Properties

Label 280.1.c.a.69.1
Level $280$
Weight $1$
Character 280.69
Analytic conductor $0.140$
Analytic rank $0$
Dimension $4$
Projective image $D_{4}$
CM discriminant -56
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 280.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.139738203537\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{4}\)
Projective field: Galois closure of 4.2.11200.2

Embedding invariants

Embedding label 69.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 280.69
Dual form 280.1.c.a.69.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +(0.707107 - 0.707107i) q^{5} -1.41421 q^{6} +1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} +(0.707107 - 0.707107i) q^{5} -1.41421 q^{6} +1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-0.707107 - 0.707107i) q^{10} +1.41421i q^{12} +1.41421i q^{13} +1.00000 q^{14} +(-1.00000 - 1.00000i) q^{15} +1.00000 q^{16} +1.00000i q^{18} -1.41421 q^{19} +(-0.707107 + 0.707107i) q^{20} +1.41421 q^{21} +1.41421 q^{24} -1.00000i q^{25} +1.41421 q^{26} -1.00000i q^{28} +(-1.00000 + 1.00000i) q^{30} -1.00000i q^{32} +(0.707107 + 0.707107i) q^{35} +1.00000 q^{36} +1.41421i q^{38} +2.00000 q^{39} +(0.707107 + 0.707107i) q^{40} -1.41421i q^{42} +(-0.707107 + 0.707107i) q^{45} -1.41421i q^{48} -1.00000 q^{49} -1.00000 q^{50} -1.41421i q^{52} -1.00000 q^{56} +2.00000i q^{57} +1.41421 q^{59} +(1.00000 + 1.00000i) q^{60} -1.41421 q^{61} -1.00000i q^{63} -1.00000 q^{64} +(1.00000 + 1.00000i) q^{65} +(0.707107 - 0.707107i) q^{70} -1.00000i q^{72} -1.41421 q^{75} +1.41421 q^{76} -2.00000i q^{78} +(0.707107 - 0.707107i) q^{80} -1.00000 q^{81} +1.41421i q^{83} -1.41421 q^{84} +(0.707107 + 0.707107i) q^{90} -1.41421 q^{91} +(-1.00000 + 1.00000i) q^{95} -1.41421 q^{96} +1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{4} - 4q^{9} + 4q^{14} - 4q^{15} + 4q^{16} - 4q^{30} + 4q^{36} + 8q^{39} - 4q^{49} - 4q^{50} - 4q^{56} + 4q^{60} - 4q^{64} + 4q^{65} - 4q^{81} - 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 1.00000i
\(3\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(4\) −1.00000 −1.00000
\(5\) 0.707107 0.707107i 0.707107 0.707107i
\(6\) −1.41421 −1.41421
\(7\) 1.00000i 1.00000i
\(8\) 1.00000i 1.00000i
\(9\) −1.00000 −1.00000
\(10\) −0.707107 0.707107i −0.707107 0.707107i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.41421i 1.41421i
\(13\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(14\) 1.00000 1.00000
\(15\) −1.00000 1.00000i −1.00000 1.00000i
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.00000i 1.00000i
\(19\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(21\) 1.41421 1.41421
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 1.41421 1.41421
\(25\) 1.00000i 1.00000i
\(26\) 1.41421 1.41421
\(27\) 0 0
\(28\) 1.00000i 1.00000i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000i 1.00000i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(36\) 1.00000 1.00000
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 1.41421i 1.41421i
\(39\) 2.00000 2.00000
\(40\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 1.41421i 1.41421i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.41421i 1.41421i
\(49\) −1.00000 −1.00000
\(50\) −1.00000 −1.00000
\(51\) 0 0
\(52\) 1.41421i 1.41421i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −1.00000
\(57\) 2.00000i 2.00000i
\(58\) 0 0
\(59\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(60\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(61\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(62\) 0 0
\(63\) 1.00000i 1.00000i
\(64\) −1.00000 −1.00000
\(65\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0.707107 0.707107i 0.707107 0.707107i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000i 1.00000i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) −1.41421 −1.41421
\(76\) 1.41421 1.41421
\(77\) 0 0
\(78\) 2.00000i 2.00000i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0.707107 0.707107i 0.707107 0.707107i
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(84\) −1.41421 −1.41421
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(91\) −1.41421 −1.41421
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(96\) −1.41421 −1.41421
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 1.00000i 1.00000i
\(99\) 0 0
\(100\) 1.00000i 1.00000i
\(101\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −1.41421 −1.41421
\(105\) 1.00000 1.00000i 1.00000 1.00000i
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000i 1.00000i
\(113\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(114\) 2.00000 2.00000
\(115\) 0 0
\(116\) 0 0
\(117\) 1.41421i 1.41421i
\(118\) 1.41421i 1.41421i
\(119\) 0 0
\(120\) 1.00000 1.00000i 1.00000 1.00000i
\(121\) 1.00000 1.00000
\(122\) 1.41421i 1.41421i
\(123\) 0 0
\(124\) 0 0
\(125\) −0.707107 0.707107i −0.707107 0.707107i
\(126\) −1.00000 −1.00000
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000i 1.00000i
\(129\) 0 0
\(130\) 1.00000 1.00000i 1.00000 1.00000i
\(131\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(132\) 0 0
\(133\) 1.41421i 1.41421i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(140\) −0.707107 0.707107i −0.707107 0.707107i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 1.41421i 1.41421i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 1.41421i 1.41421i
\(151\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(152\) 1.41421i 1.41421i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −2.00000 −2.00000
