Properties

Label 2001.1.bf.b.827.1
Level $2001$
Weight $1$
Character 2001.827
Analytic conductor $0.999$
Analytic rank $0$
Dimension $12$
Projective image $D_{28}$
CM discriminant -23
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2001.bf (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.998629090279\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\Q(\zeta_{28})\)
Defining polynomial: \(x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{28}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{28} - \cdots)\)

Embedding invariants

Embedding label 827.1
Root \(-0.433884 + 0.900969i\) of defining polynomial
Character \(\chi\) \(=\) 2001.827
Dual form 2001.1.bf.b.1655.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.222521 + 1.97493i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-2.87590 + 0.656405i) q^{4} +(-1.05737 - 1.68280i) q^{6} +(-1.27989 - 3.65773i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})\) \(q+(0.222521 + 1.97493i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-2.87590 + 0.656405i) q^{4} +(-1.05737 - 1.68280i) q^{6} +(-1.27989 - 3.65773i) q^{8} +(0.623490 - 0.781831i) q^{9} +(2.30629 - 1.83921i) q^{12} +(-0.541044 - 1.12349i) q^{13} +(4.28122 - 2.06173i) q^{16} +(1.68280 + 1.05737i) q^{18} +(0.781831 - 0.623490i) q^{23} +(2.74017 + 2.74017i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(2.09842 - 1.31852i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(0.974928 - 0.222521i) q^{29} +(-1.40532 + 0.158342i) q^{31} +(2.96269 + 4.71510i) q^{32} +(-1.27989 + 2.65773i) q^{36} +(0.974928 + 0.777479i) q^{39} +(-1.33485 - 1.33485i) q^{41} +(1.40532 + 1.40532i) q^{46} +(1.00435 + 0.351438i) q^{47} +(-2.96269 + 3.71510i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(1.87590 - 0.656405i) q^{50} +(2.29345 + 2.87590i) q^{52} +(-1.97493 - 0.222521i) q^{54} +(0.656405 + 1.87590i) q^{58} -0.445042i q^{59} +(-0.625427 - 2.74017i) q^{62} +(-4.93762 + 3.93762i) q^{64} +(-0.433884 + 0.900969i) q^{69} +(1.40881 - 0.678448i) q^{71} +(-3.65773 - 1.27989i) q^{72} +(-1.05737 - 0.119137i) q^{73} +(0.623490 + 0.781831i) q^{75} +(-1.31852 + 2.09842i) q^{78} +(-0.222521 - 0.974928i) q^{81} +(2.33921 - 2.93327i) q^{82} +(-0.781831 + 0.623490i) q^{87} +(-1.83921 + 2.30629i) q^{92} +(1.19745 - 0.752407i) q^{93} +(-0.470575 + 2.06173i) q^{94} +(-4.71510 - 2.96269i) q^{96} +(0.656405 - 1.87590i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - 2q^{3} - 14q^{4} + 2q^{6} - 2q^{9} + O(q^{10}) \) \( 12q + 2q^{2} - 2q^{3} - 14q^{4} + 2q^{6} - 2q^{9} + 12q^{16} + 2q^{18} - 2q^{25} + 4q^{26} - 2q^{27} + 2q^{31} + 2q^{32} - 2q^{41} - 2q^{46} + 2q^{47} - 2q^{48} - 2q^{49} + 2q^{50} + 10q^{52} - 12q^{54} + 2q^{58} - 4q^{62} - 14q^{64} - 14q^{72} + 2q^{73} - 2q^{75} - 10q^{78} - 2q^{81} + 4q^{82} + 2q^{92} + 2q^{93} - 4q^{94} - 12q^{96} + 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{27}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.222521 + 1.97493i 0.222521 + 1.97493i 0.222521 + 0.974928i \(0.428571\pi\)
1.00000i \(0.5\pi\)
\(3\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(4\) −2.87590 + 0.656405i −2.87590 + 0.656405i
\(5\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(6\) −1.05737 1.68280i −1.05737 1.68280i
\(7\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(8\) −1.27989 3.65773i −1.27989 3.65773i
\(9\) 0.623490 0.781831i 0.623490 0.781831i
\(10\) 0 0
\(11\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(12\) 2.30629 1.83921i 2.30629 1.83921i
\(13\) −0.541044 1.12349i −0.541044 1.12349i −0.974928 0.222521i \(-0.928571\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.28122 2.06173i 4.28122 2.06173i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 1.68280 + 1.05737i 1.68280 + 1.05737i
\(19\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.781831 0.623490i 0.781831 0.623490i
\(24\) 2.74017 + 2.74017i 2.74017 + 2.74017i
\(25\) −0.222521 0.974928i −0.222521 0.974928i
\(26\) 2.09842 1.31852i 2.09842 1.31852i
\(27\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(28\) 0 0
\(29\) 0.974928 0.222521i 0.974928 0.222521i
\(30\) 0 0
\(31\) −1.40532 + 0.158342i −1.40532 + 0.158342i −0.781831 0.623490i \(-0.785714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(32\) 2.96269 + 4.71510i 2.96269 + 4.71510i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −1.27989 + 2.65773i −1.27989 + 2.65773i
