Properties

Label 751.1.b.b.750.2
Level 751
Weight 1
Character 751.750
Analytic conductor 0.375
Analytic rank 0
Dimension 2
Projective image \(S_{4}\)
CM/RM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 751 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 751.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.374797824487\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Projective image \(S_{4}\)
Projective field Galois closure of 4.2.751.1
Artin image size \(48\)
Artin image $\GL(2,3)$
Artin field Galois closure of 8.2.423564751.1

Embedding invariants

Embedding label 750.2
Root \(-1.41421i\)
Character \(\chi\) = 751.750
Dual form 751.1.b.b.750.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.41421i q^{3}\) \(-1.41421i q^{6}\) \(-1.41421i q^{7}\) \(+1.00000 q^{8}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.41421i q^{3}\) \(-1.41421i q^{6}\) \(-1.41421i q^{7}\) \(+1.00000 q^{8}\) \(-1.00000 q^{9}\) \(-1.41421i q^{11}\) \(+1.00000 q^{13}\) \(+1.41421i q^{14}\) \(-1.00000 q^{16}\) \(-1.41421i q^{17}\) \(+1.00000 q^{18}\) \(+1.00000 q^{19}\) \(+2.00000 q^{21}\) \(+1.41421i q^{22}\) \(-1.00000 q^{23}\) \(+1.41421i q^{24}\) \(-1.00000 q^{25}\) \(-1.00000 q^{26}\) \(+2.00000 q^{33}\) \(+1.41421i q^{34}\) \(+1.00000 q^{37}\) \(-1.00000 q^{38}\) \(+1.41421i q^{39}\) \(+1.41421i q^{41}\) \(-2.00000 q^{42}\) \(+1.00000 q^{46}\) \(+1.00000 q^{47}\) \(-1.41421i q^{48}\) \(-1.00000 q^{49}\) \(+1.00000 q^{50}\) \(+2.00000 q^{51}\) \(-1.00000 q^{53}\) \(-1.41421i q^{56}\) \(+1.41421i q^{57}\) \(-1.00000 q^{59}\) \(+1.00000 q^{61}\) \(+1.41421i q^{63}\) \(+1.00000 q^{64}\) \(-2.00000 q^{66}\) \(-1.41421i q^{67}\) \(-1.41421i q^{69}\) \(-1.00000 q^{72}\) \(-1.00000 q^{74}\) \(-1.41421i q^{75}\) \(-2.00000 q^{77}\) \(-1.41421i q^{78}\) \(+1.41421i q^{79}\) \(-1.00000 q^{81}\) \(-1.41421i q^{82}\) \(-1.41421i q^{83}\) \(-1.41421i q^{88}\) \(+1.00000 q^{89}\) \(-1.41421i q^{91}\) \(-1.00000 q^{94}\) \(+1.00000 q^{97}\) \(+1.00000 q^{98}\) \(+1.41421i q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 2q^{59} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 2q^{89} \) \(\mathstrut -\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/751\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(4\) 0 0
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) − 1.41421i − 1.41421i
\(7\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(8\) 1.00000 1.00000
\(9\) −1.00000 −1.00000
\(10\) 0 0
\(11\) − 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 \(0.333333\pi\)
\(14\) 1.41421i 1.41421i
\(15\) 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
\(19\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 0 0
\(21\) 2.00000 2.00000
\(22\) 1.41421i 1.41421i
\(23\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 1.41421i 1.41421i
\(25\) −1.00000 −1.00000
\(26\) −1.00000 −1.00000
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 2.00000 2.00000
\(34\) 1.41421i 1.41421i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −1.00000 −1.00000
\(39\) 1.41421i 1.41421i
\(40\) 0 0
\(41\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(42\) −2.00000 −2.00000
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.00000 1.00000
\(47\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) − 1.41421i − 1.41421i
\(49\) −1.00000 −1.00000
\(50\) 1.00000 1.00000
\(51\) 2.00000 2.00000
\(52\) 0 0
\(53\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) − 1.41421i − 1.41421i
\(57\) 1.41421i 1.41421i
\(58\) 0 0
\(59\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) 1.41421i 1.41421i
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −2.00000 −2.00000
\(67\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(68\) 0 0
\(69\) − 1.41421i − 1.41421i
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.00000 −1.00000
