Properties

Label 8036.2.a.t.1.9
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-0.103746\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.103746 q^{3} -3.71451 q^{5} -2.98924 q^{9} +O(q^{10})\) \(q-0.103746 q^{3} -3.71451 q^{5} -2.98924 q^{9} -1.25890 q^{11} +0.166769 q^{13} +0.385366 q^{15} +5.79993 q^{17} -1.05905 q^{19} -8.98555 q^{23} +8.79757 q^{25} +0.621361 q^{27} -3.21478 q^{29} -9.67227 q^{31} +0.130606 q^{33} +1.70626 q^{37} -0.0173016 q^{39} -1.00000 q^{41} -3.83571 q^{43} +11.1035 q^{45} -7.32109 q^{47} -0.601721 q^{51} +2.82243 q^{53} +4.67619 q^{55} +0.109873 q^{57} -9.74300 q^{59} -4.82191 q^{61} -0.619464 q^{65} -1.21471 q^{67} +0.932217 q^{69} -13.4015 q^{71} +16.5739 q^{73} -0.912716 q^{75} -11.6084 q^{79} +8.90325 q^{81} +6.00621 q^{83} -21.5439 q^{85} +0.333522 q^{87} +11.0453 q^{89} +1.00346 q^{93} +3.93385 q^{95} +4.56071 q^{97} +3.76315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 4q^{3} + 8q^{5} + 16q^{9} + O(q^{10}) \) \( 20q + 4q^{3} + 8q^{5} + 16q^{9} - 8q^{11} + 12q^{13} + 8q^{15} + 8q^{17} + 24q^{19} + 8q^{23} + 20q^{25} + 16q^{27} - 12q^{29} + 44q^{33} + 12q^{37} + 12q^{39} - 20q^{41} + 4q^{43} + 40q^{45} + 4q^{47} + 4q^{51} - 12q^{53} - 16q^{55} + 28q^{57} + 16q^{59} + 68q^{61} - 8q^{65} + 4q^{67} + 32q^{69} + 8q^{71} + 48q^{73} + 60q^{75} - 20q^{79} + 32q^{81} - 8q^{83} - 28q^{85} + 60q^{89} - 16q^{93} + 20q^{95} + 40q^{97} + O(q^{100}) \)

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
\(3\) −0.103746 −0.0598979 −0.0299490 0.999551i \(-0.509534\pi\)
−0.0299490 + 0.999551i \(0.509534\pi\)
\(4\) 0 0
\(5\) −3.71451 −1.66118 −0.830589 0.556885i \(-0.811996\pi\)
−0.830589 + 0.556885i \(0.811996\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.98924 −0.996412
\(10\) 0 0
\(11\) −1.25890 −0.379573 −0.189786 0.981825i \(-0.560780\pi\)
−0.189786 + 0.981825i \(0.560780\pi\)
\(12\) 0 0
\(13\) 0.166769 0.0462533 0.0231266 0.999733i \(-0.492638\pi\)
0.0231266 + 0.999733i \(0.492638\pi\)
\(14\) 0 0
\(15\) 0.385366 0.0995012
\(16\) 0 0
\(17\) 5.79993 1.40669 0.703345 0.710849i \(-0.251689\pi\)
0.703345 + 0.710849i \(0.251689\pi\)
\(18\) 0 0
\(19\) −1.05905 −0.242963 −0.121481 0.992594i \(-0.538764\pi\)
−0.121481 + 0.992594i \(0.538764\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −8.98555 −1.87362 −0.936808 0.349844i \(-0.886235\pi\)
−0.936808 + 0.349844i \(0.886235\pi\)
\(24\) 0 0
\(25\) 8.79757 1.75951
\(26\) 0 0
\(27\) 0.621361 0.119581
\(28\) 0 0
\(29\) −3.21478 −0.596970 −0.298485 0.954414i \(-0.596481\pi\)
−0.298485 + 0.954414i \(0.596481\pi\)
\(30\) 0 0
\(31\) −9.67227 −1.73719 −0.868595 0.495522i \(-0.834977\pi\)
−0.868595 + 0.495522i \(0.834977\pi\)
\(32\) 0 0
\(33\) 0.130606 0.0227356
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.70626 0.280507 0.140253 0.990116i \(-0.455208\pi\)
0.140253 + 0.990116i \(0.455208\pi\)
\(38\) 0 0
\(39\) −0.0173016 −0.00277048
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −3.83571 −0.584940 −0.292470 0.956275i \(-0.594477\pi\)
−0.292470 + 0.956275i \(0.594477\pi\)
\(44\) 0 0
\(45\) 11.1035 1.65522
\(46\) 0 0
\(47\) −7.32109 −1.06789 −0.533945 0.845519i \(-0.679291\pi\)
−0.533945 + 0.845519i \(0.679291\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −0.601721 −0.0842579
\(52\) 0 0
\(53\) 2.82243 0.387690 0.193845 0.981032i \(-0.437904\pi\)
0.193845 + 0.981032i \(0.437904\pi\)
\(54\) 0 0
\(55\) 4.67619 0.630538
\(56\) 0 0
\(57\) 0.109873 0.0145530
\(58\) 0 0
\(59\) −9.74300 −1.26843 −0.634215 0.773157i \(-0.718677\pi\)
−0.634215 + 0.773157i \(0.718677\pi\)
\(60\) 0 0
\(61\) −4.82191 −0.617383 −0.308691 0.951162i \(-0.599891\pi\)
−0.308691 + 0.951162i \(0.599891\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.619464 −0.0768350
\(66\) 0 0
\(67\) −1.21471 −0.148401 −0.0742005 0.997243i \(-0.523640\pi\)
−0.0742005 + 0.997243i \(0.523640\pi\)
\(68\) 0 0
\(69\) 0.932217 0.112226
\(70\) 0 0
\(71\) −13.4015 −1.59046 −0.795232 0.606305i \(-0.792651\pi\)
−0.795232 + 0.606305i \(0.792651\pi\)
\(72\) 0 0
\(73\) 16.5739 1.93982 0.969912 0.243456i \(-0.0782811\pi\)
