Properties

Label 8036.2.a.p.1.8
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 10
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
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 1.8
Root \(2.58799\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.58799 q^{3} +3.78481 q^{5} +3.69770 q^{9} +O(q^{10})\) \(q+2.58799 q^{3} +3.78481 q^{5} +3.69770 q^{9} -3.59611 q^{11} +3.80530 q^{13} +9.79504 q^{15} +4.90120 q^{17} +0.726528 q^{19} +2.67934 q^{23} +9.32475 q^{25} +1.80564 q^{27} -1.31419 q^{29} +4.60193 q^{31} -9.30670 q^{33} +6.36856 q^{37} +9.84809 q^{39} +1.00000 q^{41} -6.79538 q^{43} +13.9951 q^{45} -9.58539 q^{47} +12.6843 q^{51} +3.00523 q^{53} -13.6106 q^{55} +1.88025 q^{57} +4.98541 q^{59} -2.28749 q^{61} +14.4023 q^{65} -5.58747 q^{67} +6.93410 q^{69} -1.69196 q^{71} +0.259201 q^{73} +24.1324 q^{75} +2.89788 q^{79} -6.42011 q^{81} -13.2415 q^{83} +18.5501 q^{85} -3.40110 q^{87} -17.3487 q^{89} +11.9098 q^{93} +2.74977 q^{95} +1.39398 q^{97} -13.2973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) 2.58799 1.49418 0.747089 0.664724i \(-0.231451\pi\)
0.747089 + 0.664724i \(0.231451\pi\)
\(4\) 0 0
\(5\) 3.78481 1.69262 0.846308 0.532694i \(-0.178820\pi\)
0.846308 + 0.532694i \(0.178820\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 3.69770 1.23257
\(10\) 0 0
\(11\) −3.59611 −1.08427 −0.542134 0.840292i \(-0.682383\pi\)
−0.542134 + 0.840292i \(0.682383\pi\)
\(12\) 0 0
\(13\) 3.80530 1.05540 0.527700 0.849431i \(-0.323054\pi\)
0.527700 + 0.849431i \(0.323054\pi\)
\(14\) 0 0
\(15\) 9.79504 2.52907
\(16\) 0 0
\(17\) 4.90120 1.18872 0.594358 0.804201i \(-0.297406\pi\)
0.594358 + 0.804201i \(0.297406\pi\)
\(18\) 0 0
\(19\) 0.726528 0.166677 0.0833384 0.996521i \(-0.473442\pi\)
0.0833384 + 0.996521i \(0.473442\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.67934 0.558681 0.279340 0.960192i \(-0.409884\pi\)
0.279340 + 0.960192i \(0.409884\pi\)
\(24\) 0 0
\(25\) 9.32475 1.86495
\(26\) 0 0
\(27\) 1.80564 0.347496
\(28\) 0 0
\(29\) −1.31419 −0.244038 −0.122019 0.992528i \(-0.538937\pi\)
−0.122019 + 0.992528i \(0.538937\pi\)
\(30\) 0 0
\(31\) 4.60193 0.826531 0.413266 0.910611i \(-0.364388\pi\)
0.413266 + 0.910611i \(0.364388\pi\)
\(32\) 0 0
\(33\) −9.30670 −1.62009
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.36856 1.04698 0.523492 0.852031i \(-0.324629\pi\)
0.523492 + 0.852031i \(0.324629\pi\)
\(38\) 0 0
\(39\) 9.84809 1.57696
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −6.79538 −1.03629 −0.518143 0.855294i \(-0.673376\pi\)
−0.518143 + 0.855294i \(0.673376\pi\)
\(44\) 0 0
\(45\) 13.9951 2.08626
\(46\) 0 0
\(47\) −9.58539 −1.39817 −0.699086 0.715037i \(-0.746410\pi\)
−0.699086 + 0.715037i \(0.746410\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 12.6843 1.77615
\(52\) 0 0
\(53\) 3.00523 0.412800 0.206400 0.978468i \(-0.433825\pi\)
0.206400 + 0.978468i \(0.433825\pi\)
\(54\) 0 0
\(55\) −13.6106 −1.83525
\(56\) 0 0
\(57\) 1.88025 0.249045
\(58\) 0 0
\(59\) 4.98541 0.649045 0.324522 0.945878i \(-0.394796\pi\)
0.324522 + 0.945878i \(0.394796\pi\)
\(60\) 0 0
\(61\) −2.28749 −0.292883 −0.146442 0.989219i \(-0.546782\pi\)
−0.146442 + 0.989219i \(0.546782\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 14.4023 1.78639
\(66\) 0 0
\(67\) −5.58747 −0.682618 −0.341309 0.939951i \(-0.610870\pi\)
−0.341309 + 0.939951i \(0.610870\pi\)
\(68\) 0 0
\(69\) 6.93410 0.834768
\(70\) 0 0
\(71\) −1.69196 −0.200799 −0.100400 0.994947i \(-0.532012\pi\)
−0.100400 + 0.994947i \(0.532012\pi\)
\(72\) 0 0
\(73\) 0.259201 0.0303371 0.0151686 0.999885i \(-0.495172\pi\)
0.0151686 + 0.999885i \(0.495172\pi\)
\(74\) 0 0
\(75\) 24.1324 2.78657
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.89788 0.326037 0.163019 0.986623i \(-0.447877\pi\)
0.163019 + 0.986623i \(0.447877\pi\)
\(80\) 0 0
\(81\) −6.42011 −0.713346
\(82\) 0 0
\(83\) −13.2415 −1.45344 −0.726722 0.686931i \(-0.758957\pi\)
−0.726722 + 0.686931i \(0.758957\pi\)