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −1.00000 −1.00000
\(75\) − 1.41421i − 1.41421i
\(76\) 0 0
\(77\) −2.00000 −2.00000
\(78\) − 1.41421i − 1.41421i
\(79\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(80\) 0 0
\(81\) −1.00000 −1.00000
\(82\) − 1.41421i − 1.41421i
\(83\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) − 1.41421i − 1.41421i
\(89\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0 0
\(91\) − 1.41421i − 1.41421i
\(92\) 0 0
\(93\) 0 0
\(94\) −1.00000 −1.00000
\(95\) 0 0
\(96\) 0 0
\(97\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) 1.00000 1.00000
\(99\) 1.41421i 1.41421i
\(100\) 0 0
\(101\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(102\) −2.00000 −2.00000
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 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
\(109\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 1.41421i 1.41421i
\(112\) 1.41421i 1.41421i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) − 1.41421i − 1.41421i
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −1.00000
\(118\) 1.00000 1.00000
\(119\) −2.00000 −2.00000
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) −1.00000 −1.00000
\(123\) −2.00000 −2.00000
\(124\) 0 0
\(125\) 0 0
\(126\) − 1.41421i − 1.41421i
\(127\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) −1.00000 −1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) −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
\(137\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(138\) 1.41421i 1.41421i
\(139\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(140\) 0 0
\(141\) 1.41421i 1.41421i
\(142\) 0 0
\(143\) − 1.41421i − 1.41421i
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) − 1.41421i − 1.41421i
\(148\) 0 0
\(149\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 1.41421i 1.41421i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 1.00000 1.00000
\(153\) 1.41421i 1.41421i
\(154\) 2.00000 2.00000
\(155\) 0 0
\(156\) 0 0
\(157\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) − 1.41421i − 1.41421i
\(159\) − 1.41421i − 1.41421i
\(160\) 0 0
\(161\) 1.41421i 1.41421i
\(162\) 1.00000 1.00000
\(163\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.41421i 1.41421i
\(167\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) 2.00000 2.00000
\(169\) 0 0
\(170\) 0 0
\(171\) −1.00000 −1.00000
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 1.41421i 1.41421i
\(176\) 1.41421i 1.41421i
\(177\) − 1.41421i − 1.41421i
\(178\) −1.00000 −1.00000
\(179\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 1.41421i 1.41421i
\(183\) 1.41421i 1.41421i
\(184\) −1.00000 −1.00000
\(185\) 0 0
\(186\) 0 0
\(187\) −2.00000 −2.00000
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) 1.41421i 1.41421i
\(193\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) −1.00000 −1.00000
\(195\) 0 0
\(196\) 0 0
\(197\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) − 1.41421i − 1.41421i
\(199\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) −1.00000 −1.00000
\(201\) 2.00000 2.00000
\(202\) − 1.41421i − 1.41421i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.00000 1.00000
\(208\) −1.00000 −1.00000
\(209\) − 1.41421i − 1.41421i
\(210\) 0 0
\(211\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.00000 1.00000
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −1.00000 −1.00000
\(219\) 0 0
\(220\) 0 0
\(221\) − 1.41421i − 1.41421i
\(222\) − 1.41421i − 1.41421i
\(223\) 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
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 0 0
\(231\) − 2.82843i − 2.82843i
\(232\) 0 0
\(233\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 1.00000 1.00000
\(235\) 0 0
\(236\) 0 0
\(237\) −2.00000 −2.00000
\(238\) 2.00000 2.00000
