Properties

Label 981.1.d.a.980.2
Level 981
Weight 1
Character 981.980
Analytic conductor 0.490
Analytic rank 0
Dimension 2
Projective image \(S_{4}\)
CM/RM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 981 = 3^{2} \cdot 109 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 981.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.489582777393\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Projective image \(S_{4}\)
Projective field Galois closure of 4.2.2943.1
Artin image size \(48\)
Artin image $\GL(2,3)$
Artin field Galois closure of 8.2.2832228423.1

Embedding invariants

Embedding label 980.2
Root \(-1.41421i\)
Character \(\chi\) = 981.980
Dual form 981.1.d.a.980.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.41421i q^{5}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.41421i q^{5}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(-1.41421i q^{10}\) \(-1.41421i q^{13}\) \(-1.00000 q^{14}\) \(-1.00000 q^{16}\) \(+1.00000 q^{17}\) \(+1.41421i q^{19}\) \(-1.00000 q^{23}\) \(-1.00000 q^{25}\) \(+1.41421i q^{26}\) \(+1.00000 q^{31}\) \(-1.00000 q^{34}\) \(+1.41421i q^{35}\) \(+1.41421i q^{37}\) \(-1.41421i q^{38}\) \(+1.41421i q^{40}\) \(-1.00000 q^{41}\) \(+1.00000 q^{43}\) \(+1.00000 q^{46}\) \(+1.00000 q^{47}\) \(+1.00000 q^{50}\) \(+1.00000 q^{56}\) \(+1.00000 q^{59}\) \(-1.00000 q^{61}\) \(-1.00000 q^{62}\) \(+1.00000 q^{64}\) \(+2.00000 q^{65}\) \(-1.41421i q^{70}\) \(-1.41421i q^{71}\) \(-1.00000 q^{73}\) \(-1.41421i q^{74}\) \(+1.41421i q^{79}\) \(-1.41421i q^{80}\) \(+1.00000 q^{82}\) \(+1.41421i q^{83}\) \(+1.41421i q^{85}\) \(-1.00000 q^{86}\) \(-1.41421i q^{89}\) \(-1.41421i q^{91}\) \(-1.00000 q^{94}\) \(-2.00000 q^{95}\) \(-1.00000 q^{97}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut +\mathstrut 2q^{56} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 2q^{62} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 2q^{94} \) \(\mathstrut -\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/981\mathbb{Z}\right)^\times\).

\(n\) \(110\) \(442\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) 0 0
\(4\) 0 0
\(5\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(6\) 0 0
\(7\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(8\) 1.00000 1.00000
\(9\) 0 0
\(10\) − 1.41421i − 1.41421i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(14\) −1.00000 −1.00000
\(15\) 0 0
\(16\) −1.00000 −1.00000
\(17\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 0 0
\(19\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) −1.00000 −1.00000
\(26\) 1.41421i 1.41421i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) −1.00000 −1.00000
\(35\) 1.41421i 1.41421i
\(36\) 0 0
\(37\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) − 1.41421i − 1.41421i
\(39\) 0 0
\(40\) 1.41421i 1.41421i
\(41\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.00000 1.00000
\(47\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.00000 1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 1.00000
\(57\) 0 0
\(58\) 0 0
\(59\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) 0 0
\(61\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) −1.00000 −1.00000
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 2.00000 2.00000
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) − 1.41421i − 1.41421i
\(71\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(72\) 0 0
\(73\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) − 1.41421i − 1.41421i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(80\) − 1.41421i − 1.41421i
\(81\) 0 0
\(82\) 1.00000 1.00000
\(83\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(84\) 0 0
\(85\) 1.41421i 1.41421i
\(86\) −1.00000 −1.00000
\(87\) 0 0
\(88\) 0 0
\(89\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(90\) 0 0
\(91\) − 1.41421i − 1.41421i
\(92\) 0 0
\(93\) 0 0
\(94\) −1.00000 −1.00000
\(95\) −2.00000 −2.00000
\(96\) 0 0
\(97\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) − 1.41421i − 1.41421i
\(105\) 0 0
\(106\) 0 0
\(107\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) 0 0
\(109\) 1.00000 1.00000
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −1.00000
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) − 1.41421i − 1.41421i
\(116\) 0 0
\(117\) 0 0
\(118\) −1.00000 −1.00000
\(119\) 1.00000 1.00000
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 1.00000 1.00000
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −1.00000 −1.00000
\(129\) 0 0
\(130\) −2.00000 −2.00000
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 1.41421i 1.41421i
