Properties

Label 2563.1.b.d.2562.2
Level 2563
Weight 1
Character 2563.2562
Analytic conductor 1.279
Analytic rank 0
Dimension 2
Projective image \(S_{4}\)
CM/RM No
Inner twists 2

Related objects

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Newspace parameters

Level: \( N \) = \( 2563 = 11 \cdot 233 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2563.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(1.27910362738\)
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 4.2.2563.1
Artin image size \(48\)
Artin image $\GL(2,3)$
Artin field Galois closure of 8.2.16836267547.1

Embedding invariants

Embedding label 2562.2
Root \(-1.41421i\)
Character \(\chi\) = 2563.2562
Dual form 2563.1.b.d.2562.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} -1.41421i q^{3} -1.00000 q^{4} +1.41421i q^{5} +2.00000 q^{6} -1.00000 q^{9} +O(q^{10})\) \(q+1.41421i q^{2} -1.41421i q^{3} -1.00000 q^{4} +1.41421i q^{5} +2.00000 q^{6} -1.00000 q^{9} -2.00000 q^{10} -1.00000 q^{11} +1.41421i q^{12} +2.00000 q^{15} -1.00000 q^{16} -1.00000 q^{17} -1.41421i q^{18} +1.41421i q^{19} -1.41421i q^{20} -1.41421i q^{22} -1.00000 q^{23} -1.00000 q^{25} +1.41421i q^{29} +2.82843i q^{30} -1.00000 q^{31} -1.41421i q^{32} +1.41421i q^{33} -1.41421i q^{34} +1.00000 q^{36} +1.00000 q^{37} -2.00000 q^{38} -1.00000 q^{41} +1.00000 q^{43} +1.00000 q^{44} -1.41421i q^{45} -1.41421i q^{46} -1.41421i q^{47} +1.41421i q^{48} +1.00000 q^{49} -1.41421i q^{50} +1.41421i q^{51} +1.41421i q^{53} -1.41421i q^{55} +2.00000 q^{57} -2.00000 q^{58} -2.00000 q^{60} -1.41421i q^{62} +1.00000 q^{64} -2.00000 q^{66} +1.00000 q^{68} +1.41421i q^{69} -1.00000 q^{71} +1.00000 q^{73} +1.41421i q^{74} +1.41421i q^{75} -1.41421i q^{76} -1.00000 q^{79} -1.41421i q^{80} -1.00000 q^{81} -1.41421i q^{82} -1.41421i q^{85} +1.41421i q^{86} +2.00000 q^{87} +1.00000 q^{89} +2.00000 q^{90} +1.00000 q^{92} +1.41421i q^{93} +2.00000 q^{94} -2.00000 q^{95} -2.00000 q^{96} +1.41421i q^{97} +1.41421i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} + 4q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} + 4q^{6} - 2q^{9} - 4q^{10} - 2q^{11} + 4q^{15} - 2q^{16} - 2q^{17} - 2q^{23} - 2q^{25} - 2q^{31} + 2q^{36} + 2q^{37} - 4q^{38} - 2q^{41} + 2q^{43} + 2q^{44} + 2q^{49} + 4q^{57} - 4q^{58} - 4q^{60} + 2q^{64} - 4q^{66} + 2q^{68} - 2q^{71} + 2q^{73} - 2q^{79} - 2q^{81} + 4q^{87} + 2q^{89} + 4q^{90} + 2q^{92} + 4q^{94} - 4q^{95} - 4q^{96} + 2q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2563\mathbb{Z}\right)^\times\).

