Properties

Label 6004.2.a.g.1.4
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.67388 q^{3} +3.55353 q^{5} +1.65788 q^{7} +4.14966 q^{9} +O(q^{10})\) \(q-2.67388 q^{3} +3.55353 q^{5} +1.65788 q^{7} +4.14966 q^{9} +1.12044 q^{11} -2.27561 q^{13} -9.50172 q^{15} -3.07611 q^{17} +1.00000 q^{19} -4.43298 q^{21} +4.46777 q^{23} +7.62755 q^{25} -3.07406 q^{27} -3.82490 q^{29} -4.45375 q^{31} -2.99592 q^{33} +5.89132 q^{35} -11.5926 q^{37} +6.08472 q^{39} -9.46040 q^{41} +4.63326 q^{43} +14.7459 q^{45} -2.15431 q^{47} -4.25144 q^{49} +8.22516 q^{51} -7.35612 q^{53} +3.98150 q^{55} -2.67388 q^{57} -3.21366 q^{59} +11.6415 q^{61} +6.87964 q^{63} -8.08644 q^{65} -13.1658 q^{67} -11.9463 q^{69} -12.2547 q^{71} -13.5211 q^{73} -20.3952 q^{75} +1.85755 q^{77} -1.00000 q^{79} -4.22930 q^{81} -10.9635 q^{83} -10.9310 q^{85} +10.2273 q^{87} -4.05620 q^{89} -3.77269 q^{91} +11.9088 q^{93} +3.55353 q^{95} +16.8881 q^{97} +4.64943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) −2.67388 −1.54377 −0.771884 0.635763i \(-0.780685\pi\)
−0.771884 + 0.635763i \(0.780685\pi\)
\(4\) 0 0
\(5\) 3.55353 1.58919 0.794593 0.607143i \(-0.207684\pi\)
0.794593 + 0.607143i \(0.207684\pi\)
\(6\) 0 0
\(7\) 1.65788 0.626619 0.313310 0.949651i \(-0.398562\pi\)
0.313310 + 0.949651i \(0.398562\pi\)
\(8\) 0 0
\(9\) 4.14966 1.38322
\(10\) 0 0
\(11\) 1.12044 0.337824 0.168912 0.985631i \(-0.445975\pi\)
0.168912 + 0.985631i \(0.445975\pi\)
\(12\) 0 0
\(13\) −2.27561 −0.631141 −0.315570 0.948902i \(-0.602196\pi\)
−0.315570 + 0.948902i \(0.602196\pi\)
\(14\) 0 0
\(15\) −9.50172 −2.45333
\(16\) 0 0
\(17\) −3.07611 −0.746066 −0.373033 0.927818i \(-0.621682\pi\)
−0.373033 + 0.927818i \(0.621682\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −4.43298 −0.967355
\(22\) 0 0
\(23\) 4.46777 0.931593 0.465797 0.884892i \(-0.345768\pi\)
0.465797 + 0.884892i \(0.345768\pi\)
\(24\) 0 0
\(25\) 7.62755 1.52551
\(26\) 0 0
\(27\) −3.07406 −0.591603
\(28\) 0 0
\(29\) −3.82490 −0.710266 −0.355133 0.934816i \(-0.615564\pi\)
−0.355133 + 0.934816i \(0.615564\pi\)
\(30\) 0 0
\(31\) −4.45375 −0.799917 −0.399958 0.916533i \(-0.630975\pi\)
−0.399958 + 0.916533i \(0.630975\pi\)
\(32\) 0 0
\(33\) −2.99592 −0.521523
\(34\) 0 0
\(35\) 5.89132 0.995815
\(36\) 0 0
\(37\) −11.5926 −1.90581 −0.952907 0.303264i \(-0.901924\pi\)
−0.952907 + 0.303264i \(0.901924\pi\)
\(38\) 0 0
\(39\) 6.08472 0.974335
\(40\) 0 0
\(41\) −9.46040 −1.47747 −0.738733 0.673998i \(-0.764576\pi\)
−0.738733 + 0.673998i \(0.764576\pi\)
\(42\) 0 0
\(43\) 4.63326 0.706566 0.353283 0.935516i \(-0.385065\pi\)
0.353283 + 0.935516i \(0.385065\pi\)
\(44\) 0 0
\(45\) 14.7459 2.19819
\(46\) 0 0
\(47\) −2.15431 −0.314238 −0.157119 0.987580i \(-0.550221\pi\)
−0.157119 + 0.987580i \(0.550221\pi\)
\(48\) 0 0
\(49\) −4.25144 −0.607348
\(50\) 0 0
\(51\) 8.22516 1.15175
\(52\) 0 0
\(53\) −7.35612 −1.01044 −0.505220 0.862990i \(-0.668589\pi\)
−0.505220 + 0.862990i \(0.668589\pi\)
\(54\) 0 0
\(55\) 3.98150 0.536866
\(56\) 0 0
\(57\) −2.67388 −0.354165
\(58\) 0 0
\(59\) −3.21366 −0.418383 −0.209192 0.977875i \(-0.567083\pi\)
−0.209192 + 0.977875i \(0.567083\pi\)
\(60\) 0 0
\(61\) 11.6415 1.49054 0.745269 0.666764i \(-0.232321\pi\)
0.745269 + 0.666764i \(0.232321\pi\)
\(62\) 0 0
\(63\) 6.87964 0.866753
\(64\) 0 0
\(65\) −8.08644 −1.00300
\(66\) 0 0
\(67\) −13.1658 −1.60846 −0.804228 0.594321i \(-0.797421\pi\)
−0.804228 + 0.594321i \(0.797421\pi\)
\(68\) 0 0
\(69\) −11.9463 −1.43816
\(70\) 0 0
\(71\) −12.2547 −1.45437 −0.727184 0.686443i \(-0.759171\pi\)
−0.727184 + 0.686443i \(0.759171\pi\)
\(72\) 0 0
\(73\) −13.5211 −1.58253 −0.791263 0.611476i \(-0.790576\pi\)
−0.791263 + 0.611476i \(0.790576\pi\)
\(74\) 0 0
\(75\) −20.3952 −2.35503
\(76\) 0 0
\(77\) 1.85755 0.211687
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −4.22930 −0.469922
\(82\) 0 0
\(83\) −10.9635 −1.20340 −0.601701 0.798721i \(-0.705510\pi\)
−0.601701 + 0.798721i \(0.705510\pi\)
\(84\) 0 0
\(85\) −10.9310 −1.18564
\(86\) 0 0
\(87\) 10.2273 1.09649
\(88\) 0 0