\(239\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.00000 1.00000
\(243\) − 1.41421i − 1.41421i
\(244\) 0 0
\(245\) 0 0
\(246\) 2.00000 2.00000
\(247\) 1.00000 1.00000
\(248\) 0 0
\(249\) 2.00000 2.00000
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 1.41421i 1.41421i
\(254\) 1.00000 1.00000
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) − 1.41421i − 1.41421i
\(260\) 0 0
\(261\) 0 0
\(262\) 1.00000 1.00000
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 2.00000 2.00000
\(265\) 0 0
\(266\) 1.41421i 1.41421i
\(267\) 1.41421i 1.41421i
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 1.41421i 1.41421i
\(273\) 2.00000 2.00000
\(274\) − 1.41421i − 1.41421i
\(275\) 1.41421i 1.41421i
\(276\) 0 0
\(277\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(278\) −1.00000 −1.00000
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) − 1.41421i − 1.41421i
\(283\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.41421i 1.41421i
\(287\) 2.00000 2.00000
\(288\) 0 0
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 1.41421i 1.41421i
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 1.41421i 1.41421i
\(295\) 0 0
\(296\) 1.00000 1.00000
\(297\) 0 0
\(298\) −1.00000 −1.00000
\(299\) −1.00000 −1.00000
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −2.00000 −2.00000
\(304\) −1.00000 −1.00000
\(305\) 0 0
\(306\) − 1.41421i − 1.41421i
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(312\) 1.41421i 1.41421i
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) − 1.41421i − 1.41421i
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 1.41421i 1.41421i
\(319\) 0 0
\(320\) 0 0
\(321\) − 1.41421i − 1.41421i
\(322\) − 1.41421i − 1.41421i
\(323\) − 1.41421i − 1.41421i
\(324\) 0 0
\(325\) −1.00000 −1.00000
\(326\) 2.00000 2.00000
\(327\) 1.41421i 1.41421i
\(328\) 1.41421i 1.41421i
\(329\) − 1.41421i − 1.41421i
\(330\) 0 0
\(331\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(332\) 0 0
\(333\) −1.00000 −1.00000
\(334\) 1.00000 1.00000
\(335\) 0 0
\(336\) −2.00000 −2.00000
\(337\) − 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
\(341\) 0 0
\(342\) 1.00000 1.00000
\(343\) 0 0
\(344\) 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 \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(350\) − 1.41421i − 1.41421i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 1.41421i 1.41421i
\(355\) 0 0
\(356\) 0 0
\(357\) − 2.82843i − 2.82843i
\(358\) −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
\(361\) 0 0
\(362\) 0 0
\(363\) − 1.41421i − 1.41421i
\(364\) 0 0
\(365\) 0 0
\(366\) − 1.41421i − 1.41421i
\(367\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 1.00000 1.00000
\(369\) − 1.41421i − 1.41421i
\(370\) 0 0
\(371\) 1.41421i 1.41421i
\(372\) 0 0
\(373\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(374\) 2.00000 2.00000
\(375\) 0 0
\(376\) 1.00000 1.00000
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) − 1.41421i − 1.41421i
\(382\) −1.00000 −1.00000
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) − 1.41421i − 1.41421i
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 1.41421i 1.41421i
\(392\) −1.00000 −1.00000
\(393\) − 1.41421i − 1.41421i
\(394\) 1.00000 1.00000
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 1.00000 1.00000
\(399\) 2.00000 2.00000
\(400\) 1.00000 1.00000
\(401\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) −2.00000 −2.00000
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 1.41421i − 1.41421i
\(408\) 2.00000 2.00000
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) −2.00000 −2.00000
\(412\) 0 0
\(413\) 1.41421i 1.41421i
\(414\) −1.00000 −1.00000
\(415\) 0 0
\(416\) 0 0
\(417\) 1.41421i 1.41421i
\(418\) 1.41421i 1.41421i
\(419\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(422\) −1.00000 −1.00000