\(84\) 0 0
\(85\) 18.5501 2.01204
\(86\) 0 0
\(87\) −3.40110 −0.364636
\(88\) 0 0
\(89\) −17.3487 −1.83895 −0.919477 0.393143i \(-0.871388\pi\)
−0.919477 + 0.393143i \(0.871388\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 11.9098 1.23498
\(94\) 0 0
\(95\) 2.74977 0.282120
\(96\) 0 0
\(97\) 1.39398 0.141537 0.0707687 0.997493i \(-0.477455\pi\)
0.0707687 + 0.997493i \(0.477455\pi\)
\(98\) 0 0
\(99\) −13.2973 −1.33643
\(100\) 0 0
\(101\) −20.0334 −1.99340 −0.996699 0.0811850i \(-0.974130\pi\)
−0.996699 + 0.0811850i \(0.974130\pi\)
\(102\) 0 0
\(103\) 11.2645 1.10993 0.554963 0.831875i \(-0.312732\pi\)
0.554963 + 0.831875i \(0.312732\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.9772 −1.06121 −0.530605 0.847619i \(-0.678035\pi\)
−0.530605 + 0.847619i \(0.678035\pi\)
\(108\) 0 0
\(109\) −17.3625 −1.66302 −0.831511 0.555508i \(-0.812524\pi\)
−0.831511 + 0.555508i \(0.812524\pi\)
\(110\) 0 0
\(111\) 16.4818 1.56438
\(112\) 0 0
\(113\) 14.3203 1.34714 0.673569 0.739124i \(-0.264760\pi\)
0.673569 + 0.739124i \(0.264760\pi\)
\(114\) 0 0
\(115\) 10.1408 0.945632
\(116\) 0 0
\(117\) 14.0709 1.30085
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.93200 0.175636
\(122\) 0 0
\(123\) 2.58799 0.233351
\(124\) 0 0
\(125\) 16.3683 1.46403
\(126\) 0 0
\(127\) 12.8284 1.13834 0.569169 0.822221i \(-0.307265\pi\)
0.569169 + 0.822221i \(0.307265\pi\)
\(128\) 0 0
\(129\) −17.5864 −1.54839
\(130\) 0 0
\(131\) −16.7714 −1.46532 −0.732660 0.680594i \(-0.761722\pi\)
−0.732660 + 0.680594i \(0.761722\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 6.83401 0.588178
\(136\) 0 0
\(137\) 12.3762 1.05737 0.528684 0.848818i \(-0.322686\pi\)
0.528684 + 0.848818i \(0.322686\pi\)
\(138\) 0 0
\(139\) −15.5902 −1.32235 −0.661173 0.750233i \(-0.729941\pi\)
−0.661173 + 0.750233i \(0.729941\pi\)
\(140\) 0 0
\(141\) −24.8069 −2.08912
\(142\) 0 0
\(143\) −13.6843 −1.14434
\(144\) 0 0
\(145\) −4.97394 −0.413063
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 16.5452 1.35543 0.677717 0.735323i \(-0.262970\pi\)
0.677717 + 0.735323i \(0.262970\pi\)
\(150\) 0 0
\(151\) 4.20029 0.341815 0.170907 0.985287i \(-0.445330\pi\)
0.170907 + 0.985287i \(0.445330\pi\)
\(152\) 0 0
\(153\) 18.1232 1.46517
\(154\) 0 0
\(155\) 17.4174 1.39900
\(156\) 0 0
\(157\) 18.4113 1.46939 0.734693 0.678400i \(-0.237326\pi\)
0.734693 + 0.678400i \(0.237326\pi\)
\(158\) 0 0
\(159\) 7.77750 0.616796
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.747023 0.0585114 0.0292557 0.999572i \(-0.490686\pi\)
0.0292557 + 0.999572i \(0.490686\pi\)
\(164\) 0 0
\(165\) −35.2240 −2.74219
\(166\) 0 0
\(167\) 3.55850 0.275365 0.137683 0.990476i \(-0.456035\pi\)
0.137683 + 0.990476i \(0.456035\pi\)
\(168\) 0 0
\(169\) 1.48032 0.113871
\(170\) 0 0
\(171\) 2.68648 0.205440
\(172\) 0 0
\(173\) 12.3522 0.939122 0.469561 0.882900i \(-0.344412\pi\)
0.469561 + 0.882900i \(0.344412\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.9022 0.969788
\(178\) 0 0
\(179\) 19.1605 1.43212 0.716062 0.698037i \(-0.245943\pi\)
0.716062 + 0.698037i \(0.245943\pi\)
\(180\) 0 0
\(181\) 18.1901 1.35206 0.676031 0.736873i \(-0.263698\pi\)
0.676031 + 0.736873i \(0.263698\pi\)
\(182\) 0 0
\(183\) −5.92001 −0.437620
\(184\) 0 0
\(185\) 24.1037 1.77214
\(186\) 0 0
\(187\) −17.6252 −1.28889
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −10.5726 −0.765003 −0.382502 0.923955i \(-0.624937\pi\)
−0.382502 + 0.923955i \(0.624937\pi\)
\(192\) 0 0
\(193\) −6.02663 −0.433806 −0.216903 0.976193i \(-0.569596\pi\)
−0.216903 + 0.976193i \(0.569596\pi\)
\(194\) 0 0
\(195\) 37.2731 2.66918
\(196\) 0 0
\(197\) −8.15800 −0.581233 −0.290617 0.956840i \(-0.593860\pi\)
−0.290617 + 0.956840i \(0.593860\pi\)
\(198\) 0 0
\(199\) −11.2537 −0.797751 −0.398875 0.917005i \(-0.630599\pi\)
−0.398875 + 0.917005i \(0.630599\pi\)
\(200\) 0 0
\(201\) −14.4603 −1.01995
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.78481 0.264342
\(206\) 0 0