\(89\) −4.05620 −0.429956 −0.214978 0.976619i \(-0.568968\pi\)
−0.214978 + 0.976619i \(0.568968\pi\)
\(90\) 0 0
\(91\) −3.77269 −0.395485
\(92\) 0 0
\(93\) 11.9088 1.23489
\(94\) 0 0
\(95\) 3.55353 0.364584
\(96\) 0 0
\(97\) 16.8881 1.71473 0.857365 0.514709i \(-0.172100\pi\)
0.857365 + 0.514709i \(0.172100\pi\)
\(98\) 0 0
\(99\) 4.64943 0.467285
\(100\) 0 0
\(101\) −13.0169 −1.29523 −0.647616 0.761967i \(-0.724234\pi\)
−0.647616 + 0.761967i \(0.724234\pi\)
\(102\) 0 0
\(103\) 6.86859 0.676783 0.338391 0.941005i \(-0.390117\pi\)
0.338391 + 0.941005i \(0.390117\pi\)
\(104\) 0 0
\(105\) −15.7527 −1.53731
\(106\) 0 0
\(107\) 15.7660 1.52416 0.762079 0.647484i \(-0.224179\pi\)
0.762079 + 0.647484i \(0.224179\pi\)
\(108\) 0 0
\(109\) 0.491186 0.0470471 0.0235236 0.999723i \(-0.492512\pi\)
0.0235236 + 0.999723i \(0.492512\pi\)
\(110\) 0 0
\(111\) 30.9973 2.94213
\(112\) 0 0
\(113\) 16.2508 1.52874 0.764371 0.644776i \(-0.223050\pi\)
0.764371 + 0.644776i \(0.223050\pi\)
\(114\) 0 0
\(115\) 15.8763 1.48047
\(116\) 0 0
\(117\) −9.44301 −0.873007
\(118\) 0 0
\(119\) −5.09981 −0.467499
\(120\) 0 0
\(121\) −9.74462 −0.885875
\(122\) 0 0
\(123\) 25.2960 2.28087
\(124\) 0 0
\(125\) 9.33707 0.835133
\(126\) 0 0
\(127\) −11.2558 −0.998795 −0.499397 0.866373i \(-0.666445\pi\)
−0.499397 + 0.866373i \(0.666445\pi\)
\(128\) 0 0
\(129\) −12.3888 −1.09077
\(130\) 0 0
\(131\) 15.9990 1.39784 0.698920 0.715200i \(-0.253665\pi\)
0.698920 + 0.715200i \(0.253665\pi\)
\(132\) 0 0
\(133\) 1.65788 0.143756
\(134\) 0 0
\(135\) −10.9238 −0.940167
\(136\) 0 0
\(137\) 14.2950 1.22131 0.610654 0.791898i \(-0.290907\pi\)
0.610654 + 0.791898i \(0.290907\pi\)
\(138\) 0 0
\(139\) 2.04181 0.173184 0.0865919 0.996244i \(-0.472402\pi\)
0.0865919 + 0.996244i \(0.472402\pi\)
\(140\) 0 0
\(141\) 5.76037 0.485110
\(142\) 0 0
\(143\) −2.54968 −0.213215
\(144\) 0 0
\(145\) −13.5919 −1.12874
\(146\) 0 0
\(147\) 11.3679 0.937605
\(148\) 0 0
\(149\) −11.0853 −0.908143 −0.454072 0.890965i \(-0.650029\pi\)
−0.454072 + 0.890965i \(0.650029\pi\)
\(150\) 0 0
\(151\) −2.83057 −0.230349 −0.115174 0.993345i \(-0.536743\pi\)
−0.115174 + 0.993345i \(0.536743\pi\)
\(152\) 0 0
\(153\) −12.7648 −1.03197
\(154\) 0 0
\(155\) −15.8265 −1.27122
\(156\) 0 0
\(157\) −8.00562 −0.638918 −0.319459 0.947600i \(-0.603501\pi\)
−0.319459 + 0.947600i \(0.603501\pi\)
\(158\) 0 0
\(159\) 19.6694 1.55989
\(160\) 0 0
\(161\) 7.40702 0.583755
\(162\) 0 0
\(163\) 2.75990 0.216172 0.108086 0.994142i \(-0.465528\pi\)
0.108086 + 0.994142i \(0.465528\pi\)
\(164\) 0 0
\(165\) −10.6461 −0.828796
\(166\) 0 0
\(167\) 24.6556 1.90791 0.953954 0.299952i \(-0.0969706\pi\)
0.953954 + 0.299952i \(0.0969706\pi\)
\(168\) 0 0
\(169\) −7.82160 −0.601661
\(170\) 0 0
\(171\) 4.14966 0.317332
\(172\) 0 0
\(173\) −5.44441 −0.413931 −0.206965 0.978348i \(-0.566359\pi\)
−0.206965 + 0.978348i \(0.566359\pi\)
\(174\) 0 0
\(175\) 12.6456 0.955914
\(176\) 0 0
\(177\) 8.59297 0.645887
\(178\) 0 0
\(179\) 17.6753 1.32111 0.660555 0.750777i \(-0.270321\pi\)
0.660555 + 0.750777i \(0.270321\pi\)
\(180\) 0 0
\(181\) −4.06274 −0.301981 −0.150991 0.988535i \(-0.548246\pi\)
−0.150991 + 0.988535i \(0.548246\pi\)
\(182\) 0 0
\(183\) −31.1279 −2.30104
\(184\) 0 0
\(185\) −41.1946 −3.02869
\(186\) 0 0
\(187\) −3.44658 −0.252039
\(188\) 0 0
\(189\) −5.09642 −0.370710
\(190\) 0 0
\(191\) −5.03164 −0.364077 −0.182038 0.983291i \(-0.558270\pi\)
−0.182038 + 0.983291i \(0.558270\pi\)
\(192\) 0 0
\(193\) −1.75661 −0.126444 −0.0632219 0.997999i \(-0.520138\pi\)
−0.0632219 + 0.997999i \(0.520138\pi\)
\(194\) 0 0
\(195\) 21.6222 1.54840
\(196\) 0 0
\(197\) 1.07380 0.0765053 0.0382527 0.999268i \(-0.487821\pi\)
0.0382527 + 0.999268i \(0.487821\pi\)
\(198\) 0 0
\(199\) −17.7158 −1.25584 −0.627918 0.778279i \(-0.716093\pi\)
−0.627918 + 0.778279i \(0.716093\pi\)
\(200\) 0 0
\(201\) 35.2038 2.48308
\(202\) 0 0
\(203\) −6.34122 −0.445066
\(204\) 0 0
\(205\) −33.6178 −2.34797
\(206\) 0 0
\(207\) 18.5397 1.28860
\(208\) 0 0
\(209\) 1.12044 0.0775022
\(210\) 0 0
