Properties

Label 3332.1.ce.a.1795.1
Level $3332$
Weight $1$
Character 3332.1795
Analytic conductor $1.663$
Analytic rank $0$
Dimension $16$
Projective image $D_{16}$
CM discriminant -4
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.ce (of order \(48\), degree \(16\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.66288462209\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\Q(\zeta_{48})\)
Defining polynomial: \( x^{16} - x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{16}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\)

Embedding invariants

Embedding label 1795.1
Root \(0.991445 - 0.130526i\) of defining polynomial
Character \(\chi\) \(=\) 3332.1795
Dual form 3332.1.ce.a.607.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.991445 - 0.130526i) q^{2} +(0.965926 - 0.258819i) q^{4} +(0.835400 - 0.732626i) q^{5} +(0.923880 - 0.382683i) q^{8} +(-0.608761 + 0.793353i) q^{9} +O(q^{10})\) \(q+(0.991445 - 0.130526i) q^{2} +(0.965926 - 0.258819i) q^{4} +(0.835400 - 0.732626i) q^{5} +(0.923880 - 0.382683i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(0.732626 - 0.835400i) q^{10} +(-1.00000 - 1.00000i) q^{13} +(0.866025 - 0.500000i) q^{16} +(0.793353 - 0.608761i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.617317 - 0.923880i) q^{20} +(0.0306258 - 0.232626i) q^{25} +(-1.12197 - 0.860919i) q^{26} +(-0.216773 - 1.08979i) q^{29} +(0.793353 - 0.608761i) q^{32} +(0.707107 - 0.707107i) q^{34} +(-0.382683 + 0.923880i) q^{36} +(-0.108761 + 1.65938i) q^{37} +(0.491445 - 0.996552i) q^{40} +(0.0761205 - 0.382683i) q^{41} +(0.0726721 + 1.10876i) q^{45} -0.234633i q^{50} +(-1.22474 - 0.707107i) q^{52} +(1.12484 + 1.46593i) q^{53} +(-0.357164 - 1.05217i) q^{58} +(0.630526 + 1.85747i) q^{61} +(0.707107 - 0.707107i) q^{64} +(-1.56803 - 0.102774i) q^{65} +(0.608761 - 0.793353i) q^{68} +(-0.258819 + 0.965926i) q^{72} +(-1.57469 - 0.534534i) q^{73} +(0.108761 + 1.65938i) q^{74} +(0.357164 - 1.05217i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(0.0255190 - 0.389345i) q^{82} +(0.216773 - 1.08979i) q^{85} +(0.216773 + 1.08979i) q^{90} +(-1.63099 + 0.324423i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{13} - 8 q^{18} + 16 q^{20} + 8 q^{37} - 8 q^{40} + 16 q^{41} + 8 q^{61} - 8 q^{74}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.991445 0.130526i 0.991445 0.130526i
\(3\) 0 0 −0.442289 0.896873i \(-0.645833\pi\)
0.442289 + 0.896873i \(0.354167\pi\)
\(4\) 0.965926 0.258819i 0.965926 0.258819i
\(5\) 0.835400 0.732626i 0.835400 0.732626i −0.130526 0.991445i \(-0.541667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.923880 0.382683i 0.923880 0.382683i
\(9\) −0.608761 + 0.793353i −0.608761 + 0.793353i
\(10\) 0.732626 0.835400i 0.732626 0.835400i
\(11\) 0 0 0.997859 0.0654031i \(-0.0208333\pi\)
−0.997859 + 0.0654031i \(0.979167\pi\)
\(12\) 0 0
\(13\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.866025 0.500000i 0.866025 0.500000i
\(17\) 0.793353 0.608761i 0.793353 0.608761i
\(18\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(19\) 0 0 −0.130526 0.991445i \(-0.541667\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(20\) 0.617317 0.923880i 0.617317 0.923880i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.896873 0.442289i \(-0.854167\pi\)
0.896873 + 0.442289i \(0.145833\pi\)
\(24\) 0 0
\(25\) 0.0306258 0.232626i 0.0306258 0.232626i
\(26\) −1.12197 0.860919i −1.12197 0.860919i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.216773 1.08979i −0.216773 1.08979i −0.923880 0.382683i \(-0.875000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(30\) 0 0
\(31\) 0 0 0.896873 0.442289i \(-0.145833\pi\)
−0.896873 + 0.442289i \(0.854167\pi\)
\(32\) 0.793353 0.608761i 0.793353 0.608761i
\(33\) 0 0
\(34\) 0.707107 0.707107i 0.707107 0.707107i
\(35\) 0 0