\(207\) 9.90739 0.688611
\(208\) 0 0
\(209\) −2.61267 −0.180722
\(210\) 0 0
\(211\) 11.5779 0.797055 0.398527 0.917156i \(-0.369521\pi\)
0.398527 + 0.917156i \(0.369521\pi\)
\(212\) 0 0
\(213\) −4.37879 −0.300030
\(214\) 0 0
\(215\) −25.7192 −1.75403
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0.670809 0.0453291
\(220\) 0 0
\(221\) 18.6505 1.25457
\(222\) 0 0
\(223\) −16.3491 −1.09482 −0.547410 0.836865i \(-0.684386\pi\)
−0.547410 + 0.836865i \(0.684386\pi\)
\(224\) 0 0
\(225\) 34.4801 2.29868
\(226\) 0 0
\(227\) 3.86697 0.256660 0.128330 0.991732i \(-0.459038\pi\)
0.128330 + 0.991732i \(0.459038\pi\)
\(228\) 0 0
\(229\) 26.6084 1.75833 0.879167 0.476514i \(-0.158100\pi\)
0.879167 + 0.476514i \(0.158100\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.62705 0.499665 0.249832 0.968289i \(-0.419624\pi\)
0.249832 + 0.968289i \(0.419624\pi\)
\(234\) 0 0
\(235\) −36.2788 −2.36657
\(236\) 0 0
\(237\) 7.49969 0.487157
\(238\) 0 0
\(239\) 28.2707 1.82868 0.914340 0.404948i \(-0.132710\pi\)
0.914340 + 0.404948i \(0.132710\pi\)
\(240\) 0 0
\(241\) 27.1444 1.74852 0.874261 0.485457i \(-0.161347\pi\)
0.874261 + 0.485457i \(0.161347\pi\)
\(242\) 0 0
\(243\) −22.0321 −1.41336
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.76466 0.175911
\(248\) 0 0
\(249\) −34.2689 −2.17170
\(250\) 0 0
\(251\) 15.8143 0.998188 0.499094 0.866548i \(-0.333666\pi\)
0.499094 + 0.866548i \(0.333666\pi\)
\(252\) 0 0
\(253\) −9.63519 −0.605759
\(254\) 0 0
\(255\) 48.0075 3.00634
\(256\) 0 0
\(257\) −26.8521 −1.67499 −0.837493 0.546448i \(-0.815980\pi\)
−0.837493 + 0.546448i \(0.815980\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −4.85947 −0.300793
\(262\) 0 0
\(263\) −6.32193 −0.389827 −0.194913 0.980820i \(-0.562443\pi\)
−0.194913 + 0.980820i \(0.562443\pi\)
\(264\) 0 0
\(265\) 11.3742 0.698711
\(266\) 0 0
\(267\) −44.8982 −2.74772
\(268\) 0 0
\(269\) 4.15268 0.253193 0.126597 0.991954i \(-0.459595\pi\)
0.126597 + 0.991954i \(0.459595\pi\)
\(270\) 0 0
\(271\) −3.95643 −0.240336 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −33.5328 −2.02211
\(276\) 0 0
\(277\) 2.26011 0.135797 0.0678985 0.997692i \(-0.478371\pi\)
0.0678985 + 0.997692i \(0.478371\pi\)
\(278\) 0 0
\(279\) 17.0166 1.01875
\(280\) 0 0
\(281\) 14.7417 0.879414 0.439707 0.898141i \(-0.355082\pi\)
0.439707 + 0.898141i \(0.355082\pi\)
\(282\) 0 0
\(283\) −0.419276 −0.0249234 −0.0124617 0.999922i \(-0.503967\pi\)
−0.0124617 + 0.999922i \(0.503967\pi\)
\(284\) 0 0
\(285\) 7.11637 0.421537
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 7.02174 0.413044
\(290\) 0 0
\(291\) 3.60761 0.211482
\(292\) 0 0
\(293\) 10.3460 0.604419 0.302209 0.953242i \(-0.402276\pi\)
0.302209 + 0.953242i \(0.402276\pi\)
\(294\) 0 0
\(295\) 18.8688 1.09858
\(296\) 0 0
\(297\) −6.49329 −0.376779
\(298\) 0 0
\(299\) 10.1957 0.589632
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −51.8463 −2.97849
\(304\) 0 0
\(305\) −8.65771 −0.495739
\(306\) 0 0
\(307\) 25.0647 1.43052 0.715259 0.698860i \(-0.246309\pi\)
0.715259 + 0.698860i \(0.246309\pi\)
\(308\) 0 0
\(309\) 29.1525 1.65843
\(310\) 0 0
\(311\) −1.52589 −0.0865253 −0.0432627 0.999064i \(-0.513775\pi\)
−0.0432627 + 0.999064i \(0.513775\pi\)
\(312\) 0 0
\(313\) −5.46504 −0.308902 −0.154451 0.988000i \(-0.549361\pi\)
−0.154451 + 0.988000i \(0.549361\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.45336 −0.474788 −0.237394 0.971413i \(-0.576293\pi\)
−0.237394 + 0.971413i \(0.576293\pi\)
\(318\) 0 0
\(319\) 4.72595 0.264603
\(320\) 0 0
\(321\) −28.4090 −1.58564
\(322\) 0 0
\(323\) 3.56086 0.198131
\(324\) 0 0
\(325\) 35.4835 1.96827
\(326\) 0 0
\(327\) −44.9339 −2.48485
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 17.7945 0.978075 0.489037 0.872263i \(-0.337348\pi\)
0.489037 + 0.872263i \(0.337348\pi\)
\(332\) 0 0
\(333\) 23.5490 1.29048
\(334\) 0 0
\(335\) −21.1475 −1.15541
\(336\) 0 0
\(337\) 6.12448 0.333622 0.166811 0.985989i \(-0.446653\pi\)
