Properties

Label 2183.1.d.c.2182.1
Level 2183
Weight 1
Character 2183.2182
Analytic conductor 1.089
Analytic rank 0
Dimension 2
Projective image \(S_{4}\)
CM/RM No
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 2183 = 37 \cdot 59 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2183.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(1.08945892258\)
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 4.2.2183.1
Artin image size \(48\)
Artin image $\GL(2,3)$
Artin field Galois closure of 8.2.10403062487.3

Embedding invariants

Embedding label 2182.1
Root \(1.41421i\)
Character \(\chi\) = 2183.2182
Dual form 2183.1.d.c.2182.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.41421i q^{5}\) \(-1.00000 q^{7}\) \(+1.00000 q^{8}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.41421i q^{5}\) \(-1.00000 q^{7}\) \(+1.00000 q^{8}\) \(-1.00000 q^{9}\) \(+1.41421i q^{10}\) \(-1.41421i q^{11}\) \(+1.00000 q^{13}\) \(+1.00000 q^{14}\) \(-1.00000 q^{16}\) \(-1.41421i q^{17}\) \(+1.00000 q^{18}\) \(+1.41421i q^{19}\) \(+1.41421i q^{22}\) \(-1.00000 q^{25}\) \(-1.00000 q^{26}\) \(-1.41421i q^{29}\) \(+1.00000 q^{31}\) \(+1.41421i q^{34}\) \(+1.41421i q^{35}\) \(-1.00000 q^{37}\) \(-1.41421i q^{38}\) \(-1.41421i q^{40}\) \(-1.00000 q^{41}\) \(+1.41421i q^{45}\) \(+1.41421i q^{47}\) \(+1.00000 q^{50}\) \(-1.00000 q^{53}\) \(-2.00000 q^{55}\) \(-1.00000 q^{56}\) \(+1.41421i q^{58}\) \(+1.00000 q^{59}\) \(-1.00000 q^{61}\) \(-1.00000 q^{62}\) \(+1.00000 q^{63}\) \(+1.00000 q^{64}\) \(-1.41421i q^{65}\) \(-1.41421i q^{67}\) \(-1.41421i q^{70}\) \(-1.00000 q^{71}\) \(-1.00000 q^{72}\) \(+1.41421i q^{73}\) \(+1.00000 q^{74}\) \(+1.41421i q^{77}\) \(+1.41421i q^{80}\) \(+1.00000 q^{81}\) \(+1.00000 q^{82}\) \(-2.00000 q^{85}\) \(-1.41421i q^{88}\) \(-1.00000 q^{89}\) \(-1.41421i q^{90}\) \(-1.00000 q^{91}\) \(-1.41421i q^{94}\) \(+2.00000 q^{95}\) \(-1.00000 q^{97}\) \(+1.41421i q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 2q^{56} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 2q^{62} \) \(\mathstrut +\mathstrut 2q^{63} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 2q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2183\mathbb{Z}\right)^\times\).

\(n\) \(297\) \(1889\)
\(\chi(n)\) \(-1\) \(-1\)

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