\(134\) 0 0
\(135\) 0 0
\(136\) 1.00000 1.00000
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.41421i 1.41421i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 1.00000 1.00000
\(147\) 0 0
\(148\) 0 0
\(149\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(152\) 1.41421i 1.41421i
\(153\) 0 0
\(154\) 0 0
\(155\) 1.41421i 1.41421i
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) − 1.41421i − 1.41421i
\(159\) 0 0
\(160\) 0 0
\(161\) −1.00000 −1.00000
\(162\) 0 0
\(163\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) − 1.41421i − 1.41421i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −1.00000 −1.00000
\(170\) − 1.41421i − 1.41421i
\(171\) 0 0
\(172\) 0 0
\(173\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(174\) 0 0
\(175\) −1.00000 −1.00000
\(176\) 0 0
\(177\) 0 0
\(178\) 1.41421i 1.41421i
\(179\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0 0
\(181\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(182\) 1.41421i 1.41421i
\(183\) 0 0
\(184\) −1.00000 −1.00000
\(185\) −2.00000 −2.00000
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 2.00000 2.00000
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 1.00000 1.00000
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(200\) −1.00000 −1.00000
\(201\) 0 0
\(202\) 2.00000 2.00000
\(203\) 0 0
\(204\) 0 0
\(205\) − 1.41421i − 1.41421i
\(206\) 0 0
\(207\) 0 0
\(208\) 1.41421i 1.41421i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.00000 −1.00000
\(215\) 1.41421i 1.41421i
\(216\) 0 0
\(217\) 1.00000 1.00000
\(218\) −1.00000 −1.00000
\(219\) 0 0
\(220\) 0 0
\(221\) − 1.41421i − 1.41421i
\(222\) 0 0
\(223\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(228\) 0 0
\(229\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(230\) 1.41421i 1.41421i
\(231\) 0 0
\(232\) 0 0
\(233\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(234\) 0 0
\(235\) 1.41421i 1.41421i
\(236\) 0 0
\(237\) 0 0
\(238\) −1.00000 −1.00000
\(239\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.00000 1.00000
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.00000 2.00000
\(248\) 1.00000 1.00000
\(249\) 0 0
\(250\) 0 0
\(251\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 1.41421i 1.41421i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) − 1.41421i − 1.41421i
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −1.00000 −1.00000
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 1.41421i 1.41421i
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.00000 −1.00000
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(294\) 0 0
\(295\) 1.41421i 1.41421i
\(296\) 1.41421i 1.41421i
\(297\) 0 0
\(298\) −1.00000 −1.00000
\(299\) 1.41421i 1.41421i
\(300\) 0 0
\(301\) 1.00000 1.00000
\(302\) 1.41421i 1.41421i
\(303\) 0 0
\(304\) − 1.41421i − 1.41421i
\(305\) − 1.41421i − 1.41421i
\(306\) 0 0
\(307\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) − 1.41421i − 1.41421i
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.41421i 1.41421i
\(321\) 0 0
\(322\) 1.00000 1.00000
\(323\) 1.41421i 1.41421i
\(324\) 0 0
\(325\) 1.41421i 1.41421i
\(326\) 1.41421i 1.41421i
\(327\) 0 0
\(328\) −1.00000 −1.00000
\(329\) 1.00000 1.00000
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 1.00000 1.00000
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) 1.00000 1.00000
\(345\) 0 0
\(346\) 1.41421i 1.41421i
\(347\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(348\) 0 0
\(349\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 1.00000 1.00000
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 2.00000 2.00000
\(356\) 0 0
\(357\) 0 0
\(358\) 1.00000 1.00000
\(359\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) 0 0
\(361\) −1.00000 −1.00000
\(362\) 1.41421i 1.41421i
\(363\) 0 0
\(364\) 0 0
\(365\) − 1.41421i − 1.41421i
\(366\) 0 0
\(367\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(368\) 1.00000 1.00000
\(369\) 0 0
\(370\) 2.00000 2.00000
\(371\) 0 0
\(372\) 0 0
\(373\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.00000 1.00000
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) 0 0
\(391\) −1.00000 −1.00000
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.00000 −2.00000
\(396\) 0 0
\(397\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(398\) 1.41421i 1.41421i
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) − 1.41421i − 1.41421i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 1.41421i 1.41421i
\(411\) 0 0
\(412\) 0 0
\(413\) 1.00000 1.00000
\(414\) 0 0
\(415\) −2.00000 −2.00000