0.166811 + 0.985989i \(0.446653\pi\)
\(338\) 0 0
\(339\) 37.0608 2.01286
\(340\) 0 0
\(341\) −16.5490 −0.896181
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 26.2442 1.41294
\(346\) 0 0
\(347\) 24.2673 1.30273 0.651367 0.758762i \(-0.274196\pi\)
0.651367 + 0.758762i \(0.274196\pi\)
\(348\) 0 0
\(349\) 6.76708 0.362233 0.181117 0.983462i \(-0.442029\pi\)
0.181117 + 0.983462i \(0.442029\pi\)
\(350\) 0 0
\(351\) 6.87102 0.366748
\(352\) 0 0
\(353\) 10.4903 0.558343 0.279171 0.960241i \(-0.409940\pi\)
0.279171 + 0.960241i \(0.409940\pi\)
\(354\) 0 0
\(355\) −6.40375 −0.339876
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −36.6271 −1.93310 −0.966552 0.256469i \(-0.917441\pi\)
−0.966552 + 0.256469i \(0.917441\pi\)
\(360\) 0 0
\(361\) −18.4722 −0.972219
\(362\) 0 0
\(363\) 4.99999 0.262431
\(364\) 0 0
\(365\) 0.981024 0.0513491
\(366\) 0 0
\(367\) −9.14736 −0.477488 −0.238744 0.971083i \(-0.576736\pi\)
−0.238744 + 0.971083i \(0.576736\pi\)
\(368\) 0 0
\(369\) 3.69770 0.192495
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −11.8244 −0.612242 −0.306121 0.951993i \(-0.599031\pi\)
−0.306121 + 0.951993i \(0.599031\pi\)
\(374\) 0 0
\(375\) 42.3611 2.18752
\(376\) 0 0
\(377\) −5.00087 −0.257558
\(378\) 0 0
\(379\) −17.2821 −0.887720 −0.443860 0.896096i \(-0.646391\pi\)
−0.443860 + 0.896096i \(0.646391\pi\)
\(380\) 0 0
\(381\) 33.1998 1.70088
\(382\) 0 0
\(383\) −28.3230 −1.44724 −0.723619 0.690200i \(-0.757523\pi\)
−0.723619 + 0.690200i \(0.757523\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −25.1273 −1.27729
\(388\) 0 0
\(389\) −32.3079 −1.63807 −0.819037 0.573741i \(-0.805492\pi\)
−0.819037 + 0.573741i \(0.805492\pi\)
\(390\) 0 0
\(391\) 13.1320 0.664112
\(392\) 0 0
\(393\) −43.4041 −2.18945
\(394\) 0 0
\(395\) 10.9679 0.551856
\(396\) 0 0
\(397\) 22.4571 1.12709 0.563545 0.826085i \(-0.309437\pi\)
0.563545 + 0.826085i \(0.309437\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.0371 −0.950669 −0.475335 0.879805i \(-0.657673\pi\)
−0.475335 + 0.879805i \(0.657673\pi\)
\(402\) 0 0
\(403\) 17.5117 0.872322
\(404\) 0 0
\(405\) −24.2989 −1.20742
\(406\) 0 0
\(407\) −22.9020 −1.13521
\(408\) 0 0
\(409\) −17.7091 −0.875660 −0.437830 0.899058i \(-0.644253\pi\)
−0.437830 + 0.899058i \(0.644253\pi\)
\(410\) 0 0
\(411\) 32.0295 1.57990
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −50.1165 −2.46012
\(416\) 0 0
\(417\) −40.3474 −1.97582
\(418\) 0 0
\(419\) −5.55936 −0.271593 −0.135796 0.990737i \(-0.543359\pi\)
−0.135796 + 0.990737i \(0.543359\pi\)
\(420\) 0 0
\(421\) 24.8300 1.21014 0.605071 0.796172i \(-0.293145\pi\)
0.605071 + 0.796172i \(0.293145\pi\)
\(422\) 0 0
\(423\) −35.4439 −1.72334
\(424\) 0 0
\(425\) 45.7025 2.21689
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −35.4148 −1.70984
\(430\) 0 0
\(431\) −16.6624 −0.802598 −0.401299 0.915947i \(-0.631441\pi\)
−0.401299 + 0.915947i \(0.631441\pi\)
\(432\) 0 0
\(433\) −27.0719 −1.30099 −0.650496 0.759510i \(-0.725439\pi\)
−0.650496 + 0.759510i \(0.725439\pi\)
\(434\) 0 0
\(435\) −12.8725 −0.617190
\(436\) 0 0
\(437\) 1.94661 0.0931191
\(438\) 0 0
\(439\) −9.77885 −0.466719 −0.233360 0.972391i \(-0.574972\pi\)
−0.233360 + 0.972391i \(0.574972\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −33.3426 −1.58416 −0.792078 0.610420i \(-0.791001\pi\)
−0.792078 + 0.610420i \(0.791001\pi\)
\(444\) 0 0
\(445\) −65.6613 −3.11264
\(446\) 0 0
\(447\) 42.8188 2.02526
\(448\) 0 0
\(449\) −19.5152 −0.920981 −0.460490 0.887665i \(-0.652326\pi\)
−0.460490 + 0.887665i \(0.652326\pi\)
\(450\) 0 0
\(451\) −3.59611 −0.169334
\(452\) 0 0
\(453\) 10.8703 0.510732
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0689 −0.471001 −0.235500 0.971874i \(-0.575673\pi\)
−0.235500 + 0.971874i \(0.575673\pi\)
\(458\) 0 0
\(459\) 8.84981 0.413074
\(460\) 0 0
\(461\) −10.8841 −0.506923 −0.253462 0.967345i \(-0.581569\pi\)
−0.253462 + 0.967345i \(0.581569\pi\)
\(462\) 0 0
\(463\) −7.76854 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(464\) 0 0
