Properties

Label 283.1.b.b.282.2
Level 283
Weight 1
Character 283.282
Analytic conductor 0.141
Analytic rank 0
Dimension 2
Projective image \(S_{4}\)
CM/RM No
Inner twists 2

Related objects

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Newspace parameters

Level: \( N \) = \( 283 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 283.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.141235398575\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Projective image \(S_{4}\)
Projective field Galois closure of 4.2.283.1
Artin image size \(48\)
Artin image $\GL(2,3)$
Artin field Galois closure of 8.2.22665187.3

Embedding invariants

Embedding label 282.2
Root \(-1.41421i\)
Character \(\chi\) = 283.282
Dual form 283.1.b.b.282.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.41421i q^{2}\) \(-1.41421i q^{3}\) \(-1.00000 q^{4}\) \(-1.41421i q^{5}\) \(+2.00000 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.41421i q^{2}\) \(-1.41421i q^{3}\) \(-1.00000 q^{4}\) \(-1.41421i q^{5}\) \(+2.00000 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{9}\) \(+2.00000 q^{10}\) \(+1.00000 q^{11}\) \(+1.41421i q^{12}\) \(+1.00000 q^{13}\) \(-1.41421i q^{14}\) \(-2.00000 q^{15}\) \(-1.00000 q^{16}\) \(-1.41421i q^{18}\) \(+1.41421i q^{19}\) \(+1.41421i q^{20}\) \(+1.41421i q^{21}\) \(+1.41421i q^{22}\) \(-1.00000 q^{23}\) \(-1.00000 q^{25}\) \(+1.41421i q^{26}\) \(+1.00000 q^{28}\) \(-1.00000 q^{29}\) \(-2.82843i q^{30}\) \(+1.41421i q^{31}\) \(-1.41421i q^{32}\) \(-1.41421i q^{33}\) \(+1.41421i q^{35}\) \(+1.00000 q^{36}\) \(-2.00000 q^{38}\) \(-1.41421i q^{39}\) \(+1.00000 q^{41}\) \(-2.00000 q^{42}\) \(+1.41421i q^{43}\) \(-1.00000 q^{44}\) \(+1.41421i q^{45}\) \(-1.41421i q^{46}\) \(-1.41421i q^{47}\) \(+1.41421i q^{48}\) \(-1.41421i q^{50}\) \(-1.00000 q^{52}\) \(-1.41421i q^{55}\) \(+2.00000 q^{57}\) \(-1.41421i q^{58}\) \(+1.00000 q^{59}\) \(+2.00000 q^{60}\) \(+1.00000 q^{61}\) \(-2.00000 q^{62}\) \(+1.00000 q^{63}\) \(+1.00000 q^{64}\) \(-1.41421i q^{65}\) \(+2.00000 q^{66}\) \(+1.41421i q^{69}\) \(-2.00000 q^{70}\) \(+1.41421i q^{75}\) \(-1.41421i q^{76}\) \(-1.00000 q^{77}\) \(+2.00000 q^{78}\) \(+1.41421i q^{80}\) \(-1.00000 q^{81}\) \(+1.41421i q^{82}\) \(-2.00000 q^{83}\) \(-1.41421i q^{84}\) \(-2.00000 q^{86}\) \(+1.41421i q^{87}\) \(-1.00000 q^{89}\) \(-2.00000 q^{90}\) \(-1.00000 q^{91}\) \(+1.00000 q^{92}\) \(+2.00000 q^{93}\) \(+2.00000 q^{94}\) \(+2.00000 q^{95}\) \(-2.00000 q^{96}\) \(+1.00000 q^{97}\) \(-1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut +\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 4q^{62} \) \(\mathstrut +\mathstrut 2q^{63} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 4q^{78} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 4q^{86} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut -\mathstrut 4q^{90} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 2q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/283\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(4\) −1.00000 −1.00000
\(5\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(6\) 2.00000 2.00000
\(7\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 0 0
\(9\) −1.00000 −1.00000
\(10\) 2.00000 2.00000
\(11\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) 1.41421i 1.41421i
\(13\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) − 1.41421i − 1.41421i
\(15\) −2.00000 −2.00000
\(16\) −1.00000 −1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) − 1.41421i − 1.41421i
\(19\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) 1.41421i 1.41421i
\(21\) 1.41421i 1.41421i
\(22\) 1.41421i 1.41421i
\(23\) −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
\(28\) 1.00000 1.00000
\(29\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) − 2.82843i − 2.82843i