\(211\) 21.1414 1.45543 0.727716 0.685878i \(-0.240582\pi\)
0.727716 + 0.685878i \(0.240582\pi\)
\(212\) 0 0
\(213\) 32.7677 2.24521
\(214\) 0 0
\(215\) 16.4644 1.12286
\(216\) 0 0
\(217\) −7.38378 −0.501243
\(218\) 0 0
\(219\) 36.1539 2.44305
\(220\) 0 0
\(221\) 7.00002 0.470872
\(222\) 0 0
\(223\) −4.82163 −0.322881 −0.161440 0.986882i \(-0.551614\pi\)
−0.161440 + 0.986882i \(0.551614\pi\)
\(224\) 0 0
\(225\) 31.6517 2.11012
\(226\) 0 0
\(227\) 6.60893 0.438650 0.219325 0.975652i \(-0.429615\pi\)
0.219325 + 0.975652i \(0.429615\pi\)
\(228\) 0 0
\(229\) 2.87595 0.190048 0.0950240 0.995475i \(-0.469707\pi\)
0.0950240 + 0.995475i \(0.469707\pi\)
\(230\) 0 0
\(231\) −4.96687 −0.326796
\(232\) 0 0
\(233\) −17.4858 −1.14553 −0.572765 0.819719i \(-0.694129\pi\)
−0.572765 + 0.819719i \(0.694129\pi\)
\(234\) 0 0
\(235\) −7.65538 −0.499382
\(236\) 0 0
\(237\) 2.67388 0.173687
\(238\) 0 0
\(239\) −14.8527 −0.960739 −0.480370 0.877066i \(-0.659497\pi\)
−0.480370 + 0.877066i \(0.659497\pi\)
\(240\) 0 0
\(241\) 24.4398 1.57431 0.787153 0.616758i \(-0.211554\pi\)
0.787153 + 0.616758i \(0.211554\pi\)
\(242\) 0 0
\(243\) 20.5308 1.31705
\(244\) 0 0
\(245\) −15.1076 −0.965189
\(246\) 0 0
\(247\) −2.27561 −0.144794
\(248\) 0 0
\(249\) 29.3152 1.85777
\(250\) 0 0
\(251\) 8.99518 0.567771 0.283885 0.958858i \(-0.408376\pi\)
0.283885 + 0.958858i \(0.408376\pi\)
\(252\) 0 0
\(253\) 5.00585 0.314715
\(254\) 0 0
\(255\) 29.2283 1.83035
\(256\) 0 0
\(257\) −11.2594 −0.702339 −0.351170 0.936312i \(-0.614216\pi\)
−0.351170 + 0.936312i \(0.614216\pi\)
\(258\) 0 0
\(259\) −19.2191 −1.19422
\(260\) 0 0
\(261\) −15.8720 −0.982454
\(262\) 0 0
\(263\) 11.9807 0.738759 0.369380 0.929279i \(-0.379570\pi\)
0.369380 + 0.929279i \(0.379570\pi\)
\(264\) 0 0
\(265\) −26.1402 −1.60578
\(266\) 0 0
\(267\) 10.8458 0.663752
\(268\) 0 0
\(269\) 6.31432 0.384991 0.192495 0.981298i \(-0.438342\pi\)
0.192495 + 0.981298i \(0.438342\pi\)
\(270\) 0 0
\(271\) −9.81634 −0.596300 −0.298150 0.954519i \(-0.596370\pi\)
−0.298150 + 0.954519i \(0.596370\pi\)
\(272\) 0 0
\(273\) 10.0877 0.610537
\(274\) 0 0
\(275\) 8.54619 0.515355
\(276\) 0 0
\(277\) −9.94650 −0.597628 −0.298814 0.954311i \(-0.596591\pi\)
−0.298814 + 0.954311i \(0.596591\pi\)
\(278\) 0 0
\(279\) −18.4815 −1.10646
\(280\) 0 0
\(281\) −10.3042 −0.614695 −0.307348 0.951597i \(-0.599441\pi\)
−0.307348 + 0.951597i \(0.599441\pi\)
\(282\) 0 0
\(283\) −9.10870 −0.541456 −0.270728 0.962656i \(-0.587264\pi\)
−0.270728 + 0.962656i \(0.587264\pi\)
\(284\) 0 0
\(285\) −9.50172 −0.562833
\(286\) 0 0
\(287\) −15.6842 −0.925809
\(288\) 0 0
\(289\) −7.53756 −0.443386
\(290\) 0 0
\(291\) −45.1569 −2.64714
\(292\) 0 0
\(293\) −34.2179 −1.99903 −0.999514 0.0311620i \(-0.990079\pi\)
−0.999514 + 0.0311620i \(0.990079\pi\)
\(294\) 0 0
\(295\) −11.4198 −0.664889
\(296\) 0 0
\(297\) −3.44429 −0.199858
\(298\) 0 0
\(299\) −10.1669 −0.587967
\(300\) 0 0
\(301\) 7.68139 0.442748
\(302\) 0 0
\(303\) 34.8057 1.99954
\(304\) 0 0
\(305\) 41.3683 2.36874
\(306\) 0 0
\(307\) −24.6365 −1.40608 −0.703041 0.711149i \(-0.748175\pi\)
−0.703041 + 0.711149i \(0.748175\pi\)
\(308\) 0 0
\(309\) −18.3658 −1.04480
\(310\) 0 0
\(311\) −24.1337 −1.36850 −0.684249 0.729248i \(-0.739870\pi\)
−0.684249 + 0.729248i \(0.739870\pi\)
\(312\) 0 0
\(313\) 30.2145 1.70783 0.853913 0.520416i \(-0.174223\pi\)
0.853913 + 0.520416i \(0.174223\pi\)
\(314\) 0 0
\(315\) 24.4470 1.37743
\(316\) 0 0
\(317\) 27.8375 1.56351 0.781756 0.623585i \(-0.214324\pi\)
0.781756 + 0.623585i \(0.214324\pi\)
\(318\) 0 0
\(319\) −4.28556 −0.239945
\(320\) 0 0
\(321\) −42.1565 −2.35295
\(322\) 0 0
\(323\) −3.07611 −0.171159
\(324\) 0 0
\(325\) −17.3573 −0.962812
\(326\) 0 0
\(327\) −1.31338 −0.0726298
\(328\) 0 0
\(329\) −3.57158 −0.196908
\(330\) 0 0
\(331\) 22.5351 1.23864 0.619320 0.785139i \(-0.287408\pi\)
0.619320 + 0.785139i \(0.287408\pi\)
\(332\) 0 0
\(333\) −48.1054 −2.63616
\(334\) 0 0
\(335\) −46.7849 −2.55613
\(336\) 0 0
\(337\) 16.3766 0.892092 0.446046 0.895010i \(-0.352832\pi\)
