(0.483606\pi\)
\(200\) 0 0
\(201\) −4.99917 −0.352615
\(202\) 0 0
\(203\) 4.44880 0.312245
\(204\) 0 0
\(205\) 4.26037 0.297557
\(206\) 0 0
\(207\) −15.5922 −1.08373
\(208\) 0 0
\(209\) 0.989367 0.0684359
\(210\) 0 0
\(211\) 12.9804 0.893609 0.446804 0.894632i \(-0.352562\pi\)
0.446804 + 0.894632i \(0.352562\pi\)
\(212\) 0 0
\(213\) 14.1538 0.969804
\(214\) 0 0
\(215\) 30.1215 2.05427
\(216\) 0 0
\(217\) −2.66711 −0.181055
\(218\) 0 0
\(219\) 5.97578 0.403806
\(220\) 0 0
\(221\) 6.03031 0.405643
\(222\) 0 0
\(223\) −16.2513 −1.08827 −0.544134 0.838998i \(-0.683142\pi\)
−0.544134 + 0.838998i \(0.683142\pi\)
\(224\) 0 0
\(225\) −2.05239 −0.136826
\(226\) 0 0
\(227\) 4.33488 0.287716 0.143858 0.989598i \(-0.454049\pi\)
0.143858 + 0.989598i \(0.454049\pi\)
\(228\) 0 0
\(229\) −17.2810 −1.14196 −0.570981 0.820963i \(-0.693437\pi\)
−0.570981 + 0.820963i \(0.693437\pi\)
\(230\) 0 0
\(231\) 1.10969 0.0730122
\(232\) 0 0
\(233\) 13.3970 0.877667 0.438834 0.898568i \(-0.355392\pi\)
0.438834 + 0.898568i \(0.355392\pi\)
\(234\) 0 0
\(235\) 7.36838 0.480660
\(236\) 0 0
\(237\) 5.95739 0.386974
\(238\) 0 0
\(239\) 24.4300 1.58025 0.790124 0.612947i \(-0.210016\pi\)
0.790124 + 0.612947i \(0.210016\pi\)
\(240\) 0 0
\(241\) −8.44977 −0.544298 −0.272149 0.962255i \(-0.587734\pi\)
−0.272149 + 0.962255i \(0.587734\pi\)
\(242\) 0 0
\(243\) −15.2465 −0.978064
\(244\) 0 0
\(245\) −2.48203 −0.158571
\(246\) 0 0
\(247\) −0.989367 −0.0629519
\(248\) 0 0
\(249\) 3.29505 0.208815
\(250\) 0 0
\(251\) −18.4581 −1.16507 −0.582533 0.812807i \(-0.697938\pi\)
−0.582533 + 0.812807i \(0.697938\pi\)
\(252\) 0 0
\(253\) 8.81617 0.554268
\(254\) 0 0
\(255\) −16.6092 −1.04011
\(256\) 0 0
\(257\) −27.5410 −1.71796 −0.858979 0.512010i \(-0.828901\pi\)
−0.858979 + 0.512010i \(0.828901\pi\)
\(258\) 0 0
\(259\) 10.0381 0.623739
\(260\) 0 0
\(261\) 7.86810 0.487023
\(262\) 0 0
\(263\) 27.4646 1.69354 0.846770 0.531960i \(-0.178544\pi\)
0.846770 + 0.531960i \(0.178544\pi\)
\(264\) 0 0
\(265\) 17.8494 1.09648
\(266\) 0 0
\(267\) −3.62507 −0.221851
\(268\) 0 0
\(269\) −12.4947 −0.761816 −0.380908 0.924613i \(-0.624389\pi\)
−0.380908 + 0.924613i \(0.624389\pi\)
\(270\) 0 0
\(271\) −27.4898 −1.66989 −0.834944 0.550334i \(-0.814500\pi\)
−0.834944 + 0.550334i \(0.814500\pi\)
\(272\) 0 0
\(273\) −1.10969 −0.0671615
\(274\) 0 0
\(275\) 1.16047 0.0699787
\(276\) 0 0
\(277\) −3.64683 −0.219117 −0.109558 0.993980i \(-0.534944\pi\)
−0.109558 + 0.993980i \(0.534944\pi\)
\(278\) 0 0
\(279\) −4.71702 −0.282401
\(280\) 0 0
\(281\) 11.5085 0.686540 0.343270 0.939237i \(-0.388465\pi\)
0.343270 + 0.939237i \(0.388465\pi\)
\(282\) 0 0
\(283\) 24.1367 1.43478 0.717389 0.696673i \(-0.245337\pi\)
0.717389 + 0.696673i \(0.245337\pi\)
\(284\) 0 0
\(285\) 2.72500 0.161415
\(286\) 0 0
\(287\) 1.71649 0.101321
\(288\) 0 0
\(289\) 19.3647 1.13910
\(290\) 0 0
\(291\) 16.7335 0.980934
\(292\) 0 0
\(293\) −2.14442 −0.125278 −0.0626391 0.998036i \(-0.519952\pi\)
−0.0626391 + 0.998036i \(0.519952\pi\)
\(294\) 0 0
\(295\) 19.1745 1.11638
\(296\) 0 0