\(31\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(32\) − 1.41421i − 1.41421i
\(33\) − 1.41421i − 1.41421i
\(34\) 0 0
\(35\) 1.41421i 1.41421i
\(36\) 1.00000 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −2.00000 −2.00000
\(39\) − 1.41421i − 1.41421i
\(40\) 0 0
\(41\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(42\) −2.00000 −2.00000
\(43\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) −1.00000 −1.00000
\(45\) 1.41421i 1.41421i
\(46\) − 1.41421i − 1.41421i
\(47\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(48\) 1.41421i 1.41421i
\(49\) 0 0
\(50\) − 1.41421i − 1.41421i
\(51\) 0 0
\(52\) −1.00000 −1.00000
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) − 1.41421i − 1.41421i
\(56\) 0 0
\(57\) 2.00000 2.00000
\(58\) − 1.41421i − 1.41421i
\(59\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) 2.00000 2.00000
\(61\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) −2.00000 −2.00000
\(63\) 1.00000 1.00000
\(64\) 1.00000 1.00000
\(65\) − 1.41421i − 1.41421i
\(66\) 2.00000 2.00000
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 1.41421i 1.41421i
\(70\) −2.00000 −2.00000
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 1.41421i 1.41421i
\(76\) − 1.41421i − 1.41421i
\(77\) −1.00000 −1.00000
\(78\) 2.00000 2.00000
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 1.41421i 1.41421i
\(81\) −1.00000 −1.00000
\(82\) 1.41421i 1.41421i
\(83\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(84\) − 1.41421i − 1.41421i
\(85\) 0 0
\(86\) −2.00000 −2.00000
\(87\) 1.41421i 1.41421i
\(88\) 0 0
\(89\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) −2.00000 −2.00000
\(91\) −1.00000 −1.00000
\(92\) 1.00000 1.00000
\(93\) 2.00000 2.00000
\(94\) 2.00000 2.00000
\(95\) 2.00000 2.00000
\(96\) −2.00000 −2.00000
\(97\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) 0 0
\(99\) −1.00000 −1.00000
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) 0 0
\(105\) 2.00000 2.00000
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(110\) 2.00000 2.00000
\(111\) 0 0
\(112\) 1.00000 1.00000
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 2.82843i 2.82843i
\(115\) 1.41421i 1.41421i
\(116\) 1.00000 1.00000
\(117\) −1.00000 −1.00000
\(118\) 1.41421i 1.41421i
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 1.41421i 1.41421i
\(123\) − 1.41421i − 1.41421i
\(124\) − 1.41421i − 1.41421i
\(125\) 0 0
\(126\) 1.41421i 1.41421i
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 2.00000 2.00000
\(130\) 2.00000 2.00000
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 1.41421i 1.41421i
\(133\) − 1.41421i − 1.41421i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) −2.00000 −2.00000
\(139\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(140\) − 1.41421i − 1.41421i
\(141\) −2.00000 −2.00000
\(142\) 0 0
\(143\) 1.00000 1.00000
\(144\) 1.00000 1.00000
\(145\) 1.41421i 1.41421i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(150\) −2.00000 −2.00000
\(151\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) − 1.41421i − 1.41421i
\(155\) 2.00000 2.00000
\(156\) 1.41421i 1.41421i
\(157\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −2.00000 −2.00000
\(161\) 1.00000 1.00000
\(162\) − 1.41421i − 1.41421i
\(163\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) −1.00000 −1.00000
\(165\) −2.00000 −2.00000
\(166\) − 2.82843i − 2.82843i
\(167\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) − 1.41421i − 1.41421i
\(172\) − 1.41421i − 1.41421i
\(173\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(174\) −2.00000 −2.00000
\(175\) 1.00000 1.00000
\(176\) −1.00000 −1.00000
\(177\) − 1.41421i − 1.41421i
\(178\) − 1.41421i − 1.41421i