0.969912 + 0.243456i \(0.0782811\pi\)
\(74\) 0 0
\(75\) −0.912716 −0.105391
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −11.6084 −1.30605 −0.653024 0.757337i \(-0.726500\pi\)
−0.653024 + 0.757337i \(0.726500\pi\)
\(80\) 0 0
\(81\) 8.90325 0.989250
\(82\) 0 0
\(83\) 6.00621 0.659267 0.329633 0.944109i \(-0.393075\pi\)
0.329633 + 0.944109i \(0.393075\pi\)
\(84\) 0 0
\(85\) −21.5439 −2.33676
\(86\) 0 0
\(87\) 0.333522 0.0357573
\(88\) 0 0
\(89\) 11.0453 1.17080 0.585402 0.810743i \(-0.300937\pi\)
0.585402 + 0.810743i \(0.300937\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.00346 0.104054
\(94\) 0 0
\(95\) 3.93385 0.403605
\(96\) 0 0
\(97\) 4.56071 0.463070 0.231535 0.972827i \(-0.425625\pi\)
0.231535 + 0.972827i \(0.425625\pi\)
\(98\) 0 0
\(99\) 3.76315 0.378211
\(100\) 0 0
\(101\) −16.1605 −1.60803 −0.804015 0.594609i \(-0.797307\pi\)
−0.804015 + 0.594609i \(0.797307\pi\)
\(102\) 0 0
\(103\) −0.212217 −0.0209103 −0.0104552 0.999945i \(-0.503328\pi\)
−0.0104552 + 0.999945i \(0.503328\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.6381 1.12510 0.562550 0.826763i \(-0.309821\pi\)
0.562550 + 0.826763i \(0.309821\pi\)
\(108\) 0 0
\(109\) −16.9891 −1.62726 −0.813632 0.581380i \(-0.802513\pi\)
−0.813632 + 0.581380i \(0.802513\pi\)
\(110\) 0 0
\(111\) −0.177018 −0.0168018
\(112\) 0 0
\(113\) −5.66265 −0.532697 −0.266348 0.963877i \(-0.585817\pi\)
−0.266348 + 0.963877i \(0.585817\pi\)
\(114\) 0 0
\(115\) 33.3769 3.11241
\(116\) 0 0
\(117\) −0.498511 −0.0460874
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −9.41517 −0.855925
\(122\) 0 0
\(123\) 0.103746 0.00935449
\(124\) 0 0
\(125\) −14.1061 −1.26169
\(126\) 0 0
\(127\) −8.30382 −0.736845 −0.368423 0.929658i \(-0.620102\pi\)
−0.368423 + 0.929658i \(0.620102\pi\)
\(128\) 0 0
\(129\) 0.397941 0.0350367
\(130\) 0 0
\(131\) 7.30755 0.638464 0.319232 0.947677i \(-0.396575\pi\)
0.319232 + 0.947677i \(0.396575\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.30805 −0.198645
\(136\) 0 0
\(137\) −10.4686 −0.894395 −0.447198 0.894435i \(-0.647578\pi\)
−0.447198 + 0.894435i \(0.647578\pi\)
\(138\) 0 0
\(139\) 17.4396 1.47921 0.739606 0.673040i \(-0.235012\pi\)
0.739606 + 0.673040i \(0.235012\pi\)
\(140\) 0 0
\(141\) 0.759536 0.0639644
\(142\) 0 0
\(143\) −0.209945 −0.0175565
\(144\) 0 0
\(145\) 11.9413 0.991674
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −16.2645 −1.33244 −0.666219 0.745756i \(-0.732088\pi\)
−0.666219 + 0.745756i \(0.732088\pi\)
\(150\) 0 0
\(151\) 11.0691 0.900792 0.450396 0.892829i \(-0.351283\pi\)
0.450396 + 0.892829i \(0.351283\pi\)
\(152\) 0 0
\(153\) −17.3374 −1.40164
\(154\) 0 0
\(155\) 35.9277 2.88578
\(156\) 0 0
\(157\) 12.8519 1.02569 0.512845 0.858481i \(-0.328592\pi\)
0.512845 + 0.858481i \(0.328592\pi\)
\(158\) 0 0
\(159\) −0.292816 −0.0232219
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.63928 0.206724 0.103362 0.994644i \(-0.467040\pi\)
0.103362 + 0.994644i \(0.467040\pi\)
\(164\) 0 0
\(165\) −0.485138 −0.0377679
\(166\) 0 0
\(167\) −11.7990 −0.913031 −0.456516 0.889715i \(-0.650903\pi\)
−0.456516 + 0.889715i \(0.650903\pi\)
\(168\) 0 0
\(169\) −12.9722 −0.997861
\(170\) 0 0
\(171\) 3.16575 0.242091
\(172\) 0 0
\(173\) 7.75018 0.589235 0.294618 0.955615i \(-0.404808\pi\)
0.294618 + 0.955615i \(0.404808\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.01080 0.0759764
\(178\) 0 0
\(179\) −3.88020 −0.290019 −0.145010 0.989430i \(-0.546321\pi\)
−0.145010 + 0.989430i \(0.546321\pi\)
\(180\) 0 0
\(181\) 23.1868 1.72346 0.861730 0.507366i \(-0.169381\pi\)
0.861730 + 0.507366i \(0.169381\pi\)
\(182\) 0 0
\(183\) 0.500255 0.0369799
\(184\) 0 0
\(185\) −6.33791 −0.465972
\(186\) 0 0
\(187\) −7.30153 −0.533941
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −16.8532 −1.21945 −0.609726 0.792613i \(-0.708720\pi\)
−0.609726 + 0.792613i \(0.708720\pi\)
\(192\) 0 0
\(193\) 11.5599 0.832102 0.416051 0.909341i \(-0.363414\pi\)
0.416051 + 0.909341i \(0.363414\pi\)
\(194\) 0 0
\(195\) 0.0642670 0.00460226
\(196\) 0 0