\(37\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(38\) 0 0
\(39\) 0.974928 + 0.777479i 0.974928 + 0.777479i
\(40\) 0 0
\(41\) −1.33485 1.33485i −1.33485 1.33485i −0.900969 0.433884i \(-0.857143\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(42\) 0 0
\(43\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.40532 + 1.40532i 1.40532 + 1.40532i
\(47\) 1.00435 + 0.351438i 1.00435 + 0.351438i 0.781831 0.623490i \(-0.214286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(48\) −2.96269 + 3.71510i −2.96269 + 3.71510i
\(49\) −0.900969 0.433884i −0.900969 0.433884i
\(50\) 1.87590 0.656405i 1.87590 0.656405i
\(51\) 0 0
\(52\) 2.29345 + 2.87590i 2.29345 + 2.87590i
\(53\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(54\) −1.97493 0.222521i −1.97493 0.222521i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.656405 + 1.87590i 0.656405 + 1.87590i
\(59\) 0.445042i 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(60\) 0 0
\(61\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(62\) −0.625427 2.74017i −0.625427 2.74017i
\(63\) 0 0
\(64\) −4.93762 + 3.93762i −4.93762 + 3.93762i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(68\) 0 0
\(69\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(70\) 0 0
\(71\) 1.40881 0.678448i 1.40881 0.678448i 0.433884 0.900969i \(-0.357143\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(72\) −3.65773 1.27989i −3.65773 1.27989i
\(73\) −1.05737 0.119137i −1.05737 0.119137i −0.433884 0.900969i \(-0.642857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(74\) 0 0
\(75\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(76\) 0 0
\(77\) 0 0
\(78\) −1.31852 + 2.09842i −1.31852 + 2.09842i
\(79\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(80\) 0 0
\(81\) −0.222521 0.974928i −0.222521 0.974928i
\(82\) 2.33921 2.93327i 2.33921 2.93327i
\(83\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(88\) 0 0
\(89\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.83921 + 2.30629i −1.83921 + 2.30629i
\(93\) 1.19745 0.752407i 1.19745 0.752407i
\(94\) −0.470575 + 2.06173i −0.470575 + 2.06173i
\(95\) 0 0
\(96\) −4.71510 2.96269i −4.71510 2.96269i
\(97\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(98\) 0.656405 1.87590i 0.656405 1.87590i
\(99\) 0 0
\(100\) 1.27989 + 2.65773i 1.27989 + 2.65773i
\(101\) 1.05737 + 0.119137i 1.05737 + 0.119137i 0.623490 0.781831i \(-0.285714\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(102\) 0 0
\(103\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(104\) −3.41694 + 3.41694i −3.41694 + 3.41694i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(108\) 2.94986i 2.94986i
\(109\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.65773 + 1.27989i −2.65773 + 1.27989i
\(117\) −1.21572 0.277479i −1.21572 0.277479i
\(118\) 0.878926 0.0990311i 0.878926 0.0990311i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.781831 0.623490i −0.781831 0.623490i
\(122\) 0 0
\(123\) 1.78183 + 0.623490i 1.78183 + 0.623490i
\(124\) 3.93762 1.37783i 3.93762 1.37783i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.78183 0.623490i −1.78183 0.623490i −0.781831 0.623490i \(-0.785714\pi\)
−1.00000 \(\pi\)
\(128\) −4.93762 4.93762i −4.93762 4.93762i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.0250721 0.222521i 0.0250721 0.222521i −0.974928 0.222521i \(-0.928571\pi\)
1.00000 \(0\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(138\) −1.87590 0.656405i −1.87590 0.656405i
\(139\) 0.974928 + 1.22252i 0.974928 + 1.22252i 0.974928 + 0.222521i \(0.0714286\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −1.05737 + 0.119137i −1.05737 + 0.119137i
\(142\) 1.65338 + 2.63133i 1.65338 + 2.63133i
\(143\) 0 0
\(144\) 1.05737 4.63266i 1.05737 4.63266i
\(145\) 0 0
\(146\) 2.11475i 2.11475i
\(147\) 1.00000 1.00000
\(148\) 0 0
\(149\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(150\) −1.40532 + 1.40532i −1.40532 + 1.40532i
\(151\) 1.56366 1.24698i 1.56366 1.24698i 0.781831 0.623490i \(-0.214286\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −3.31413 1.59600i −3.31413 1.59600i
\(157\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.87590 0.656405i 1.87590 0.656405i
\(163\) −0.351438 + 1.00435i −0.351438 + 1.00435i 0.623490 + 0.781831i \(0.285714\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(164\) 4.71510 + 2.96269i 4.71510 + 2.96269i
\(165\) 0 0
\(166\) 0 0
