Properties

Label 1823.1.b.b.1822.1
Level 1823
Weight 1
Character 1823.1822
Analytic conductor 0.910
Analytic rank 0
Dimension 2
Projective image \(S_{4}\)
CM/RM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 1823 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 1823.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.90979551803\)
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 4.2.1823.1
Artin image size \(48\)
Artin image $\GL(2,3)$
Artin field Galois closure of 8.2.6058428767.1

Embedding invariants

Embedding label 1822.1
Root \(1.41421i\)
Character \(\chi\) = 1823.1822
Dual form 1823.1.b.b.1822.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.00000 q^{3}\) \(-1.41421i q^{5}\) \(-1.00000 q^{6}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.00000 q^{3}\) \(-1.41421i q^{5}\) \(-1.00000 q^{6}\) \(-1.00000 q^{8}\) \(-1.41421i q^{10}\) \(+1.41421i q^{15}\) \(-1.00000 q^{16}\) \(-1.00000 q^{17}\) \(-1.00000 q^{19}\) \(+1.41421i q^{23}\) \(+1.00000 q^{24}\) \(-1.00000 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(+1.41421i q^{30}\) \(-1.00000 q^{34}\) \(-1.00000 q^{37}\) \(-1.00000 q^{38}\) \(+1.41421i q^{40}\) \(-1.41421i q^{41}\) \(-1.41421i q^{43}\) \(+1.41421i q^{46}\) \(+1.41421i q^{47}\) \(+1.00000 q^{48}\) \(-1.00000 q^{49}\) \(-1.00000 q^{50}\) \(+1.00000 q^{51}\) \(+1.00000 q^{54}\) \(+1.00000 q^{57}\) \(-1.00000 q^{58}\) \(-1.41421i q^{59}\) \(+1.00000 q^{64}\) \(-1.41421i q^{69}\) \(-1.00000 q^{73}\) \(-1.00000 q^{74}\) \(+1.00000 q^{75}\) \(-1.00000 q^{79}\) \(+1.41421i q^{80}\) \(-1.00000 q^{81}\) \(-1.41421i q^{82}\) \(+1.00000 q^{83}\) \(+1.41421i q^{85}\) \(-1.41421i q^{86}\) \(+1.00000 q^{87}\) \(-1.41421i q^{89}\) \(+1.41421i q^{94}\) \(+1.41421i q^{95}\) \(-1.00000 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 2q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 2q^{83} \) \(\mathstrut +\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1823\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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