Properties

Label 1805.1.h.b.654.2
Level $1805$
Weight $1$
Character 1805.654
Analytic conductor $0.901$
Analytic rank $0$
Dimension $4$
Projective image $D_{4}$
CM discriminant -95
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1805.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.900812347803\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Projective image: \(D_{4}\)
Projective field: Galois closure of 4.2.475.1
Artin image: $C_3\times D_8$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{24} - \cdots)\)

Embedding invariants

Embedding label 654.2
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1805.654
Dual form 1805.1.h.b.69.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{9} +(-0.707107 - 1.22474i) q^{10} +1.41421 q^{12} +(0.707107 + 1.22474i) q^{13} +(0.707107 + 1.22474i) q^{15} +(0.500000 - 0.866025i) q^{16} -1.41421 q^{18} -1.00000 q^{20} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{26} +2.00000 q^{30} +(-0.707107 - 1.22474i) q^{32} +(-0.500000 + 0.866025i) q^{36} +1.41421 q^{37} -2.00000 q^{39} -1.00000 q^{45} +(0.707107 + 1.22474i) q^{48} +1.00000 q^{49} -1.41421 q^{50} +(0.707107 - 1.22474i) q^{52} +(-0.707107 - 1.22474i) q^{53} +(0.707107 - 1.22474i) q^{60} -1.00000 q^{64} +1.41421 q^{65} +(0.707107 + 1.22474i) q^{67} +(1.00000 - 1.73205i) q^{74} +1.41421 q^{75} +(-1.41421 + 2.44949i) q^{78} +(-0.500000 - 0.866025i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.707107 + 1.22474i) q^{90} +2.00000 q^{96} +(-0.707107 + 1.22474i) q^{97} +(0.707107 - 1.22474i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{9} + 2 q^{16} - 4 q^{20} - 2 q^{25} + 8 q^{26} + 8 q^{30} - 2 q^{36} - 8 q^{39} - 4 q^{45} + 4 q^{49} - 4 q^{64} + 4 q^{74} - 2 q^{80} + 2 q^{81} + 8 q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(4\) −0.500000 0.866025i −0.500000 0.866025i
\(5\) 0.500000 0.866025i 0.500000 0.866025i
\(6\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.500000 0.866025i
\(10\) −0.707107 1.22474i −0.707107 1.22474i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.41421 1.41421
\(13\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(14\) 0 0
\(15\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(16\) 0.500000 0.866025i 0.500000 0.866025i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) −1.41421 −1.41421
\(19\) 0 0
\(20\) −1.00000 −1.00000
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.500000 0.866025i
\(26\) 2.00000 2.00000
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 2.00000 2.00000
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −0.707107 1.22474i −0.707107 1.22474i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(37\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) 0 0
\(39\) −2.00000 −2.00000
\(40\) 0 0
\(41\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(44\) 0 0
\(45\) −1.00000 −1.00000
\(46\) 0 0
\(47\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(49\) 1.00000 1.00000
\(50\) −1.41421 −1.41421
\(51\) 0 0
\(52\) 0.707107 1.22474i 0.707107 1.22474i
\(53\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0.707107 1.22474i 0.707107 1.22474i
\(61\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) 1.41421 1.41421
\(66\) 0 0
\(67\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0 0
\(73\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 1.00000 1.73205i 1.00000 1.73205i
\(75\) 1.41421 1.41421
\(76\) 0 0
\(77\) 0 0
\(78\) −1.41421 + 2.44949i −1.41421 + 2.44949i
\(79\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) −0.500000 0.866025i −0.500000 0.866025i
\(81\) 0.500000 0.866025i 0.500000 0.866025i
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 2.00000 2.00000
\(97\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(98\) 0.707107 1.22474i 0.707107 1.22474i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.00000 −2.00000
\(107\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(108\) 0 0
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0 0
\(111\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(112\) 0 0
\(113\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.707107 1.22474i 0.707107 1.22474i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −1.00000
\(126\) 0 0
\(127\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 1.00000 1.73205i 1.00000 1.73205i
\(131\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.00000 2.00000
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 0 0
\(139\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(148\) −0.707107 1.22474i −0.707107 1.22474i
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 1.00000 1.73205i 1.00000 1.73205i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(157\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0 0
\(159\) 2.00000 2.00000
\(160\) −1.41421 −1.41421