\(297\) 5.29165 0.307053
\(298\) 0 0
\(299\) −8.81617 −0.509852
\(300\) 0 0
\(301\) 12.1359 0.699499
\(302\) 0 0
\(303\) 7.75049 0.445254
\(304\) 0 0
\(305\) 2.28092 0.130605
\(306\) 0 0
\(307\) −9.54498 −0.544761 −0.272380 0.962190i \(-0.587811\pi\)
−0.272380 + 0.962190i \(0.587811\pi\)
\(308\) 0 0
\(309\) 9.80985 0.558063
\(310\) 0 0
\(311\) 2.82475 0.160177 0.0800885 0.996788i \(-0.474480\pi\)
0.0800885 + 0.996788i \(0.474480\pi\)
\(312\) 0 0
\(313\) −35.0812 −1.98291 −0.991454 0.130459i \(-0.958355\pi\)
−0.991454 + 0.130459i \(0.958355\pi\)
\(314\) 0 0
\(315\) −4.38969 −0.247331
\(316\) 0 0
\(317\) −15.0605 −0.845880 −0.422940 0.906158i \(-0.639002\pi\)
−0.422940 + 0.906158i \(0.639002\pi\)
\(318\) 0 0
\(319\) −4.44880 −0.249085
\(320\) 0 0
\(321\) −16.2059 −0.904523
\(322\) 0 0
\(323\) −5.96619 −0.331968
\(324\) 0 0
\(325\) −1.16047 −0.0643710
\(326\) 0 0
\(327\) −9.56484 −0.528937
\(328\) 0 0
\(329\) 2.96869 0.163669
\(330\) 0 0
\(331\) −29.9479 −1.64609 −0.823044 0.567978i \(-0.807726\pi\)
−0.823044 + 0.567978i \(0.807726\pi\)
\(332\) 0 0
\(333\) 17.7533 0.972875
\(334\) 0 0
\(335\) −11.1816 −0.610915
\(336\) 0 0
\(337\) 34.0878 1.85688 0.928440 0.371482i \(-0.121150\pi\)
0.928440 + 0.371482i \(0.121150\pi\)
\(338\) 0 0
\(339\) −4.86360 −0.264155
\(340\) 0 0
\(341\) 2.66711 0.144432
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 24.2822 1.30731
\(346\) 0 0
\(347\) 16.4981 0.885665 0.442833 0.896604i \(-0.353974\pi\)
0.442833 + 0.896604i \(0.353974\pi\)
\(348\) 0 0
\(349\) −1.40543 −0.0752312 −0.0376156 0.999292i \(-0.511976\pi\)
−0.0376156 + 0.999292i \(0.511976\pi\)
\(350\) 0 0
\(351\) −5.29165 −0.282448
\(352\) 0 0
\(353\) −8.42294 −0.448308 −0.224154 0.974554i \(-0.571962\pi\)
−0.224154 + 0.974554i \(0.571962\pi\)
\(354\) 0 0
\(355\) 31.6577 1.68022
\(356\) 0 0
\(357\) −6.69178 −0.354166
\(358\) 0 0
\(359\) 19.1778 1.01216 0.506082 0.862485i \(-0.331093\pi\)
0.506082 + 0.862485i \(0.331093\pi\)
\(360\) 0 0
\(361\) −18.0212 −0.948482
\(362\) 0 0
\(363\) −1.10969 −0.0582436
\(364\) 0 0
\(365\) 13.3660 0.699606
\(366\) 0 0
\(367\) −10.4832 −0.547218 −0.273609 0.961841i \(-0.588217\pi\)
−0.273609 + 0.961841i \(0.588217\pi\)
\(368\) 0 0
\(369\) 3.03576 0.158035
\(370\) 0 0
\(371\) 7.19148 0.373363
\(372\) 0 0
\(373\) −19.6005 −1.01488 −0.507438 0.861688i \(-0.669407\pi\)
−0.507438 + 0.861688i \(0.669407\pi\)
\(374\) 0 0
\(375\) −10.5752 −0.546099
\(376\) 0 0
\(377\) 4.44880 0.229125
\(378\) 0 0
\(379\) 6.64649 0.341407 0.170704 0.985322i \(-0.445396\pi\)
0.170704 + 0.985322i \(0.445396\pi\)
\(380\) 0 0
\(381\) −6.78577 −0.347645
\(382\) 0 0
\(383\) 20.0950 1.02681 0.513403 0.858148i \(-0.328385\pi\)
0.513403 + 0.858148i \(0.328385\pi\)
\(384\) 0 0
\(385\) 2.48203 0.126496
\(386\) 0 0
\(387\) 21.4633 1.09104
\(388\) 0 0
\(389\) 26.1801 1.32738 0.663692 0.748006i \(-0.268989\pi\)
0.663692 + 0.748006i \(0.268989\pi\)
\(390\) 0 0
\(391\) −53.1643 −2.68863
\(392\) 0 0
\(393\) 19.8675 1.00218
\(394\) 0 0
\(395\) 13.3248 0.670444
\(396\) 0 0
\(397\) 10.5177 0.527867 0.263934 0.964541i \(-0.414980\pi\)
