Properties

Label 2001.1.bf.a.68.1
Level $2001$
Weight $1$
Character 2001.68
Analytic conductor $0.999$
Analytic rank $0$
Dimension $12$
Projective image $D_{28}$
CM discriminant -23
Inner twists $4$

Related objects

Downloads

Learn more

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 68.1
Root \(-0.781831 - 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 2001.68
Dual form 2001.1.bf.a.206.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.900969 - 1.43388i) q^{2} +(0.974928 - 0.222521i) q^{3} +(-0.810394 + 1.68280i) q^{4} +(-1.19745 - 1.19745i) q^{6} +(1.46028 - 0.164534i) q^{8} +(0.900969 - 0.433884i) q^{9} +O(q^{10})\) \(q+(-0.900969 - 1.43388i) q^{2} +(0.974928 - 0.222521i) q^{3} +(-0.810394 + 1.68280i) q^{4} +(-1.19745 - 1.19745i) q^{6} +(1.46028 - 0.164534i) q^{8} +(0.900969 - 0.433884i) q^{9} +(-0.415617 + 1.82094i) q^{12} +(0.347948 - 0.277479i) q^{13} +(-0.387055 - 0.485352i) q^{16} +(-1.43388 - 0.900969i) q^{18} +(0.974928 - 0.222521i) q^{23} +(1.38705 - 0.485352i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-0.711363 - 0.248917i) q^{26} +(0.781831 - 0.623490i) q^{27} +(-0.433884 + 0.900969i) q^{29} +(1.19745 - 0.752407i) q^{31} +(0.138138 - 0.394777i) q^{32} +1.86777i q^{36} +(0.277479 - 0.347948i) q^{39} +(0.158342 + 0.158342i) q^{41} +(-1.19745 - 1.19745i) q^{46} +(0.0739590 - 0.656405i) q^{47} +(-0.485352 - 0.387055i) q^{48} +(0.623490 - 0.781831i) q^{49} +(0.189606 + 1.68280i) q^{50} +(0.184967 + 0.810394i) q^{52} +(-1.59842 - 0.559311i) q^{54} +(1.68280 - 0.189606i) q^{58} +1.80194i q^{59} +(-2.15773 - 1.03911i) q^{62} +(-1.29575 + 0.295745i) q^{64} +(0.900969 - 0.433884i) q^{69} +(-1.21572 - 1.52446i) q^{71} +(1.24428 - 0.781831i) q^{72} +(-0.559311 - 0.351438i) q^{73} +(-0.974928 - 0.222521i) q^{75} +(-0.748917 - 0.0843826i) q^{78} +(0.623490 - 0.781831i) q^{81} +(0.0843826 - 0.369704i) q^{82} +(-0.222521 + 0.974928i) q^{87} +(-0.415617 + 1.82094i) q^{92} +(1.00000 - 1.00000i) q^{93} +(-1.00784 + 0.485352i) q^{94} +(0.0468288 - 0.415617i) q^{96} +(-1.68280 - 0.189606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 14q^{4} - 2q^{6} + 2q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - 14q^{4} - 2q^{6} + 2q^{9} - 2q^{12} + 12q^{16} - 12q^{18} - 2q^{25} - 4q^{26} + 2q^{31} - 2q^{32} + 4q^{39} + 2q^{41} - 2q^{46} - 2q^{47} - 2q^{49} - 2q^{50} + 10q^{52} + 2q^{54} + 2q^{58} + 4q^{62} - 14q^{64} + 2q^{69} + 14q^{72} + 2q^{73} + 4q^{78} - 2q^{81} + 4q^{82} - 2q^{87} - 2q^{92} + 12q^{93} - 4q^{94} + 12q^{96} - 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{23}{28}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.900969 1.43388i −0.900969 1.43388i −0.900969 0.433884i \(-0.857143\pi\)
1.00000i \(-0.5\pi\)
\(3\) 0.974928 0.222521i 0.974928 0.222521i
\(4\) −0.810394 + 1.68280i −0.810394 + 1.68280i
\(5\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(6\) −1.19745 1.19745i −1.19745 1.19745i
\(7\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(8\) 1.46028 0.164534i 1.46028 0.164534i
\(9\) 0.900969 0.433884i 0.900969 0.433884i
\(10\) 0 0
\(11\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(12\) −0.415617 + 1.82094i −0.415617 + 1.82094i
\(13\) 0.347948 0.277479i 0.347948 0.277479i −0.433884 0.900969i \(-0.642857\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.387055 0.485352i −0.387055 0.485352i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −1.43388 0.900969i −1.43388 0.900969i
\(19\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.974928 0.222521i 0.974928 0.222521i
\(24\) 1.38705 0.485352i 1.38705 0.485352i
\(25\) −0.900969 0.433884i −0.900969 0.433884i
\(26\) −0.711363 0.248917i −0.711363 0.248917i
\(27\) 0.781831 0.623490i 0.781831 0.623490i
\(28\) 0 0
\(29\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(30\) 0 0
\(31\) 1.19745 0.752407i 1.19745 0.752407i 0.222521 0.974928i \(-0.428571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(32\) 0.138138 0.394777i 0.138138 0.394777i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.86777i 1.86777i
\(37\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(38\) 0 0
\(39\) 0.277479 0.347948i 0.277479 0.347948i
\(40\) 0 0
\(41\) 0.158342 + 0.158342i 0.158342 + 0.158342i 0.781831 0.623490i \(-0.214286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(42\) 0 0
\(43\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −1.19745 1.19745i −1.19745 1.19745i