\(157\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.707107 0.707107i −0.707107 0.707107i
\(161\) 0 0
\(162\) 1.00000i 1.00000i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.41421 1.41421
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 1.41421i 1.41421i
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) 1.41421 1.41421
\(172\) 0 0
\(173\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(174\) 0 0
\(175\) 1.00000 1.00000
\(176\) 0 0
\(177\) 2.00000i 2.00000i
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.707107 0.707107i 0.707107 0.707107i
\(181\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(182\) 1.41421i 1.41421i
\(183\) 2.00000i 2.00000i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.41421i 1.41421i
\(193\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 1.41421 1.41421i 1.41421 1.41421i
\(196\) 1.00000 1.00000
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) 1.41421i 1.41421i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.41421i 1.41421i
\(209\) 0 0
\(210\) −1.00000 1.00000i −1.00000 1.00000i
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 1.00000 1.00000
\(225\) 1.00000i 1.00000i
\(226\) −2.00000 −2.00000
\(227\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(228\) 2.00000i 2.00000i
\(229\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) −1.41421 −1.41421
\(235\) 0 0
\(236\) −1.41421 −1.41421
\(237\) 0 0
\(238\) 0 0
\(239\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(240\) −1.00000 1.00000i −1.00000 1.00000i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.00000i 1.00000i
\(243\) 1.41421i 1.41421i
\(244\) 1.41421 1.41421
\(245\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(246\) 0 0
\(247\) 2.00000i 2.00000i
\(248\) 0 0
\(249\) 2.00000 2.00000
\(250\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(251\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(252\) 1.00000i 1.00000i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.00000 1.00000i −1.00000 1.00000i
\(261\) 0 0
\(262\) 1.41421i 1.41421i
\(263\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.41421 −1.41421
\(267\) 0 0
\(268\) 0 0
\(269\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 2.00000i 2.00000i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 1.41421i 1.41421i
\(279\) 0 0
\(280\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(281\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(284\) 0 0
\(285\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000i 1.00000i
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(294\) 1.41421 1.41421
\(295\) 1.00000 1.00000i 1.00000 1.00000i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 1.41421 1.41421
\(301\) 0 0
\(302\) 2.00000i 2.00000i
\(303\) 2.00000i 2.00000i
\(304\) −1.41421 −1.41421
\(305\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(306\) 0 0
\(307\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 2.00000i 2.00000i
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 1.41421 1.41421
\(315\) −0.707107 0.707107i −0.707107 0.707107i
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) 1.41421 1.41421
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 1.41421i 1.41421i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 1.41421 1.41421
\(337\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(338\) 1.00000i 1.00000i
\(339\) −2.82843 −2.82843
\(340\) 0 0
\(341\) 0 0
\(342\) 1.41421i 1.41421i
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) −1.41421 −1.41421
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(350\) 1.00000i 1.00000i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) −2.00000 −2.00000
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(360\) −0.707107 0.707107i −0.707107 0.707107i
\(361\) 1.00000 1.00000
\(362\) 1.41421i 1.41421i
\(363\) 1.41421i 1.41421i
\(364\) 1.41421 1.41421
\(365\) 0 0
\(366\) 2.00000 2.00000
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 1.00000 1.00000i 1.00000 1.00000i
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 1.41421 1.41421
\(385\) 0 0
\(386\) 2.00000 2.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −1.41421 1.41421i −1.41421 1.41421i
\(391\) 0 0
\(392\) 1.00000i 1.00000i
\(393\) 2.00000i 2.00000i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(398\) 0 0
\(399\) −2.00000 −2.00000
\(400\) 1.00000i 1.00000i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.41421 1.41421
\(405\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.41421i 1.41421i
\(414\) 0 0
\(415\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(416\) 1.41421 1.41421
\(417\) 2.00000i 2.00000i
\(418\) 0 0
\(419\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(420\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.41421i 1.41421i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 1.00000i 1.00000i
\(449\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(450\) 1.00000 1.00000
\(451\) 0 0
\(452\) 2.00000i 2.00000i
\(453\) 2.82843i 2.82843i
\(454\) −1.41421 −1.41421
\(455\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(456\) −2.00000 −2.00000
\(457\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 1.41421i 1.41421i
\(459\) 0 0
\(460\) 0 0
\(461\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(462\) 0 0
\(463\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 1.41421i 1.41421i
\(469\) 0 0
\(470\) 0 0
\(471\) 2.00000 2.00000