\(36\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(37\) −0.108761 + 1.65938i −0.108761 + 1.65938i 0.500000 + 0.866025i \(0.333333\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.491445 0.996552i 0.491445 0.996552i
\(41\) 0.0761205 0.382683i 0.0761205 0.382683i −0.923880 0.382683i \(-0.875000\pi\)
1.00000 \(0\)
\(42\) 0 0
\(43\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(44\) 0 0
\(45\) 0.0726721 + 1.10876i 0.0726721 + 1.10876i
\(46\) 0 0
\(47\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.234633i 0.234633i
\(51\) 0 0
\(52\) −1.22474 0.707107i −1.22474 0.707107i
\(53\) 1.12484 + 1.46593i 1.12484 + 1.46593i 0.866025 + 0.500000i \(0.166667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.357164 1.05217i −0.357164 1.05217i
\(59\) 0 0 −0.991445 0.130526i \(-0.958333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(60\) 0 0
\(61\) 0.630526 + 1.85747i 0.630526 + 1.85747i 0.500000 + 0.866025i \(0.333333\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.707107 0.707107i 0.707107 0.707107i
\(65\) −1.56803 0.102774i −1.56803 0.102774i
\(66\) 0 0
\(67\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(68\) 0.608761 0.793353i 0.608761 0.793353i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(72\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(73\) −1.57469 0.534534i −1.57469 0.534534i −0.608761 0.793353i \(-0.708333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(74\) 0.108761 + 1.65938i 0.108761 + 1.65938i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.442289 0.896873i \(-0.354167\pi\)
−0.442289 + 0.896873i \(0.645833\pi\)
\(80\) 0.357164 1.05217i 0.357164 1.05217i
\(81\) −0.258819 0.965926i −0.258819 0.965926i
\(82\) 0.0255190 0.389345i 0.0255190 0.389345i
\(83\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(84\) 0 0
\(85\) 0.216773 1.08979i 0.216773 1.08979i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(90\) 0.216773 + 1.08979i 0.216773 + 1.08979i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.63099 + 0.324423i −1.63099 + 0.324423i −0.923880 0.382683i \(-0.875000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.0306258 0.232626i −0.0306258 0.232626i
\(101\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) −1.30656 0.541196i −1.30656 0.541196i
\(105\) 0 0
\(106\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(107\) 0 0 −0.659346 0.751840i \(-0.729167\pi\)
0.659346 + 0.751840i \(0.270833\pi\)
\(108\) 0 0
\(109\) −0.257264 + 0.293353i −0.257264 + 0.293353i −0.866025 0.500000i \(-0.833333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.08979 1.63099i −1.08979 1.63099i −0.707107 0.707107i \(-0.750000\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.491445 0.996552i −0.491445 0.996552i
\(117\) 1.40211 0.184592i 1.40211 0.184592i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.991445 0.130526i 0.991445 0.130526i
\(122\) 0.867580 + 1.75928i 0.867580 + 1.75928i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.472474 + 0.707107i 0.472474 + 0.707107i
\(126\) 0 0
\(127\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(128\) 0.608761 0.793353i 0.608761 0.793353i
\(129\) 0 0
\(130\) −1.56803 + 0.102774i −1.56803 + 0.102774i
\(131\) 0 0 −0.659346 0.751840i \(-0.729167\pi\)
0.659346 + 0.751840i \(0.270833\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.500000 0.866025i 0.500000 0.866025i
\(137\) −0.923880 + 1.60021i −0.923880 + 1.60021i −0.130526 + 0.991445i \(0.541667\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(138\) 0 0
\(139\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.130526 + 0.991445i −0.130526 + 0.991445i
\(145\) −0.979500 0.751597i −0.979500 0.751597i
\(146\) −1.63099 0.324423i −1.63099 0.324423i
\(147\) 0 0
\(148\) 0.324423 + 1.63099i 0.324423 + 1.63099i
\(149\) −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 0 0