\(n\) \(1399\) \(2333\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 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 \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(6\) 2.00000 2.00000
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) −1.00000 −1.00000
\(10\) −2.00000 −2.00000
\(11\) −1.00000 −1.00000
\(12\) 1.41421i 1.41421i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 2.00000 2.00000
\(16\) −1.00000 −1.00000
\(17\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) − 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
\(21\) 0 0
\(22\) − 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
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(30\) 2.82843i 2.82843i
\(31\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) − 1.41421i − 1.41421i
\(33\) 1.41421i 1.41421i
\(34\) − 1.41421i − 1.41421i
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −2.00000 −2.00000
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 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
\(49\) 1.00000 1.00000
\(50\) − 1.41421i − 1.41421i
\(51\) 1.41421i 1.41421i
\(52\) 0 0
\(53\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(54\) 0 0
\(55\) − 1.41421i − 1.41421i
\(56\) 0 0
\(57\) 2.00000 2.00000
\(58\) −2.00000 −2.00000
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) −2.00000 −2.00000
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) − 1.41421i − 1.41421i
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −2.00000 −2.00000
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 1.00000 1.00000
\(69\) 1.41421i 1.41421i
\(70\) 0 0
\(71\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0 0
\(73\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 1.41421i 1.41421i
\(75\) 1.41421i 1.41421i
\(76\) − 1.41421i − 1.41421i
\(77\) 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
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) − 1.41421i − 1.41421i
\(86\) 1.41421i 1.41421i
\(87\) 2.00000 2.00000
\(88\) 0 0
\(89\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 2.00000 2.00000
\(91\) 0 0
\(92\) 1.00000 1.00000
\(93\) 1.41421i 1.41421i
\(94\) 2.00000 2.00000
\(95\) −2.00000 −2.00000
\(96\) −2.00000 −2.00000
\(97\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(98\) 1.41421i 1.41421i
\(99\) 1.00000 1.00000
\(100\) 1.00000 1.00000
\(101\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(102\) −2.00000 −2.00000
\(103\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.00000 −2.00000
\(107\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(108\) 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
\(111\) − 1.41421i − 1.41421i
\(112\) 0 0
\(113\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) 2.82843i 2.82843i
\(115\) − 1.41421i − 1.41421i
\(116\) − 1.41421i − 1.41421i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 1.41421i 1.41421i
\(124\) 1.00000 1.00000
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) − 1.41421i − 1.41421i
\(130\) 0 0
\(131\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(132\) − 1.41421i − 1.41421i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −2.00000 −2.00000
\(139\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) −2.00000 −2.00000
\(142\) − 1.41421i − 1.41421i
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) −2.00000 −2.00000
\(146\) 1.41421i 1.41421i
\(147\) − 1.41421i − 1.41421i
\(148\) −1.00000 −1.00000
\(149\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) −2.00000 −2.00000
\(151\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 0 0
\(153\) 1.00000 1.00000
\(154\) 0 0
\(155\) − 1.41421i − 1.41421i
\(156\) 0 0
\(157\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) − 1.41421i − 1.41421i
\(159\) 2.00000 2.00000
\(160\) 2.00000 2.00000
\(161\) 0 0
\(162\) − 1.41421i − 1.41421i