\(423\) −1.00000 −1.00000
\(424\) −1.00000 −1.00000
\(425\) 1.41421i 1.41421i
\(426\) 0 0
\(427\) − 1.41421i − 1.41421i
\(428\) 0 0
\(429\) 2.00000 2.00000
\(430\) 0 0
\(431\) 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 \(0.333333\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.00000 −1.00000
\(438\) 0 0
\(439\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 1.41421i 1.41421i
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) − 1.41421i − 1.41421i
\(447\) 1.41421i 1.41421i
\(448\) − 1.41421i − 1.41421i
\(449\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(450\) −1.00000 −1.00000
\(451\) 2.00000 2.00000
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 1.41421i 1.41421i
\(457\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 1.00000 1.00000
\(459\) 0 0
\(460\) 0 0
\(461\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) 2.82843i 2.82843i
\(463\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.00000 −1.00000
\(467\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(468\) 0 0
\(469\) −2.00000 −2.00000
\(470\) 0 0
\(471\) −2.00000 −2.00000
\(472\) −1.00000 −1.00000
\(473\) 0 0
\(474\) 2.00000 2.00000
\(475\) −1.00000 −1.00000
\(476\) 0 0
\(477\) 1.00000 1.00000
\(478\) 1.41421i 1.41421i
\(479\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0 0
\(481\) 1.00000 1.00000
\(482\) 0 0
\(483\) −2.00000 −2.00000
\(484\) 0 0
\(485\) 0 0
\(486\) 1.41421i 1.41421i
\(487\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(488\) 1.00000 1.00000
\(489\) − 2.82843i − 2.82843i
\(490\) 0 0
\(491\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.00000 −1.00000
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −2.00000 −2.00000
\(499\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) − 1.41421i − 1.41421i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 1.41421i 1.41421i
\(505\) 0 0
\(506\) − 1.41421i − 1.41421i
\(507\) 0 0
\(508\) 0 0
\(509\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) − 1.41421i − 1.41421i
\(518\) 1.41421i 1.41421i
\(519\) 0 0
\(520\) 0 0
\(521\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(522\) 0 0
\(523\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) 0 0
\(525\) −2.00000 −2.00000
\(526\) 0 0
\(527\) 0 0
\(528\) −2.00000 −2.00000
\(529\) 0 0
\(530\) 0 0
\(531\) 1.00000 1.00000
\(532\) 0 0
\(533\) 1.41421i 1.41421i
\(534\) − 1.41421i − 1.41421i
\(535\) 0 0
\(536\) − 1.41421i − 1.41421i
\(537\) 2.82843i 2.82843i
\(538\) 0 0
\(539\) 1.41421i 1.41421i
\(540\) 0 0
\(541\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) −2.00000 −2.00000
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) −1.00000 −1.00000
\(550\) − 1.41421i − 1.41421i
\(551\) 0 0
\(552\) − 1.41421i − 1.41421i
\(553\) 2.00000 2.00000
\(554\) − 1.41421i − 1.41421i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) − 2.82843i − 2.82843i
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.41421i 1.41421i
\(567\) 1.41421i 1.41421i
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 1.41421i 1.41421i
\(574\) −2.00000 −2.00000
\(575\) 1.00000 1.00000
\(576\) −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
\(579\) 1.41421i 1.41421i
\(580\) 0 0
\(581\) −2.00000 −2.00000
\(582\) − 1.41421i − 1.41421i
\(583\) 1.41421i 1.41421i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) − 1.41421i − 1.41421i
\(592\) −1.00000 −1.00000
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) − 1.41421i − 1.41421i
\(598\) 1.00000 1.00000
\(599\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(600\) − 1.41421i − 1.41421i
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 1.41421i 1.41421i
\(604\) 0 0
\(605\) 0 0
\(606\) 2.00000 2.00000
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.00000 1.00000
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −2.00000 −2.00000