\(161\) 0 0
\(162\) −0.707107 1.22474i −0.707107 1.22474i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(168\) 0 0
\(169\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(181\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.707107 1.22474i 0.707107 1.22474i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(192\) 0.707107 1.22474i 0.707107 1.22474i
\(193\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(194\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(195\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(196\) −0.500000 0.866025i −0.500000 0.866025i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(200\) 0 0
\(201\) −2.00000 −2.00000
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(207\) 0 0
\(208\) 1.41421 1.41421
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(213\) 0 0
\(214\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 1.41421 + 2.44949i 1.41421 + 2.44949i
\(223\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(224\) 0 0
\(225\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(226\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(227\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) −1.00000 1.73205i −1.00000 1.73205i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(240\) 1.41421 1.41421
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(243\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(244\) 0 0
\(245\) 0.500000 0.866025i 0.500000 0.866025i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(251\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −2.00000 −2.00000
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.707107 1.22474i −0.707107 1.22474i
\(261\) 0 0
\(262\) 1.41421 + 2.44949i 1.41421 + 2.44949i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) −1.41421 −1.41421
\(266\) 0 0
\(267\) 0 0
\(268\) 0.707107 1.22474i 0.707107 1.22474i
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(282\) 0 0
\(283\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(289\) −0.500000 0.866025i −0.500000 0.866025i
\(290\) 0 0
\(291\) −1.00000 1.73205i −1.00000 1.73205i
\(292\) 0 0
\(293\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(294\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −0.707107 1.22474i −0.707107 1.22474i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(308\) 0 0
\(309\) 1.00000 1.73205i 1.00000 1.73205i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(318\) 1.41421 2.44949i 1.41421 2.44949i
\(319\) 0 0
\(320\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(321\) 1.00000 1.73205i 1.00000 1.73205i
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 0.707107 1.22474i 0.707107 1.22474i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −0.707107 1.22474i −0.707107 1.22474i
\(334\) −2.00000 −2.00000
\(335\) 1.41421 1.41421
\(336\) 0 0
\(337\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(338\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(339\) 1.00000 1.73205i 1.00000 1.73205i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −1.00000 1.73205i −1.00000 1.73205i
\(347\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 0.707107 1.22474i 0.707107 1.22474i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −1.00000 1.73205i −1.00000 1.73205i
\(371\) 0 0
\(372\) 0 0
\(373\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(374\) 0 0
\(375\) 0.707107 1.22474i 0.707107 1.22474i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 2.00000 2.00000
\(382\) −1.41421 + 2.44949i −1.41421 + 2.44949i
\(383\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(387\) 0 0
\(388\) 1.41421 1.41421
\(389\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(390\) 1.41421 + 2.44949i 1.41421 + 2.44949i
\(391\) 0 0
\(392\) 0 0
\(393\) −1.41421 2.44949i −1.41421 2.44949i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 2.82843 2.82843
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) −1.41421 + 2.44949i −1.41421 + 2.44949i
\(403\) 0 0
\(404\) 0 0
\(405\) −0.500000 0.866025i −0.500000 0.866025i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000 1.73205i 1.00000 1.73205i
\(417\) 0 0
\(418\) 0 0
\(419\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 0 0
\(433\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) −0.500000 0.866025i −0.500000 0.866025i
\(442\) 0 0
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 2.00000 2.00000
\(445\) 0 0
\(446\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(451\) 0 0
\(452\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(453\) 0 0
\(454\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.00000 + 1.73205i −1.00000 + 1.73205i −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 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −1.41421 −1.41421