0.446046 + 0.895010i \(0.352832\pi\)
\(338\) 0 0
\(339\) −43.4526 −2.36002
\(340\) 0 0
\(341\) −4.99014 −0.270231
\(342\) 0 0
\(343\) −18.6535 −1.00720
\(344\) 0 0
\(345\) −42.4515 −2.28551
\(346\) 0 0
\(347\) 16.9785 0.911453 0.455726 0.890120i \(-0.349380\pi\)
0.455726 + 0.890120i \(0.349380\pi\)
\(348\) 0 0
\(349\) −0.913351 −0.0488906 −0.0244453 0.999701i \(-0.507782\pi\)
−0.0244453 + 0.999701i \(0.507782\pi\)
\(350\) 0 0
\(351\) 6.99536 0.373385
\(352\) 0 0
\(353\) 20.6531 1.09926 0.549628 0.835409i \(-0.314769\pi\)
0.549628 + 0.835409i \(0.314769\pi\)
\(354\) 0 0
\(355\) −43.5475 −2.31126
\(356\) 0 0
\(357\) 13.6363 0.721710
\(358\) 0 0
\(359\) −30.7753 −1.62426 −0.812129 0.583477i \(-0.801692\pi\)
−0.812129 + 0.583477i \(0.801692\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 26.0560 1.36759
\(364\) 0 0
\(365\) −48.0476 −2.51493
\(366\) 0 0
\(367\) 21.3499 1.11445 0.557227 0.830360i \(-0.311865\pi\)
0.557227 + 0.830360i \(0.311865\pi\)
\(368\) 0 0
\(369\) −39.2575 −2.04366
\(370\) 0 0
\(371\) −12.1956 −0.633162
\(372\) 0 0
\(373\) −31.6340 −1.63795 −0.818973 0.573832i \(-0.805456\pi\)
−0.818973 + 0.573832i \(0.805456\pi\)
\(374\) 0 0
\(375\) −24.9663 −1.28925
\(376\) 0 0
\(377\) 8.70398 0.448278
\(378\) 0 0
\(379\) −12.6379 −0.649164 −0.324582 0.945858i \(-0.605224\pi\)
−0.324582 + 0.945858i \(0.605224\pi\)
\(380\) 0 0
\(381\) 30.0968 1.54191
\(382\) 0 0
\(383\) 35.1877 1.79801 0.899004 0.437941i \(-0.144292\pi\)
0.899004 + 0.437941i \(0.144292\pi\)
\(384\) 0 0
\(385\) 6.60085 0.336410
\(386\) 0 0
\(387\) 19.2265 0.977337
\(388\) 0 0
\(389\) −21.1628 −1.07300 −0.536499 0.843901i \(-0.680253\pi\)
−0.536499 + 0.843901i \(0.680253\pi\)
\(390\) 0 0
\(391\) −13.7433 −0.695030
\(392\) 0 0
\(393\) −42.7795 −2.15794
\(394\) 0 0
\(395\) −3.55353 −0.178797
\(396\) 0 0
\(397\) 23.3841 1.17362 0.586808 0.809726i \(-0.300385\pi\)
0.586808 + 0.809726i \(0.300385\pi\)
\(398\) 0 0
\(399\) −4.43298 −0.221926
\(400\) 0 0
\(401\) −36.4905 −1.82225 −0.911125 0.412131i \(-0.864785\pi\)
−0.911125 + 0.412131i \(0.864785\pi\)
\(402\) 0 0
\(403\) 10.1350 0.504860
\(404\) 0 0
\(405\) −15.0289 −0.746793
\(406\) 0 0
\(407\) −12.9888 −0.643830
\(408\) 0 0
\(409\) 28.2626 1.39749 0.698747 0.715368i \(-0.253741\pi\)
0.698747 + 0.715368i \(0.253741\pi\)
\(410\) 0 0
\(411\) −38.2233 −1.88542
\(412\) 0 0
\(413\) −5.32787 −0.262167
\(414\) 0 0
\(415\) −38.9591 −1.91243
\(416\) 0 0
\(417\) −5.45956 −0.267356
\(418\) 0 0
\(419\) −6.34208 −0.309831 −0.154915 0.987928i \(-0.549510\pi\)
−0.154915 + 0.987928i \(0.549510\pi\)
\(420\) 0 0
\(421\) 21.7007 1.05763 0.528813 0.848739i \(-0.322637\pi\)
0.528813 + 0.848739i \(0.322637\pi\)
\(422\) 0 0
\(423\) −8.93964 −0.434660
\(424\) 0 0
\(425\) −23.4632 −1.13813
\(426\) 0 0
\(427\) 19.3002 0.934000
\(428\) 0 0
\(429\) 6.81754 0.329154
\(430\) 0 0
\(431\) −4.81459 −0.231911 −0.115955 0.993254i \(-0.536993\pi\)
−0.115955 + 0.993254i \(0.536993\pi\)
\(432\) 0 0
\(433\) −32.0527 −1.54035 −0.770177 0.637830i \(-0.779832\pi\)
−0.770177 + 0.637830i \(0.779832\pi\)
\(434\) 0 0
\(435\) 36.3431 1.74252
\(436\) 0 0
\(437\) 4.46777 0.213722
\(438\) 0 0
\(439\) 33.3217 1.59036 0.795178 0.606376i \(-0.207377\pi\)
0.795178 + 0.606376i \(0.207377\pi\)
\(440\) 0 0
\(441\) −17.6420 −0.840096
\(442\) 0 0
\(443\) 6.26155 0.297495 0.148748 0.988875i \(-0.452476\pi\)
0.148748 + 0.988875i \(0.452476\pi\)
\(444\) 0 0
\(445\) −14.4138 −0.683280
\(446\) 0 0
\(447\) 29.6408 1.40196
\(448\) 0 0
\(449\) −28.0340 −1.32301 −0.661504 0.749942i \(-0.730082\pi\)
−0.661504 + 0.749942i \(0.730082\pi\)
\(450\) 0 0
\(451\) −10.5998 −0.499124
\(452\) 0 0
\(453\) 7.56862 0.355605
\(454\) 0 0
\(455\) −13.4063 −0.628499
\(456\) 0 0
\(457\) −30.5800 −1.43047 −0.715236 0.698883i \(-0.753681\pi\)
−0.715236 + 0.698883i \(0.753681\pi\)
\(458\) 0 0
\(459\) 9.45614 0.441375
\(460\) 0 0
\(461\) −2.71325 −0.126369 −0.0631844 0.998002i \(-0.520126\pi\)
−0.0631844 + 0.998002i \(0.520126\pi\)
\(462\) 0 0
\(463\) −26.9595 −1.25291 −0.626456 0.779457i \(-0.715495\pi\)