0.263934 + 0.964541i \(0.414980\pi\)
\(398\) 0 0
\(399\) 1.09789 0.0549633
\(400\) 0 0
\(401\) 3.09285 0.154449 0.0772247 0.997014i \(-0.475394\pi\)
0.0772247 + 0.997014i \(0.475394\pi\)
\(402\) 0 0
\(403\) −2.66711 −0.132858
\(404\) 0 0
\(405\) 1.40565 0.0698471
\(406\) 0 0
\(407\) −10.0381 −0.497571
\(408\) 0 0
\(409\) 38.2833 1.89299 0.946493 0.322724i \(-0.104599\pi\)
0.946493 + 0.322724i \(0.104599\pi\)
\(410\) 0 0
\(411\) −21.2621 −1.04878
\(412\) 0 0
\(413\) 7.72532 0.380138
\(414\) 0 0
\(415\) 7.36999 0.361779
\(416\) 0 0
\(417\) −5.91221 −0.289522
\(418\) 0 0
\(419\) 6.97905 0.340949 0.170474 0.985362i \(-0.445470\pi\)
0.170474 + 0.985362i \(0.445470\pi\)
\(420\) 0 0
\(421\) 33.1636 1.61630 0.808148 0.588979i \(-0.200470\pi\)
0.808148 + 0.588979i \(0.200470\pi\)
\(422\) 0 0
\(423\) 5.25040 0.255283
\(424\) 0 0
\(425\) −6.99797 −0.339451
\(426\) 0 0
\(427\) 0.918973 0.0444722
\(428\) 0 0
\(429\) 1.10969 0.0535763
\(430\) 0 0
\(431\) 11.0412 0.531837 0.265918 0.963996i \(-0.414325\pi\)
0.265918 + 0.963996i \(0.414325\pi\)
\(432\) 0 0
\(433\) 19.7428 0.948781 0.474390 0.880315i \(-0.342669\pi\)
0.474390 + 0.880315i \(0.342669\pi\)
\(434\) 0 0
\(435\) −12.2533 −0.587499
\(436\) 0 0
\(437\) 8.72243 0.417250
\(438\) 0 0
\(439\) 14.1100 0.673434 0.336717 0.941606i \(-0.390684\pi\)
0.336717 + 0.941606i \(0.390684\pi\)
\(440\) 0 0
\(441\) −1.76859 −0.0842185
\(442\) 0 0
\(443\) 36.5077 1.73453 0.867267 0.497843i \(-0.165874\pi\)
0.867267 + 0.497843i \(0.165874\pi\)
\(444\) 0 0
\(445\) −8.10814 −0.384363
\(446\) 0 0
\(447\) 10.4242 0.493047
\(448\) 0 0
\(449\) −36.4557 −1.72045 −0.860225 0.509915i \(-0.829677\pi\)
−0.860225 + 0.509915i \(0.829677\pi\)
\(450\) 0 0
\(451\) −1.71649 −0.0808262
\(452\) 0 0
\(453\) 11.0953 0.521303
\(454\) 0 0
\(455\) −2.48203 −0.116359
\(456\) 0 0
\(457\) −33.5370 −1.56880 −0.784398 0.620258i \(-0.787028\pi\)
−0.784398 + 0.620258i \(0.787028\pi\)
\(458\) 0 0
\(459\) −31.9103 −1.48945
\(460\) 0 0
\(461\) 23.9111 1.11365 0.556827 0.830629i \(-0.312019\pi\)
0.556827 + 0.830629i \(0.312019\pi\)
\(462\) 0 0
\(463\) 41.4760 1.92755 0.963776 0.266713i \(-0.0859375\pi\)
0.963776 + 0.266713i \(0.0859375\pi\)
\(464\) 0 0
\(465\) 7.34597 0.340661
\(466\) 0 0
\(467\) 27.4556 1.27049 0.635247 0.772309i \(-0.280898\pi\)
0.635247 + 0.772309i \(0.280898\pi\)
\(468\) 0 0
\(469\) −4.50502 −0.208022
\(470\) 0 0
\(471\) −17.7509 −0.817918
\(472\) 0 0
\(473\) −12.1359 −0.558007
\(474\) 0 0
\(475\) 1.14813 0.0526796
\(476\) 0 0
\(477\) 12.7188 0.582352
\(478\) 0 0
\(479\) 14.0378 0.641406 0.320703 0.947180i \(-0.396081\pi\)
0.320703 + 0.947180i \(0.396081\pi\)
\(480\) 0 0
\(481\) 10.0381 0.457699
\(482\) 0 0
\(483\) 9.78321 0.445152
\(484\) 0 0
\(485\) 37.4275 1.69950
\(486\) 0 0
\(487\) 34.2433 1.55171 0.775855 0.630911i \(-0.217319\pi\)
0.775855 + 0.630911i \(0.217319\pi\)
\(488\) 0 0
\(489\) −5.79028 −0.261846
\(490\) 0 0
\(491\) −8.53084 −0.384991 −0.192496 0.981298i \(-0.561658\pi\)
−0.192496 + 0.981298i \(0.561658\pi\)
\(492\) 0 0
\(493\) 26.8277 1.20826