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(478\) 1.41421 2.44949i 1.41421 2.44949i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 1.00000 1.73205i 1.00000 1.73205i
\(481\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(482\) 0 0
\(483\) 0 0
\(484\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(485\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(486\) 2.00000 2.00000
\(487\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.707107 1.22474i −0.707107 1.22474i
\(491\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(500\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(501\) 2.00000 2.00000
\(502\) 2.82843 2.82843
\(503\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.707107 1.22474i −0.707107 1.22474i
\(508\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(509\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.41421 −1.41421
\(513\) 0 0
\(514\) −2.00000 −2.00000
\(515\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(524\) 2.00000 2.00000
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(530\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(556\) 0 0
\(557\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) 0 0
\(565\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 1.41421 2.44949i 1.41421 2.44949i
\(574\) 0 0
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −1.41421 −1.41421
\(579\) −1.00000 1.73205i −1.00000 1.73205i
\(580\) 0 0
\(581\) 0 0
\(582\) −2.82843 −2.82843
\(583\) 0 0
\(584\) 0 0
\(585\) −0.707107 1.22474i −0.707107 1.22474i
\(586\) 1.00000 1.73205i 1.00000 1.73205i
\(587\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 1.41421 1.41421
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.707107 1.22474i 0.707107 1.22474i
\(593\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.82843 −2.82843
\(598\) 0 0
\(599\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0.707107 1.22474i 0.707107 1.22474i
\(604\) 0 0
\(605\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(606\) 0 0
\(607\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) −1.00000 1.73205i −1.00000 1.73205i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(618\) −1.41421 2.44949i −1.41421 2.44949i
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(625\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 2.00000 2.00000
\(635\) −1.41421 −1.41421
\(636\) −1.00000 1.73205i −1.00000 1.73205i
\(637\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) −1.41421 2.44949i −1.41421 2.44949i
\(643\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −1.00000 1.73205i −1.00000 1.73205i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −2.00000 −2.00000
\(667\) 0 0
\(668\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(669\) −1.00000 1.73205i −1.00000 1.73205i
\(670\) 1.00000 1.73205i 1.00000 1.73205i
\(671\) 0 0
\(672\) 0 0
\(673\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(674\) −1.00000 1.73205i −1.00000 1.73205i
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(678\) −1.41421 2.44949i −1.41421 2.44949i
\(679\) 0 0
\(680\) 0 0
\(681\) 1.00000 1.73205i 1.00000 1.73205i
\(682\) 0 0
\(683\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.00000 1.73205i 1.00000 1.73205i
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) −1.41421 −1.41421
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −1.41421 + 2.44949i −1.41421 + 2.44949i
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.41421 + 2.44949i −1.41421 + 2.44949i
\(718\) 0 0
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −1.00000 1.73205i −1.00000 1.73205i
\(727\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(728\) 0 0
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(740\) −1.41421 −1.41421
\(741\) 0 0
\(742\) 0 0
\(743\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.00000 1.73205i 1.00000 1.73205i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −1.00000 1.73205i −1.00000 1.73205i
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) −2.82843 −2.82843
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 1.41421 2.44949i 1.41421 2.44949i
\(763\) 0 0
\(764\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(765\) 0 0
\(766\) −1.00000 1.73205i −1.00000 1.73205i
\(767\) 0 0
\(768\) 1.41421 1.41421
\(769\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(770\) 0 0
\(771\) 2.00000 2.00000
\(772\) 1.41421 1.41421
\(773\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −2.82843 −2.82843
\(779\) 0 0
\(780\) 2.00000 2.00000
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.500000 0.866025i 0.500000 0.866025i
\(785\) 0 0
\(786\) −4.00000 −4.00000
\(787\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1.00000 1.73205i 1.00000 1.73205i
\(796\) 1.00000 1.73205i 1.00000 1.73205i
\(797\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(805\) 0 0
\(806\)