\(197\) 14.6526 1.04395 0.521977 0.852960i \(-0.325195\pi\)
0.521977 + 0.852960i \(0.325195\pi\)
\(198\) 0 0
\(199\) 11.3345 0.803480 0.401740 0.915754i \(-0.368406\pi\)
0.401740 + 0.915754i \(0.368406\pi\)
\(200\) 0 0
\(201\) 0.126022 0.00888891
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.71451 0.259433
\(206\) 0 0
\(207\) 26.8599 1.86689
\(208\) 0 0
\(209\) 1.33324 0.0922220
\(210\) 0 0
\(211\) −15.4952 −1.06673 −0.533366 0.845885i \(-0.679073\pi\)
−0.533366 + 0.845885i \(0.679073\pi\)
\(212\) 0 0
\(213\) 1.39035 0.0952655
\(214\) 0 0
\(215\) 14.2478 0.971690
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.71948 −0.116191
\(220\) 0 0
\(221\) 0.967247 0.0650641
\(222\) 0 0
\(223\) 19.7332 1.32143 0.660715 0.750637i \(-0.270253\pi\)
0.660715 + 0.750637i \(0.270253\pi\)
\(224\) 0 0
\(225\) −26.2980 −1.75320
\(226\) 0 0
\(227\) −3.27003 −0.217040 −0.108520 0.994094i \(-0.534611\pi\)
−0.108520 + 0.994094i \(0.534611\pi\)
\(228\) 0 0
\(229\) 18.1500 1.19938 0.599692 0.800231i \(-0.295290\pi\)
0.599692 + 0.800231i \(0.295290\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.0356 0.788476 0.394238 0.919008i \(-0.371009\pi\)
0.394238 + 0.919008i \(0.371009\pi\)
\(234\) 0 0
\(235\) 27.1942 1.77396
\(236\) 0 0
\(237\) 1.20433 0.0782296
\(238\) 0 0
\(239\) 14.9782 0.968861 0.484431 0.874830i \(-0.339027\pi\)
0.484431 + 0.874830i \(0.339027\pi\)
\(240\) 0 0
\(241\) −2.73474 −0.176160 −0.0880802 0.996113i \(-0.528073\pi\)
−0.0880802 + 0.996113i \(0.528073\pi\)
\(242\) 0 0
\(243\) −2.78776 −0.178835
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −0.176616 −0.0112378
\(248\) 0 0
\(249\) −0.623121 −0.0394887
\(250\) 0 0
\(251\) 6.33313 0.399743 0.199872 0.979822i \(-0.435947\pi\)
0.199872 + 0.979822i \(0.435947\pi\)
\(252\) 0 0
\(253\) 11.3119 0.711173
\(254\) 0 0
\(255\) 2.23510 0.139967
\(256\) 0 0
\(257\) 29.3821 1.83281 0.916403 0.400258i \(-0.131079\pi\)
0.916403 + 0.400258i \(0.131079\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 9.60974 0.594828
\(262\) 0 0
\(263\) 10.1326 0.624804 0.312402 0.949950i \(-0.398866\pi\)
0.312402 + 0.949950i \(0.398866\pi\)
\(264\) 0 0
\(265\) −10.4839 −0.644023
\(266\) 0 0
\(267\) −1.14591 −0.0701287
\(268\) 0 0
\(269\) 5.47385 0.333746 0.166873 0.985978i \(-0.446633\pi\)
0.166873 + 0.985978i \(0.446633\pi\)
\(270\) 0 0
\(271\) 10.6123 0.644651 0.322326 0.946629i \(-0.395535\pi\)
0.322326 + 0.946629i \(0.395535\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −11.0753 −0.667864
\(276\) 0 0
\(277\) 22.1170 1.32888 0.664441 0.747341i \(-0.268670\pi\)
0.664441 + 0.747341i \(0.268670\pi\)
\(278\) 0 0
\(279\) 28.9127 1.73096
\(280\) 0 0
\(281\) −8.60380 −0.513260 −0.256630 0.966510i \(-0.582612\pi\)
−0.256630 + 0.966510i \(0.582612\pi\)
\(282\) 0 0
\(283\) −19.4778 −1.15783 −0.578917 0.815387i \(-0.696524\pi\)
−0.578917 + 0.815387i \(0.696524\pi\)
\(284\) 0 0
\(285\) −0.408123 −0.0241751
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 16.6392 0.978777
\(290\) 0 0
\(291\) −0.473156 −0.0277369
\(292\) 0 0
\(293\) −0.507171 −0.0296292 −0.0148146 0.999890i \(-0.504716\pi\)
−0.0148146 + 0.999890i \(0.504716\pi\)
\(294\) 0 0
\(295\) 36.1904 2.10709
\(296\) 0 0
\(297\) −0.782231 −0.0453897
\(298\) 0 0
\(299\) −1.49851 −0.0866609
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1.67659 0.0963177
\(304\) 0 0
\(305\) 17.9110 1.02558
\(306\) 0 0
\(307\) −19.3930 −1.10682 −0.553410 0.832909i \(-0.686674\pi\)
−0.553410 + 0.832909i \(0.686674\pi\)
\(308\) 0 0
\(309\) 0.0220167 0.00125249
\(310\) 0 0
\(311\) −30.2720 −1.71657 −0.858285 0.513174i \(-0.828470\pi\)
−0.858285 + 0.513174i \(0.828470\pi\)
\(312\) 0 0
\(313\) −2.36212 −0.133515 −0.0667575 0.997769i \(-0.521265\pi\)
−0.0667575 + 0.997769i \(0.521265\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.7324 1.27678 0.638390 0.769713i \(-0.279601\pi\)
0.638390 + 0.769713i \(0.279601\pi\)
\(318\) 0 0
\(319\) 4.04709 0.226593
\(320\) 0 0
\(321\) −1.20741 −0.0673911
\(322\) 0 0
\(323\) −6.14242 −0.341773
\(324\) 0 0
\(325\) 1.46716 0.0813834
\(326\) 0 0
\(327\) 1.76256 0.0974698