\(472\) 1.41421i 1.41421i
\(473\) 0 0
\(474\) 0 0
\(475\) 1.41421i 1.41421i
\(476\) 0 0
\(477\) 0 0
\(478\) 2.00000i 2.00000i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.00000 −1.00000
\(485\) 0 0
\(486\) 1.41421 1.41421
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 1.41421i 1.41421i
\(489\) 0 0
\(490\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −2.00000 −2.00000
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 2.00000i 2.00000i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(501\) 0 0
\(502\) 1.41421i 1.41421i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 1.00000 1.00000
\(505\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(506\) 0 0
\(507\) 1.41421i 1.41421i
\(508\) 0 0
\(509\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −2.00000 −2.00000
\(520\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(524\) −1.41421 −1.41421
\(525\) 1.41421i 1.41421i
\(526\) −2.00000 −2.00000
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) −1.41421 −1.41421
\(532\) 1.41421i 1.41421i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.41421i 1.41421i
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 2.00000i 2.00000i
\(544\) 0 0
\(545\) 0 0
\(546\) 2.00000 2.00000
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 1.41421 1.41421
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.41421 −1.41421
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(561\) 0 0
\(562\) 2.00000i 2.00000i
\(563\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(564\) 0 0
\(565\) −1.41421 1.41421i −1.41421 1.41421i
\(566\) 1.41421 1.41421
\(567\) 1.00000i 1.00000i
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 1.41421 1.41421i 1.41421 1.41421i
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 1.00000i 1.00000i
\(579\) 2.82843 2.82843
\(580\) 0 0
\(581\) −1.41421 −1.41421
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −1.00000 1.00000i −1.00000 1.00000i
\(586\) −1.41421 −1.41421
\(587\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 1.41421i 1.41421i
\(589\) 0 0
\(590\) −1.00000 1.00000i −1.00000 1.00000i
\(591\) 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
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 1.41421i 1.41421i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2.00000 2.00000
\(605\) 0.707107 0.707107i 0.707107 0.707107i
\(606\) 2.00000 2.00000
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 1.41421i 1.41421i
\(609\) 0 0
\(610\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) −1.41421 −1.41421
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 2.00000 2.00000
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 1.41421i 1.41421i
\(629\) 0 0
\(630\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.41421i 1.41421i
\(638\) 0 0
\(639\) 0 0
\(640\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) 1.41421i 1.41421i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 1.00000 1.00000i 1.00000 1.00000i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.41421 −1.41421
\(665\) −1.00000 1.00000i −1.00000 1.00000i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 1.41421i 1.41421i
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) −2.00000 −2.00000
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) 2.82843i 2.82843i
\(679\) 0 0
\(680\) 0 0
\(681\) −2.00000 −2.00000
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −1.41421 −1.41421
\(685\) 0 0
\(686\) −1.00000 −1.00000
\(687\) 2.00000i 2.00000i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(692\) 1.41421i 1.41421i
\(693\) 0 0
\(694\) 0 0
\(695\) 1.00000 1.00000i 1.00000 1.00000i
\(696\) 0 0
\(697\) 0 0
\(698\) 1.41421i 1.41421i
\(699\) 0 0
\(700\) −1.00000 −1.00000
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.41421i 1.41421i
\(708\) 2.00000i 2.00000i
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 2.82843i 2.82843i
\(718\) 2.00000i 2.00000i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(721\) 0 0
\(722\) 1.00000i 1.00000i
\(723\) 0 0
\(724\) −1.41421 −1.41421
\(725\) 0 0
\(726\) −1.41421 −1.41421
\(727\) 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
\(732\) 2.00000i 2.00000i
\(733\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(734\) 0 0
\(735\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) −2.82843 −2.82843
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.41421i 1.41421i
\(748\) 0 0
\(749\) 0 0
\(750\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(751\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 2.00000i 2.00000i
\(754\) 0 0
\(755\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −1.00000 1.00000i −1.00000 1.00000i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.00000i 2.00000i
\(768\) 1.41421i 1.41421i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.00000i 2.00000i
\(773\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −1.00000 −1.00000
\(785\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(786\) −2.00000 −2.00000
\(787\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(788\) 0 0
\(789\) −2.82843 −2.82843
\(790\) 0 0
\(791\) 2.00000 2.00000
\(792\) 0 0
\(793\) 2.00000i 2.00000i
\(794\) 1.41421 1.41421
\(795\) 0 0
\(796\) 0 0
\(797\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(798\) 2.00000i 2.00000i
\(799\) 0 0
\(800\) −1.00000 −1.00000
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.00000i 2.00000i
\(808\) 1.41421i 1.41421i
\(809\) 0 0 1.00000i \(-0.5\pi\)