\(465\) 45.0761 2.09035
\(466\) 0 0
\(467\) −3.61280 −0.167180 −0.0835902 0.996500i \(-0.526639\pi\)
−0.0835902 + 0.996500i \(0.526639\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 47.6484 2.19552
\(472\) 0 0
\(473\) 24.4369 1.12361
\(474\) 0 0
\(475\) 6.77469 0.310844
\(476\) 0 0
\(477\) 11.1124 0.508803
\(478\) 0 0
\(479\) 26.6680 1.21849 0.609247 0.792981i \(-0.291472\pi\)
0.609247 + 0.792981i \(0.291472\pi\)
\(480\) 0 0
\(481\) 24.2343 1.10499
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.27595 0.239568
\(486\) 0 0
\(487\) 13.5887 0.615763 0.307882 0.951425i \(-0.400380\pi\)
0.307882 + 0.951425i \(0.400380\pi\)
\(488\) 0 0
\(489\) 1.93329 0.0874264
\(490\) 0 0
\(491\) −25.9300 −1.17021 −0.585103 0.810959i \(-0.698946\pi\)
−0.585103 + 0.810959i \(0.698946\pi\)
\(492\) 0 0
\(493\) −6.44108 −0.290092
\(494\) 0 0
\(495\) −50.3278 −2.26207
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 10.5967 0.474371 0.237186 0.971464i \(-0.423775\pi\)
0.237186 + 0.971464i \(0.423775\pi\)
\(500\) 0 0
\(501\) 9.20938 0.411445
\(502\) 0 0
\(503\) −1.10153 −0.0491148 −0.0245574 0.999698i \(-0.507818\pi\)
−0.0245574 + 0.999698i \(0.507818\pi\)
\(504\) 0 0
\(505\) −75.8225 −3.37406
\(506\) 0 0
\(507\) 3.83107 0.170144
\(508\) 0 0
\(509\) 11.6687 0.517208 0.258604 0.965983i \(-0.416738\pi\)
0.258604 + 0.965983i \(0.416738\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1.31185 0.0579196
\(514\) 0 0
\(515\) 42.6340 1.87868
\(516\) 0 0
\(517\) 34.4701 1.51599
\(518\) 0 0
\(519\) 31.9674 1.40322
\(520\) 0 0
\(521\) 3.47208 0.152115 0.0760573 0.997103i \(-0.475767\pi\)
0.0760573 + 0.997103i \(0.475767\pi\)
\(522\) 0 0
\(523\) −18.1404 −0.793223 −0.396611 0.917987i \(-0.629814\pi\)
−0.396611 + 0.917987i \(0.629814\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 22.5550 0.982510
\(528\) 0 0
\(529\) −15.8211 −0.687876
\(530\) 0 0
\(531\) 18.4345 0.799991
\(532\) 0 0
\(533\) 3.80530 0.164826
\(534\) 0 0
\(535\) −41.5467 −1.79622
\(536\) 0 0
\(537\) 49.5872 2.13985
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −31.7015 −1.36295 −0.681477 0.731840i \(-0.738662\pi\)
−0.681477 + 0.731840i \(0.738662\pi\)
\(542\) 0 0
\(543\) 47.0759 2.02022
\(544\) 0 0
\(545\) −65.7135 −2.81486
\(546\) 0 0
\(547\) 14.3885 0.615207 0.307603 0.951515i \(-0.400473\pi\)
0.307603 + 0.951515i \(0.400473\pi\)
\(548\) 0 0
\(549\) −8.45846 −0.360998
\(550\) 0 0
\(551\) −0.954792 −0.0406755
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 62.3803 2.64790
\(556\) 0 0
\(557\) 2.52585 0.107024 0.0535118 0.998567i \(-0.482959\pi\)
0.0535118 + 0.998567i \(0.482959\pi\)
\(558\) 0 0
\(559\) −25.8585 −1.09370
\(560\) 0 0
\(561\) −45.6140 −1.92582
\(562\) 0 0
\(563\) −10.6852 −0.450325 −0.225163 0.974321i \(-0.572291\pi\)
−0.225163 + 0.974321i \(0.572291\pi\)
\(564\) 0 0
\(565\) 54.1995 2.28019
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −19.0959 −0.800541 −0.400271 0.916397i \(-0.631084\pi\)
−0.400271 + 0.916397i \(0.631084\pi\)
\(570\) 0 0
\(571\) −38.3286 −1.60400 −0.802001 0.597323i \(-0.796231\pi\)
−0.802001 + 0.597323i \(0.796231\pi\)
\(572\) 0 0
\(573\) −27.3617 −1.14305
\(574\) 0 0
\(575\) 24.9842 1.04191
\(576\) 0 0
\(577\) −26.9868 −1.12347 −0.561737 0.827316i \(-0.689867\pi\)
−0.561737 + 0.827316i \(0.689867\pi\)
\(578\) 0 0
\(579\) −15.5969 −0.648184
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −10.8071 −0.447585
\(584\) 0 0
\(585\) 53.2555 2.20184
\(586\) 0 0
\(587\) 29.5370 1.21912 0.609560 0.792740i \(-0.291346\pi\)
0.609560 + 0.792740i \(0.291346\pi\)
\(588\) 0 0
\(589\) 3.34343 0.137764
\(590\) 0 0
\(591\) −21.1128 −0.868466
\(592\) 0 0
\(593\) −28.4935 −1.17009 −0.585044 0.811002i \(-0.698923\pi\)
−0.585044 + 0.811002i \(0.698923\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −29.1244 −1.19198
\(598\) 0 0
\(599\) 34.9502 1.42803 0.714014 0.700132i \(-0.246875\pi\)
0.714014 + 0.700132i \(0.246875\pi\)
\(600\) 0 0