\(167\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(168\) 0 0
\(169\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(174\) −1.40532 1.40532i −1.40532 1.40532i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.193096 + 0.400969i 0.193096 + 0.400969i
\(178\) 0 0
\(179\) 1.12349 1.40881i 1.12349 1.40881i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(180\) 0 0
\(181\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.28122 2.06173i −3.28122 2.06173i
\(185\) 0 0
\(186\) 1.75241 + 2.19745i 1.75241 + 2.19745i
\(187\) 0 0
\(188\) −3.11910 0.351438i −3.11910 0.351438i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) 2.74017 5.69003i 2.74017 5.69003i
\(193\) 0.900969 1.43388i 0.900969 1.43388i 1.00000i \(-0.5\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.87590 + 0.656405i 2.87590 + 0.656405i
\(197\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(198\) 0 0
\(199\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(200\) −3.28122 + 2.06173i −3.28122 + 2.06173i
\(201\) 0 0
\(202\) 2.11475i 2.11475i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.00000i 1.00000i
\(208\) −4.63266 3.69442i −4.63266 3.69442i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.33485 0.467085i 1.33485 0.467085i 0.433884 0.900969i \(-0.357143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(212\) 0 0
\(213\) −0.974928 + 1.22252i −0.974928 + 1.22252i
\(214\) 0 0
\(215\) 0 0
\(216\) 3.85082 0.433884i 3.85082 0.433884i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.00435 0.351438i 1.00435 0.351438i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −0.900969 0.433884i −0.900969 0.433884i
\(226\) 0 0
\(227\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(228\) 0 0
\(229\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2.06173 3.28122i −2.06173 3.28122i
\(233\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(234\) 0.277479 2.46269i 0.277479 2.46269i
\(235\) 0 0
\(236\) 0.292128 + 1.27989i 0.292128 + 1.27989i
\(237\) 0 0
\(238\) 0 0
\(239\) −0.846011 0.193096i −0.846011 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(240\) 0 0
\(241\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(242\) 1.05737 1.68280i 1.05737 1.68280i
\(243\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(244\) 0 0
\(245\) 0 0
\(246\) −0.834853 + 3.65773i −0.834853 + 3.65773i
\(247\) 0 0
\(248\) 2.37783 + 4.93762i 2.37783 + 4.93762i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.834853 3.65773i 0.834853 3.65773i
\(255\) 0 0
\(256\) 4.71510 5.91255i 4.71510 5.91255i
\(257\) 1.90097 0.433884i 1.90097 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
1.00000 \(0\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.433884 0.900969i 0.433884 0.900969i
\(262\) 0.445042 0.445042
\(263\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.623490 1.78183i −0.623490 1.78183i −0.623490 0.781831i \(-0.714286\pi\)
1.00000i \(-0.5\pi\)
\(270\) 0 0
\(271\) 0.189606 + 0.119137i 0.189606 + 0.119137i 0.623490 0.781831i \(-0.285714\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0.656405 2.87590i 0.656405 2.87590i
\(277\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(278\) −2.19745 + 2.19745i −2.19745 + 2.19745i
\(279\) −0.752407 + 1.19745i −0.752407 + 1.19745i
\(280\) 0 0
\(281\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(282\) −0.470575 2.06173i −0.470575 2.06173i
\(283\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(284\) −3.60626 + 2.87590i −3.60626 + 2.87590i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 5.53363 + 0.623490i 5.53363 + 0.623490i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 3.11910 0.351438i 3.11910 0.351438i
\(293\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(294\) 0.222521 + 1.97493i 0.222521 + 1.97493i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.12349 0.541044i −1.12349 0.541044i
\(300\) −2.30629 1.83921i −2.30629 1.83921i
\(301\) 0 0
\(302\) 2.81064 + 2.81064i 2.81064 + 2.81064i
\(303\) −1.00435 + 0.351438i −1.00435 + 0.351438i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.19745 + 1.19745i 1.19745 + 1.19745i 0.974928 + 0.222521i \(0.0714286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.87590 + 0.656405i −1.87590 + 0.656405i −0.900969 + 0.433884i \(0.857143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(312\) 1.59600 4.56111i 1.59600 4.56111i