\(163\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(164\) 1.00000 1.00000
\(165\) −2.00000 −2.00000
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 2.00000 2.00000
\(171\) − 1.41421i − 1.41421i
\(172\) −1.00000 −1.00000
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 2.82843i 2.82843i
\(175\) 0 0
\(176\) 1.00000 1.00000
\(177\) 0 0
\(178\) 1.41421i 1.41421i
\(179\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(180\) 1.41421i 1.41421i
\(181\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.41421i 1.41421i
\(186\) −2.00000 −2.00000
\(187\) 1.00000 1.00000
\(188\) 1.41421i 1.41421i
\(189\) 0 0
\(190\) − 2.82843i − 2.82843i
\(191\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(192\) − 1.41421i − 1.41421i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) −2.00000 −2.00000
\(195\) 0 0
\(196\) −1.00000 −1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 1.41421i 1.41421i
\(199\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −2.00000 −2.00000
\(203\) 0 0
\(204\) − 1.41421i − 1.41421i
\(205\) − 1.41421i − 1.41421i
\(206\) −2.00000 −2.00000
\(207\) 1.00000 1.00000
\(208\) 0 0
\(209\) − 1.41421i − 1.41421i
\(210\) 0 0
\(211\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) − 1.41421i − 1.41421i
\(213\) 1.41421i 1.41421i
\(214\) −2.00000 −2.00000
\(215\) 1.41421i 1.41421i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.00000 2.00000
\(219\) − 1.41421i − 1.41421i
\(220\) 1.41421i 1.41421i
\(221\) 0 0
\(222\) 2.00000 2.00000
\(223\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) 0 0
\(225\) 1.00000 1.00000
\(226\) 1.41421i 1.41421i
\(227\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) −2.00000 −2.00000
\(229\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 2.00000 2.00000
\(231\) 0 0
\(232\) 0 0
\(233\) 1.00000 1.00000
\(234\) 0 0
\(235\) 2.00000 2.00000
\(236\) 0 0
\(237\) 1.41421i 1.41421i
\(238\) 0 0
\(239\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) −2.00000 −2.00000
\(241\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(242\) 1.41421i 1.41421i
\(243\) 1.41421i 1.41421i
\(244\) 0 0
\(245\) 1.41421i 1.41421i
\(246\) −2.00000 −2.00000
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(252\) 0 0
\(253\) 1.00000 1.00000
\(254\) 0 0
\(255\) −2.00000 −2.00000
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 2.00000 2.00000
\(259\) 0 0
\(260\) 0 0
\(261\) − 1.41421i − 1.41421i
\(262\) 2.00000 2.00000
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) −2.00000 −2.00000
\(266\) 0 0
\(267\) − 1.41421i − 1.41421i
\(268\) 0 0
\(269\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(270\) 0 0
\(271\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(272\) 1.00000 1.00000
\(273\) 0 0
\(274\) 0 0
\(275\) 1.00000 1.00000
\(276\) − 1.41421i − 1.41421i
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) − 1.41421i − 1.41421i
\(279\) 1.00000 1.00000
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) − 2.82843i − 2.82843i
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 1.00000 1.00000
\(285\) 2.82843i 2.82843i
\(286\) 0 0
\(287\) 0 0
\(288\) 1.41421i 1.41421i
\(289\) 0 0
\(290\) − 2.82843i − 2.82843i
\(291\) 2.00000 2.00000
\(292\) −1.00000 −1.00000
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 2.00000 2.00000
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) − 1.41421i − 1.41421i
\(299\) 0 0
\(300\) − 1.41421i − 1.41421i
\(301\) 0 0
\(302\) 1.41421i 1.41421i
\(303\) 2.00000 2.00000
\(304\) − 1.41421i − 1.41421i
\(305\) 0 0
\(306\) 1.41421i 1.41421i
\(307\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(308\) 0 0
\(309\) 2.00000 2.00000
\(310\) 2.00000 2.00000
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) − 1.41421i − 1.41421i
\(315\) 0 0
\(316\) 1.00000 1.00000
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 2.82843i 2.82843i