\(601\) 15.2328 0.621360 0.310680 0.950515i \(-0.399443\pi\)
0.310680 + 0.950515i \(0.399443\pi\)
\(602\) 0 0
\(603\) −20.6608 −0.841372
\(604\) 0 0
\(605\) 7.31223 0.297284
\(606\) 0 0
\(607\) 15.9275 0.646476 0.323238 0.946318i \(-0.395228\pi\)
0.323238 + 0.946318i \(0.395228\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −36.4753 −1.47563
\(612\) 0 0
\(613\) 12.2603 0.495189 0.247594 0.968864i \(-0.420360\pi\)
0.247594 + 0.968864i \(0.420360\pi\)
\(614\) 0 0
\(615\) 9.79504 0.394974
\(616\) 0 0
\(617\) −35.8405 −1.44288 −0.721441 0.692475i \(-0.756520\pi\)
−0.721441 + 0.692475i \(0.756520\pi\)
\(618\) 0 0
\(619\) 2.41570 0.0970953 0.0485476 0.998821i \(-0.484541\pi\)
0.0485476 + 0.998821i \(0.484541\pi\)
\(620\) 0 0
\(621\) 4.83793 0.194139
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15.3272 0.613090
\(626\) 0 0
\(627\) −6.76157 −0.270031
\(628\) 0 0
\(629\) 31.2136 1.24457
\(630\) 0 0
\(631\) −30.1822 −1.20154 −0.600768 0.799423i \(-0.705138\pi\)
−0.600768 + 0.799423i \(0.705138\pi\)
\(632\) 0 0
\(633\) 29.9635 1.19094
\(634\) 0 0
\(635\) 48.5531 1.92677
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −6.25638 −0.247498
\(640\) 0 0
\(641\) −16.9868 −0.670938 −0.335469 0.942051i \(-0.608895\pi\)
−0.335469 + 0.942051i \(0.608895\pi\)
\(642\) 0 0
\(643\) −0.216985 −0.00855705 −0.00427853 0.999991i \(-0.501362\pi\)
−0.00427853 + 0.999991i \(0.501362\pi\)
\(644\) 0 0
\(645\) −66.5610 −2.62084
\(646\) 0 0
\(647\) 19.3789 0.761863 0.380931 0.924603i \(-0.375603\pi\)
0.380931 + 0.924603i \(0.375603\pi\)
\(648\) 0 0
\(649\) −17.9281 −0.703738
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 42.7962 1.67475 0.837373 0.546632i \(-0.184090\pi\)
0.837373 + 0.546632i \(0.184090\pi\)
\(654\) 0 0
\(655\) −63.4763 −2.48023
\(656\) 0 0
\(657\) 0.958446 0.0373925
\(658\) 0 0
\(659\) 9.67207 0.376770 0.188385 0.982095i \(-0.439675\pi\)
0.188385 + 0.982095i \(0.439675\pi\)
\(660\) 0 0
\(661\) 5.74266 0.223363 0.111682 0.993744i \(-0.464376\pi\)
0.111682 + 0.993744i \(0.464376\pi\)
\(662\) 0 0
\(663\) 48.2674 1.87455
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3.52115 −0.136339
\(668\) 0 0
\(669\) −42.3115 −1.63586
\(670\) 0 0
\(671\) 8.22607 0.317564
\(672\) 0 0
\(673\) −9.67554 −0.372965 −0.186482 0.982458i \(-0.559709\pi\)
−0.186482 + 0.982458i \(0.559709\pi\)
\(674\) 0 0
\(675\) 16.8372 0.648063
\(676\) 0 0
\(677\) −20.8582 −0.801646 −0.400823 0.916155i \(-0.631276\pi\)
−0.400823 + 0.916155i \(0.631276\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 10.0077 0.383495
\(682\) 0 0
\(683\) 30.5389 1.16854 0.584270 0.811560i \(-0.301381\pi\)
0.584270 + 0.811560i \(0.301381\pi\)
\(684\) 0 0
\(685\) 46.8414 1.78972
\(686\) 0 0
\(687\) 68.8624 2.62726
\(688\) 0 0
\(689\) 11.4358 0.435669
\(690\) 0 0
\(691\) −46.9732 −1.78694 −0.893472 0.449119i \(-0.851738\pi\)
−0.893472 + 0.449119i \(0.851738\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −59.0060 −2.23823
\(696\) 0 0
\(697\) 4.90120 0.185646
\(698\) 0 0
\(699\) 19.7388 0.746588
\(700\) 0 0
\(701\) 32.8159 1.23944 0.619719 0.784824i \(-0.287247\pi\)
0.619719 + 0.784824i \(0.287247\pi\)
\(702\) 0 0
\(703\) 4.62693 0.174508
\(704\) 0 0
\(705\) −93.8893 −3.53608
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −16.6674 −0.625957 −0.312979 0.949760i \(-0.601327\pi\)
−0.312979 + 0.949760i \(0.601327\pi\)
\(710\) 0 0
\(711\) 10.7155 0.401862
\(712\) 0 0
\(713\) 12.3301 0.461767
\(714\) 0 0
\(715\) −51.7923 −1.93692
\(716\) 0 0
\(717\) 73.1643 2.73237
\(718\) 0 0
\(719\) −5.33891 −0.199108 −0.0995538 0.995032i \(-0.531742\pi\)
−0.0995538 + 0.995032i \(0.531742\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 70.2493 2.61260
\(724\) 0 0
\(725\) −12.2545 −0.455119
\(726\) 0 0
\(727\) −16.2839 −0.603938 −0.301969 0.953318i \(-0.597644\pi\)
−0.301969 + 0.953318i \(0.597644\pi\)
\(728\) 0 0
\(729\) −37.7586 −1.39847
\(730\) 0 0
\(731\) −33.3055 −1.23185
\(732\) 0 0