−0.626456 + 0.779457i \(0.715495\pi\)
\(464\) 0 0
\(465\) 42.3183 1.96246
\(466\) 0 0
\(467\) 6.51255 0.301365 0.150682 0.988582i \(-0.451853\pi\)
0.150682 + 0.988582i \(0.451853\pi\)
\(468\) 0 0
\(469\) −21.8273 −1.00789
\(470\) 0 0
\(471\) 21.4061 0.986342
\(472\) 0 0
\(473\) 5.19128 0.238695
\(474\) 0 0
\(475\) 7.62755 0.349976
\(476\) 0 0
\(477\) −30.5254 −1.39766
\(478\) 0 0
\(479\) −0.765359 −0.0349701 −0.0174851 0.999847i \(-0.505566\pi\)
−0.0174851 + 0.999847i \(0.505566\pi\)
\(480\) 0 0
\(481\) 26.3803 1.20284
\(482\) 0 0
\(483\) −19.8055 −0.901182
\(484\) 0 0
\(485\) 60.0124 2.72502
\(486\) 0 0
\(487\) −14.7915 −0.670269 −0.335134 0.942170i \(-0.608782\pi\)
−0.335134 + 0.942170i \(0.608782\pi\)
\(488\) 0 0
\(489\) −7.37966 −0.333720
\(490\) 0 0
\(491\) −12.8798 −0.581257 −0.290629 0.956836i \(-0.593864\pi\)
−0.290629 + 0.956836i \(0.593864\pi\)
\(492\) 0 0
\(493\) 11.7658 0.529905
\(494\) 0 0
\(495\) 16.5219 0.742603
\(496\) 0 0
\(497\) −20.3168 −0.911335
\(498\) 0 0
\(499\) −7.29526 −0.326581 −0.163290 0.986578i \(-0.552211\pi\)
−0.163290 + 0.986578i \(0.552211\pi\)
\(500\) 0 0
\(501\) −65.9263 −2.94537
\(502\) 0 0
\(503\) −36.6667 −1.63489 −0.817443 0.576010i \(-0.804609\pi\)
−0.817443 + 0.576010i \(0.804609\pi\)
\(504\) 0 0
\(505\) −46.2560 −2.05836
\(506\) 0 0
\(507\) 20.9141 0.928826
\(508\) 0 0
\(509\) −14.7564 −0.654064 −0.327032 0.945013i \(-0.606048\pi\)
−0.327032 + 0.945013i \(0.606048\pi\)
\(510\) 0 0
\(511\) −22.4164 −0.991642
\(512\) 0 0
\(513\) −3.07406 −0.135723
\(514\) 0 0
\(515\) 24.4077 1.07553
\(516\) 0 0
\(517\) −2.41376 −0.106157
\(518\) 0 0
\(519\) 14.5577 0.639013
\(520\) 0 0
\(521\) −19.0319 −0.833804 −0.416902 0.908951i \(-0.636884\pi\)
−0.416902 + 0.908951i \(0.636884\pi\)
\(522\) 0 0
\(523\) 27.2712 1.19249 0.596244 0.802804i \(-0.296659\pi\)
0.596244 + 0.802804i \(0.296659\pi\)
\(524\) 0 0
\(525\) −33.8128 −1.47571
\(526\) 0 0
\(527\) 13.7002 0.596790
\(528\) 0 0
\(529\) −3.03907 −0.132134
\(530\) 0 0
\(531\) −13.3356 −0.578716
\(532\) 0 0
\(533\) 21.5282 0.932489
\(534\) 0 0
\(535\) 56.0250 2.42217
\(536\) 0 0
\(537\) −47.2616 −2.03949
\(538\) 0 0
\(539\) −4.76347 −0.205177
\(540\) 0 0
\(541\) −6.74519 −0.289998 −0.144999 0.989432i \(-0.546318\pi\)
−0.144999 + 0.989432i \(0.546318\pi\)
\(542\) 0 0
\(543\) 10.8633 0.466189
\(544\) 0 0
\(545\) 1.74544 0.0747666
\(546\) 0 0
\(547\) −29.9655 −1.28123 −0.640615 0.767862i \(-0.721321\pi\)
−0.640615 + 0.767862i \(0.721321\pi\)
\(548\) 0 0
\(549\) 48.3081 2.06174
\(550\) 0 0
\(551\) −3.82490 −0.162946
\(552\) 0 0
\(553\) −1.65788 −0.0705002
\(554\) 0 0
\(555\) 110.150 4.67560
\(556\) 0 0
\(557\) −5.29491 −0.224352 −0.112176 0.993688i \(-0.535782\pi\)
−0.112176 + 0.993688i \(0.535782\pi\)
\(558\) 0 0
\(559\) −10.5435 −0.445943
\(560\) 0 0
\(561\) 9.21577 0.389090
\(562\) 0 0
\(563\) 7.16828 0.302107 0.151054 0.988526i \(-0.451733\pi\)
0.151054 + 0.988526i \(0.451733\pi\)
\(564\) 0 0
\(565\) 57.7475 2.42946
\(566\) 0 0
\(567\) −7.01167 −0.294462
\(568\) 0 0
\(569\) 44.8609 1.88067 0.940334 0.340252i \(-0.110512\pi\)
0.940334 + 0.340252i \(0.110512\pi\)
\(570\) 0 0
\(571\) 2.96675 0.124154 0.0620772 0.998071i \(-0.480227\pi\)
0.0620772 + 0.998071i \(0.480227\pi\)
\(572\) 0 0
\(573\) 13.4540 0.562050
\(574\) 0 0
\(575\) 34.0781 1.42116
\(576\) 0 0
\(577\) 6.29065 0.261883 0.130942 0.991390i \(-0.458200\pi\)
0.130942 + 0.991390i \(0.458200\pi\)
\(578\) 0 0
\(579\) 4.69698 0.195200
\(580\) 0 0
\(581\) −18.1762 −0.754075
\(582\) 0 0
\(583\) −8.24207 −0.341352
\(584\) 0 0
\(585\) −33.5560 −1.38737
\(586\) 0 0
\(587\) 26.4920 1.09344 0.546722 0.837314i \(-0.315876\pi\)
0.546722 + 0.837314i \(0.315876\pi\)
\(588\) 0 0
\(589\) −4.45375 −0.183513
\(590\) 0 0
\(591\) −2.87123 −0.118106
\(592\) 0 0
\(593\) 11.2771 0.463095 0.231548 0.972824i \(-0.425621\pi\)
0.231548 + 0.972824i \(0.425621\pi\)
\(594\) 0 0
\(595\) −18.1223 −0.742943
\(596\) 0 0
\(597\) 47.3699 1.93872
\(598\) 0 0
\(599\) 20.2223 0.826262 0.413131 0.910672i \(-0.364435\pi\)