\(319\) − 1.41421i − 1.41421i
\(320\) 1.41421i 1.41421i
\(321\) 2.00000 2.00000
\(322\) 0 0
\(323\) − 1.41421i − 1.41421i
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) 2.00000 2.00000
\(327\) −2.00000 −2.00000
\(328\) 0 0
\(329\) 0 0
\(330\) − 2.82843i − 2.82843i
\(331\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 0 0
\(333\) −1.00000 −1.00000
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(338\) 1.41421i 1.41421i
\(339\) − 1.41421i − 1.41421i
\(340\) 1.41421i 1.41421i
\(341\) 1.00000 1.00000
\(342\) 2.00000 2.00000
\(343\) 0 0
\(344\) 0 0
\(345\) −2.00000 −2.00000
\(346\) 0 0
\(347\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) −2.00000 −2.00000
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.41421i 1.41421i
\(353\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) − 1.41421i − 1.41421i
\(356\) −1.00000 −1.00000
\(357\) 0 0
\(358\) −2.00000 −2.00000
\(359\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(360\) 0 0
\(361\) −1.00000 −1.00000
\(362\) − 1.41421i − 1.41421i
\(363\) − 1.41421i − 1.41421i
\(364\) 0 0
\(365\) 1.41421i 1.41421i
\(366\) 0 0
\(367\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(368\) 1.00000 1.00000
\(369\) 1.00000 1.00000
\(370\) −2.00000 −2.00000
\(371\) 0 0
\(372\) − 1.41421i − 1.41421i
\(373\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 1.41421i 1.41421i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(380\) 2.00000 2.00000
\(381\) 0 0
\(382\) 2.00000 2.00000
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.00000 −1.00000
\(388\) − 1.41421i − 1.41421i
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 1.00000 1.00000
\(392\) 0 0
\(393\) −2.00000 −2.00000
\(394\) 0 0
\(395\) − 1.41421i − 1.41421i
\(396\) −1.00000 −1.00000
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −2.00000 −2.00000
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) − 1.41421i − 1.41421i
\(405\) − 1.41421i − 1.41421i
\(406\) 0 0
\(407\) −1.00000 −1.00000
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 2.00000 2.00000
\(411\) 0 0
\(412\) − 1.41421i − 1.41421i
\(413\) 0 0
\(414\) 1.41421i 1.41421i
\(415\) 0 0
\(416\) 0 0
\(417\) 1.41421i 1.41421i
\(418\) 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
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 1.41421i 1.41421i
\(423\) 1.41421i 1.41421i
\(424\) 0 0
\(425\) 1.00000 1.00000
\(426\) −2.00000 −2.00000
\(427\) 0 0
\(428\) − 1.41421i − 1.41421i
\(429\) 0 0
\(430\) −2.00000 −2.00000
\(431\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0 0
\(433\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(434\) 0 0
\(435\) 2.82843i 2.82843i
\(436\) 1.41421i 1.41421i
\(437\) − 1.41421i − 1.41421i
\(438\) 2.00000 2.00000
\(439\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 1.41421i 1.41421i
\(445\) 1.41421i 1.41421i
\(446\) −2.00000 −2.00000
\(447\) 1.41421i 1.41421i
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.41421i 1.41421i
\(451\) 1.00000 1.00000
\(452\) −1.00000 −1.00000
\(453\) − 1.41421i − 1.41421i
\(454\) 1.41421i 1.41421i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 1.41421i 1.41421i
\(459\) 0 0
\(460\) 1.41421i 1.41421i
\(461\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) − 1.41421i − 1.41421i
\(465\) −2.00000 −2.00000
\(466\) 1.41421i 1.41421i
\(467\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 2.82843i 2.82843i
\(471\) 1.41421i 1.41421i
\(472\) 0 0
\(473\) −1.00000 −1.00000
\(474\) −2.00000 −2.00000
\(475\) − 1.41421i − 1.41421i
\(476\) 0 0
\(477\) − 1.41421i − 1.41421i
\(478\) 1.41421i 1.41421i
\(479\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(480\) − 2.82843i − 2.82843i
\(481\) 0 0
\(482\) 2.00000 2.00000
\(483\) 0 0
\(484\) −1.00000 −1.00000
\(485\) −2.00000 −2.00000
\(486\) −2.00000 −2.00000
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −2.00000 −2.00000