\(313\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.97493 + 0.222521i −1.97493 + 0.222521i −0.974928 + 0.222521i \(0.928571\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.27989 + 2.65773i 1.27989 + 2.65773i
\(325\) −0.974928 + 0.777479i −0.974928 + 0.777479i
\(326\) −2.06173 0.470575i −2.06173 0.470575i
\(327\) 0 0
\(328\) −3.17406 + 6.59100i −3.17406 + 6.59100i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.467085 + 0.467085i −0.467085 + 0.467085i −0.900969 0.433884i \(-0.857143\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −2.46269 0.277479i −2.46269 0.277479i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(338\) −0.933884 0.586798i −0.933884 0.586798i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.400969 + 3.55870i 0.400969 + 3.55870i
\(347\) −0.867767 −0.867767 −0.433884 0.900969i \(-0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(348\) 1.83921 2.30629i 1.83921 2.30629i
\(349\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(350\) 0 0
\(351\) 1.21572 0.277479i 1.21572 0.277479i
\(352\) 0 0
\(353\) −0.541044 + 0.678448i −0.541044 + 0.678448i −0.974928 0.222521i \(-0.928571\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(354\) −0.748917 + 0.470575i −0.748917 + 0.470575i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 3.03230 + 1.90532i 3.03230 + 1.90532i
\(359\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(360\) 0 0
\(361\) −0.433884 0.900969i −0.433884 0.900969i
\(362\) 0 0
\(363\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(368\) 2.06173 4.28122i 2.06173 4.28122i
\(369\) −1.87590 + 0.211363i −1.87590 + 0.211363i
\(370\) 0 0
\(371\) 0 0
\(372\) −2.94986 + 2.94986i −2.94986 + 2.94986i
\(373\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.12345i 4.12345i
\(377\) −0.777479 0.974928i −0.777479 0.974928i
\(378\) 0 0
\(379\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(380\) 0 0
\(381\) 1.87590 0.211363i 1.87590 0.211363i
\(382\) 0 0
\(383\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(384\) 6.59100 + 2.30629i 6.59100 + 2.30629i
\(385\) 0 0
\(386\) 3.03230 + 1.46028i 3.03230 + 1.46028i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.433884 + 3.85082i −0.433884 + 3.85082i
\(393\) 0.0739590 + 0.211363i 0.0739590 + 0.211363i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −0.781831 0.376510i −0.781831 0.376510i 1.00000i \(-0.5\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.96269 3.71510i −2.96269 3.71510i
\(401\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(402\) 0 0
\(403\) 0.938236 + 1.49319i 0.938236 + 1.49319i
\(404\) −3.11910 + 0.351438i −3.11910 + 0.351438i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 1.59842 1.00435i 1.59842 1.00435i 0.623490 0.781831i \(-0.285714\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 1.97493 0.222521i 1.97493 0.222521i
\(415\) 0 0
\(416\) 3.69442 5.87964i 3.69442 5.87964i
\(417\) −1.40881 0.678448i −1.40881 0.678448i
\(418\) 0 0
\(419\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(420\) 0 0
\(421\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(422\) 1.21949 + 2.53230i 1.21949 + 2.53230i
\(423\) 0.900969 0.566116i 0.900969 0.566116i
\(424\) 0 0
\(425\) 0 0
\(426\) −2.63133 1.65338i −2.63133 1.65338i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(432\) 1.05737 + 4.63266i 1.05737 + 4.63266i
\(433\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.917554 + 1.90532i 0.917554 + 1.90532i
\(439\) −0.846011 + 0.193096i −0.846011 + 0.193096i −0.623490 0.781831i \(-0.714286\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(440\) 0 0
\(441\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(442\) 0 0
\(443\) 0.559311 + 1.59842i 0.559311 + 1.59842i 0.781831 + 0.623490i \(0.214286\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 1.18280 3.38025i 1.18280 3.38025i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.222521 0.0250721i −0.222521 0.0250721i 1.00000i \(-0.5\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(450\) 0.656405 1.87590i 0.656405 1.87590i
\(451\) 0 0
\(452\) 0 0
\(453\) −0.867767 + 1.80194i −0.867767 + 1.80194i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −0.559311 + 0.351438i −0.559311 + 0.351438i −0.781831 0.623490i \(-0.785714\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(462\) 0 0
\(463\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(464\) 3.71510 2.96269i 3.71510 2.96269i