\(494\) 0 0
\(495\) 4.38969 0.197302
\(496\) 0 0
\(497\) 12.7548 0.572129
\(498\) 0 0
\(499\) −26.0063 −1.16420 −0.582101 0.813116i \(-0.697769\pi\)
−0.582101 + 0.813116i \(0.697769\pi\)
\(500\) 0 0
\(501\) −21.3261 −0.952782
\(502\) 0 0
\(503\) 34.7598 1.54986 0.774932 0.632044i \(-0.217784\pi\)
0.774932 + 0.632044i \(0.217784\pi\)
\(504\) 0 0
\(505\) 17.3354 0.771416
\(506\) 0 0
\(507\) −1.10969 −0.0492831
\(508\) 0 0
\(509\) 28.0026 1.24119 0.620597 0.784130i \(-0.286890\pi\)
0.620597 + 0.784130i \(0.286890\pi\)
\(510\) 0 0
\(511\) 5.38509 0.238222
\(512\) 0 0
\(513\) 5.23539 0.231148
\(514\) 0 0
\(515\) 21.9416 0.966861
\(516\) 0 0
\(517\) −2.96869 −0.130563
\(518\) 0 0
\(519\) 13.0304 0.571970
\(520\) 0 0
\(521\) −15.2247 −0.667005 −0.333503 0.942749i \(-0.608231\pi\)
−0.333503 + 0.942749i \(0.608231\pi\)
\(522\) 0 0
\(523\) −42.4646 −1.85685 −0.928425 0.371521i \(-0.878836\pi\)
−0.928425 + 0.371521i \(0.878836\pi\)
\(524\) 0 0
\(525\) 1.28776 0.0562023
\(526\) 0 0
\(527\) −16.0835 −0.700608
\(528\) 0 0
\(529\) 54.7249 2.37934
\(530\) 0 0
\(531\) 13.6629 0.592920
\(532\) 0 0
\(533\) 1.71649 0.0743493
\(534\) 0 0
\(535\) −36.2474 −1.56711
\(536\) 0 0
\(537\) −2.52037 −0.108762
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −1.92402 −0.0827200 −0.0413600 0.999144i \(-0.513169\pi\)
−0.0413600 + 0.999144i \(0.513169\pi\)
\(542\) 0 0
\(543\) −11.7889 −0.505909
\(544\) 0 0
\(545\) −21.3936 −0.916399
\(546\) 0 0
\(547\) −10.7332 −0.458917 −0.229458 0.973318i \(-0.573695\pi\)
−0.229458 + 0.973318i \(0.573695\pi\)
\(548\) 0 0
\(549\) 1.62529 0.0693655
\(550\) 0 0
\(551\) −4.40150 −0.187510
\(552\) 0 0
\(553\) 5.36852 0.228293
\(554\) 0 0
\(555\) −27.6478 −1.17358
\(556\) 0 0
\(557\) −27.5557 −1.16757 −0.583787 0.811907i \(-0.698430\pi\)
−0.583787 + 0.811907i \(0.698430\pi\)
\(558\) 0 0
\(559\) 12.1359 0.513292
\(560\) 0 0
\(561\) 6.69178 0.282527
\(562\) 0 0
\(563\) −7.04575 −0.296943 −0.148471 0.988917i \(-0.547435\pi\)
−0.148471 + 0.988917i \(0.547435\pi\)
\(564\) 0 0
\(565\) −10.8784 −0.457656
\(566\) 0 0
\(567\) 0.566329 0.0237836
\(568\) 0 0
\(569\) 0.387835 0.0162589 0.00812945 0.999967i \(-0.497412\pi\)
0.00812945 + 0.999967i \(0.497412\pi\)
\(570\) 0 0
\(571\) −44.7970 −1.87469 −0.937347 0.348397i \(-0.886726\pi\)
−0.937347 + 0.348397i \(0.886726\pi\)
\(572\) 0 0
\(573\) 15.4377 0.644920
\(574\) 0 0
\(575\) 10.2309 0.426656
\(576\) 0 0
\(577\) 0.851144 0.0354336 0.0177168 0.999843i \(-0.494360\pi\)
0.0177168 + 0.999843i \(0.494360\pi\)
\(578\) 0 0
\(579\) −24.4041 −1.01420
\(580\) 0 0
\(581\) 2.96934 0.123189
\(582\) 0 0
\(583\) −7.19148 −0.297841
\(584\) 0 0
\(585\) −4.38969 −0.181491
\(586\) 0 0
\(587\) 8.49139 0.350477 0.175239 0.984526i \(-0.443930\pi\)
0.175239 + 0.984526i \(0.443930\pi\)
\(588\) 0 0
\(589\) 2.63875 0.108728
\(590\) 0 0
\(591\) −10.2729 −0.422572
\(592\) 0 0
\(593\) 8.03257 0.329858 0.164929 0.986305i \(-0.447260\pi\)
0.164929 + 0.986305i \(0.447260\pi\)
\(594\) 0 0
\(595\) −14.9674 −0.613604
\(596\) 0 0
\(597\) −1.61177 −0.0659652
\(598\) 0 0