\(179\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) − 1.41421i − 1.41421i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) − 1.41421i − 1.41421i
\(183\) − 1.41421i − 1.41421i
\(184\) 0 0
\(185\) 0 0
\(186\) 2.82843i 2.82843i
\(187\) 0 0
\(188\) 1.41421i 1.41421i
\(189\) 0 0
\(190\) 2.82843i 2.82843i
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) − 1.41421i − 1.41421i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 1.41421i 1.41421i
\(195\) −2.00000 −2.00000
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) − 1.41421i − 1.41421i
\(199\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.00000 1.00000
\(204\) 0 0
\(205\) − 1.41421i − 1.41421i
\(206\) − 1.41421i − 1.41421i
\(207\) 1.00000 1.00000
\(208\) −1.00000 −1.00000
\(209\) 1.41421i 1.41421i
\(210\) 2.82843i 2.82843i
\(211\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.00000 2.00000
\(216\) 0 0
\(217\) − 1.41421i − 1.41421i
\(218\) 2.00000 2.00000
\(219\) 0 0
\(220\) 1.41421i 1.41421i
\(221\) 0 0
\(222\) 0 0
\(223\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(224\) 1.41421i 1.41421i
\(225\) 1.00000 1.00000
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) −2.00000 −2.00000
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) −2.00000 −2.00000
\(231\) 1.41421i 1.41421i
\(232\) 0 0
\(233\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) − 1.41421i − 1.41421i
\(235\) −2.00000 −2.00000
\(236\) −1.00000 −1.00000
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 2.00000 2.00000
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 1.41421i 1.41421i
\(244\) −1.00000 −1.00000
\(245\) 0 0
\(246\) 2.00000 2.00000
\(247\) 1.41421i 1.41421i
\(248\) 0 0
\(249\) 2.82843i 2.82843i
\(250\) 0 0
\(251\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(252\) −1.00000 −1.00000
\(253\) −1.00000 −1.00000
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 2.82843i 2.82843i
\(259\) 0 0
\(260\) 1.41421i 1.41421i
\(261\) 1.00000 1.00000
\(262\) 0 0
\(263\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.00000 2.00000
\(267\) 1.41421i 1.41421i
\(268\) 0 0
\(269\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0 0
\(273\) 1.41421i 1.41421i
\(274\) 1.41421i 1.41421i
\(275\) −1.00000 −1.00000
\(276\) − 1.41421i − 1.41421i
\(277\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(278\) 2.00000 2.00000
\(279\) − 1.41421i − 1.41421i
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) − 2.82843i − 2.82843i
\(283\) 1.00000 1.00000
\(284\) 0 0
\(285\) − 2.82843i − 2.82843i
\(286\) 1.41421i 1.41421i
\(287\) −1.00000 −1.00000
\(288\) 1.41421i 1.41421i
\(289\) 1.00000 1.00000
\(290\) −2.00000 −2.00000
\(291\) − 1.41421i − 1.41421i
\(292\) 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
\(296\) 0 0
\(297\) 0 0
\(298\) −2.00000 −2.00000
\(299\) −1.00000 −1.00000
\(300\) − 1.41421i − 1.41421i
\(301\) − 1.41421i − 1.41421i
\(302\) − 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 \(0.333333\pi\)
\(308\) 1.00000 1.00000
\(309\) 1.41421i 1.41421i
\(310\) 2.82843i 2.82843i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(314\) − 1.41421i − 1.41421i
\(315\) − 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
\(319\) −1.00000 −1.00000
\(320\) − 1.41421i − 1.41421i
\(321\) 0 0
\(322\) 1.41421i 1.41421i
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) −1.00000 −1.00000
\(326\) − 1.41421i − 1.41421i
\(327\) −2.00000 −2.00000
\(328\) 0 0
\(329\) 1.41421i 1.41421i
\(330\) − 2.82843i − 2.82843i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 2.00000 2.00000
\(333\) 0 0
\(334\) 2.00000 2.00000
\(335\) 0 0
\(336\) − 1.41421i − 1.41421i
\(337\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.41421i 1.41421i
\(342\) 2.00000 2.00000
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) 2.00000 2.00000