\(465\) 0 0
\(466\) −3.55870 + 0.400969i −3.55870 + 0.400969i
\(467\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(468\) 3.67841 3.67841
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.62784 + 0.569607i −1.62784 + 0.569607i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.193096 1.71378i 0.193096 1.71378i
\(479\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 2.65773 + 1.27989i 2.65773 + 1.27989i
\(485\) 0 0
\(486\) −1.40532 + 1.40532i −1.40532 + 1.40532i
\(487\) −0.541044 0.678448i −0.541044 0.678448i 0.433884 0.900969i \(-0.357143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(488\) 0 0
\(489\) −0.119137 1.05737i −0.119137 1.05737i
\(490\) 0 0
\(491\) 0.656405 0.0739590i 0.656405 0.0739590i 0.222521 0.974928i \(-0.428571\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(492\) −5.53363 0.623490i −5.53363 0.623490i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −5.69003 + 3.57528i −5.69003 + 3.57528i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.347948 0.277479i 0.347948 0.277479i −0.433884 0.900969i \(-0.642857\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(500\) 0 0
\(501\) −0.277479 1.21572i −0.277479 1.21572i
\(502\) 0 0
\(503\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.123490 0.541044i 0.123490 0.541044i
\(508\) 5.53363 + 0.623490i 5.53363 + 0.623490i
\(509\) −0.846011 1.75676i −0.846011 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 6.81352 + 4.28122i 6.81352 + 4.28122i
\(513\) 0 0
\(514\) 1.27989 + 3.65773i 1.27989 + 3.65773i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 1.87590 + 0.656405i 1.87590 + 0.656405i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0.0739590 + 0.656405i 0.0739590 + 0.656405i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.222521 0.974928i 0.222521 0.974928i
\(530\) 0 0
\(531\) −0.347948 0.277479i −0.347948 0.277479i
\(532\) 0 0
\(533\) −0.777479 + 2.22191i −0.777479 + 2.22191i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(538\) 3.38025 1.62784i 3.38025 1.62784i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.900969 1.43388i 0.900969 1.43388i 1.00000i \(-0.5\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(542\) −0.193096 + 0.400969i −0.193096 + 0.400969i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 3.85082 + 0.433884i 3.85082 + 0.433884i
\(553\) 0 0
\(554\) −1.31852 2.09842i −1.31852 2.09842i
\(555\) 0 0
\(556\) −3.60626 2.87590i −3.60626 2.87590i
\(557\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(558\) −2.53230 1.21949i −2.53230 1.21949i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) 2.96269 1.03669i 2.96269 1.03669i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −4.28471 4.28471i −4.28471 4.28471i
\(569\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(570\) 0 0
\(571\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.781831 0.623490i −0.781831 0.623490i
\(576\) 6.31546i 6.31546i
\(577\) 0.351438 + 0.559311i 0.351438 + 0.559311i 0.974928 0.222521i \(-0.0714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(578\) 1.97493 0.222521i 1.97493 0.222521i
\(579\) −0.189606 + 1.68280i −0.189606 + 1.68280i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.917554 + 4.02007i 0.917554 + 4.02007i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.846011 + 0.193096i 0.846011 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(588\) −2.87590 + 0.656405i −2.87590 + 0.656405i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i \(-0.785714\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.818523 2.33921i 0.818523 2.33921i
\(599\) −0.189606 0.119137i −0.189606 0.119137i 0.433884 0.900969i \(-0.357143\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(600\) 2.06173 3.28122i 2.06173 3.28122i
\(601\) 0.467085 + 1.33485i 0.467085 + 1.33485i 0.900969 + 0.433884i \(0.142857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3.67841 + 4.61258i −3.67841 + 4.61258i
\(605\) 0 0
\(606\) −0.917554 1.90532i −0.917554 1.90532i
\(607\) −0.0739590 0.656405i −0.0739590 0.656405i −0.974928 0.222521i \(-0.928571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.148562 1.31852i −0.148562 1.31852i
\(612\) 0 0
\(613\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(614\) −2.09842 + 2.63133i −2.09842 + 2.63133i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(618\) 0 0