\(599\) −9.57221 −0.391110 −0.195555 0.980693i \(-0.562651\pi\)
−0.195555 + 0.980693i \(0.562651\pi\)
\(600\) 0 0
\(601\) 25.4101 1.03650 0.518250 0.855229i \(-0.326584\pi\)
0.518250 + 0.855229i \(0.326584\pi\)
\(602\) 0 0
\(603\) −7.96753 −0.324463
\(604\) 0 0
\(605\) −2.48203 −0.100909
\(606\) 0 0
\(607\) −19.9052 −0.807928 −0.403964 0.914775i \(-0.632368\pi\)
−0.403964 + 0.914775i \(0.632368\pi\)
\(608\) 0 0
\(609\) −4.93679 −0.200049
\(610\) 0 0
\(611\) 2.96869 0.120100
\(612\) 0 0
\(613\) −20.6275 −0.833137 −0.416569 0.909104i \(-0.636767\pi\)
−0.416569 + 0.909104i \(0.636767\pi\)
\(614\) 0 0
\(615\) −4.72769 −0.190639
\(616\) 0 0
\(617\) −3.60189 −0.145006 −0.0725032 0.997368i \(-0.523099\pi\)
−0.0725032 + 0.997368i \(0.523099\pi\)
\(618\) 0 0
\(619\) −14.8811 −0.598122 −0.299061 0.954234i \(-0.596673\pi\)
−0.299061 + 0.954234i \(0.596673\pi\)
\(620\) 0 0
\(621\) 46.6521 1.87209
\(622\) 0 0
\(623\) −3.26674 −0.130879
\(624\) 0 0
\(625\) −29.4556 −1.17823
\(626\) 0 0
\(627\) −1.09789 −0.0438455
\(628\) 0 0
\(629\) 60.5330 2.41361
\(630\) 0 0
\(631\) 29.2235 1.16337 0.581685 0.813414i \(-0.302394\pi\)
0.581685 + 0.813414i \(0.302394\pi\)
\(632\) 0 0
\(633\) −14.4042 −0.572517
\(634\) 0 0
\(635\) −15.1776 −0.602306
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 22.5579 0.892378
\(640\) 0 0
\(641\) 41.4385 1.63672 0.818361 0.574705i \(-0.194883\pi\)
0.818361 + 0.574705i \(0.194883\pi\)
\(642\) 0 0
\(643\) −8.05683 −0.317730 −0.158865 0.987300i \(-0.550784\pi\)
−0.158865 + 0.987300i \(0.550784\pi\)
\(644\) 0 0
\(645\) −33.4256 −1.31613
\(646\) 0 0
\(647\) −4.54677 −0.178752 −0.0893760 0.995998i \(-0.528487\pi\)
−0.0893760 + 0.995998i \(0.528487\pi\)
\(648\) 0 0
\(649\) −7.72532 −0.303246
\(650\) 0 0
\(651\) 2.95966 0.115998
\(652\) 0 0
\(653\) 6.68144 0.261465 0.130732 0.991418i \(-0.458267\pi\)
0.130732 + 0.991418i \(0.458267\pi\)
\(654\) 0 0
\(655\) 44.4374 1.73631
\(656\) 0 0
\(657\) 9.52401 0.371567
\(658\) 0 0
\(659\) −19.7669 −0.770008 −0.385004 0.922915i \(-0.625800\pi\)
−0.385004 + 0.922915i \(0.625800\pi\)
\(660\) 0 0
\(661\) −28.8726 −1.12301 −0.561507 0.827472i \(-0.689778\pi\)
−0.561507 + 0.827472i \(0.689778\pi\)
\(662\) 0 0
\(663\) −6.69178 −0.259887
\(664\) 0 0
\(665\) 2.45564 0.0952255
\(666\) 0 0
\(667\) −39.2214 −1.51866
\(668\) 0 0
\(669\) 18.0339 0.697231
\(670\) 0 0
\(671\) −0.918973 −0.0354766
\(672\) 0 0
\(673\) −9.94704 −0.383430 −0.191715 0.981451i \(-0.561405\pi\)
−0.191715 + 0.981451i \(0.561405\pi\)
\(674\) 0 0
\(675\) 6.14078 0.236359
\(676\) 0 0
\(677\) 10.6891 0.410814 0.205407 0.978677i \(-0.434148\pi\)
0.205407 + 0.978677i \(0.434148\pi\)
\(678\) 0 0
\(679\) 15.0794 0.578695
\(680\) 0 0
\(681\) −4.81038 −0.184334
\(682\) 0 0
\(683\) −46.4976 −1.77918 −0.889591 0.456759i \(-0.849010\pi\)
−0.889591 + 0.456759i \(0.849010\pi\)
\(684\) 0 0
\(685\) −47.5567 −1.81705
\(686\) 0 0
\(687\) 19.1766 0.731632
\(688\) 0 0
\(689\) 7.19148 0.273973
\(690\) 0 0
\(691\) −22.3058 −0.848552 −0.424276 0.905533i \(-0.639471\pi\)
−0.424276 + 0.905533i \(0.639471\pi\)