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 4.97931 0.273688 0.136844 0.990593i \(-0.456304\pi\)
0.136844 + 0.990593i \(0.456304\pi\)
\(332\) 0 0
\(333\) −5.10041 −0.279501
\(334\) 0 0
\(335\) 4.51207 0.246521
\(336\) 0 0
\(337\) −9.28389 −0.505726 −0.252863 0.967502i \(-0.581372\pi\)
−0.252863 + 0.967502i \(0.581372\pi\)
\(338\) 0 0
\(339\) 0.587478 0.0319075
\(340\) 0 0
\(341\) 12.1764 0.659390
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −3.46273 −0.186427
\(346\) 0 0
\(347\) 27.9523 1.50056 0.750278 0.661123i \(-0.229920\pi\)
0.750278 + 0.661123i \(0.229920\pi\)
\(348\) 0 0
\(349\) −2.76798 −0.148166 −0.0740832 0.997252i \(-0.523603\pi\)
−0.0740832 + 0.997252i \(0.523603\pi\)
\(350\) 0 0
\(351\) 0.103624 0.00553102
\(352\) 0 0
\(353\) −26.4071 −1.40551 −0.702754 0.711433i \(-0.748046\pi\)
−0.702754 + 0.711433i \(0.748046\pi\)
\(354\) 0 0
\(355\) 49.7799 2.64204
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −14.9493 −0.788994 −0.394497 0.918897i \(-0.629081\pi\)
−0.394497 + 0.918897i \(0.629081\pi\)
\(360\) 0 0
\(361\) −17.8784 −0.940969
\(362\) 0 0
\(363\) 0.976789 0.0512681
\(364\) 0 0
\(365\) −61.5638 −3.22239
\(366\) 0 0
\(367\) 18.1485 0.947342 0.473671 0.880702i \(-0.342929\pi\)
0.473671 + 0.880702i \(0.342929\pi\)
\(368\) 0 0
\(369\) 2.98924 0.155613
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 13.5184 0.699955 0.349977 0.936758i \(-0.386189\pi\)
0.349977 + 0.936758i \(0.386189\pi\)
\(374\) 0 0
\(375\) 1.46346 0.0755726
\(376\) 0 0
\(377\) −0.536125 −0.0276118
\(378\) 0 0
\(379\) 19.5253 1.00295 0.501474 0.865173i \(-0.332791\pi\)
0.501474 + 0.865173i \(0.332791\pi\)
\(380\) 0 0
\(381\) 0.861491 0.0441355
\(382\) 0 0
\(383\) 32.6971 1.67074 0.835372 0.549685i \(-0.185252\pi\)
0.835372 + 0.549685i \(0.185252\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 11.4658 0.582842
\(388\) 0 0
\(389\) −18.6007 −0.943092 −0.471546 0.881841i \(-0.656304\pi\)
−0.471546 + 0.881841i \(0.656304\pi\)
\(390\) 0 0
\(391\) −52.1156 −2.63560
\(392\) 0 0
\(393\) −0.758131 −0.0382427
\(394\) 0 0
\(395\) 43.1195 2.16958
\(396\) 0 0
\(397\) 16.6724 0.836762 0.418381 0.908272i \(-0.362598\pi\)
0.418381 + 0.908272i \(0.362598\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −18.1863 −0.908183 −0.454091 0.890955i \(-0.650036\pi\)
−0.454091 + 0.890955i \(0.650036\pi\)
\(402\) 0 0
\(403\) −1.61303 −0.0803508
\(404\) 0 0
\(405\) −33.0712 −1.64332
\(406\) 0 0
\(407\) −2.14801 −0.106473
\(408\) 0 0
\(409\) 21.8086 1.07837 0.539183 0.842188i \(-0.318733\pi\)
0.539183 + 0.842188i \(0.318733\pi\)
\(410\) 0 0
\(411\) 1.08608 0.0535724
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −22.3101 −1.09516
\(416\) 0 0
\(417\) −1.80930 −0.0886017
\(418\) 0 0
\(419\) −25.3082 −1.23639 −0.618194 0.786025i \(-0.712136\pi\)
−0.618194 + 0.786025i \(0.712136\pi\)
\(420\) 0 0
\(421\) 13.5708 0.661400 0.330700 0.943736i \(-0.392715\pi\)
0.330700 + 0.943736i \(0.392715\pi\)
\(422\) 0 0
\(423\) 21.8845 1.06406
\(424\) 0 0
\(425\) 51.0253 2.47509
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.0217810 0.00105160
\(430\) 0 0
\(431\) 32.6571 1.57303 0.786517 0.617568i \(-0.211882\pi\)
0.786517 + 0.617568i \(0.211882\pi\)
\(432\) 0 0
\(433\) −19.2443 −0.924820 −0.462410 0.886666i \(-0.653015\pi\)
−0.462410 + 0.886666i \(0.653015\pi\)
\(434\) 0 0
\(435\) −1.23887 −0.0593992
\(436\) 0 0
\(437\) 9.51615 0.455219
\(438\) 0 0
\(439\) −11.3365 −0.541061 −0.270531 0.962711i \(-0.587199\pi\)
−0.270531 + 0.962711i \(0.587199\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.47862 −0.307808 −0.153904 0.988086i \(-0.549185\pi\)
−0.153904 + 0.988086i \(0.549185\pi\)
\(444\) 0 0
\(445\) −41.0280 −1.94491
\(446\) 0 0
\(447\) 1.68738 0.0798103
\(448\) 0 0
\(449\) 24.8694 1.17366 0.586830 0.809710i \(-0.300376\pi\)
0.586830 + 0.809710i \(0.300376\pi\)
\(450\) 0 0
\(451\) 1.25890 0.0592793
\(452\) 0 0
\(453\) −1.14838 −0.0539556
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −24.6254 −1.15193 −0.575963 0.817476i \(-0.695373\pi\)