\(346\) −2.00000 −2.00000
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) − 1.41421i − 1.41421i
\(349\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 1.41421i 1.41421i
\(351\) 0 0
\(352\) − 1.41421i − 1.41421i
\(353\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 2.00000 2.00000
\(355\) 0 0
\(356\) 1.00000 1.00000
\(357\) 0 0
\(358\) 1.41421i 1.41421i
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −1.00000 −1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 1.00000 1.00000
\(365\) 0 0
\(366\) 2.00000 2.00000
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 1.00000 1.00000
\(369\) −1.00000 −1.00000
\(370\) 0 0
\(371\) 0 0
\(372\) −2.00000 −2.00000
\(373\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.00000 −1.00000
\(378\) 0 0
\(379\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(380\) −2.00000 −2.00000
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 1.41421i 1.41421i
\(386\) 0 0
\(387\) − 1.41421i − 1.41421i
\(388\) −1.00000 −1.00000
\(389\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) − 2.82843i − 2.82843i
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 1.00000 1.00000
\(397\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(398\) 1.41421i 1.41421i
\(399\) −2.00000 −2.00000
\(400\) 1.00000 1.00000
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 1.41421i 1.41421i
\(404\) 0 0
\(405\) 1.41421i 1.41421i
\(406\) 1.41421i 1.41421i
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 2.00000 2.00000
\(411\) − 1.41421i − 1.41421i
\(412\) 1.00000 1.00000
\(413\) −1.00000 −1.00000
\(414\) 1.41421i 1.41421i
\(415\) 2.82843i 2.82843i
\(416\) − 1.41421i − 1.41421i
\(417\) −2.00000 −2.00000
\(418\) −2.00000 −2.00000
\(419\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) −2.00000 −2.00000
\(421\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(422\) − 1.41421i − 1.41421i
\(423\) 1.41421i 1.41421i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.00000 −1.00000
\(428\) 0 0
\(429\) − 1.41421i − 1.41421i
\(430\) 2.82843i 2.82843i
\(431\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(432\) 0 0
\(433\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(434\) 2.00000 2.00000
\(435\) 2.00000 2.00000
\(436\) 1.41421i 1.41421i
\(437\) − 1.41421i − 1.41421i
\(438\) 0 0
\(439\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 0 0
\(445\) 1.41421i 1.41421i
\(446\) 2.00000 2.00000
\(447\) 2.00000 2.00000
\(448\) −1.00000 −1.00000
\(449\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(450\) 1.41421i 1.41421i
\(451\) 1.00000 1.00000
\(452\) 0 0
\(453\) 1.41421i 1.41421i
\(454\) 0 0
\(455\) 1.41421i 1.41421i
\(456\) 0 0
\(457\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) − 1.41421i − 1.41421i
\(461\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(462\) −2.00000 −2.00000
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 1.00000 1.00000
\(465\) − 2.82843i − 2.82843i
\(466\) − 1.41421i − 1.41421i
\(467\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 1.00000 1.00000
\(469\) 0 0
\(470\) − 2.82843i − 2.82843i
\(471\) 1.41421i 1.41421i
\(472\) 0 0
\(473\) 1.41421i 1.41421i
\(474\) 0 0
\(475\) − 1.41421i − 1.41421i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 2.82843i 2.82843i
\(481\) 0 0
\(482\) 0 0
\(483\) − 1.41421i − 1.41421i
\(484\) 0 0
\(485\) − 1.41421i − 1.41421i
\(486\) −2.00000 −2.00000
\(487\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) 1.41421i 1.41421i
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 1.41421i 1.41421i
\(493\) 0 0
\(494\) −2.00000 −2.00000
\(495\) 1.41421i 1.41421i
\(496\) − 1.41421i − 1.41421i
\(497\) 0 0
\(498\) −4.00000 −4.00000
\(499\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 0 0
\(501\) −2.00000 −2.00000