\(692\) 0 0
\(693\) 1.76859 0.0671831
\(694\) 0 0
\(695\) −13.2238 −0.501606
\(696\) 0 0
\(697\) 10.3510 0.392070
\(698\) 0 0
\(699\) −14.8665 −0.562303
\(700\) 0 0
\(701\) −24.8494 −0.938550 −0.469275 0.883052i \(-0.655485\pi\)
−0.469275 + 0.883052i \(0.655485\pi\)
\(702\) 0 0
\(703\) −9.93139 −0.374569
\(704\) 0 0
\(705\) −8.17662 −0.307949
\(706\) 0 0
\(707\) 6.98437 0.262674
\(708\) 0 0
\(709\) −5.07357 −0.190542 −0.0952710 0.995451i \(-0.530372\pi\)
−0.0952710 + 0.995451i \(0.530372\pi\)
\(710\) 0 0
\(711\) 9.49470 0.356079
\(712\) 0 0
\(713\) 23.5137 0.880595
\(714\) 0 0
\(715\) 2.48203 0.0928226
\(716\) 0 0
\(717\) −27.1098 −1.01243
\(718\) 0 0
\(719\) 24.5939 0.917198 0.458599 0.888643i \(-0.348351\pi\)
0.458599 + 0.888643i \(0.348351\pi\)
\(720\) 0 0
\(721\) 8.84018 0.329225
\(722\) 0 0
\(723\) 9.37663 0.348721
\(724\) 0 0
\(725\) −5.16268 −0.191737
\(726\) 0 0
\(727\) −35.9708 −1.33408 −0.667041 0.745021i \(-0.732439\pi\)
−0.667041 + 0.745021i \(0.732439\pi\)
\(728\) 0 0
\(729\) 18.6179 0.689551
\(730\) 0 0
\(731\) 73.1830 2.70677
\(732\) 0 0
\(733\) −26.0419 −0.961881 −0.480940 0.876753i \(-0.659705\pi\)
−0.480940 + 0.876753i \(0.659705\pi\)
\(734\) 0 0
\(735\) 2.75428 0.101593
\(736\) 0 0
\(737\) 4.50502 0.165945
\(738\) 0 0
\(739\) −1.49861 −0.0551273 −0.0275637 0.999620i \(-0.508775\pi\)
−0.0275637 + 0.999620i \(0.508775\pi\)
\(740\) 0 0
\(741\) 1.09789 0.0403320
\(742\) 0 0
\(743\) 29.7628 1.09189 0.545946 0.837821i \(-0.316170\pi\)
0.545946 + 0.837821i \(0.316170\pi\)
\(744\) 0 0
\(745\) 23.3156 0.854218
\(746\) 0 0
\(747\) 5.25154 0.192144
\(748\) 0 0
\(749\) −14.6040 −0.533617
\(750\) 0 0
\(751\) 33.7513 1.23160 0.615801 0.787902i \(-0.288833\pi\)
0.615801 + 0.787902i \(0.288833\pi\)
\(752\) 0 0
\(753\) 20.4828 0.746434
\(754\) 0 0
\(755\) 24.8167 0.903173
\(756\) 0 0
\(757\) 5.04320 0.183298 0.0916492 0.995791i \(-0.470786\pi\)
0.0916492 + 0.995791i \(0.470786\pi\)
\(758\) 0 0
\(759\) −9.78321 −0.355108
\(760\) 0 0
\(761\) −16.4530 −0.596419 −0.298210 0.954500i \(-0.596389\pi\)
−0.298210 + 0.954500i \(0.596389\pi\)
\(762\) 0 0
\(763\) −8.61938 −0.312043
\(764\) 0 0
\(765\) −26.4712 −0.957068
\(766\) 0 0
\(767\) 7.72532 0.278945
\(768\) 0 0
\(769\) −35.3313 −1.27408 −0.637040 0.770831i \(-0.719841\pi\)
−0.637040 + 0.770831i \(0.719841\pi\)
\(770\) 0 0
\(771\) 30.5619 1.10066
\(772\) 0 0
\(773\) −5.95778 −0.214286 −0.107143 0.994244i \(-0.534170\pi\)
−0.107143 + 0.994244i \(0.534170\pi\)
\(774\) 0 0
\(775\) 3.09509 0.111179
\(776\) 0 0
\(777\) −11.1392 −0.399617
\(778\) 0 0
\(779\) −1.69824 −0.0608456
\(780\) 0 0
\(781\) −12.7548 −0.456401
\(782\) 0 0
\(783\) −23.5415 −0.841306
\(784\) 0 0
\(785\) −39.7032 −1.41707
\(786\) 0 0
\(787\) −51.9245 −1.85091 −0.925455 0.378858i \(-0.876317\pi\)
−0.925455 + 0.378858i \(0.876317\pi\)
\(788\) 0 0
\(789\) −30.4772 −1.08502
\(790\) 0 0
\(791\) −4.38285 −0.155836
\(792\) 0 0
\(793\) 0.918973 0.0326337
\(794\) 0 0
\(795\) −19.8074 −0.702494
\(796\) 0 0
\(797\) 1.30557 0.0462458 0.0231229 0.999733i \(-0.492639\pi\)