\(151\) 0 0 0.793353 0.608761i \(-0.208333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(152\) 0 0
\(153\) 1.00000i 1.00000i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.478235 + 1.78480i 0.478235 + 1.78480i 0.608761 + 0.793353i \(0.291667\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.216773 1.08979i 0.216773 1.08979i
\(161\) 0 0
\(162\) −0.382683 0.923880i −0.382683 0.923880i
\(163\) 0 0 0.946930 0.321439i \(-0.104167\pi\)
−0.946930 + 0.321439i \(0.895833\pi\)
\(164\) −0.0255190 0.389345i −0.0255190 0.389345i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(168\) 0 0
\(169\) 1.00000i 1.00000i
\(170\) 0.0726721 1.10876i 0.0726721 1.10876i
\(171\) 0 0
\(172\) 0 0
\(173\) 0.389345 + 0.0255190i 0.389345 + 0.0255190i 0.258819 0.965926i \(-0.416667\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.991445 0.130526i \(-0.958333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(180\) 0.357164 + 1.05217i 0.357164 + 1.05217i
\(181\) 1.63099 1.08979i 1.63099 1.08979i 0.707107 0.707107i \(-0.250000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.12484 + 1.46593i 1.12484 + 1.46593i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(192\) 0 0
\(193\) −0.108761 1.65938i −0.108761 1.65938i −0.608761 0.793353i \(-0.708333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(194\) −1.57469 + 0.534534i −1.57469 + 0.534534i
\(195\) 0 0
\(196\) 0 0
\(197\) 0.382683 1.92388i 0.382683 1.92388i 1.00000i \(-0.5\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(198\) 0 0
\(199\) 0 0 0.321439 0.946930i \(-0.395833\pi\)
−0.321439 + 0.946930i \(0.604167\pi\)
\(200\) −0.0607275 0.226638i −0.0607275 0.226638i
\(201\) 0 0
\(202\) −0.765367 + 1.84776i −0.765367 + 1.84776i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.216773 0.375461i −0.216773 0.375461i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.36603 0.366025i −1.36603 0.366025i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(212\) 1.46593 + 1.12484i 1.46593 + 1.12484i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −0.216773 + 0.324423i −0.216773 + 0.324423i
\(219\) 0 0
\(220\) 0 0
\(221\) −1.40211 0.184592i −1.40211 0.184592i
\(222\) 0 0
\(223\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(224\) 0 0
\(225\) 0.165911 + 0.165911i 0.165911 + 0.165911i
\(226\) −1.29335 1.47479i −1.29335 1.47479i
\(227\) 0 0 0.997859 0.0654031i \(-0.0208333\pi\)
−0.997859 + 0.0654031i \(0.979167\pi\)
\(228\) 0 0
\(229\) −0.465926 + 0.607206i −0.465926 + 0.607206i −0.965926 0.258819i \(-0.916667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.617317 0.923880i −0.617317 0.923880i
\(233\) 0.293353 0.257264i 0.293353 0.257264i −0.500000 0.866025i \(-0.666667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(234\) 1.36603 0.366025i 1.36603 0.366025i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −0.735499 1.49144i −0.735499 1.49144i −0.866025 0.500000i \(-0.833333\pi\)
0.130526 0.991445i \(-0.458333\pi\)
\(242\) 0.965926 0.258819i 0.965926 0.258819i
\(243\) 0 0
\(244\) 1.08979 + 1.63099i 1.08979 + 1.63099i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0.560728 + 0.639387i 0.560728 + 0.639387i
\(251\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.500000 0.866025i 0.500000 0.866025i
\(257\) 0.0999004 + 0.758819i 0.0999004 + 0.758819i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.54120 + 0.306563i −1.54120 + 0.306563i
\(261\) 0.996552 + 0.491445i 0.996552 + 0.491445i
\(262\) 0 0
\(263\) 0 0 0.130526 0.991445i \(-0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(264\) 0 0
\(265\) 2.01367 + 0.400544i 2.01367 + 0.400544i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.49144 0.735499i 1.49144 0.735499i 0.500000 0.866025i \(-0.333333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(270\) 0 0