\(502\) 1.41421i 1.41421i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) − 1.41421i − 1.41421i
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.41421i 1.41421i
\(513\) 0 0
\(514\) − 1.41421i − 1.41421i
\(515\) 1.41421i 1.41421i
\(516\) −2.00000 −2.00000
\(517\) − 1.41421i − 1.41421i
\(518\) 0 0
\(519\) 2.00000 2.00000
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 1.41421i 1.41421i
\(523\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) 0 0
\(525\) − 1.41421i − 1.41421i
\(526\) − 1.41421i − 1.41421i
\(527\) 0 0
\(528\) 1.41421i 1.41421i
\(529\) 0 0
\(530\) 0 0
\(531\) −1.00000 −1.00000
\(532\) 1.41421i 1.41421i
\(533\) 1.00000 1.00000
\(534\) −2.00000 −2.00000
\(535\) 0 0
\(536\) 0 0
\(537\) − 1.41421i − 1.41421i
\(538\) − 1.41421i − 1.41421i
\(539\) 0 0
\(540\) 0 0
\(541\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(542\) 1.41421i 1.41421i
\(543\) 0 0
\(544\) 0 0
\(545\) −2.00000 −2.00000
\(546\) −2.00000 −2.00000
\(547\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(548\) −1.00000 −1.00000
\(549\) −1.00000 −1.00000
\(550\) − 1.41421i − 1.41421i
\(551\) − 1.41421i − 1.41421i
\(552\) 0 0
\(553\) 0 0
\(554\) −2.00000 −2.00000
\(555\) 0 0
\(556\) 1.41421i 1.41421i
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 2.00000 2.00000
\(559\) 1.41421i 1.41421i
\(560\) − 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 \(0.666667\pi\)
\(564\) 2.00000 2.00000
\(565\) 0 0
\(566\) 1.41421i 1.41421i
\(567\) 1.00000 1.00000
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 4.00000 4.00000
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) −1.00000 −1.00000
\(573\) 0 0
\(574\) − 1.41421i − 1.41421i
\(575\) 1.00000 1.00000
\(576\) −1.00000 −1.00000
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 1.41421i 1.41421i
\(579\) 0 0
\(580\) − 1.41421i − 1.41421i
\(581\) 2.00000 2.00000
\(582\) 2.00000 2.00000
\(583\) 0 0
\(584\) 0 0
\(585\) 1.41421i 1.41421i
\(586\) 1.41421i 1.41421i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) −2.00000 −2.00000
\(590\) 2.00000 2.00000
\(591\) 0 0
\(592\) 0 0
\(593\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) − 1.41421i − 1.41421i
\(597\) − 1.41421i − 1.41421i
\(598\) − 1.41421i − 1.41421i
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(602\) 2.00000 2.00000
\(603\) 0 0
\(604\) 1.00000 1.00000
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 2.00000 2.00000
\(609\) − 1.41421i − 1.41421i
\(610\) 2.00000 2.00000
\(611\) − 1.41421i − 1.41421i
\(612\) 0 0
\(613\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) 1.41421i 1.41421i
\(615\) −2.00000 −2.00000
\(616\) 0 0
\(617\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(618\) −2.00000 −2.00000
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) −2.00000 −2.00000
\(621\) 0 0
\(622\) 0 0
\(623\) 1.00000 1.00000
\(624\) 1.41421i 1.41421i
\(625\) −1.00000 −1.00000
\(626\) −2.00000 −2.00000
\(627\) 2.00000 2.00000
\(628\) 1.00000 1.00000
\(629\) 0 0
\(630\) 2.00000 2.00000
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 1.41421i 1.41421i
\(634\) 1.41421i 1.41421i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) − 1.41421i − 1.41421i
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(644\) −1.00000 −1.00000
\(645\) − 2.82843i − 2.82843i
\(646\) 0 0
\(647\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) 0 0
\(649\) 1.00000 1.00000
\(650\) − 1.41421i − 1.41421i
\(651\) −2.00000 −2.00000
\(652\) 1.00000 1.00000
\(653\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(654\) − 2.82843i − 2.82843i
\(655\) 0 0
\(656\) −1.00000 −1.00000
\(657\) 0 0
\(658\) −2.00000 −2.00000
\(659\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) 2.00000 2.00000
\(661\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.00000 −2.00000
