Properties

Label 2001.1.i.b.1931.1
Level 2001
Weight 1
Character 2001.1931
Analytic conductor 0.999
Analytic rank 0
Dimension 2
Projective image \(D_{4}\)
CM disc. -23
Inner twists 4

Related objects

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Newspace parameters

Level: \( N \) = \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2001.i (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.998629090279\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Projective image \(D_{4}\)
Projective field Galois closure of 4.0.116116029.1

Embedding invariants

Embedding label 1931.1
Root \(-1.00000i\)
Character \(\chi\) = 2001.1931
Dual form 2001.1.i.b.1172.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(1.00000 + 1.00000i) q^{2}\) \(-1.00000i q^{3}\) \(+1.00000i q^{4}\) \(+(1.00000 - 1.00000i) q^{6}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+(1.00000 + 1.00000i) q^{2}\) \(-1.00000i q^{3}\) \(+1.00000i q^{4}\) \(+(1.00000 - 1.00000i) q^{6}\) \(-1.00000 q^{9}\) \(+1.00000 q^{12}\) \(-2.00000i q^{13}\) \(+1.00000 q^{16}\) \(+(-1.00000 - 1.00000i) q^{18}\) \(-1.00000i q^{23}\) \(+1.00000 q^{25}\) \(+(2.00000 - 2.00000i) q^{26}\) \(+1.00000i q^{27}\) \(+1.00000i q^{29}\) \(+(-1.00000 + 1.00000i) q^{31}\) \(+(1.00000 + 1.00000i) q^{32}\) \(-1.00000i q^{36}\) \(-2.00000 q^{39}\) \(+(-1.00000 + 1.00000i) q^{41}\) \(+(1.00000 - 1.00000i) q^{46}\) \(+(1.00000 - 1.00000i) q^{47}\) \(-1.00000i q^{48}\) \(+1.00000 q^{49}\) \(+(1.00000 + 1.00000i) q^{50}\) \(+2.00000 q^{52}\) \(+(-1.00000 + 1.00000i) q^{54}\) \(+(-1.00000 + 1.00000i) q^{58}\) \(+2.00000i q^{59}\) \(-2.00000 q^{62}\) \(+1.00000i q^{64}\) \(-1.00000 q^{69}\) \(+(-1.00000 - 1.00000i) q^{73}\) \(-1.00000i q^{75}\) \(+(-2.00000 - 2.00000i) q^{78}\) \(+1.00000 q^{81}\) \(-2.00000 q^{82}\) \(+1.00000 q^{87}\) \(+1.00000 q^{92}\) \(+(1.00000 + 1.00000i) q^{93}\) \(+2.00000 q^{94}\) \(+(1.00000 - 1.00000i) q^{96}\) \(+(1.00000 + 1.00000i) q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut +\mathstrut 2q^{32} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut +\mathstrut 4q^{52} \) \(\mathstrut -\mathstrut 2q^{54} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 4q^{82} \) \(\mathstrut +\mathstrut 2q^{87} \) \(\mathstrut +\mathstrut 2q^{92} \) \(\mathstrut +\mathstrut 2q^{93} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times\).