\(271\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0.382683 0.923880i 0.382683 0.923880i
\(273\) 0 0
\(274\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(275\) 0 0
\(276\) 0 0
\(277\) 0.125419 0.369474i 0.125419 0.369474i −0.866025 0.500000i \(-0.833333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.707107 + 1.70711i 0.707107 + 1.70711i 0.707107 + 0.707107i \(0.250000\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 −0.0654031 0.997859i \(-0.520833\pi\)
0.0654031 + 0.997859i \(0.479167\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000i 1.00000i
\(289\) 0.258819 0.965926i 0.258819 0.965926i
\(290\) −1.06922 0.617317i −1.06922 0.617317i
\(291\) 0 0
\(292\) −1.65938 0.108761i −1.65938 0.108761i
\(293\) −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i \(0.625000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.534534 + 1.57469i 0.534534 + 1.57469i
\(297\) 0 0
\(298\) −1.40211 0.184592i −1.40211 0.184592i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.88757 + 1.08979i 1.88757 + 1.08979i
\(306\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.946930 0.321439i \(-0.895833\pi\)
0.946930 + 0.321439i \(0.104167\pi\)
\(312\) 0 0
\(313\) −1.85747 + 0.630526i −1.85747 + 0.630526i −0.866025 + 0.500000i \(0.833333\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(314\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(315\) 0 0
\(316\) 0 0
\(317\) −0.491445 + 0.996552i −0.491445 + 0.996552i 0.500000 + 0.866025i \(0.333333\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.0726721 1.10876i 0.0726721 1.10876i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.500000 0.866025i
\(325\) −0.263252 + 0.202000i −0.263252 + 0.202000i
\(326\) 0 0
\(327\) 0 0
\(328\) −0.0761205 0.382683i −0.0761205 0.382683i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.793353 0.608761i \(-0.791667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(332\) 0 0
\(333\) −1.25026 1.09645i −1.25026 1.09645i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.08979 + 1.63099i −1.08979 + 1.63099i −0.382683 + 0.923880i \(0.625000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(338\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(339\) 0 0
\(340\) −0.0726721 1.10876i −0.0726721 1.10876i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.389345 0.0255190i 0.389345 0.0255190i
\(347\) 0 0 0.659346 0.751840i \(-0.270833\pi\)
−0.659346 + 0.751840i \(0.729167\pi\)
\(348\) 0 0
\(349\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.739288 0.198092i 0.739288 0.198092i 0.130526 0.991445i \(-0.458333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.991445 0.130526i \(-0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(360\) 0.491445 + 0.996552i 0.491445 + 0.996552i
\(361\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(362\) 1.47479 1.29335i 1.47479 1.29335i
\(363\) 0 0
\(364\) 0 0
\(365\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(366\) 0 0
\(367\) 0 0 0.659346 0.751840i \(-0.270833\pi\)
−0.659346 + 0.751840i \(0.729167\pi\)
\(368\) 0 0
\(369\) 0.257264 + 0.293353i 0.257264 + 0.293353i
\(370\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(371\) 0 0
\(372\) 0 0
\(373\) 0.662827 0.382683i 0.662827 0.382683i −0.130526 0.991445i \(-0.541667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.873017 + 1.30656i −0.873017 + 1.30656i
\(378\) 0 0
\(379\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.793353 0.608761i \(-0.791667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.324423 1.63099i −0.324423 1.63099i
\(387\) 0 0
\(388\) −1.49144 + 0.735499i −1.49144 + 0.735499i
\(389\) 1.12197 0.860919i 1.12197 0.860919i 0.130526 0.991445i \(-0.458333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0.128293 1.95737i 0.128293 1.95737i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.172572 + 0.349942i −0.172572 + 0.349942i −0.965926 0.258819i \(-0.916667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.0897902 0.216773i −0.0897902 0.216773i