\(490\) −2.00000 −2.00000
\(491\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(492\) − 1.41421i − 1.41421i
\(493\) − 1.41421i − 1.41421i
\(494\) 0 0
\(495\) 1.41421i 1.41421i
\(496\) 1.00000 1.00000
\(497\) 0 0
\(498\) 0 0
\(499\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.41421i 1.41421i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) −2.00000 −2.00000
\(506\) 1.41421i 1.41421i
\(507\) − 1.41421i − 1.41421i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) − 2.82843i − 2.82843i
\(511\) 0 0
\(512\) 1.41421i 1.41421i
\(513\) 0 0
\(514\) 0 0
\(515\) −2.00000 −2.00000
\(516\) 1.41421i 1.41421i
\(517\) 1.41421i 1.41421i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 2.00000 2.00000
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 1.41421i 1.41421i
\(525\) 0 0
\(526\) 0 0
\(527\) 1.00000 1.00000
\(528\) − 1.41421i − 1.41421i
\(529\) 0 0
\(530\) − 2.82843i − 2.82843i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 2.00000 2.00000
\(535\) −2.00000 −2.00000
\(536\) 0 0
\(537\) 2.00000 2.00000
\(538\) 1.41421i 1.41421i
\(539\) −1.00000 −1.00000
\(540\) 0 0
\(541\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 2.00000 2.00000
\(543\) 1.41421i 1.41421i
\(544\) 1.41421i 1.41421i
\(545\) 2.00000 2.00000
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.41421i 1.41421i
\(551\) −2.00000 −2.00000
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 2.00000 2.00000
\(556\) 1.00000 1.00000
\(557\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 1.41421i 1.41421i
\(559\) 0 0
\(560\) 0 0
\(561\) − 1.41421i − 1.41421i
\(562\) 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
\(565\) 1.41421i 1.41421i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) −4.00000 −4.00000
\(571\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(572\) 0 0
\(573\) −2.00000 −2.00000
\(574\) 0 0
\(575\) 1.00000 1.00000
\(576\) −1.00000 −1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 2.00000 2.00000
\(581\) 0 0
\(582\) 2.82843i 2.82843i
\(583\) − 1.41421i − 1.41421i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 1.41421i 1.41421i
\(589\) − 1.41421i − 1.41421i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 −1.00000
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.00000 1.00000
\(597\) 2.00000 2.00000
\(598\) 0 0
\(599\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.00000 −1.00000
\(605\) 1.41421i 1.41421i
\(606\) 2.82843i 2.82843i
\(607\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(608\) 2.00000 2.00000
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −1.00000 −1.00000
\(613\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(614\) 2.00000 2.00000
\(615\) −2.00000 −2.00000
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 2.82843i 2.82843i
\(619\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) 1.41421i 1.41421i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) −2.00000 −2.00000
\(628\) 1.00000 1.00000
\(629\) −1.00000 −1.00000
\(630\) 0 0
\(631\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(632\) 0 0
\(633\) − 1.41421i − 1.41421i
\(634\) 0 0
\(635\) 0 0
\(636\) −2.00000 −2.00000
\(637\) 0 0
\(638\) 2.00000 2.00000
\(639\) 1.00000 1.00000
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 2.82843i 2.82843i
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 2.00000 2.00000
\(646\) 2.00000 2.00000
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1.41421i 1.41421i
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) − 2.82843i − 2.82843i
\(655\) 2.00000 2.00000
\(656\) 1.00000 1.00000
\(657\) −1.00000 −1.00000
\(658\) 0 0
\(659\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(660\) 2.00000 2.00000
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 1.41421i 1.41421i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) − 1.41421i − 1.41421i