\(47\) 0.0739590 0.656405i 0.0739590 0.656405i −0.900969 0.433884i \(-0.857143\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(48\) −0.485352 0.387055i −0.485352 0.387055i
\(49\) 0.623490 0.781831i 0.623490 0.781831i
\(50\) 0.189606 + 1.68280i 0.189606 + 1.68280i
\(51\) 0 0
\(52\) 0.184967 + 0.810394i 0.184967 + 0.810394i
\(53\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(54\) −1.59842 0.559311i −1.59842 0.559311i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 1.68280 0.189606i 1.68280 0.189606i
\(59\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(60\) 0 0
\(61\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(62\) −2.15773 1.03911i −2.15773 1.03911i
\(63\) 0 0
\(64\) −1.29575 + 0.295745i −1.29575 + 0.295745i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(68\) 0 0
\(69\) 0.900969 0.433884i 0.900969 0.433884i
\(70\) 0 0
\(71\) −1.21572 1.52446i −1.21572 1.52446i −0.781831 0.623490i \(-0.785714\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(72\) 1.24428 0.781831i 1.24428 0.781831i
\(73\) −0.559311 0.351438i −0.559311 0.351438i 0.222521 0.974928i \(-0.428571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(74\) 0 0
\(75\) −0.974928 0.222521i −0.974928 0.222521i
\(76\) 0 0
\(77\) 0 0
\(78\) −0.748917 0.0843826i −0.748917 0.0843826i
\(79\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(80\) 0 0
\(81\) 0.623490 0.781831i 0.623490 0.781831i
\(82\) 0.0843826 0.369704i 0.0843826 0.369704i
\(83\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(88\) 0 0
\(89\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.415617 + 1.82094i −0.415617 + 1.82094i
\(93\) 1.00000 1.00000i 1.00000 1.00000i
\(94\) −1.00784 + 0.485352i −1.00784 + 0.485352i
\(95\) 0 0
\(96\) 0.0468288 0.415617i 0.0468288 0.415617i
\(97\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(98\) −1.68280 0.189606i −1.68280 0.189606i
\(99\) 0 0
\(100\) 1.46028 1.16453i 1.46028 1.16453i
\(101\) −0.559311 0.351438i −0.559311 0.351438i 0.222521 0.974928i \(-0.428571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(102\) 0 0
\(103\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(104\) 0.462446 0.462446i 0.462446 0.462446i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(108\) 0.415617 + 1.82094i 0.415617 + 1.82094i
\(109\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.16453 1.46028i −1.16453 1.46028i
\(117\) 0.193096 0.400969i 0.193096 0.400969i
\(118\) 2.58377 1.62349i 2.58377 1.62349i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(122\) 0 0
\(123\) 0.189606 + 0.119137i 0.189606 + 0.119137i
\(124\) 0.295745 + 2.62481i 0.295745 + 2.62481i
\(125\) 0 0
\(126\) 0 0
\(127\) −0.0250721 + 0.222521i −0.0250721 + 0.222521i 0.974928 + 0.222521i \(0.0714286\pi\)
−1.00000 \(\pi\)
\(128\) 1.29575 + 1.29575i 1.29575 + 1.29575i
\(129\) 0 0
\(130\) 0 0
\(131\) −0.566116 + 0.900969i −0.566116 + 0.900969i 0.433884 + 0.900969i \(0.357143\pi\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(138\) −1.43388 0.900969i −1.43388 0.900969i
\(139\) 0.433884 + 1.90097i 0.433884 + 1.90097i 0.433884 + 0.900969i \(0.357143\pi\)
1.00000i \(0.500000\pi\)
\(140\) 0 0
\(141\) −0.0739590 0.656405i −0.0739590 0.656405i
\(142\) −1.09057 + 3.11668i −1.09057 + 3.11668i
\(143\) 0 0
\(144\) −0.559311 0.269350i −0.559311 0.269350i
\(145\) 0 0
\(146\) 1.11862i 1.11862i
\(147\) 0.433884 0.900969i 0.433884 0.900969i
\(148\) 0 0
\(149\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(150\) 0.559311 + 1.59842i 0.559311 + 1.59842i
\(151\) −1.94986 + 0.445042i −1.94986 + 0.445042i −0.974928 + 0.222521i \(0.928571\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.360659 + 0.748917i 0.360659 + 0.748917i
\(157\) 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
\(162\) −1.68280 0.189606i −1.68280 0.189606i
\(163\) −0.656405 0.0739590i −0.656405 0.0739590i −0.222521 0.974928i \(-0.571429\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(164\) −0.394777 + 0.138138i −0.394777 + 0.138138i
\(165\) 0 0
\(166\) 0 0
\(167\) −0.400969 + 0.193096i −0.400969 + 0.193096i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(168\) 0 0
\(169\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(174\) 1.59842 0.559311i 1.59842 0.559311i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(178\) 0 0
\(179\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(180\) 0 0
\(181\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.38705 0.485352i 1.38705 0.485352i
\(185\) 0 0