0.413131 + 0.910672i \(0.364435\pi\)
\(600\) 0 0
\(601\) −11.7713 −0.480162 −0.240081 0.970753i \(-0.577174\pi\)
−0.240081 + 0.970753i \(0.577174\pi\)
\(602\) 0 0
\(603\) −54.6335 −2.22485
\(604\) 0 0
\(605\) −34.6278 −1.40782
\(606\) 0 0
\(607\) −7.12655 −0.289258 −0.144629 0.989486i \(-0.546199\pi\)
−0.144629 + 0.989486i \(0.546199\pi\)
\(608\) 0 0
\(609\) 16.9557 0.687079
\(610\) 0 0
\(611\) 4.90236 0.198328
\(612\) 0 0
\(613\) 30.9321 1.24934 0.624668 0.780890i \(-0.285234\pi\)
0.624668 + 0.780890i \(0.285234\pi\)
\(614\) 0 0
\(615\) 89.8901 3.62472
\(616\) 0 0
\(617\) −5.22160 −0.210214 −0.105107 0.994461i \(-0.533518\pi\)
−0.105107 + 0.994461i \(0.533518\pi\)
\(618\) 0 0
\(619\) 20.5205 0.824788 0.412394 0.911006i \(-0.364693\pi\)
0.412394 + 0.911006i \(0.364693\pi\)
\(620\) 0 0
\(621\) −13.7342 −0.551134
\(622\) 0 0
\(623\) −6.72468 −0.269419
\(624\) 0 0
\(625\) −4.95821 −0.198329
\(626\) 0 0
\(627\) −2.99592 −0.119645
\(628\) 0 0
\(629\) 35.6601 1.42186
\(630\) 0 0
\(631\) −44.9891 −1.79099 −0.895493 0.445075i \(-0.853177\pi\)
−0.895493 + 0.445075i \(0.853177\pi\)
\(632\) 0 0
\(633\) −56.5296 −2.24685
\(634\) 0 0
\(635\) −39.9980 −1.58727
\(636\) 0 0
\(637\) 9.67461 0.383322
\(638\) 0 0
\(639\) −50.8529 −2.01171
\(640\) 0 0
\(641\) 34.6930 1.37029 0.685145 0.728407i \(-0.259739\pi\)
0.685145 + 0.728407i \(0.259739\pi\)
\(642\) 0 0
\(643\) −30.7380 −1.21219 −0.606094 0.795393i \(-0.707264\pi\)
−0.606094 + 0.795393i \(0.707264\pi\)
\(644\) 0 0
\(645\) −44.0240 −1.73344
\(646\) 0 0
\(647\) −25.5916 −1.00611 −0.503055 0.864255i \(-0.667791\pi\)
−0.503055 + 0.864255i \(0.667791\pi\)
\(648\) 0 0
\(649\) −3.60071 −0.141340
\(650\) 0 0
\(651\) 19.7434 0.773804
\(652\) 0 0
\(653\) 13.5682 0.530966 0.265483 0.964116i \(-0.414469\pi\)
0.265483 + 0.964116i \(0.414469\pi\)
\(654\) 0 0
\(655\) 56.8529 2.22143
\(656\) 0 0
\(657\) −56.1080 −2.18898
\(658\) 0 0
\(659\) 10.7621 0.419234 0.209617 0.977784i \(-0.432778\pi\)
0.209617 + 0.977784i \(0.432778\pi\)
\(660\) 0 0
\(661\) 13.2305 0.514606 0.257303 0.966331i \(-0.417166\pi\)
0.257303 + 0.966331i \(0.417166\pi\)
\(662\) 0 0
\(663\) −18.7173 −0.726918
\(664\) 0 0
\(665\) 5.89132 0.228456
\(666\) 0 0
\(667\) −17.0887 −0.661679
\(668\) 0 0
\(669\) 12.8925 0.498453
\(670\) 0 0
\(671\) 13.0435 0.503540
\(672\) 0 0
\(673\) 37.4043 1.44183 0.720914 0.693024i \(-0.243722\pi\)
0.720914 + 0.693024i \(0.243722\pi\)
\(674\) 0 0
\(675\) −23.4476 −0.902497
\(676\) 0 0
\(677\) 31.3234 1.20386 0.601928 0.798550i \(-0.294399\pi\)
0.601928 + 0.798550i \(0.294399\pi\)
\(678\) 0 0
\(679\) 27.9985 1.07448
\(680\) 0 0
\(681\) −17.6715 −0.677174
\(682\) 0 0
\(683\) −6.56990 −0.251390 −0.125695 0.992069i \(-0.540116\pi\)
−0.125695 + 0.992069i \(0.540116\pi\)
\(684\) 0 0
\(685\) 50.7978 1.94088
\(686\) 0 0
\(687\) −7.68995 −0.293390
\(688\) 0 0
\(689\) 16.7397 0.637730
\(690\) 0 0
\(691\) −11.3562 −0.432009 −0.216005 0.976392i \(-0.569303\pi\)
−0.216005 + 0.976392i \(0.569303\pi\)
\(692\) 0 0
\(693\) 7.70820 0.292810
\(694\) 0 0
\(695\) 7.25562 0.275221
\(696\) 0 0
\(697\) 29.1012 1.10229
\(698\) 0 0
\(699\) 46.7549 1.76843
\(700\) 0 0
\(701\) −13.9697 −0.527628 −0.263814 0.964574i \(-0.584981\pi\)
−0.263814 + 0.964574i \(0.584981\pi\)
\(702\) 0 0
\(703\) −11.5926 −0.437224
\(704\) 0 0
\(705\) 20.4696 0.770930
\(706\) 0 0
\(707\) −21.5805 −0.811617
\(708\) 0 0
\(709\) −23.3876 −0.878341 −0.439170 0.898404i \(-0.644728\pi\)
−0.439170 + 0.898404i \(0.644728\pi\)
\(710\) 0 0
\(711\) −4.14966 −0.155624
\(712\) 0 0
\(713\) −19.8983 −0.745197
\(714\) 0 0
\(715\) −9.06035 −0.338838
\(716\) 0 0
\(717\) 39.7143 1.48316
\(718\) 0 0
\(719\) 18.2219 0.679564 0.339782 0.940504i \(-0.389647\pi\)
0.339782 + 0.940504i \(0.389647\pi\)
\(720\) 0 0
\(721\) 11.3873 0.424085
\(722\) 0 0
\(723\) −65.3492 −2.43036
\(724\) 0 0
\(725\) −29.1746 −1.08352
\(726\) 0 0
\(727\) 12.7594 0.473221 0.236611 0.971605i \(-0.423963\pi\)
0.236611 + 0.971605i \(0.423963\pi\)
\(728\) 0 0
\(729\) −42.2092 −1.56330
\(730\) 0 0
\(731\) −14.2524 −0.527145