\(401\) 1.57469 0.534534i 1.57469 0.534534i 0.608761 0.793353i \(-0.291667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.517638 + 1.93185i −0.517638 + 1.93185i
\(405\) −0.923880 0.617317i −0.923880 0.617317i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.60021 0.923880i −1.60021 0.923880i −0.991445 0.130526i \(-0.958333\pi\)
−0.608761 0.793353i \(-0.708333\pi\)
\(410\) −0.263926 0.343955i −0.263926 0.343955i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −1.40211 0.184592i −1.40211 0.184592i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(420\) 0 0
\(421\) −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i \(-0.875000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 1.60021 + 0.923880i 1.60021 + 0.923880i
\(425\) −0.117317 0.203198i −0.117317 0.203198i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.0654031 0.997859i \(-0.520833\pi\)
0.0654031 + 0.997859i \(0.479167\pi\)
\(432\) 0 0
\(433\) −0.707107 1.70711i −0.707107 1.70711i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(-0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.172572 + 0.349942i −0.172572 + 0.349942i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.0654031 0.997859i \(-0.479167\pi\)
−0.0654031 + 0.997859i \(0.520833\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1.41421 −1.41421
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.08979 + 0.216773i 1.08979 + 0.216773i 0.707107 0.707107i \(-0.250000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(450\) 0.186147 + 0.142836i 0.186147 + 0.142836i
\(451\) 0 0
\(452\) −1.47479 1.29335i −1.47479 1.29335i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.184592 1.40211i −0.184592 1.40211i −0.793353 0.608761i \(-0.791667\pi\)
0.608761 0.793353i \(-0.291667\pi\)
\(458\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(459\) 0 0
\(460\) 0 0
\(461\) 1.84776 + 0.765367i 1.84776 + 0.765367i 0.923880 + 0.382683i \(0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(462\) 0 0
\(463\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(464\) −0.732626 0.835400i −0.732626 0.835400i
\(465\) 0 0
\(466\) 0.257264 0.293353i 0.257264 0.293353i
\(467\) 0 0 0.608761 0.793353i \(-0.291667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(468\) 1.30656 0.541196i 1.30656 0.541196i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.84776 −1.84776
\(478\) 0 0
\(479\) 0 0 −0.442289 0.896873i \(-0.645833\pi\)
0.442289 + 0.896873i \(0.354167\pi\)
\(480\) 0 0
\(481\) 1.76814 1.55062i 1.76814 1.55062i
\(482\) −0.923880 1.38268i −0.923880 1.38268i
\(483\) 0 0
\(484\) 0.923880 0.382683i 0.923880 0.382683i
\(485\) −1.12484 + 1.46593i −1.12484 + 1.46593i
\(486\) 0 0
\(487\) 0 0 0.997859 0.0654031i \(-0.0208333\pi\)
−0.997859 + 0.0654031i \(0.979167\pi\)
\(488\) 1.29335 + 1.47479i 1.29335 + 1.47479i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(492\) 0 0
\(493\) −0.835400 0.732626i −0.835400 0.732626i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.896873 0.442289i \(-0.854167\pi\)
0.896873 + 0.442289i \(0.145833\pi\)
\(500\) 0.639387 + 0.560728i 0.639387 + 0.560728i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(504\) 0 0
\(505\) 0.433546 + 2.17958i 0.433546 + 2.17958i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i \(-0.0416667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.382683 0.923880i 0.382683 0.923880i
\(513\) 0 0
\(514\) 0.198092 + 0.739288i 0.198092 + 0.739288i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −1.48800 + 0.505107i −1.48800 + 0.505107i
\(521\) −0.0255190 0.389345i −0.0255190 0.389345i −0.991445 0.130526i \(-0.958333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(522\) 1.05217 + 0.357164i 1.05217 + 0.357164i