\(186\) −2.33485 0.532915i −2.33485 0.532915i
\(187\) 0 0
\(188\) 1.04466 + 0.656405i 1.04466 + 0.656405i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −1.19745 + 0.576661i −1.19745 + 0.576661i
\(193\) −0.623490 1.78183i −0.623490 1.78183i −0.623490 0.781831i \(-0.714286\pi\)
1.00000i \(-0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.810394 + 1.68280i 0.810394 + 1.68280i
\(197\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(198\) 0 0
\(199\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(200\) −1.38705 0.485352i −1.38705 0.485352i
\(201\) 0 0
\(202\) 1.11862i 1.11862i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.781831 0.623490i 0.781831 0.623490i
\(208\) −0.269350 0.0614773i −0.269350 0.0614773i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.158342 + 1.40532i 0.158342 + 1.40532i 0.781831 + 0.623490i \(0.214286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(212\) 0 0
\(213\) −1.52446 1.21572i −1.52446 1.21572i
\(214\) 0 0
\(215\) 0 0
\(216\) 1.03911 1.03911i 1.03911 1.03911i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.623490 0.218169i −0.623490 0.218169i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −1.00000 −1.00000
\(226\) 0 0
\(227\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(228\) 0 0
\(229\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.485352 + 1.38705i −0.485352 + 1.38705i
\(233\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(234\) −0.748917 + 0.0843826i −0.748917 + 0.0843826i
\(235\) 0 0
\(236\) −3.03230 1.46028i −3.03230 1.46028i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.678448 + 1.40881i 0.678448 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(240\) 0 0
\(241\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(242\) −0.559311 1.59842i −0.559311 1.59842i
\(243\) 0.433884 0.900969i 0.433884 0.900969i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.379212i 0.379212i
\(247\) 0 0
\(248\) 1.62481 1.29575i 1.62481 1.29575i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.341658 0.164534i 0.341658 0.164534i
\(255\) 0 0
\(256\) 0.394777 1.72963i 0.394777 1.72963i
\(257\) −0.376510 + 0.781831i −0.376510 + 0.781831i 0.623490 + 0.781831i \(0.285714\pi\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.00000i 1.00000i
\(262\) 1.80194 1.80194
\(263\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.222521 + 0.0250721i −0.222521 + 0.0250721i −0.222521 0.974928i \(-0.571429\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −1.00435 + 0.351438i −1.00435 + 0.351438i −0.781831 0.623490i \(-0.785714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.86777i 1.86777i
\(277\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(278\) 2.33485 2.33485i 2.33485 2.33485i
\(279\) 0.752407 1.19745i 0.752407 1.19745i
\(280\) 0 0
\(281\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(282\) −0.874573 + 0.697449i −0.874573 + 0.697449i
\(283\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(284\) 3.55057 0.810394i 3.55057 0.810394i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.0468288 0.415617i −0.0468288 0.415617i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 1.04466 0.656405i 1.04466 0.656405i
\(293\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(294\) −1.68280 + 0.189606i −1.68280 + 0.189606i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.277479 0.347948i 0.277479 0.347948i
\(300\) 1.16453 1.46028i 1.16453 1.46028i
\(301\) 0 0
\(302\) 2.39490 + 2.39490i 2.39490 + 2.39490i
\(303\) −0.623490 0.218169i −0.623490 0.218169i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.33485 + 1.33485i 1.33485 + 1.33485i 0.900969 + 0.433884i \(0.142857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −0.189606 1.68280i −0.189606 1.68280i −0.623490 0.781831i \(-0.714286\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(312\) 0.347948 0.553756i 0.347948 0.553756i
\(313\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.43388 0.900969i 1.43388 0.900969i 0.433884 0.900969i \(-0.357143\pi\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.810394 + 1.68280i 0.810394 + 1.68280i
\(325\) −0.433884 + 0.0990311i −0.433884 + 0.0990311i
\(326\) 0.485352 + 1.00784i 0.485352 + 1.00784i
\(327\) 0 0
\(328\) 0.257276 + 0.205171i 0.257276 + 0.205171i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.40532 1.40532i 1.40532 1.40532i 0.623490 0.781831i \(-0.285714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.638138 + 0.400969i 0.638138 + 0.400969i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(338\) 1.28183 0.448532i 1.28183 0.448532i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −1.12349 1.78802i −1.12349 1.78802i