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −1.00000 −1.00000
\(623\) − 1.41421i − 1.41421i
\(624\) − 1.41421i − 1.41421i
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 2.00000 2.00000
\(628\) 0 0
\(629\) − 1.41421i − 1.41421i
\(630\) 0 0
\(631\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(632\) 1.41421i 1.41421i
\(633\) 1.41421i 1.41421i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.00000 −1.00000
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 1.41421i 1.41421i
\(643\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.41421i 1.41421i
\(647\) 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
\(653\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(654\) − 1.41421i − 1.41421i
\(655\) 0 0
\(656\) − 1.41421i − 1.41421i
\(657\) 0 0
\(658\) 1.41421i 1.41421i
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) − 1.41421i − 1.41421i
\(663\) 2.00000 2.00000
\(664\) − 1.41421i − 1.41421i
\(665\) 0 0
\(666\) 1.00000 1.00000
\(667\) 0 0
\(668\) 0 0
\(669\) −2.00000 −2.00000
\(670\) 0 0
\(671\) − 1.41421i − 1.41421i
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 1.41421i 1.41421i
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) − 1.41421i − 1.41421i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) − 1.41421i − 1.41421i
\(688\) 0 0
\(689\) −1.00000 −1.00000
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 2.00000 2.00000
\(694\) −1.00000 −1.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 2.00000 2.00000
\(698\) − 1.41421i − 1.41421i
\(699\) 1.41421i 1.41421i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 1.00000 1.00000
\(704\) − 1.41421i − 1.41421i
\(705\) 0 0
\(706\) 0 0
\(707\) 2.00000 2.00000
\(708\) 0 0
\(709\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(710\) 0 0
\(711\) − 1.41421i − 1.41421i
\(712\) 1.00000 1.00000
\(713\) 0 0
\(714\) 2.82843i 2.82843i
\(715\) 0 0
\(716\) 0 0
\(717\) 2.00000 2.00000
\(718\) − 1.41421i − 1.41421i
\(719\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 1.41421i 1.41421i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) − 1.41421i − 1.41421i
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 1.00000 1.00000
\(735\) 0 0
\(736\) 0 0
\(737\) −2.00000 −2.00000
\(738\) 1.41421i 1.41421i
\(739\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 0 0
\(741\) 1.41421i 1.41421i
\(742\) − 1.41421i − 1.41421i
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.41421i 1.41421i
\(747\) 1.41421i 1.41421i
\(748\) 0 0
\(749\) 1.41421i 1.41421i
\(750\) 0 0
\(751\) 1.00000 1.00000
\(752\) −1.00000 −1.00000
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) −2.00000 −2.00000
\(760\) 0 0
\(761\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) 1.41421i 1.41421i
\(763\) − 1.41421i − 1.41421i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.00000 −1.00000
\(768\) 0 0
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.00000 1.00000
\(777\) 2.00000 2.00000
\(778\) − 1.41421i − 1.41421i
\(779\) 1.41421i 1.41421i
\(780\) 0 0
\(781\) 0 0
\(782\) − 1.41421i − 1.41421i
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 1.41421i 1.41421i
\(787\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.41421i 1.41421i
\(793\) 1.00000 1.00000
\(794\) 1.00000 1.00000
\(795\) 0 0
\(796\) 0 0
\(797\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) −2.00000 −2.00000
\(799\) − 1.41421i − 1.41421i
\(800\) 0 0
\(801\) −1.00000 −1.00000
\(802\) 1.00000 1.00000
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 1.41421i 1.41421i
\(809\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 1.41421i 1.41421i
\(815\) 0 0
\(816\) −2.00000 −2.00000
\(817\) 0 0
\(818\) 0 0
\(819\) 1.41421i 1.41421i
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 2.00000 2.00000
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) −2.00000 −2.00000