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 1.00000 1.00000
\(423\) 0 0
\(424\) 0 0
\(425\) −1.00000 −1.00000
\(426\) 0 0
\(427\) −1.00000 −1.00000
\(428\) 0 0
\(429\) 0 0
\(430\) − 1.41421i − 1.41421i
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(434\) −1.00000 −1.00000
\(435\) 0 0
\(436\) 0 0
\(437\) − 1.41421i − 1.41421i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 1.41421i 1.41421i
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 2.00000 2.00000
\(446\) −1.00000 −1.00000
\(447\) 0 0
\(448\) 1.00000 1.00000
\(449\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) − 1.41421i − 1.41421i
\(455\) 2.00000 2.00000
\(456\) 0 0
\(457\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 1.41421i 1.41421i
\(459\) 0 0
\(460\) 0 0
\(461\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.41421i 1.41421i
\(467\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) − 1.41421i − 1.41421i
\(471\) 0 0
\(472\) 1.00000 1.00000
\(473\) 0 0
\(474\) 0 0
\(475\) − 1.41421i − 1.41421i
\(476\) 0 0
\(477\) 0 0
\(478\) 1.41421i 1.41421i
\(479\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(480\) 0 0
\(481\) 2.00000 2.00000
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 1.41421i − 1.41421i
\(486\) 0 0
\(487\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(488\) −1.00000 −1.00000
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −2.00000 −2.00000
\(495\) 0 0
\(496\) −1.00000 −1.00000
\(497\) − 1.41421i − 1.41421i
\(498\) 0 0
\(499\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.00000 −1.00000
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) − 2.82843i − 2.82843i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −1.00000 −1.00000
\(512\) 1.00000 1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) − 1.41421i − 1.41421i
\(519\) 0 0
\(520\) 2.00000 2.00000
\(521\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 1.41421i 1.41421i
\(527\) 1.00000 1.00000
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.41421i 1.41421i
\(534\) 0 0
\(535\) 1.41421i 1.41421i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.41421i 1.41421i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.41421i 1.41421i
\(554\) 1.41421i 1.41421i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) − 1.41421i − 1.41421i
\(560\) − 1.41421i − 1.41421i
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) − 1.41421i − 1.41421i
\(567\) 0 0
\(568\) − 1.41421i − 1.41421i
\(569\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) 0 0
\(571\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1.00000 1.00000
\(575\) 1.00000 1.00000
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.41421i 1.41421i
\(582\) 0 0
\(583\) 0 0
\(584\) −1.00000 −1.00000
\(585\) 0 0
\(586\) − 1.41421i − 1.41421i
\(587\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 1.41421i 1.41421i
\(590\) − 1.41421i − 1.41421i
\(591\) 0 0
\(592\) − 1.41421i − 1.41421i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 1.41421i 1.41421i
\(596\) 0 0
\(597\) 0 0
\(598\) − 1.41421i − 1.41421i
\(599\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0 0
\(601\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(602\) −1.00000 −1.00000
\(603\) 0 0
\(604\) 0 0
\(605\) − 1.41421i − 1.41421i
\(606\) 0 0
\(607\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.41421i 1.41421i
\(611\) − 1.41421i − 1.41421i
\(612\) 0 0
\(613\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(614\) −1.00000 −1.00000
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) − 1.41421i − 1.41421i
\(624\) 0 0
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.41421i 1.41421i
\(630\) 0 0
\(631\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(632\) 1.41421i 1.41421i
\(633\) 0 0
\(634\) −1.00000 −1.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) − 1.41421i − 1.41421i
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) − 1.41421i − 1.41421i
\(647\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) − 1.41421i − 1.41421i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.00000 1.00000
\(657\) 0 0
\(658\) −1.00000 −1.00000
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.41421i 1.41421i
\(665\) −2.00000 −2.00000
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0 0
\(679\) −1.00000 −1.00000
\(680\) 1.41421i 1.41421i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 1.00000
\(687\) 0 0
\(688\) −1.00000 −1.00000
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) − 1.41421i − 1.41421i
\(695\) 0 0
\(696\) 0 0
\(697\) −1.00000 −1.00000
\(698\) 1.00000 1.00000
\(699\) 0 0