\(619\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(620\) 0 0
\(621\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(622\) −1.71378 3.55870i −1.71378 3.55870i
\(623\) 0 0
\(624\) 5.77683 + 1.31852i 5.77683 + 1.31852i
\(625\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(632\) 0 0
\(633\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(634\) −0.878926 3.85082i −0.878926 3.85082i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.24698i 1.24698i
\(638\) 0 0
\(639\) 0.347948 1.52446i 0.347948 1.52446i
\(640\) 0 0
\(641\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(642\) 0 0
\(643\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.75676 0.846011i −1.75676 0.846011i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(648\) −3.28122 + 2.06173i −3.28122 + 2.06173i
\(649\) 0 0
\(650\) −1.75241 1.75241i −1.75241 1.75241i
\(651\) 0 0
\(652\) 0.351438 3.11910i 0.351438 3.11910i
\(653\) −0.158342 + 1.40532i −0.158342 + 1.40532i 0.623490 + 0.781831i \(0.285714\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −8.46690 2.96269i −8.46690 2.96269i
\(657\) −0.752407 + 0.752407i −0.752407 + 0.752407i
\(658\) 0 0
\(659\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(660\) 0 0
\(661\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(662\) −1.02640 0.818523i −1.02640 0.818523i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.623490 0.781831i 0.623490 0.781831i
\(668\) 3.67841i 3.67841i
\(669\) 1.80194 1.80194
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.678448 0.541044i 0.678448 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) 0.710288 1.47493i 0.710288 1.47493i
\(677\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.846011 + 1.75676i 0.846011 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.974928 + 1.22252i −0.974928 + 1.22252i 1.00000i \(0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(692\) −5.18219 + 1.18280i −5.18219 + 1.18280i
\(693\) 0 0
\(694\) −0.193096 1.71378i −0.193096 1.71378i
\(695\) 0 0
\(696\) 3.28122 + 2.06173i 3.28122 + 2.06173i
\(697\) 0 0
\(698\) −0.0990311 0.878926i −0.0990311 0.878926i
\(699\) −0.781831 1.62349i −0.781831 1.62349i
\(700\) 0 0
\(701\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(702\) 0.818523 + 2.33921i 0.818523 + 2.33921i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.46028 0.917554i −1.46028 0.917554i
\(707\) 0 0
\(708\) −0.818523 1.02640i −0.818523 1.02640i
\(709\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(714\) 0 0
\(715\) 0 0
\(716\) −2.30629 + 4.78906i −2.30629 + 4.78906i
\(717\) 0.846011 0.193096i 0.846011 0.193096i
\(718\) 0 0
\(719\) 1.22252 0.974928i 1.22252 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.68280 1.05737i 1.68280 1.05737i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.433884 0.900969i −0.433884 0.900969i
\(726\) −0.222521 + 1.97493i −0.222521 + 1.97493i
\(727\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(728\) 0 0
\(729\) −0.900969 0.433884i −0.900969 0.433884i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 5.25615 + 1.83921i 5.25615 + 1.83921i
\(737\) 0 0
\(738\) −0.834853 3.65773i −0.834853 3.65773i
\(739\) −0.211363 + 1.87590i −0.211363 + 1.87590i 0.222521 + 0.974928i \(0.428571\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(744\) −4.28471 3.41694i −4.28471 3.41694i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(752\) 5.02442 0.566116i 5.02442 0.566116i
\(753\) 0 0
\(754\) 1.75241 1.75241i 1.75241 1.75241i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.21572 + 0.277479i 1.21572 + 0.277479i 0.781831 0.623490i \(-0.214286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(762\) 0.834853 + 3.65773i 0.834853 + 3.65773i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(768\) −1.68280 + 7.37283i −1.68280 + 7.37283i
\(769\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(770\) 0 0
\(771\) −1.52446 + 1.21572i −1.52446 + 1.21572i
\(772\) −1.64989 + 4.71510i −1.64989 + 4.71510i
\(773\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(774\) 0 0
\(775\) 0.467085 + 1.33485i 0.467085 + 1.33485i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 1.00000i 1.00000i
\(784\) −4.75179 −4.75179
\(785\) 0 0
\(786\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(787\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0.569607 1.62784i 0.569607 1.62784i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(798\) 0 0