\(733\) −35.7554 −1.32066 −0.660328 0.750978i \(-0.729583\pi\)
−0.660328 + 0.750978i \(0.729583\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 20.0931 0.740140
\(738\) 0 0
\(739\) 13.2364 0.486910 0.243455 0.969912i \(-0.421719\pi\)
0.243455 + 0.969912i \(0.421719\pi\)
\(740\) 0 0
\(741\) 7.15491 0.262842
\(742\) 0 0
\(743\) 39.0119 1.43121 0.715604 0.698506i \(-0.246151\pi\)
0.715604 + 0.698506i \(0.246151\pi\)
\(744\) 0 0
\(745\) 62.6203 2.29423
\(746\) 0 0
\(747\) −48.9631 −1.79147
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 18.0871 0.660008 0.330004 0.943980i \(-0.392950\pi\)
0.330004 + 0.943980i \(0.392950\pi\)
\(752\) 0 0
\(753\) 40.9272 1.49147
\(754\) 0 0
\(755\) 15.8973 0.578561
\(756\) 0 0
\(757\) −3.57240 −0.129841 −0.0649205 0.997890i \(-0.520679\pi\)
−0.0649205 + 0.997890i \(0.520679\pi\)
\(758\) 0 0
\(759\) −24.9358 −0.905112
\(760\) 0 0
\(761\) 8.71186 0.315804 0.157902 0.987455i \(-0.449527\pi\)
0.157902 + 0.987455i \(0.449527\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 68.5926 2.47997
\(766\) 0 0
\(767\) 18.9710 0.685002
\(768\) 0 0
\(769\) 4.38267 0.158043 0.0790216 0.996873i \(-0.474820\pi\)
0.0790216 + 0.996873i \(0.474820\pi\)
\(770\) 0 0
\(771\) −69.4930 −2.50273
\(772\) 0 0
\(773\) 32.7723 1.17874 0.589370 0.807863i \(-0.299376\pi\)
0.589370 + 0.807863i \(0.299376\pi\)
\(774\) 0 0
\(775\) 42.9119 1.54144
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.726528 0.0260306
\(780\) 0 0
\(781\) 6.08449 0.217720
\(782\) 0 0
\(783\) −2.37295 −0.0848023
\(784\) 0 0
\(785\) 69.6834 2.48711
\(786\) 0 0
\(787\) −35.7887 −1.27573 −0.637865 0.770148i \(-0.720182\pi\)
−0.637865 + 0.770148i \(0.720182\pi\)
\(788\) 0 0
\(789\) −16.3611 −0.582470
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −8.70460 −0.309109
\(794\) 0 0
\(795\) 29.4363 1.04400
\(796\) 0 0
\(797\) 46.6956 1.65404 0.827022 0.562170i \(-0.190033\pi\)
0.827022 + 0.562170i \(0.190033\pi\)
\(798\) 0 0
\(799\) −46.9799 −1.66203
\(800\) 0 0
\(801\) −64.1501 −2.26663
\(802\) 0 0
\(803\) −0.932113 −0.0328936
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 10.7471 0.378315
\(808\) 0 0
\(809\) −52.6645 −1.85159 −0.925793 0.378030i \(-0.876602\pi\)
−0.925793 + 0.378030i \(0.876602\pi\)
\(810\) 0 0
\(811\) 51.2790 1.80065 0.900324 0.435220i \(-0.143329\pi\)
0.900324 + 0.435220i \(0.143329\pi\)
\(812\) 0 0
\(813\) −10.2392 −0.359105
\(814\) 0 0
\(815\) 2.82734 0.0990373
\(816\) 0 0
\(817\) −4.93703 −0.172725
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15.6346 −0.545651 −0.272825 0.962064i \(-0.587958\pi\)
−0.272825 + 0.962064i \(0.587958\pi\)
\(822\) 0 0
\(823\) 41.5894 1.44972 0.724858 0.688898i \(-0.241905\pi\)
0.724858 + 0.688898i \(0.241905\pi\)
\(824\) 0 0
\(825\) −86.7827 −3.02138
\(826\) 0 0
\(827\) 20.1201 0.699645 0.349823 0.936816i \(-0.386242\pi\)
0.349823 + 0.936816i \(0.386242\pi\)
\(828\) 0 0
\(829\) −54.9561 −1.90870 −0.954352 0.298684i \(-0.903452\pi\)
−0.954352 + 0.298684i \(0.903452\pi\)
\(830\) 0 0
\(831\) 5.84916 0.202905
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 13.4682 0.466088
\(836\) 0 0
\(837\) 8.30944 0.287216
\(838\) 0 0
\(839\) −32.4924 −1.12176 −0.560881 0.827896i \(-0.689537\pi\)
−0.560881 + 0.827896i \(0.689537\pi\)
\(840\) 0 0
\(841\) −27.2729 −0.940445
\(842\) 0 0
\(843\) 38.1513 1.31400
\(844\) 0 0
\(845\) 5.60274 0.192740
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −1.08508 −0.0372400
\(850\) 0 0
\(851\) 17.0635 0.584930
\(852\) 0 0
\(853\) −20.7697 −0.711140 −0.355570 0.934650i \(-0.615713\pi\)
−0.355570 + 0.934650i \(0.615713\pi\)
\(854\) 0 0
\(855\) 10.1678 0.347732
\(856\) 0 0
\(857\) −40.2776 −1.37586 −0.687928 0.725779i \(-0.741479\pi\)
−0.687928 + 0.725779i \(0.741479\pi\)
\(858\) 0 0
\(859\) −48.9883 −1.67146 −0.835730 0.549141i \(-0.814955\pi\)
−0.835730 + 0.549141i \(0.814955\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −27.1659 −0.924739 −0.462370 0.886687i \(-0.653001\pi\)