−0.575963 + 0.817476i \(0.695373\pi\)
\(458\) 0 0
\(459\) 3.60385 0.168213
\(460\) 0 0
\(461\) −0.483177 −0.0225038 −0.0112519 0.999937i \(-0.503582\pi\)
−0.0112519 + 0.999937i \(0.503582\pi\)
\(462\) 0 0
\(463\) 1.07820 0.0501081 0.0250541 0.999686i \(-0.492024\pi\)
0.0250541 + 0.999686i \(0.492024\pi\)
\(464\) 0 0
\(465\) −3.72737 −0.172853
\(466\) 0 0
\(467\) −31.6546 −1.46480 −0.732400 0.680875i \(-0.761600\pi\)
−0.732400 + 0.680875i \(0.761600\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.33333 −0.0614367
\(472\) 0 0
\(473\) 4.82877 0.222027
\(474\) 0 0
\(475\) −9.31708 −0.427497
\(476\) 0 0
\(477\) −8.43690 −0.386299
\(478\) 0 0
\(479\) 1.94043 0.0886605 0.0443303 0.999017i \(-0.485885\pi\)
0.0443303 + 0.999017i \(0.485885\pi\)
\(480\) 0 0
\(481\) 0.284550 0.0129744
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.9408 −0.769242
\(486\) 0 0
\(487\) 20.7650 0.940951 0.470476 0.882413i \(-0.344082\pi\)
0.470476 + 0.882413i \(0.344082\pi\)
\(488\) 0 0
\(489\) −0.273815 −0.0123823
\(490\) 0 0
\(491\) 32.2595 1.45585 0.727925 0.685657i \(-0.240485\pi\)
0.727925 + 0.685657i \(0.240485\pi\)
\(492\) 0 0
\(493\) −18.6455 −0.839752
\(494\) 0 0
\(495\) −13.9783 −0.628276
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 20.5390 0.919453 0.459726 0.888061i \(-0.347948\pi\)
0.459726 + 0.888061i \(0.347948\pi\)
\(500\) 0 0
\(501\) 1.22410 0.0546887
\(502\) 0 0
\(503\) 18.9911 0.846772 0.423386 0.905949i \(-0.360841\pi\)
0.423386 + 0.905949i \(0.360841\pi\)
\(504\) 0 0
\(505\) 60.0283 2.67123
\(506\) 0 0
\(507\) 1.34582 0.0597698
\(508\) 0 0
\(509\) −19.4017 −0.859964 −0.429982 0.902837i \(-0.641480\pi\)
−0.429982 + 0.902837i \(0.641480\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −0.658053 −0.0290537
\(514\) 0 0
\(515\) 0.788281 0.0347358
\(516\) 0 0
\(517\) 9.21651 0.405342
\(518\) 0 0
\(519\) −0.804053 −0.0352940
\(520\) 0 0
\(521\) −10.6858 −0.468155 −0.234078 0.972218i \(-0.575207\pi\)
−0.234078 + 0.972218i \(0.575207\pi\)
\(522\) 0 0
\(523\) −24.7762 −1.08339 −0.541694 0.840576i \(-0.682217\pi\)
−0.541694 + 0.840576i \(0.682217\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −56.0985 −2.44369
\(528\) 0 0
\(529\) 57.7400 2.51044
\(530\) 0 0
\(531\) 29.1241 1.26388
\(532\) 0 0
\(533\) −0.166769 −0.00722355
\(534\) 0 0
\(535\) −43.2299 −1.86899
\(536\) 0 0
\(537\) 0.402556 0.0173716
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −30.3160 −1.30339 −0.651694 0.758482i \(-0.725941\pi\)
−0.651694 + 0.758482i \(0.725941\pi\)
\(542\) 0 0
\(543\) −2.40554 −0.103232
\(544\) 0 0
\(545\) 63.1063 2.70318
\(546\) 0 0
\(547\) 11.8145 0.505152 0.252576 0.967577i \(-0.418722\pi\)
0.252576 + 0.967577i \(0.418722\pi\)
\(548\) 0 0
\(549\) 14.4138 0.615168
\(550\) 0 0
\(551\) 3.40462 0.145042
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.657534 0.0279108
\(556\) 0 0
\(557\) 39.7423 1.68394 0.841968 0.539528i \(-0.181397\pi\)
0.841968 + 0.539528i \(0.181397\pi\)
\(558\) 0 0
\(559\) −0.639676 −0.0270554
\(560\) 0 0
\(561\) 0.757507 0.0319820
\(562\) 0 0
\(563\) −29.5515 −1.24545 −0.622723 0.782442i \(-0.713974\pi\)
−0.622723 + 0.782442i \(0.713974\pi\)
\(564\) 0 0
\(565\) 21.0339 0.884905
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.29222 0.347628 0.173814 0.984779i \(-0.444391\pi\)
0.173814 + 0.984779i \(0.444391\pi\)
\(570\) 0 0
\(571\) 17.4987 0.732296 0.366148 0.930557i \(-0.380676\pi\)
0.366148 + 0.930557i \(0.380676\pi\)
\(572\) 0 0
\(573\) 1.74845 0.0730426
\(574\) 0 0
\(575\) −79.0510 −3.29665
\(576\) 0 0
\(577\) 44.4641 1.85106 0.925531 0.378671i \(-0.123619\pi\)
0.925531 + 0.378671i \(0.123619\pi\)
\(578\) 0 0
\(579\) −1.19930 −0.0498412
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −3.55315 −0.147157
\(584\) 0 0
\(585\) 1.85172 0.0765593
\(586\) 0 0
\(587\) −28.3564 −1.17039 −0.585197 0.810891i \(-0.698983\pi\)
−0.585197 + 0.810891i \(0.698983\pi\)
\(588\) 0 0
\(589\) 10.2434 0.422073
\(590\) 0 0
\(591\) −1.52015 −0.0625307
\(592\) 0 0
\(593\) −4.32320 −0.177533 −0.0887663 0.996052i \(-0.528292\pi\)