\(732\) 0 0
\(733\) −14.5936 −0.539029 −0.269514 0.962996i \(-0.586863\pi\)
−0.269514 + 0.962996i \(0.586863\pi\)
\(734\) 0 0
\(735\) 40.3960 1.49003
\(736\) 0 0
\(737\) −14.7514 −0.543375
\(738\) 0 0
\(739\) −7.44091 −0.273718 −0.136859 0.990591i \(-0.543701\pi\)
−0.136859 + 0.990591i \(0.543701\pi\)
\(740\) 0 0
\(741\) 6.08472 0.223528
\(742\) 0 0
\(743\) −34.1645 −1.25337 −0.626687 0.779271i \(-0.715590\pi\)
−0.626687 + 0.779271i \(0.715590\pi\)
\(744\) 0 0
\(745\) −39.3919 −1.44321
\(746\) 0 0
\(747\) −45.4949 −1.66457
\(748\) 0 0
\(749\) 26.1382 0.955068
\(750\) 0 0
\(751\) 13.7963 0.503435 0.251718 0.967801i \(-0.419005\pi\)
0.251718 + 0.967801i \(0.419005\pi\)
\(752\) 0 0
\(753\) −24.0521 −0.876507
\(754\) 0 0
\(755\) −10.0585 −0.366067
\(756\) 0 0
\(757\) −15.7598 −0.572798 −0.286399 0.958110i \(-0.592458\pi\)
−0.286399 + 0.958110i \(0.592458\pi\)
\(758\) 0 0
\(759\) −13.3851 −0.485847
\(760\) 0 0
\(761\) 13.7578 0.498720 0.249360 0.968411i \(-0.419780\pi\)
0.249360 + 0.968411i \(0.419780\pi\)
\(762\) 0 0
\(763\) 0.814328 0.0294806
\(764\) 0 0
\(765\) −45.3601 −1.64000
\(766\) 0 0
\(767\) 7.31305 0.264059
\(768\) 0 0
\(769\) −53.0357 −1.91252 −0.956259 0.292522i \(-0.905506\pi\)
−0.956259 + 0.292522i \(0.905506\pi\)
\(770\) 0 0
\(771\) 30.1062 1.08425
\(772\) 0 0
\(773\) 42.8442 1.54100 0.770500 0.637440i \(-0.220007\pi\)
0.770500 + 0.637440i \(0.220007\pi\)
\(774\) 0 0
\(775\) −33.9712 −1.22028
\(776\) 0 0
\(777\) 51.3898 1.84360
\(778\) 0 0
\(779\) −9.46040 −0.338954
\(780\) 0 0
\(781\) −13.7306 −0.491321
\(782\) 0 0
\(783\) 11.7580 0.420195
\(784\) 0 0
\(785\) −28.4482 −1.01536
\(786\) 0 0
\(787\) −11.7335 −0.418256 −0.209128 0.977888i \(-0.567062\pi\)
−0.209128 + 0.977888i \(0.567062\pi\)
\(788\) 0 0
\(789\) −32.0349 −1.14047
\(790\) 0 0
\(791\) 26.9418 0.957940
\(792\) 0 0
\(793\) −26.4914 −0.940739
\(794\) 0 0
\(795\) 69.8958 2.47895
\(796\) 0 0
\(797\) 44.3184 1.56984 0.784920 0.619598i \(-0.212704\pi\)
0.784920 + 0.619598i \(0.212704\pi\)
\(798\) 0 0
\(799\) 6.62688 0.234442
\(800\) 0 0
\(801\) −16.8318 −0.594724
\(802\) 0 0
\(803\) −15.1495 −0.534616
\(804\) 0 0
\(805\) 26.3210 0.927694
\(806\) 0 0
\(807\) −16.8838 −0.594336
\(808\) 0 0
\(809\) 30.8365 1.08415 0.542077 0.840329i \(-0.317638\pi\)
0.542077 + 0.840329i \(0.317638\pi\)
\(810\) 0 0
\(811\) −9.70574 −0.340815 −0.170407 0.985374i \(-0.554508\pi\)
−0.170407 + 0.985374i \(0.554508\pi\)
\(812\) 0 0
\(813\) 26.2478 0.920549
\(814\) 0 0
\(815\) 9.80739 0.343538
\(816\) 0 0
\(817\) 4.63326 0.162097
\(818\) 0 0
\(819\) −15.6554 −0.547043
\(820\) 0 0
\(821\) 3.55255 0.123985 0.0619924 0.998077i \(-0.480255\pi\)
0.0619924 + 0.998077i \(0.480255\pi\)
\(822\) 0 0
\(823\) 39.8774 1.39004 0.695020 0.718990i \(-0.255395\pi\)
0.695020 + 0.718990i \(0.255395\pi\)
\(824\) 0 0
\(825\) −22.8515 −0.795588
\(826\) 0 0
\(827\) −14.0469 −0.488460 −0.244230 0.969717i \(-0.578535\pi\)
−0.244230 + 0.969717i \(0.578535\pi\)
\(828\) 0 0
\(829\) −15.9389 −0.553581 −0.276791 0.960930i \(-0.589271\pi\)
−0.276791 + 0.960930i \(0.589271\pi\)
\(830\) 0 0
\(831\) 26.5958 0.922598
\(832\) 0 0
\(833\) 13.0779 0.453121
\(834\) 0 0
\(835\) 87.6144 3.03202
\(836\) 0 0
\(837\) 13.6911 0.473233
\(838\) 0 0
\(839\) −12.5192 −0.432210 −0.216105 0.976370i \(-0.569335\pi\)
−0.216105 + 0.976370i \(0.569335\pi\)
\(840\) 0 0
\(841\) −14.3702 −0.495522
\(842\) 0 0
\(843\) 27.5522 0.948947
\(844\) 0 0
\(845\) −27.7943 −0.956151
\(846\) 0 0
\(847\) −16.1554 −0.555106
\(848\) 0 0
\(849\) 24.3556 0.835883
\(850\) 0 0
\(851\) −51.7931 −1.77544
\(852\) 0 0
\(853\) 46.4699 1.59110 0.795549 0.605890i \(-0.207183\pi\)
0.795549 + 0.605890i \(0.207183\pi\)
\(854\) 0 0
\(855\) 14.7459 0.504300
\(856\) 0 0
\(857\) −15.0247 −0.513235 −0.256617 0.966513i \(-0.582608\pi\)
−0.256617 + 0.966513i \(0.582608\pi\)
\(858\) 0 0
\(859\) 9.36733 0.319609 0.159805 0.987149i \(-0.448914\pi\)
0.159805 + 0.987149i \(0.448914\pi\)
\(860\) 0 0
\(861\) 41.9378 1.42924
\(862\) 0 0
\(863\) −42.2506 −1.43823 −0.719114 0.694893i \(-0.755452\pi\)