\(826\) − 1.41421i − 1.41421i
\(827\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(828\) 0 0
\(829\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(830\) 0 0
\(831\) −2.00000 −2.00000
\(832\) 1.00000 1.00000
\(833\) 1.41421i 1.41421i
\(834\) − 1.41421i − 1.41421i
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 1.00000 1.00000
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) − 1.41421i − 1.41421i
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 1.00000 1.00000
\(847\) 1.41421i 1.41421i
\(848\) 1.00000 1.00000
\(849\) 2.00000 2.00000
\(850\) − 1.41421i − 1.41421i
\(851\) −1.00000 −1.00000
\(852\) 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
\(855\) 0 0
\(856\) −1.00000 −1.00000
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) −2.00000 −2.00000
\(859\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(860\) 0 0
\(861\) 2.82843i 2.82843i
\(862\) − 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
\(866\) −1.00000 −1.00000
\(867\) − 1.41421i − 1.41421i
\(868\) 0 0
\(869\) 2.00000 2.00000
\(870\) 0 0
\(871\) − 1.41421i − 1.41421i
\(872\) 1.00000 1.00000
\(873\) −1.00000 −1.00000
\(874\) 1.00000 1.00000
\(875\) 0 0
\(876\) 0 0
\(877\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(878\) 2.00000 2.00000
\(879\) 0 0
\(880\) 0 0
\(881\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(882\) −1.00000 −1.00000
\(883\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 1.41421i 1.41421i
\(889\) 1.41421i 1.41421i
\(890\) 0 0
\(891\) 1.41421i 1.41421i
\(892\) 0 0
\(893\) 1.00000 1.00000
\(894\) − 1.41421i − 1.41421i
\(895\) 0 0
\(896\) 1.41421i 1.41421i
\(897\) − 1.41421i − 1.41421i
\(898\) 1.41421i 1.41421i
\(899\) 0 0
\(900\) 0 0
\(901\) 1.41421i 1.41421i
\(902\) −2.00000 −2.00000
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) − 1.41421i − 1.41421i
\(910\) 0 0
\(911\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(912\) − 1.41421i − 1.41421i
\(913\) −2.00000 −2.00000
\(914\) 1.00000 1.00000
\(915\) 0 0
\(916\) 0 0
\(917\) 1.41421i 1.41421i
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1.00000 1.00000
\(923\) 0 0
\(924\) 0 0
\(925\) −1.00000 −1.00000
\(926\) − 1.41421i − 1.41421i
\(927\) 0 0
\(928\) 0 0
\(929\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(930\) 0 0
\(931\) −1.00000 −1.00000
\(932\) 0 0
\(933\) 1.41421i 1.41421i
\(934\) 1.41421i 1.41421i
\(935\) 0 0
\(936\) −1.00000 −1.00000
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 2.00000 2.00000
\(939\) 0 0
\(940\) 0 0
\(941\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(942\) 2.00000 2.00000
\(943\) − 1.41421i − 1.41421i
\(944\) 1.00000 1.00000
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 1.00000 1.00000
\(951\) 0 0
\(952\) −2.00000 −2.00000
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) −1.00000 −1.00000
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −1.00000 −1.00000
\(959\) 2.00000 2.00000
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) −1.00000 −1.00000
\(963\) 1.00000 1.00000
\(964\) 0 0
\(965\) 0 0
\(966\) 2.00000 2.00000
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −1.00000 −1.00000
\(969\) 2.00000 2.00000
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) − 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 \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(978\) 2.82843i 2.82843i
\(979\) − 1.41421i − 1.41421i
\(980\) 0 0
\(981\) −1.00000 −1.00000
\(982\) − 1.41421i − 1.41421i
\(983\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(984\) −2.00000 −2.00000
\(985\) 0 0
\(986\) 0 0
\(987\) 2.00000 2.00000
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −2.00000 −2.00000
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) 1.00000 1.00000
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))