−0.462370 + 0.886687i \(0.653001\pi\)
\(864\) 0 0
\(865\) 46.7508 1.58957
\(866\) 0 0
\(867\) 18.1722 0.617160
\(868\) 0 0
\(869\) −10.4211 −0.353511
\(870\) 0 0
\(871\) −21.2620 −0.720436
\(872\) 0 0
\(873\) 5.15453 0.174454
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −40.8059 −1.37792 −0.688959 0.724800i \(-0.741932\pi\)
−0.688959 + 0.724800i \(0.741932\pi\)
\(878\) 0 0
\(879\) 26.7753 0.903109
\(880\) 0 0
\(881\) 47.3129 1.59401 0.797005 0.603972i \(-0.206416\pi\)
0.797005 + 0.603972i \(0.206416\pi\)
\(882\) 0 0
\(883\) 38.7892 1.30536 0.652680 0.757633i \(-0.273644\pi\)
0.652680 + 0.757633i \(0.273644\pi\)
\(884\) 0 0
\(885\) 48.8323 1.64148
\(886\) 0 0
\(887\) −2.43098 −0.0816243 −0.0408122 0.999167i \(-0.512995\pi\)
−0.0408122 + 0.999167i \(0.512995\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 23.0874 0.773458
\(892\) 0 0
\(893\) −6.96405 −0.233043
\(894\) 0 0
\(895\) 72.5188 2.42404
\(896\) 0 0
\(897\) 26.3864 0.881015
\(898\) 0 0
\(899\) −6.04779 −0.201705
\(900\) 0 0
\(901\) 14.7292 0.490701
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 68.8462 2.28852
\(906\) 0 0
\(907\) 45.0206 1.49488 0.747442 0.664327i \(-0.231282\pi\)
0.747442 + 0.664327i \(0.231282\pi\)
\(908\) 0 0
\(909\) −74.0775 −2.45700
\(910\) 0 0
\(911\) 45.0034 1.49103 0.745515 0.666489i \(-0.232204\pi\)
0.745515 + 0.666489i \(0.232204\pi\)
\(912\) 0 0
\(913\) 47.6179 1.57592
\(914\) 0 0
\(915\) −22.4061 −0.740722
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −44.8526 −1.47955 −0.739775 0.672854i \(-0.765068\pi\)
−0.739775 + 0.672854i \(0.765068\pi\)
\(920\) 0 0
\(921\) 64.8672 2.13745
\(922\) 0 0
\(923\) −6.43843 −0.211924
\(924\) 0 0
\(925\) 59.3852 1.95257
\(926\) 0 0
\(927\) 41.6528 1.36806
\(928\) 0 0
\(929\) 31.8648 1.04545 0.522724 0.852502i \(-0.324916\pi\)
0.522724 + 0.852502i \(0.324916\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −3.94899 −0.129284
\(934\) 0 0
\(935\) −66.7081 −2.18159
\(936\) 0 0
\(937\) 26.1454 0.854134 0.427067 0.904220i \(-0.359547\pi\)
0.427067 + 0.904220i \(0.359547\pi\)
\(938\) 0 0
\(939\) −14.1435 −0.461555
\(940\) 0 0
\(941\) −49.8800 −1.62604 −0.813021 0.582234i \(-0.802179\pi\)
−0.813021 + 0.582234i \(0.802179\pi\)
\(942\) 0 0
\(943\) 2.67934 0.0872512
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −20.0360 −0.651081 −0.325541 0.945528i \(-0.605546\pi\)
−0.325541 + 0.945528i \(0.605546\pi\)
\(948\) 0 0
\(949\) 0.986336 0.0320178
\(950\) 0 0
\(951\) −21.8772 −0.709418
\(952\) 0 0
\(953\) 48.9363 1.58520 0.792601 0.609741i \(-0.208726\pi\)
0.792601 + 0.609741i \(0.208726\pi\)
\(954\) 0 0
\(955\) −40.0151 −1.29486
\(956\) 0 0
\(957\) 12.2307 0.395363
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −9.82223 −0.316846
\(962\) 0 0
\(963\) −40.5906 −1.30801
\(964\) 0 0
\(965\) −22.8096 −0.734268
\(966\) 0 0
\(967\) −1.69266 −0.0544324 −0.0272162 0.999630i \(-0.508664\pi\)
−0.0272162 + 0.999630i \(0.508664\pi\)
\(968\) 0 0
\(969\) 9.21547 0.296043
\(970\) 0 0
\(971\) 26.8308 0.861042 0.430521 0.902580i \(-0.358330\pi\)
0.430521 + 0.902580i \(0.358330\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 91.8310 2.94095
\(976\) 0 0
\(977\) 54.1829 1.73347 0.866733 0.498772i \(-0.166216\pi\)
0.866733 + 0.498772i \(0.166216\pi\)
\(978\) 0 0
\(979\) 62.3877 1.99392
\(980\) 0 0
\(981\) −64.2012 −2.04979
\(982\) 0 0
\(983\) −48.8385 −1.55771 −0.778853 0.627207i \(-0.784198\pi\)
−0.778853 + 0.627207i \(0.784198\pi\)
\(984\) 0 0
\(985\) −30.8764 −0.983805
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −18.2071 −0.578953
\(990\) 0 0
\(991\) 31.6007 1.00383 0.501914 0.864917i \(-0.332629\pi\)
0.501914 + 0.864917i \(0.332629\pi\)
\(992\) 0 0
\(993\) 46.0520 1.46142
\(994\) 0 0
\(995\) −42.5929 −1.35029
\(996\) 0 0
\(997\) −21.2713 −0.673668 −0.336834 0.941564i \(-0.609356\pi\)
−0.336834 + 0.941564i \(0.609356\pi\)
\(998\) 0 0
\(999\) 11.4993 0.363823
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 \(a_p\))