\(667\) − 1.41421i − 1.41421i
\(668\) 0 0
\(669\) 2.00000 2.00000
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(674\) −2.00000 −2.00000
\(675\) 0 0
\(676\) −1.00000 −1.00000
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 2.00000 2.00000
\(679\) 0 0
\(680\) 0 0
\(681\) − 1.41421i − 1.41421i
\(682\) 1.41421i 1.41421i
\(683\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(684\) 1.41421i 1.41421i
\(685\) 0 0
\(686\) 0 0
\(687\) − 1.41421i − 1.41421i
\(688\) −1.00000 −1.00000
\(689\) 0 0
\(690\) − 2.82843i − 2.82843i
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.41421i 1.41421i
\(695\) − 1.41421i − 1.41421i
\(696\) 0 0
\(697\) 1.00000 1.00000
\(698\) 0 0
\(699\) − 1.41421i − 1.41421i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 1.41421i 1.41421i
\(704\) −1.00000 −1.00000
\(705\) − 2.82843i − 2.82843i
\(706\) − 1.41421i − 1.41421i
\(707\) 0 0
\(708\) 0 0
\(709\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(710\) 2.00000 2.00000
\(711\) 1.00000 1.00000
\(712\) 0 0
\(713\) 1.00000 1.00000
\(714\) 0 0
\(715\) 0 0
\(716\) − 1.41421i − 1.41421i
\(717\) − 1.41421i − 1.41421i
\(718\) −2.00000 −2.00000
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 1.41421i 1.41421i
\(721\) 0 0
\(722\) − 1.41421i − 1.41421i
\(723\) −2.00000 −2.00000
\(724\) 1.00000 1.00000
\(725\) − 1.41421i − 1.41421i
\(726\) 2.00000 2.00000
\(727\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) −2.00000 −2.00000
\(731\) −1.00000 −1.00000
\(732\) 0 0
\(733\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) −2.00000 −2.00000
\(735\) 2.00000 2.00000
\(736\) 1.41421i 1.41421i
\(737\) 0 0
\(738\) 1.41421i 1.41421i
\(739\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) − 1.41421i − 1.41421i
\(741\) 0 0
\(742\) 0 0
\(743\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(744\) 0 0
\(745\) − 1.41421i − 1.41421i
\(746\) 1.41421i 1.41421i
\(747\) 0 0
\(748\) −1.00000 −1.00000
\(749\) 0 0
\(750\) 0 0
\(751\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(752\) 1.41421i 1.41421i
\(753\) − 1.41421i − 1.41421i
\(754\) 0 0
\(755\) 1.41421i 1.41421i
\(756\) 0 0
\(757\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) −2.00000 −2.00000
\(759\) − 1.41421i − 1.41421i
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.41421i 1.41421i
\(765\) 1.41421i 1.41421i
\(766\) 0 0
\(767\) 0 0
\(768\) − 1.41421i − 1.41421i
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) − 1.41421i − 1.41421i
\(775\) 1.00000 1.00000
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 1.41421i − 1.41421i
\(780\) 0 0
\(781\) 1.00000 1.00000
\(782\) 1.41421i 1.41421i
\(783\) 0 0
\(784\) −1.00000 −1.00000
\(785\) − 1.41421i − 1.41421i
\(786\) − 2.82843i − 2.82843i
\(787\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 2.00000 2.00000
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 2.82843i 2.82843i
\(796\) − 1.41421i − 1.41421i
\(797\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(798\) 0 0
\(799\) 1.41421i 1.41421i
\(800\) 1.41421i 1.41421i
\(801\) −1.00000 −1.00000
\(802\) 2.00000 2.00000
\(803\) −1.00000 −1.00000
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) − 1.41421i − 1.41421i
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 2.00000 2.00000
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) −2.00000 −2.00000
\(814\) − 1.41421i − 1.41421i
\(815\) 2.00000 2.00000
\(816\) − 1.41421i − 1.41421i
\(817\) 1.41421i 1.41421i
\(818\) 0 0
\(819\) 0 0
\(820\) 1.41421i 1.41421i
\(821\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(822\) 0 0
\(823\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) − 1.41421i − 1.41421i
\(826\) 0 0
\(827\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(828\) −1.00000 −1.00000
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.00000 −1.00000