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(3\) 1.00000i 1.00000i
\(4\) 1.00000i 1.00000i
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 1.00000 1.00000i 1.00000 1.00000i
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) −1.00000 −1.00000
\(10\) 0 0
\(11\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(12\) 1.00000 1.00000
\(13\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) −1.00000 1.00000i −1.00000 1.00000i
\(19\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000i 1.00000i
\(24\) 0 0
\(25\) 1.00000 1.00000
\(26\) 2.00000 2.00000i 2.00000 2.00000i
\(27\) 1.00000i 1.00000i
\(28\) 0 0
\(29\) 1.00000i 1.00000i
\(30\) 0 0
\(31\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(32\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000i 1.00000i
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) 0 0
\(39\) −2.00000 −2.00000
\(40\) 0 0
\(41\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.00000 1.00000i 1.00000 1.00000i
\(47\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(48\) 1.00000i 1.00000i
\(49\) 1.00000 1.00000
\(50\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(51\) 0 0
\(52\) 2.00000 2.00000
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(59\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(62\) −2.00000 −2.00000
\(63\) 0 0
\(64\) 1.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) −1.00000 −1.00000
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 1.00000i 1.00000i
\(76\) 0 0
\(77\) 0 0
\(78\) −2.00000 2.00000i −2.00000 2.00000i
\(79\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(80\) 0 0
\(81\) 1.00000 1.00000
\(82\) −2.00000 −2.00000
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1.00000 1.00000
\(88\) 0 0
\(89\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.00000 1.00000
\(93\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(94\) 2.00000 2.00000
\(95\) 0 0
\(96\) 1.00000 1.00000i 1.00000 1.00000i
\(97\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(99\) 0 0
\(100\) 1.00000i 1.00000i
\(101\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −1.00000 −1.00000
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.00000 −1.00000
\(117\) 2.00000i 2.00000i
\(118\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000i 1.00000i
\(122\) 0 0
\(123\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(124\) −1.00000 1.00000i −1.00000 1.00000i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(138\) −1.00000 1.00000i −1.00000 1.00000i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −1.00000 1.00000i −1.00000 1.00000i
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 0 0
\(146\) 2.00000i 2.00000i
\(147\) 1.00000i 1.00000i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 1.00000 1.00000i 1.00000 1.00000i
\(151\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 2.00000i 2.00000i
\(157\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(163\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(164\) −1.00000 1.00000i −1.00000 1.00000i
\(165\) 0 0
\(166\) 0 0
\(167\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −3.00000 −3.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(174\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(175\) 0 0
\(176\) 0 0
\(177\) 2.00000 2.00000
\(178\) 0 0
\(179\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 2.00000i 2.00000i
\(187\) 0 0
\(188\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(192\) 1.00000 1.00000
\(193\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.00000i 1.00000i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 2.00000i 2.00000i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.00000i 1.00000i
\(208\) 2.00000i 2.00000i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −1.00000 −1.00000
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(234\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(235\) 0 0
\(236\) −2.00000 −2.00000
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(243\) 1.00000i 1.00000i
\(244\) 0 0
\(245\) 0 0
\(246\) 2.00000i 2.00000i
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −2.00000 −2.00000
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.00000i 1.00000i
\(262\) −2.00000 −2.00000
\(263\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(270\) 0 0
\(271\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.00000i 1.00000i
\(277\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(278\) 0 0
\(279\) 1.00000 1.00000i 1.00000 1.00000i
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 2.00000i 2.00000i
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 1.00000i −1.00000 1.00000i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 1.00000 1.00000i 1.00000 1.00000i
\(293\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(294\) 1.00000 1.00000i 1.00000 1.00000i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.00000 −2.00000
\(300\) 1.00000 1.00000
\(301\) 0 0
\(302\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(303\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000i 1.00000i
\(325\) 2.00000i 2.00000i
\(326\) 2.00000i 2.00000i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −2.00000 2.00000i −2.00000 2.00000i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(338\) −3.00000 3.00000i −3.00000 3.00000i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 1.00000i 1.00000i
\(349\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(350\) 0 0
\(351\) 2.00000 2.00000
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(359\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(360\) 0 0
\(361\) 1.00000i 1.00000i
\(362\) 0 0
\(363\) 1.00000 1.00000
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(368\) 1.00000i 1.00000i
\(369\) 1.00000 1.00000i 1.00000 1.00000i
\(370\) 0 0
\(371\) 0 0
\(372\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.00000 2.00000
\(378\) 0 0
\(379\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(380\) 0 0
\(381\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.00000 −2.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(404\) 1.00000 1.00000i 1.00000 1.00000i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(415\) 0 0
\(416\) 2.00000 2.00000i 2.00000 2.00000i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(422\) 2.00000i 2.00000i
\(423\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 1.00000i 1.00000i
\(433\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −2.00000 −2.00000
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 0 0
\(443\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −2.00000 2.00000i −2.00000 2.00000i
\(447\) 0 0
\(448\) 0 0
\(449\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(450\) −1.00000 1.00000i −1.00000 1.00000i
\(451\) 0 0
\(452\) 0 0
\(453\) 2.00000 2.00000
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(462\) 0 0
\(463\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(464\) 1.00000i 1.00000i
\(465\) 0 0
\(466\) 2.00000 2.00000i 2.00000 2.00000i
\(467\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(468\) −2.00000 −2.00000
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.00000 −1.00000
\(485\) 0 0
\(486\) 1.00000 1.00000i 1.00000 1.00000i
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 1.00000 1.00000i 1.00000 1.00000i
\(490\) 0 0
\(491\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(492\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(500\) 0 0
\(501\) 2.00000i 2.00000i
\(502\) 0 0
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000i 3.00000i
\(508\) −1.00000 1.00000i −1.00000 1.00000i
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 2.00000i 2.00000i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 1.00000 1.00000i 1.00000 1.00000i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −1.00000 1.00000i −1.00000 1.00000i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) 2.00000i 2.00000i
\(532\) 0 0
\(533\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.00000i 2.00000i
\(538\) 2.00000 2.00000
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(542\) 2.00000i 2.00000i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 2.00000 2.00000
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) 1.00000 1.00000i 1.00000 1.00000i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000i 1.00000i
\(576\) 1.00000i 1.00000i
\(577\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(578\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(579\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 1.00000 1.00000
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −2.00000 2.00000i −2.00000 2.00000i
\(599\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2.00000 −2.00000
\(605\) 0 0
\(606\) −2.00000 −2.00000
\(607\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.00000 2.00000i −2.00000 2.00000i
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) −2.00000 −2.00000
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(620\) 0 0
\(621\) 1.00000 1.00000
\(622\) 2.00000i 2.00000i
\(623\) 0 0
\(624\) −2.00000 −2.00000
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(634\) 2.00000 2.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 2.00000i 2.00000i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 2.00000 2.00000i 2.00000 2.00000i
\(651\) 0 0
\(652\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(653\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(657\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(658\) 0 0
\(659\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 2.00000i 2.00000i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.00000 1.00000
\(668\) 2.00000i 2.00000i
\(669\) 2.00000i 2.00000i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 1.00000i 1.00000i
\(676\) 3.00000i 3.00000i
\(677\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 2.00000i 2.00000i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(699\) −2.00000 −2.00000
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 2.00000i 2.00000i
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(714\) 0 0
\(715\) 0 0
\(716\) 2.00000i 2.00000i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000 1.00000i 1.00000 1.00000i
\(723\) 0 0
\(724\) 0 0
\(725\) 1.00000i 1.00000i
\(726\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(727\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(728\) 0 0
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1.00000 1.00000i 1.00000 1.00000i
\(737\) 0 0
\(738\) 2.00000 2.00000
\(739\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(752\) 1.00000 1.00000i 1.00000 1.00000i
\(753\) 0 0
\(754\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(762\) 2.00000i 2.00000i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.00000 4.00000
\(768\) 1.00000i 1.00000i
\(769\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 1.00000i −1.00000 1.00000i
\(773\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(774\) 0 0
\(775\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −1.00000 −1.00000
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 2.00000i 2.00000i
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 4.00000i 4.00000i
\(807\) −1.00000 1.00000i −1.00000 1.00000i
\(808\) 0 0
\(809\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 1.00000 1.00000i 1.00000 1.00000i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 2.00000 2.00000
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)