\(523\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.608761 + 0.793353i 0.608761 + 0.793353i
\(530\) 2.04872 + 0.134280i 2.04872 + 0.134280i
\(531\) 0 0
\(532\) 0 0
\(533\) −0.458804 + 0.306563i −0.458804 + 0.306563i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.38268 0.923880i 1.38268 0.923880i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.95737 0.128293i −1.95737 0.128293i −0.965926 0.258819i \(-0.916667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.258819 0.965926i 0.258819 0.965926i
\(545\) 0.433546i 0.433546i
\(546\) 0 0
\(547\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(548\) −0.478235 + 1.78480i −0.478235 + 1.78480i
\(549\) −1.85747 0.630526i −1.85747 0.630526i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.0761205 0.382683i 0.0761205 0.382683i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.198092 0.739288i −0.198092 0.739288i −0.991445 0.130526i \(-0.958333\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.923880 + 1.60021i 0.923880 + 1.60021i
\(563\) 0 0 0.793353 0.608761i \(-0.208333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(564\) 0 0
\(565\) −2.10531 0.564117i −2.10531 0.564117i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.607206 0.465926i −0.607206 0.465926i 0.258819 0.965926i \(-0.416667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) 0 0
\(571\) 0 0 −0.751840 0.659346i \(-0.770833\pi\)
0.751840 + 0.659346i \(0.229167\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(577\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(578\) 0.130526 0.991445i 0.130526 0.991445i
\(579\) 0 0
\(580\) −1.14065 0.472474i −1.14065 0.472474i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.65938 + 0.108761i −1.65938 + 0.108761i
\(585\) 1.03609 1.18143i 1.03609 1.18143i
\(586\) −1.12484 + 1.46593i −1.12484 + 1.46593i
\(587\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.735499 + 1.49144i 0.735499 + 1.49144i
\(593\) −1.98289 + 0.261052i −1.98289 + 0.261052i −0.991445 + 0.130526i \(0.958333\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.41421 −1.41421
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(600\) 0 0
\(601\) −1.08979 1.63099i −1.08979 1.63099i −0.707107 0.707107i \(-0.750000\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.732626 0.835400i 0.732626 0.835400i
\(606\) 0 0
\(607\) 0 0 −0.659346 0.751840i \(-0.729167\pi\)
0.659346 + 0.751840i \(0.270833\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 2.01367 + 0.834089i 2.01367 + 0.834089i
\(611\) 0 0
\(612\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(613\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.382683 + 0.0761205i −0.382683 + 0.0761205i −0.382683 0.923880i \(-0.625000\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 0 0 −0.751840 0.659346i \(-0.770833\pi\)
0.751840 + 0.659346i \(0.229167\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.13939 + 0.305298i 1.13939 + 0.305298i
\(626\) −1.75928 + 0.867580i −1.75928 + 0.867580i
\(627\) 0 0
\(628\) 0.923880 + 1.60021i 0.923880 + 1.60021i
\(629\) 0.923880 + 1.38268i 0.923880 + 1.38268i
\(630\) 0 0
\(631\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −0.357164 + 1.05217i −0.357164 + 1.05217i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.0726721 1.10876i −0.0726721 1.10876i
\(641\) −0.369474 0.125419i −0.369474 0.125419i 0.130526 0.991445i \(-0.458333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0 0
\(643\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) −0.608761 0.793353i −0.608761 0.793353i
\(649\) 0 0
\(650\) −0.234633 + 0.234633i −0.234633 + 0.234633i
\(651\) 0 0
\(652\) 0 0
\(653\) 0.534534 + 1.57469i 0.534534 + 1.57469i 0.793353 + 0.608761i \(0.208333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.125419 0.369474i −0.125419 0.369474i