−0.719114 + 0.694893i \(0.755452\pi\)
\(864\) 0 0
\(865\) −19.3468 −0.657812
\(866\) 0 0
\(867\) 20.1546 0.684485
\(868\) 0 0
\(869\) −1.12044 −0.0380082
\(870\) 0 0
\(871\) 29.9602 1.01516
\(872\) 0 0
\(873\) 70.0800 2.37185
\(874\) 0 0
\(875\) 15.4797 0.523311
\(876\) 0 0
\(877\) −44.0007 −1.48580 −0.742899 0.669403i \(-0.766550\pi\)
−0.742899 + 0.669403i \(0.766550\pi\)
\(878\) 0 0
\(879\) 91.4946 3.08604
\(880\) 0 0
\(881\) −44.6224 −1.50337 −0.751683 0.659525i \(-0.770758\pi\)
−0.751683 + 0.659525i \(0.770758\pi\)
\(882\) 0 0
\(883\) 23.5680 0.793126 0.396563 0.918008i \(-0.370203\pi\)
0.396563 + 0.918008i \(0.370203\pi\)
\(884\) 0 0
\(885\) 30.5353 1.02643
\(886\) 0 0
\(887\) 23.3974 0.785609 0.392804 0.919622i \(-0.371505\pi\)
0.392804 + 0.919622i \(0.371505\pi\)
\(888\) 0 0
\(889\) −18.6608 −0.625864
\(890\) 0 0
\(891\) −4.73866 −0.158751
\(892\) 0 0
\(893\) −2.15431 −0.0720911
\(894\) 0 0
\(895\) 62.8095 2.09949
\(896\) 0 0
\(897\) 27.1851 0.907684
\(898\) 0 0
\(899\) 17.0351 0.568153
\(900\) 0 0
\(901\) 22.6282 0.753855
\(902\) 0 0
\(903\) −20.5392 −0.683501
\(904\) 0 0
\(905\) −14.4371 −0.479904
\(906\) 0 0
\(907\) −38.9279 −1.29258 −0.646290 0.763092i \(-0.723680\pi\)
−0.646290 + 0.763092i \(0.723680\pi\)
\(908\) 0 0
\(909\) −54.0158 −1.79159
\(910\) 0 0
\(911\) −3.05729 −0.101293 −0.0506463 0.998717i \(-0.516128\pi\)
−0.0506463 + 0.998717i \(0.516128\pi\)
\(912\) 0 0
\(913\) −12.2839 −0.406539
\(914\) 0 0
\(915\) −110.614 −3.65679
\(916\) 0 0
\(917\) 26.5244 0.875913
\(918\) 0 0
\(919\) 33.2902 1.09814 0.549071 0.835776i \(-0.314982\pi\)
0.549071 + 0.835776i \(0.314982\pi\)
\(920\) 0 0
\(921\) 65.8753 2.17066
\(922\) 0 0
\(923\) 27.8870 0.917910
\(924\) 0 0
\(925\) −88.4232 −2.90734
\(926\) 0 0
\(927\) 28.5023 0.936139
\(928\) 0 0
\(929\) −22.0090 −0.722093 −0.361046 0.932548i \(-0.617580\pi\)
−0.361046 + 0.932548i \(0.617580\pi\)
\(930\) 0 0
\(931\) −4.25144 −0.139335
\(932\) 0 0
\(933\) 64.5308 2.11264
\(934\) 0 0
\(935\) −12.2475 −0.400537
\(936\) 0 0
\(937\) 52.5179 1.71569 0.857843 0.513911i \(-0.171804\pi\)
0.857843 + 0.513911i \(0.171804\pi\)
\(938\) 0 0
\(939\) −80.7901 −2.63649
\(940\) 0 0
\(941\) 28.9536 0.943862 0.471931 0.881636i \(-0.343557\pi\)
0.471931 + 0.881636i \(0.343557\pi\)
\(942\) 0 0
\(943\) −42.2669 −1.37640
\(944\) 0 0
\(945\) −18.1103 −0.589127
\(946\) 0 0
\(947\) 54.9697 1.78628 0.893138 0.449782i \(-0.148498\pi\)
0.893138 + 0.449782i \(0.148498\pi\)
\(948\) 0 0
\(949\) 30.7688 0.998797
\(950\) 0 0
\(951\) −74.4343 −2.41370
\(952\) 0 0
\(953\) −55.1084 −1.78514 −0.892568 0.450913i \(-0.851098\pi\)
−0.892568 + 0.450913i \(0.851098\pi\)
\(954\) 0 0
\(955\) −17.8801 −0.578586
\(956\) 0 0
\(957\) 11.4591 0.370420
\(958\) 0 0
\(959\) 23.6995 0.765295
\(960\) 0 0
\(961\) −11.1641 −0.360133
\(962\) 0 0
\(963\) 65.4236 2.10825
\(964\) 0 0
\(965\) −6.24217 −0.200943
\(966\) 0 0
\(967\) 10.1313 0.325801 0.162900 0.986643i \(-0.447915\pi\)
0.162900 + 0.986643i \(0.447915\pi\)
\(968\) 0 0
\(969\) 8.22516 0.264230
\(970\) 0 0
\(971\) 56.7893 1.82246 0.911228 0.411901i \(-0.135135\pi\)
0.911228 + 0.411901i \(0.135135\pi\)
\(972\) 0 0
\(973\) 3.38507 0.108520
\(974\) 0 0
\(975\) 46.4115 1.48636
\(976\) 0 0
\(977\) 24.3146 0.777894 0.388947 0.921260i \(-0.372839\pi\)
0.388947 + 0.921260i \(0.372839\pi\)
\(978\) 0 0
\(979\) −4.54471 −0.145250
\(980\) 0 0
\(981\) 2.03826 0.0650765
\(982\) 0 0
\(983\) −36.6882 −1.17017 −0.585087 0.810971i \(-0.698940\pi\)
−0.585087 + 0.810971i \(0.698940\pi\)
\(984\) 0 0
\(985\) 3.81579 0.121581
\(986\) 0 0
\(987\) 9.54999 0.303980
\(988\) 0 0
\(989\) 20.7003 0.658233
\(990\) 0 0
\(991\) −38.6198 −1.22680 −0.613399 0.789773i \(-0.710198\pi\)
−0.613399 + 0.789773i \(0.710198\pi\)
\(992\) 0 0
\(993\) −60.2562 −1.91217
\(994\) 0 0
\(995\) −62.9534 −1.99576
\(996\) 0 0
\(997\) −58.0512 −1.83850 −0.919251 0.393673i \(-0.871204\pi\)
−0.919251 + 0.393673i \(0.871204\pi\)
\(998\) 0 0
\(999\) 35.6364 1.12748
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 \(a_p\))