\(666\) 0 0
\(667\) 1.00000 1.00000
\(668\) 1.41421i 1.41421i
\(669\) −2.00000 −2.00000
\(670\) 0 0
\(671\) 1.00000 1.00000
\(672\) 2.00000 2.00000
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 1.41421i 1.41421i
\(675\) 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
\(680\) 0 0
\(681\) 0 0
\(682\) −2.00000 −2.00000
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 1.41421i 1.41421i
\(685\) − 1.41421i − 1.41421i
\(686\) 1.41421i 1.41421i
\(687\) 0 0
\(688\) − 1.41421i − 1.41421i
\(689\) 0 0
\(690\) 2.82843i 2.82843i
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) − 1.41421i − 1.41421i
\(693\) 1.00000 1.00000
\(694\) 0 0
\(695\) −2.00000 −2.00000
\(696\) 0 0
\(697\) 0 0
\(698\) − 1.41421i − 1.41421i
\(699\) 1.41421i 1.41421i
\(700\) −1.00000 −1.00000
\(701\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.00000 1.00000
\(705\) 2.82843i 2.82843i
\(706\) 1.41421i 1.41421i
\(707\) 0 0
\(708\) 1.41421i 1.41421i
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 1.41421i − 1.41421i
\(714\) 0 0
\(715\) − 1.41421i − 1.41421i
\(716\) −1.00000 −1.00000
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) − 1.41421i − 1.41421i
\(721\) 1.00000 1.00000
\(722\) − 1.41421i − 1.41421i
\(723\) 0 0
\(724\) 0 0
\(725\) 1.00000 1.00000
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 1.41421i 1.41421i
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1.41421i 1.41421i
\(737\) 0 0
\(738\) − 1.41421i − 1.41421i
\(739\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(740\) 0 0
\(741\) 2.00000 2.00000
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 2.00000 2.00000
\(746\) − 1.41421i − 1.41421i
\(747\) 2.00000 2.00000
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 1.41421i 1.41421i
\(753\) − 1.41421i − 1.41421i
\(754\) − 1.41421i − 1.41421i
\(755\) 1.41421i 1.41421i
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 1.41421i 1.41421i
\(759\) 1.41421i 1.41421i
\(760\) 0 0
\(761\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0 0
\(763\) 1.41421i 1.41421i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.00000 1.00000
\(768\) − 1.41421i − 1.41421i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) −2.00000 −2.00000
\(771\) 1.41421i 1.41421i
\(772\) 0 0
\(773\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(774\) 2.00000 2.00000
\(775\) − 1.41421i − 1.41421i
\(776\) 0 0
\(777\) 0 0
\(778\) − 1.41421i − 1.41421i
\(779\) 1.41421i 1.41421i
\(780\) 2.00000 2.00000
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.41421i 1.41421i
\(786\) 0 0
\(787\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(788\) 0 0
\(789\) 1.41421i 1.41421i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1.00000 1.00000
\(794\) 2.00000 2.00000
\(795\) 0 0
\(796\) −1.00000 −1.00000
\(797\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) − 2.82843i − 2.82843i
\(799\) 0 0
\(800\) 1.41421i 1.41421i
\(801\) 1.00000 1.00000
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) − 1.41421i − 1.41421i
\(806\) −2.00000 −2.00000
\(807\) 1.41421i 1.41421i
\(808\) 0 0
\(809\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(810\) −2.00000 −2.00000
\(811\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(812\) −1.00000 −1.00000
\(813\) − 1.41421i − 1.41421i
\(814\) 0 0
\(815\) 1.41421i 1.41421i
\(816\) 0 0
\(817\) −2.00000 −2.00000
\(818\) 0 0
\(819\) 1.00000 1.00000
\(820\) 1.41421i 1.41421i
\(821\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(822\) 2.00000 2.00000
\(823\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(824\) 0 0
\(825\) 1.41421i 1.41421i
\(826\) − 1.41421i − 1.41421i
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) −1.00000 −1.00000
\(829\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(830\) −4.00000 −4.00000