0.0231229 + 0.999733i \(0.492639\pi\)
\(798\) 0 0
\(799\) 17.9021 0.633332
\(800\) 0 0
\(801\) −5.77752 −0.204139
\(802\) 0 0
\(803\) −5.38509 −0.190036
\(804\) 0 0
\(805\) 21.8820 0.771239
\(806\) 0 0
\(807\) 13.8653 0.488080
\(808\) 0 0
\(809\) −10.6414 −0.374132 −0.187066 0.982347i \(-0.559898\pi\)
−0.187066 + 0.982347i \(0.559898\pi\)
\(810\) 0 0
\(811\) 43.5136 1.52797 0.763985 0.645234i \(-0.223240\pi\)
0.763985 + 0.645234i \(0.223240\pi\)
\(812\) 0 0
\(813\) 30.5052 1.06986
\(814\) 0 0
\(815\) −12.9511 −0.453656
\(816\) 0 0
\(817\) −12.0068 −0.420065
\(818\) 0 0
\(819\) −1.76859 −0.0617995
\(820\) 0 0
\(821\) −31.9076 −1.11358 −0.556792 0.830652i \(-0.687968\pi\)
−0.556792 + 0.830652i \(0.687968\pi\)
\(822\) 0 0
\(823\) −13.2277 −0.461088 −0.230544 0.973062i \(-0.574051\pi\)
−0.230544 + 0.973062i \(0.574051\pi\)
\(824\) 0 0
\(825\) −1.28776 −0.0448339
\(826\) 0 0
\(827\) 24.9894 0.868965 0.434483 0.900680i \(-0.356931\pi\)
0.434483 + 0.900680i \(0.356931\pi\)
\(828\) 0 0
\(829\) 34.8946 1.21194 0.605970 0.795488i \(-0.292785\pi\)
0.605970 + 0.795488i \(0.292785\pi\)
\(830\) 0 0
\(831\) 4.04685 0.140384
\(832\) 0 0
\(833\) −6.03031 −0.208938
\(834\) 0 0
\(835\) −47.6999 −1.65072
\(836\) 0 0
\(837\) 14.1134 0.487831
\(838\) 0 0
\(839\) −50.3788 −1.73927 −0.869635 0.493695i \(-0.835646\pi\)
−0.869635 + 0.493695i \(0.835646\pi\)
\(840\) 0 0
\(841\) −9.20814 −0.317522
\(842\) 0 0
\(843\) −12.7709 −0.439852
\(844\) 0 0
\(845\) −2.48203 −0.0853844
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −26.7843 −0.919233
\(850\) 0 0
\(851\) −88.4978 −3.03367
\(852\) 0 0
\(853\) 47.0728 1.61174 0.805870 0.592092i \(-0.201698\pi\)
0.805870 + 0.592092i \(0.201698\pi\)
\(854\) 0 0
\(855\) 4.34301 0.148528
\(856\) 0 0
\(857\) 30.9002 1.05553 0.527765 0.849390i \(-0.323030\pi\)
0.527765 + 0.849390i \(0.323030\pi\)
\(858\) 0 0
\(859\) −14.0452 −0.479218 −0.239609 0.970870i \(-0.577019\pi\)
−0.239609 + 0.970870i \(0.577019\pi\)
\(860\) 0 0
\(861\) −1.90477 −0.0649143
\(862\) 0 0
\(863\) 51.5784 1.75575 0.877874 0.478892i \(-0.158961\pi\)
0.877874 + 0.478892i \(0.158961\pi\)
\(864\) 0 0
\(865\) 29.1449 0.990955
\(866\) 0 0
\(867\) −21.4888 −0.729797
\(868\) 0 0
\(869\) −5.36852 −0.182115
\(870\) 0 0
\(871\) −4.50502 −0.152647
\(872\) 0 0
\(873\) 26.6693 0.902619
\(874\) 0 0
\(875\) −9.52983 −0.322167
\(876\) 0 0
\(877\) 41.2824 1.39401 0.697004 0.717067i \(-0.254516\pi\)
0.697004 + 0.717067i \(0.254516\pi\)
\(878\) 0 0
\(879\) 2.37964 0.0802632
\(880\) 0 0
\(881\) 22.8066 0.768374 0.384187 0.923255i \(-0.374482\pi\)
0.384187 + 0.923255i \(0.374482\pi\)
\(882\) 0 0
\(883\) −45.7317 −1.53899 −0.769497 0.638650i \(-0.779493\pi\)
−0.769497 + 0.638650i \(0.779493\pi\)
\(884\) 0 0
\(885\) −21.2777 −0.715243
\(886\) 0 0
\(887\) 39.6335 1.33076 0.665382 0.746503i \(-0.268269\pi\)
0.665382 + 0.746503i \(0.268269\pi\)
\(888\) 0 0
\(889\) −6.11501 −0.205091
\(890\) 0 0
\(891\) −0.566329 −0.0189727
\(892\) 0 0
\(893\) −2.93713 −0.0982872
\(894\) 0 0
\(895\) −5.63727 −0.188433
\(896\) 0 0