−0.0887663 + 0.996052i \(0.528292\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.17591 −0.0481268
\(598\) 0 0
\(599\) −9.43799 −0.385626 −0.192813 0.981236i \(-0.561761\pi\)
−0.192813 + 0.981236i \(0.561761\pi\)
\(600\) 0 0
\(601\) −19.7128 −0.804100 −0.402050 0.915618i \(-0.631702\pi\)
−0.402050 + 0.915618i \(0.631702\pi\)
\(602\) 0 0
\(603\) 3.63107 0.147869
\(604\) 0 0
\(605\) 34.9727 1.42184
\(606\) 0 0
\(607\) −14.8565 −0.603008 −0.301504 0.953465i \(-0.597489\pi\)
−0.301504 + 0.953465i \(0.597489\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.22093 −0.0493934
\(612\) 0 0
\(613\) 13.8325 0.558688 0.279344 0.960191i \(-0.409883\pi\)
0.279344 + 0.960191i \(0.409883\pi\)
\(614\) 0 0
\(615\) −0.385366 −0.0155395
\(616\) 0 0
\(617\) −21.5481 −0.867492 −0.433746 0.901035i \(-0.642808\pi\)
−0.433746 + 0.901035i \(0.642808\pi\)
\(618\) 0 0
\(619\) 8.11291 0.326085 0.163043 0.986619i \(-0.447869\pi\)
0.163043 + 0.986619i \(0.447869\pi\)
\(620\) 0 0
\(621\) −5.58327 −0.224049
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 8.40943 0.336377
\(626\) 0 0
\(627\) −0.138319 −0.00552391
\(628\) 0 0
\(629\) 9.89617 0.394586
\(630\) 0 0
\(631\) −30.1578 −1.20056 −0.600282 0.799788i \(-0.704945\pi\)
−0.600282 + 0.799788i \(0.704945\pi\)
\(632\) 0 0
\(633\) 1.60757 0.0638951
\(634\) 0 0
\(635\) 30.8446 1.22403
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 40.0602 1.58476
\(640\) 0 0
\(641\) −43.1257 −1.70336 −0.851681 0.524060i \(-0.824417\pi\)
−0.851681 + 0.524060i \(0.824417\pi\)
\(642\) 0 0
\(643\) 16.9922 0.670107 0.335054 0.942199i \(-0.391246\pi\)
0.335054 + 0.942199i \(0.391246\pi\)
\(644\) 0 0
\(645\) −1.47815 −0.0582022
\(646\) 0 0
\(647\) −40.6985 −1.60002 −0.800012 0.599985i \(-0.795173\pi\)
−0.800012 + 0.599985i \(0.795173\pi\)
\(648\) 0 0
\(649\) 12.2655 0.481461
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −10.0267 −0.392377 −0.196188 0.980566i \(-0.562856\pi\)
−0.196188 + 0.980566i \(0.562856\pi\)
\(654\) 0 0
\(655\) −27.1440 −1.06060
\(656\) 0 0
\(657\) −49.5432 −1.93286
\(658\) 0 0
\(659\) 22.1913 0.864452 0.432226 0.901765i \(-0.357728\pi\)
0.432226 + 0.901765i \(0.357728\pi\)
\(660\) 0 0
\(661\) 13.9938 0.544298 0.272149 0.962255i \(-0.412266\pi\)
0.272149 + 0.962255i \(0.412266\pi\)
\(662\) 0 0
\(663\) −0.100348 −0.00389720
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 28.8866 1.11849
\(668\) 0 0
\(669\) −2.04724 −0.0791509
\(670\) 0 0
\(671\) 6.07030 0.234342
\(672\) 0 0
\(673\) −9.56955 −0.368879 −0.184440 0.982844i \(-0.559047\pi\)
−0.184440 + 0.982844i \(0.559047\pi\)
\(674\) 0 0
\(675\) 5.46647 0.210405
\(676\) 0 0
\(677\) −33.0781 −1.27130 −0.635648 0.771979i \(-0.719267\pi\)
−0.635648 + 0.771979i \(0.719267\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.339254 0.0130002
\(682\) 0 0
\(683\) 12.2408 0.468379 0.234190 0.972191i \(-0.424756\pi\)
0.234190 + 0.972191i \(0.424756\pi\)
\(684\) 0 0
\(685\) 38.8858 1.48575
\(686\) 0 0
\(687\) −1.88299 −0.0718407
\(688\) 0 0
\(689\) 0.470692 0.0179320
\(690\) 0 0
\(691\) −1.86970 −0.0711268 −0.0355634 0.999367i \(-0.511323\pi\)
−0.0355634 + 0.999367i \(0.511323\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −64.7797 −2.45723
\(696\) 0 0
\(697\) −5.79993 −0.219688
\(698\) 0 0
\(699\) −1.24865 −0.0472281
\(700\) 0 0
\(701\) −49.8538 −1.88295 −0.941475 0.337082i \(-0.890560\pi\)
−0.941475 + 0.337082i \(0.890560\pi\)
\(702\) 0 0
\(703\) −1.80701 −0.0681528
\(704\) 0 0
\(705\) −2.82130 −0.106256
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 7.14510 0.268340 0.134170 0.990958i \(-0.457163\pi\)
0.134170 + 0.990958i \(0.457163\pi\)
\(710\) 0 0
\(711\) 34.7003 1.30136
\(712\) 0 0
\(713\) 86.9106 3.25483
\(714\) 0 0
\(715\) 0.779843 0.0291645
\(716\) 0 0
\(717\) −1.55394 −0.0580328
\(718\) 0 0
\(719\) 41.9999 1.56633 0.783165 0.621813i \(-0.213604\pi\)
0.783165 + 0.621813i \(0.213604\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0.283720 0.0105516
\(724\) 0 0
\(725\) −28.2823 −1.05038
\(726\) 0 0
\(727\) 1.39778 0.0518408 0.0259204 0.999664i \(-0.491748\pi\)