\(831\) 2.00000 2.00000
\(832\) 1.00000 1.00000
\(833\) 0 0
\(834\) − 2.82843i − 2.82843i
\(835\) −2.00000 −2.00000
\(836\) − 1.41421i − 1.41421i
\(837\) 0 0
\(838\) − 1.41421i − 1.41421i
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 0 0
\(842\) 1.41421i 1.41421i
\(843\) 0 0
\(844\) 1.00000 1.00000
\(845\) 0 0
\(846\) −2.00000 −2.00000
\(847\) 0 0
\(848\) 0 0
\(849\) − 1.41421i − 1.41421i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(854\) − 1.41421i − 1.41421i
\(855\) −2.00000 −2.00000
\(856\) 0 0
\(857\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(858\) 2.00000 2.00000
\(859\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(860\) −2.00000 −2.00000
\(861\) 1.41421i 1.41421i
\(862\) −2.00000 −2.00000
\(863\) − 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
\(866\) 1.41421i 1.41421i
\(867\) − 1.41421i − 1.41421i
\(868\) 1.41421i 1.41421i
\(869\) 0 0
\(870\) 2.82843i 2.82843i
\(871\) 0 0
\(872\) 0 0
\(873\) −1.00000 −1.00000
\(874\) 2.00000 2.00000
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 2.00000 2.00000
\(879\) − 1.41421i − 1.41421i
\(880\) 1.41421i 1.41421i
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) −2.00000 −2.00000
\(886\) 1.41421i 1.41421i
\(887\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −2.00000 −2.00000
\(891\) −1.00000 −1.00000
\(892\) 1.41421i 1.41421i
\(893\) 2.00000 2.00000
\(894\) 2.82843i 2.82843i
\(895\) − 1.41421i − 1.41421i
\(896\) 0 0
\(897\) 1.41421i 1.41421i
\(898\) 2.00000 2.00000
\(899\) − 1.41421i − 1.41421i
\(900\) −1.00000 −1.00000
\(901\) 0 0
\(902\) 1.41421i 1.41421i
\(903\) −2.00000 −2.00000
\(904\) 0 0
\(905\) 0 0
\(906\) −2.00000 −2.00000
\(907\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(908\) 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 \(0.666667\pi\)
\(912\) −2.00000 −2.00000
\(913\) −2.00000 −2.00000
\(914\) − 1.41421i − 1.41421i
\(915\) −2.00000 −2.00000
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(920\) 0 0
\(921\) − 1.41421i − 1.41421i
\(922\) 2.00000 2.00000
\(923\) 0 0
\(924\) − 1.41421i − 1.41421i
\(925\) 0 0
\(926\) 0 0
\(927\) 1.00000 1.00000
\(928\) 1.41421i 1.41421i
\(929\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(930\) 4.00000 4.00000
\(931\) 0 0
\(932\) 1.00000 1.00000
\(933\) 0 0
\(934\) −2.00000 −2.00000
\(935\) 0 0
\(936\) 0 0
\(937\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(938\) 0 0
\(939\) 2.00000 2.00000
\(940\) 2.00000 2.00000
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) −2.00000 −2.00000
\(943\) −1.00000 −1.00000
\(944\) −1.00000 −1.00000
\(945\) 0 0
\(946\) −2.00000 −2.00000
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 2.00000 2.00000
\(951\) − 1.41421i − 1.41421i
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.41421i 1.41421i
\(958\) 0 0
\(959\) −1.00000 −1.00000
\(960\) −2.00000 −2.00000
\(961\) −1.00000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 2.00000 2.00000
\(967\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 2.00000 2.00000
\(971\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(972\) − 1.41421i − 1.41421i
\(973\) 1.41421i 1.41421i
\(974\) − 1.41421i − 1.41421i
\(975\) 1.41421i 1.41421i
\(976\) −1.00000 −1.00000
\(977\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(978\) −2.00000 −2.00000
\(979\) −1.00000 −1.00000
\(980\) 0 0
\(981\) 1.41421i 1.41421i
\(982\) 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
\(987\) 2.00000 2.00000
\(988\) − 1.41421i − 1.41421i
\(989\) − 1.41421i − 1.41421i
\(990\) −2.00000 −2.00000
\(991\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(992\) 2.00000 2.00000
\(993\) 0 0
\(994\) 0 0
\(995\) − 1.41421i − 1.41421i
\(996\) − 2.82843i − 2.82843i
\(997\) 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 \(a_p\))