\(834\) −2.00000 −2.00000
\(835\) 0 0
\(836\) 1.41421i 1.41421i
\(837\) 0 0
\(838\) 2.00000 2.00000
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −1.00000 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −1.00000 −1.00000
\(845\) 1.41421i 1.41421i
\(846\) −2.00000 −2.00000
\(847\) 0 0
\(848\) − 1.41421i − 1.41421i
\(849\) 0 0
\(850\) 1.41421i 1.41421i
\(851\) −1.00000 −1.00000
\(852\) − 1.41421i − 1.41421i
\(853\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(854\) 0 0
\(855\) 2.00000 2.00000
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) − 1.41421i − 1.41421i
\(861\) 0 0
\(862\) − 1.41421i − 1.41421i
\(863\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) − 1.41421i − 1.41421i
\(867\) 0 0
\(868\) 0 0
\(869\) 1.00000 1.00000
\(870\) −4.00000 −4.00000
\(871\) 0 0
\(872\) 0 0
\(873\) − 1.41421i − 1.41421i
\(874\) 2.00000 2.00000
\(875\) 0 0
\(876\) 1.41421i 1.41421i
\(877\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(878\) − 1.41421i − 1.41421i
\(879\) 0 0
\(880\) 1.41421i 1.41421i
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) − 1.41421i − 1.41421i
\(883\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.41421i 1.41421i
\(887\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(888\) 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
\(894\) −2.00000 −2.00000
\(895\) −2.00000 −2.00000
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 1.41421i − 1.41421i
\(900\) −1.00000 −1.00000
\(901\) − 1.41421i − 1.41421i
\(902\) 1.41421i 1.41421i
\(903\) 0 0
\(904\) 0 0
\(905\) − 1.41421i − 1.41421i
\(906\) 2.00000 2.00000
\(907\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(908\) −1.00000 −1.00000
\(909\) − 1.41421i − 1.41421i
\(910\) 0 0
\(911\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(912\) −2.00000 −2.00000
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −1.00000 −1.00000
\(917\) 0 0
\(918\) 0 0
\(919\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(920\) 0 0
\(921\) −2.00000 −2.00000
\(922\) − 1.41421i − 1.41421i
\(923\) 0 0
\(924\) 0 0
\(925\) −1.00000 −1.00000
\(926\) 0 0
\(927\) − 1.41421i − 1.41421i
\(928\) 2.00000 2.00000
\(929\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(930\) − 2.82843i − 2.82843i
\(931\) 1.41421i 1.41421i
\(932\) −1.00000 −1.00000
\(933\) 0 0
\(934\) 1.41421i 1.41421i
\(935\) 1.41421i 1.41421i
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −2.00000 −2.00000
\(941\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(942\) −2.00000 −2.00000
\(943\) 1.00000 1.00000
\(944\) 0 0
\(945\) 0 0
\(946\) − 1.41421i − 1.41421i
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) − 1.41421i − 1.41421i
\(949\) 0 0
\(950\) 2.00000 2.00000
\(951\) 0 0
\(952\) 0 0
\(953\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(954\) 2.00000 2.00000
\(955\) 2.00000 2.00000
\(956\) −1.00000 −1.00000
\(957\) −2.00000 −2.00000
\(958\) 2.00000 2.00000
\(959\) 0 0
\(960\) 2.00000 2.00000
\(961\) 0 0
\(962\) 0 0
\(963\) − 1.41421i − 1.41421i
\(964\) 1.41421i 1.41421i
\(965\) 0 0
\(966\) 0 0
\(967\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 0 0
\(969\) −2.00000 −2.00000
\(970\) − 2.82843i − 2.82843i
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) − 1.41421i − 1.41421i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) − 2.82843i − 2.82843i
\(979\) −1.00000 −1.00000
\(980\) − 1.41421i − 1.41421i
\(981\) 1.41421i 1.41421i
\(982\) 2.00000 2.00000
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 2.00000 2.00000
\(987\) 0 0
\(988\) 0 0
\(989\) −1.00000 −1.00000
\(990\) −2.00000 −2.00000
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 1.41421i 1.41421i
\(993\) − 1.41421i − 1.41421i
\(994\) 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 \(0.333333\pi\)
\(998\) − 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 \(a_p\))