0.0259204 + 0.999664i \(0.491748\pi\)
\(728\) 0 0
\(729\) −26.4205 −0.978538
\(730\) 0 0
\(731\) −22.2469 −0.822830
\(732\) 0 0
\(733\) 28.1491 1.03971 0.519856 0.854254i \(-0.325986\pi\)
0.519856 + 0.854254i \(0.325986\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.52920 0.0563289
\(738\) 0 0
\(739\) 22.6496 0.833179 0.416590 0.909095i \(-0.363225\pi\)
0.416590 + 0.909095i \(0.363225\pi\)
\(740\) 0 0
\(741\) 0.0183233 0.000673123 0
\(742\) 0 0
\(743\) −16.2233 −0.595175 −0.297587 0.954695i \(-0.596182\pi\)
−0.297587 + 0.954695i \(0.596182\pi\)
\(744\) 0 0
\(745\) 60.4146 2.21342
\(746\) 0 0
\(747\) −17.9540 −0.656901
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −28.6190 −1.04432 −0.522161 0.852847i \(-0.674874\pi\)
−0.522161 + 0.852847i \(0.674874\pi\)
\(752\) 0 0
\(753\) −0.657038 −0.0239438
\(754\) 0 0
\(755\) −41.1163 −1.49638
\(756\) 0 0
\(757\) 40.5494 1.47379 0.736897 0.676005i \(-0.236290\pi\)
0.736897 + 0.676005i \(0.236290\pi\)
\(758\) 0 0
\(759\) −1.17357 −0.0425978
\(760\) 0 0
\(761\) −9.16931 −0.332387 −0.166194 0.986093i \(-0.553148\pi\)
−0.166194 + 0.986093i \(0.553148\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 64.3998 2.32838
\(766\) 0 0
\(767\) −1.62483 −0.0586691
\(768\) 0 0
\(769\) 16.7231 0.603052 0.301526 0.953458i \(-0.402504\pi\)
0.301526 + 0.953458i \(0.402504\pi\)
\(770\) 0 0
\(771\) −3.04828 −0.109781
\(772\) 0 0
\(773\) 39.9783 1.43792 0.718960 0.695052i \(-0.244619\pi\)
0.718960 + 0.695052i \(0.244619\pi\)
\(774\) 0 0
\(775\) −85.0925 −3.05661
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.05905 0.0379444
\(780\) 0 0
\(781\) 16.8711 0.603697
\(782\) 0 0
\(783\) −1.99754 −0.0713863
\(784\) 0 0
\(785\) −47.7383 −1.70385
\(786\) 0 0
\(787\) 22.2939 0.794693 0.397346 0.917669i \(-0.369931\pi\)
0.397346 + 0.917669i \(0.369931\pi\)
\(788\) 0 0
\(789\) −1.05122 −0.0374245
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.804144 −0.0285560
\(794\) 0 0
\(795\) 1.08767 0.0385756
\(796\) 0 0
\(797\) 30.7525 1.08931 0.544654 0.838661i \(-0.316661\pi\)
0.544654 + 0.838661i \(0.316661\pi\)
\(798\) 0 0
\(799\) −42.4618 −1.50219
\(800\) 0 0
\(801\) −33.0171 −1.16660
\(802\) 0 0
\(803\) −20.8648 −0.736304
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −0.567891 −0.0199907
\(808\) 0 0
\(809\) −34.2468 −1.20405 −0.602027 0.798476i \(-0.705640\pi\)
−0.602027 + 0.798476i \(0.705640\pi\)
\(810\) 0 0
\(811\) 7.17378 0.251905 0.125953 0.992036i \(-0.459801\pi\)
0.125953 + 0.992036i \(0.459801\pi\)
\(812\) 0 0
\(813\) −1.10099 −0.0386133
\(814\) 0 0
\(815\) −9.80361 −0.343406
\(816\) 0 0
\(817\) 4.06221 0.142119
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 49.9117 1.74193 0.870965 0.491346i \(-0.163495\pi\)
0.870965 + 0.491346i \(0.163495\pi\)
\(822\) 0 0
\(823\) −28.7584 −1.00246 −0.501228 0.865315i \(-0.667118\pi\)
−0.501228 + 0.865315i \(0.667118\pi\)
\(824\) 0 0
\(825\) 1.14902 0.0400037
\(826\) 0 0
\(827\) 10.5598 0.367199 0.183600 0.983001i \(-0.441225\pi\)
0.183600 + 0.983001i \(0.441225\pi\)
\(828\) 0 0
\(829\) −1.66400 −0.0577930 −0.0288965 0.999582i \(-0.509199\pi\)
−0.0288965 + 0.999582i \(0.509199\pi\)
\(830\) 0 0
\(831\) −2.29456 −0.0795973
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 43.8273 1.51671
\(836\) 0 0
\(837\) −6.00997 −0.207735
\(838\) 0 0
\(839\) 8.18432 0.282554 0.141277 0.989970i \(-0.454879\pi\)
0.141277 + 0.989970i \(0.454879\pi\)
\(840\) 0 0
\(841\) −18.6652 −0.643627
\(842\) 0 0
\(843\) 0.892613 0.0307432
\(844\) 0 0
\(845\) 48.1853 1.65762
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 2.02075 0.0693519
\(850\) 0 0
\(851\) −15.3317 −0.525562
\(852\) 0 0
\(853\) 14.6872 0.502882 0.251441 0.967873i \(-0.419096\pi\)
0.251441 + 0.967873i \(0.419096\pi\)
\(854\) 0 0
\(855\) −11.7592 −0.402157
\(856\) 0 0
\(857\) −8.41864 −0.287575 −0.143788 0.989609i \(-0.545928\pi\)
−0.143788 + 0.989609i \(0.545928\pi\)
\(858\) 0 0
\(859\) −42.9116 −1.46412 −0.732062 0.681238i \(-0.761442\pi\)
−0.732062 + 0.681238i \(0.761442\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −19.0445 −0.648282 −0.324141 0.946009i \(-0.605075\pi\)