\(700\) 0 0
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 0 0
\(703\) −2.00000 −2.00000
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.00000 −2.00000
\(708\) 0 0
\(709\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(710\) −2.00000 −2.00000
\(711\) 0 0
\(712\) − 1.41421i − 1.41421i
\(713\) −1.00000 −1.00000
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 1.00000 1.00000
\(719\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000 1.00000
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) − 1.41421i − 1.41421i
\(729\) 0 0
\(730\) 1.41421i 1.41421i
\(731\) 1.00000 1.00000
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) − 1.41421i − 1.41421i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(744\) 0 0
\(745\) 1.41421i 1.41421i
\(746\) 1.00000 1.00000
\(747\) 0 0
\(748\) 0 0
\(749\) 1.00000 1.00000
\(750\) 0 0
\(751\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) −1.00000 −1.00000
\(753\) 0 0
\(754\) 0 0
\(755\) 2.00000 2.00000
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −2.00000 −2.00000
\(761\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(762\) 0 0
\(763\) 1.00000 1.00000
\(764\) 0 0
\(765\) 0 0
\(766\) −1.00000 −1.00000
\(767\) − 1.41421i − 1.41421i
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 0 0
\(775\) −1.00000 −1.00000
\(776\) −1.00000 −1.00000
\(777\) 0 0
\(778\) −1.00000 −1.00000
\(779\) − 1.41421i − 1.41421i
\(780\) 0 0
\(781\) 0 0
\(782\) 1.00000 1.00000
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 2.00000 2.00000
\(791\) 0 0
\(792\) 0 0
\(793\) 1.41421i 1.41421i
\(794\) − 1.41421i − 1.41421i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 1.00000 1.00000
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) − 1.41421i − 1.41421i
\(806\) 1.41421i 1.41421i
\(807\) 0 0
\(808\) −2.00000 −2.00000
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2.00000 2.00000
\(816\) 0 0
\(817\) 1.41421i 1.41421i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(822\) 0 0
\(823\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −1.00000 −1.00000
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 2.00000 2.00000
\(831\) 0 0
\(832\) − 1.41421i − 1.41421i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 1.00000 1.00000
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 1.00000 1.00000
\(843\) 0 0
\(844\) 0 0
\(845\) − 1.41421i − 1.41421i
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) 0 0
\(849\) 0 0
\(850\) 1.00000 1.00000
\(851\) − 1.41421i − 1.41421i
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 1.00000 1.00000
\(855\) 0 0
\(856\) 1.00000 1.00000
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(864\) 0 0
\(865\) 2.00000 2.00000
\(866\) −1.00000 −1.00000
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 1.00000 1.00000
\(873\) 0 0
\(874\) 1.41421i 1.41421i
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −2.00000 −2.00000
\(891\) 0 0
\(892\) 0 0
\(893\) 1.41421i 1.41421i
\(894\) 0 0
\(895\) − 1.41421i − 1.41421i
\(896\) −1.00000 −1.00000
\(897\) 0 0
\(898\) 1.00000 1.00000
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.00000 2.00000
\(906\) 0 0
\(907\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) −2.00000 −2.00000
\(911\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 1.00000 1.00000
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(920\) − 1.41421i − 1.41421i
\(921\) 0 0
\(922\) 1.41421i 1.41421i
\(923\) −2.00000 −2.00000
\(924\) 0 0
\(925\) − 1.41421i − 1.41421i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) − 1.41421i − 1.41421i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(942\) 0 0
\(943\) 1.00000 1.00000
\(944\) −1.00000 −1.00000
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 1.41421i 1.41421i
\(950\) 1.41421i 1.41421i
\(951\) 0 0
\(952\) 1.00000 1.00000
\(953\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 1.41421i 1.41421i
\(959\) 0 0
\(960\) 0 0
\(961\) 0 0
\(962\) −2.00000 −2.00000
\(963\) 0 0
\(964\) 0 0
\(965\) 1.41421i 1.41421i
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) 1.41421i 1.41421i
\(971\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 1.41421i 1.41421i
\(975\) 0 0
\(976\) 1.00000 1.00000
\(977\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.00000 −1.00000
\(990\) 0 0
\(991\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 1.41421i 1.41421i
\(995\) 2.00000 2.00000
\(996\) 0 0
\(997\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) −1.00000 −1.00000
\(999\) 0 0
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 \(a_p\))