\(657\) 1.38268 0.923880i 1.38268 0.923880i
\(658\) 0 0
\(659\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(660\) 0 0
\(661\) 0.860919 + 1.12197i 0.860919 + 1.12197i 0.991445 + 0.130526i \(0.0416667\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −1.38268 0.923880i −1.38268 0.923880i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.382683 1.92388i 0.382683 1.92388i 1.00000i \(-0.5\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(674\) −0.867580 + 1.75928i −0.867580 + 1.75928i
\(675\) 0 0
\(676\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(677\) 0.108761 1.65938i 0.108761 1.65938i −0.500000 0.866025i \(-0.666667\pi\)
0.608761 0.793353i \(-0.291667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.216773 1.08979i −0.216773 1.08979i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.896873 0.442289i \(-0.145833\pi\)
−0.896873 + 0.442289i \(0.854167\pi\)
\(684\) 0 0
\(685\) 0.400544 + 2.01367i 0.400544 + 2.01367i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.341081 2.59077i 0.341081 2.59077i
\(690\) 0 0
\(691\) 0 0 −0.896873 0.442289i \(-0.854167\pi\)
0.896873 + 0.442289i \(0.145833\pi\)
\(692\) 0.382683 0.0761205i 0.382683 0.0761205i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.172572 0.349942i −0.172572 0.349942i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i \(-0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.707107 0.292893i 0.707107 0.292893i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.835400 0.732626i 0.835400 0.732626i −0.130526 0.991445i \(-0.541667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.751840 0.659346i \(-0.229167\pi\)
−0.751840 + 0.659346i \(0.770833\pi\)
\(720\) 0.617317 + 0.923880i 0.617317 + 0.923880i
\(721\) 0 0
\(722\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(723\) 0 0
\(724\) 1.29335 1.47479i 1.29335 1.47479i
\(725\) −0.260152 + 0.0170513i −0.260152 + 0.0170513i
\(726\) 0 0
\(727\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) 0 0
\(729\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(730\) −1.60021 + 0.923880i −1.60021 + 0.923880i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.991445 0.130526i \(-0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0.293353 + 0.257264i 0.293353 + 0.257264i
\(739\) 0 0 0.130526 0.991445i \(-0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(740\) 1.46593 + 1.12484i 1.46593 + 1.12484i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(744\) 0 0
\(745\) −1.40934 + 0.695008i −1.40934 + 0.695008i
\(746\) 0.607206 0.465926i 0.607206 0.465926i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.0654031 0.997859i \(-0.479167\pi\)
−0.0654031 + 0.997859i \(0.520833\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −0.695008 + 1.40934i −0.695008 + 1.40934i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.732626 + 0.835400i 0.732626 + 0.835400i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i \(-0.250000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.534534 1.57469i −0.534534 1.57469i
\(773\) 0.758819 + 0.0999004i 0.758819 + 0.0999004i 0.500000 0.866025i \(-0.333333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −1.38268 + 0.923880i −1.38268 + 0.923880i
\(777\) 0 0
\(778\) 1.00000 1.00000i 1.00000 1.00000i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.70711 + 1.14065i 1.70711 + 1.14065i
\(786\) 0 0
\(787\) 0 0 −0.946930 0.321439i \(-0.895833\pi\)
0.946930 + 0.321439i \(0.104167\pi\)
\(788\) −0.128293 1.95737i −0.128293 1.95737i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1.22694 2.48800i 1.22694 2.48800i
\(794\) −0.125419 + 0.369474i −0.125419 + 0.369474i
\(795\) 0 0
\(796\) 0 0
\(797\) 0.541196 1.30656i 0.541196 1.30656i −0.382683 0.923880i \(-0.625000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.117317 0.203198i