−0.324141 + 0.946009i \(0.605075\pi\)
\(864\) 0 0
\(865\) −28.7881 −0.978825
\(866\) 0 0
\(867\) −1.72626 −0.0586267
\(868\) 0 0
\(869\) 14.6138 0.495740
\(870\) 0 0
\(871\) −0.202576 −0.00686403
\(872\) 0 0
\(873\) −13.6330 −0.461408
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −36.9819 −1.24879 −0.624395 0.781109i \(-0.714654\pi\)
−0.624395 + 0.781109i \(0.714654\pi\)
\(878\) 0 0
\(879\) 0.0526171 0.00177473
\(880\) 0 0
\(881\) 38.9419 1.31199 0.655993 0.754767i \(-0.272250\pi\)
0.655993 + 0.754767i \(0.272250\pi\)
\(882\) 0 0
\(883\) 37.2257 1.25274 0.626371 0.779525i \(-0.284539\pi\)
0.626371 + 0.779525i \(0.284539\pi\)
\(884\) 0 0
\(885\) −3.75462 −0.126210
\(886\) 0 0
\(887\) 7.85934 0.263891 0.131945 0.991257i \(-0.457878\pi\)
0.131945 + 0.991257i \(0.457878\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −11.2083 −0.375492
\(892\) 0 0
\(893\) 7.75340 0.259458
\(894\) 0 0
\(895\) 14.4130 0.481774
\(896\) 0 0
\(897\) 0.155465 0.00519081
\(898\) 0 0
\(899\) 31.0942 1.03705
\(900\) 0 0
\(901\) 16.3699 0.545360
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −86.1275 −2.86298
\(906\) 0 0
\(907\) 3.40729 0.113137 0.0565686 0.998399i \(-0.481984\pi\)
0.0565686 + 0.998399i \(0.481984\pi\)
\(908\) 0 0
\(909\) 48.3076 1.60226
\(910\) 0 0
\(911\) −40.5842 −1.34462 −0.672308 0.740272i \(-0.734697\pi\)
−0.672308 + 0.740272i \(0.734697\pi\)
\(912\) 0 0
\(913\) −7.56121 −0.250240
\(914\) 0 0
\(915\) −1.85820 −0.0614303
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −21.0834 −0.695477 −0.347738 0.937592i \(-0.613050\pi\)
−0.347738 + 0.937592i \(0.613050\pi\)
\(920\) 0 0
\(921\) 2.01196 0.0662962
\(922\) 0 0
\(923\) −2.23495 −0.0735642
\(924\) 0 0
\(925\) 15.0109 0.493556
\(926\) 0 0
\(927\) 0.634366 0.0208353
\(928\) 0 0
\(929\) −48.8096 −1.60139 −0.800696 0.599072i \(-0.795536\pi\)
−0.800696 + 0.599072i \(0.795536\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 3.14061 0.102819
\(934\) 0 0
\(935\) 27.1216 0.886972
\(936\) 0 0
\(937\) 3.91878 0.128021 0.0640104 0.997949i \(-0.479611\pi\)
0.0640104 + 0.997949i \(0.479611\pi\)
\(938\) 0 0
\(939\) 0.245062 0.00799728
\(940\) 0 0
\(941\) −51.6312 −1.68313 −0.841564 0.540157i \(-0.818365\pi\)
−0.841564 + 0.540157i \(0.818365\pi\)
\(942\) 0 0
\(943\) 8.98555 0.292610
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5.80509 0.188640 0.0943200 0.995542i \(-0.469932\pi\)
0.0943200 + 0.995542i \(0.469932\pi\)
\(948\) 0 0
\(949\) 2.76400 0.0897233
\(950\) 0 0
\(951\) −2.35840 −0.0764765
\(952\) 0 0
\(953\) −2.18025 −0.0706253 −0.0353126 0.999376i \(-0.511243\pi\)
−0.0353126 + 0.999376i \(0.511243\pi\)
\(954\) 0 0
\(955\) 62.6012 2.02573
\(956\) 0 0
\(957\) −0.419870 −0.0135725
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 62.5528 2.01783
\(962\) 0 0
\(963\) −34.7891 −1.12106
\(964\) 0 0
\(965\) −42.9394 −1.38227
\(966\) 0 0
\(967\) 28.1312 0.904638 0.452319 0.891856i \(-0.350597\pi\)
0.452319 + 0.891856i \(0.350597\pi\)
\(968\) 0 0
\(969\) 0.637253 0.0204715
\(970\) 0 0
\(971\) 4.15681 0.133398 0.0666991 0.997773i \(-0.478753\pi\)
0.0666991 + 0.997773i \(0.478753\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −0.152212 −0.00487470
\(976\) 0 0
\(977\) 2.34657 0.0750736 0.0375368 0.999295i \(-0.488049\pi\)
0.0375368 + 0.999295i \(0.488049\pi\)
\(978\) 0 0
\(979\) −13.9050 −0.444405
\(980\) 0 0
\(981\) 50.7846 1.62143
\(982\) 0 0
\(983\) 2.21649 0.0706950 0.0353475 0.999375i \(-0.488746\pi\)
0.0353475 + 0.999375i \(0.488746\pi\)
\(984\) 0 0
\(985\) −54.4272 −1.73419
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 34.4659 1.09595
\(990\) 0 0
\(991\) −43.7956 −1.39121 −0.695607 0.718422i \(-0.744865\pi\)
−0.695607 + 0.718422i \(0.744865\pi\)
\(992\) 0 0
\(993\) −0.516585 −0.0163933
\(994\) 0 0
\(995\) −42.1020 −1.33472
\(996\) 0 0
\(997\) 2.41535 0.0764951 0.0382475 0.999268i \(-0.487822\pi\)
0.0382475 + 0.999268i \(0.487822\pi\)
\(998\) 0 0
\(999\) 1.06020 0.0335433
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 \(a_p\))