\(897\) 9.78321 0.326652
\(898\) 0 0
\(899\) −11.8655 −0.395735
\(900\) 0 0
\(901\) 43.3668 1.44476
\(902\) 0 0
\(903\) −13.4670 −0.448155
\(904\) 0 0
\(905\) −26.3680 −0.876503
\(906\) 0 0
\(907\) 13.4277 0.445861 0.222930 0.974834i \(-0.428438\pi\)
0.222930 + 0.974834i \(0.428438\pi\)
\(908\) 0 0
\(909\) 12.3525 0.409706
\(910\) 0 0
\(911\) −42.6266 −1.41228 −0.706142 0.708070i \(-0.749566\pi\)
−0.706142 + 0.708070i \(0.749566\pi\)
\(912\) 0 0
\(913\) −2.96934 −0.0982708
\(914\) 0 0
\(915\) −2.53111 −0.0836759
\(916\) 0 0
\(917\) 17.9037 0.591231
\(918\) 0 0
\(919\) 12.1665 0.401335 0.200667 0.979659i \(-0.435689\pi\)
0.200667 + 0.979659i \(0.435689\pi\)
\(920\) 0 0
\(921\) 10.5920 0.349017
\(922\) 0 0
\(923\) 12.7548 0.419828
\(924\) 0 0
\(925\) −11.6489 −0.383013
\(926\) 0 0
\(927\) 15.6346 0.513509
\(928\) 0 0
\(929\) 6.25073 0.205080 0.102540 0.994729i \(-0.467303\pi\)
0.102540 + 0.994729i \(0.467303\pi\)
\(930\) 0 0
\(931\) 0.989367 0.0324252
\(932\) 0 0
\(933\) −3.13460 −0.102622
\(934\) 0 0
\(935\) 14.9674 0.489486
\(936\) 0 0
\(937\) 17.0576 0.557247 0.278623 0.960400i \(-0.410122\pi\)
0.278623 + 0.960400i \(0.410122\pi\)
\(938\) 0 0
\(939\) 38.9293 1.27041
\(940\) 0 0
\(941\) 4.68141 0.152610 0.0763048 0.997085i \(-0.475688\pi\)
0.0763048 + 0.997085i \(0.475688\pi\)
\(942\) 0 0
\(943\) −15.1328 −0.492793
\(944\) 0 0
\(945\) 13.1340 0.427250
\(946\) 0 0
\(947\) −27.1306 −0.881625 −0.440813 0.897599i \(-0.645310\pi\)
−0.440813 + 0.897599i \(0.645310\pi\)
\(948\) 0 0
\(949\) 5.38509 0.174808
\(950\) 0 0
\(951\) 16.7124 0.541938
\(952\) 0 0
\(953\) 14.4961 0.469576 0.234788 0.972047i \(-0.424560\pi\)
0.234788 + 0.972047i \(0.424560\pi\)
\(954\) 0 0
\(955\) 34.5293 1.11734
\(956\) 0 0
\(957\) 4.93679 0.159584
\(958\) 0 0
\(959\) −19.1604 −0.618722
\(960\) 0 0
\(961\) −23.8865 −0.770533
\(962\) 0 0
\(963\) −25.8284 −0.832308
\(964\) 0 0
\(965\) −54.5844 −1.75713
\(966\) 0 0
\(967\) 43.2518 1.39088 0.695442 0.718582i \(-0.255209\pi\)
0.695442 + 0.718582i \(0.255209\pi\)
\(968\) 0 0
\(969\) 6.62062 0.212685
\(970\) 0 0
\(971\) 4.64313 0.149005 0.0745026 0.997221i \(-0.476263\pi\)
0.0745026 + 0.997221i \(0.476263\pi\)
\(972\) 0 0
\(973\) −5.32781 −0.170802
\(974\) 0 0
\(975\) 1.28776 0.0412412
\(976\) 0 0
\(977\) 59.7703 1.91222 0.956110 0.293008i \(-0.0946562\pi\)
0.956110 + 0.293008i \(0.0946562\pi\)
\(978\) 0 0
\(979\) 3.26674 0.104405
\(980\) 0 0
\(981\) −15.2441 −0.486708
\(982\) 0 0
\(983\) 14.0910 0.449435 0.224717 0.974424i \(-0.427854\pi\)
0.224717 + 0.974424i \(0.427854\pi\)
\(984\) 0 0
\(985\) −22.9773 −0.732119
\(986\) 0 0
\(987\) −3.29433 −0.104860
\(988\) 0 0
\(989\) −106.992 −3.40214
\(990\) 0 0
\(991\) 48.3445 1.53571 0.767857 0.640621i \(-0.221323\pi\)
0.767857 + 0.640621i \(0.221323\pi\)
\(992\) 0 0
\(993\) 33.2329 1.05462
\(994\) 0 0
\(995\) −3.60501 −0.114287
\(996\) 0 0
\(997\) −37.9703 −1.20253 −0.601266 0.799049i \(-0.705337\pi\)
−0.601266 + 0.799049i \(0.705337\pi\)
\(998\) 0 0
\(999\) −53.1183 −1.68059
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 \(a_p\))