\(347\) 1.56366 1.56366 0.781831 0.623490i \(-0.214286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(348\) −1.46028 1.16453i −1.46028 1.16453i
\(349\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(350\) 0 0
\(351\) 0.0990311 0.433884i 0.0990311 0.433884i
\(352\) 0 0
\(353\) −0.347948 + 1.52446i −0.347948 + 1.52446i 0.433884 + 0.900969i \(0.357143\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(354\) 2.15773 2.15773i 2.15773 2.15773i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.99319 0.697449i 1.99319 0.697449i
\(359\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(360\) 0 0
\(361\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(362\) 0 0
\(363\) 1.00000 1.00000
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(368\) −0.485352 0.387055i −0.485352 0.387055i
\(369\) 0.211363 + 0.0739590i 0.211363 + 0.0739590i
\(370\) 0 0
\(371\) 0 0
\(372\) 0.872406 + 2.49319i 0.872406 + 2.49319i
\(373\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.970703i 0.970703i
\(377\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(378\) 0 0
\(379\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(380\) 0 0
\(381\) 0.0250721 + 0.222521i 0.0250721 + 0.222521i
\(382\) 0 0
\(383\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(384\) 1.55159 + 0.974928i 1.55159 + 0.974928i
\(385\) 0 0
\(386\) −1.99319 + 2.49939i −1.99319 + 2.49939i
\(387\) 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
\(392\) 0.781831 1.24428i 0.781831 1.24428i
\(393\) −0.351438 + 1.00435i −0.351438 + 1.00435i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.974928 1.22252i 0.974928 1.22252i 1.00000i \(-0.5\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.138138 + 0.605223i 0.138138 + 0.605223i
\(401\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(402\) 0 0
\(403\) 0.207872 0.594065i 0.207872 0.594065i
\(404\) 1.04466 0.656405i 1.04466 0.656405i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.211363 + 0.0739590i 0.211363 + 0.0739590i 0.433884 0.900969i \(-0.357143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −1.59842 0.559311i −1.59842 0.559311i
\(415\) 0 0
\(416\) −0.0614773 0.175692i −0.0614773 0.175692i
\(417\) 0.846011 + 1.75676i 0.846011 + 1.75676i
\(418\) 0 0
\(419\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(420\) 0 0
\(421\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(422\) 1.87241 1.49319i 1.87241 1.49319i
\(423\) −0.218169 0.623490i −0.218169 0.623490i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.369704 + 3.28122i −0.369704 + 3.28122i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(432\) −0.605223 0.138138i −0.605223 0.138138i
\(433\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.248917 + 1.09057i 0.248917 + 1.09057i
\(439\) −0.678448 + 1.40881i −0.678448 + 1.40881i 0.222521 + 0.974928i \(0.428571\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(440\) 0 0
\(441\) 0.222521 0.974928i 0.222521 0.974928i
\(442\) 0 0
\(443\) 1.87590 0.211363i 1.87590 0.211363i 0.900969 0.433884i \(-0.142857\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 2.09842 + 0.236435i 2.09842 + 0.236435i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.900969 + 0.566116i 0.900969 + 0.566116i 0.900969 0.433884i \(-0.142857\pi\)
1.00000i \(0.5\pi\)
\(450\) 0.900969 + 1.43388i 0.900969 + 1.43388i
\(451\) 0 0
\(452\) 0 0
\(453\) −1.80194 + 0.867767i −1.80194 + 0.867767i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.87590 0.656405i −1.87590 0.656405i −0.974928 0.222521i \(-0.928571\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(462\) 0 0
\(463\) 0.445042i 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(464\) 0.605223 0.138138i 0.605223 0.138138i
\(465\) 0 0
\(466\) 1.78802 1.12349i 1.78802 1.12349i
\(467\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(468\) 0.518266 + 0.649885i 0.518266 + 0.649885i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.296480 + 2.63133i 0.296480 + 2.63133i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 1.40881 2.24211i 1.40881 2.24211i
\(479\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.16453 + 1.46028i −1.16453 + 1.46028i
\(485\) 0 0
\(486\) −1.68280 + 0.189606i −1.68280 + 0.189606i
\(487\) 0.347948 + 1.52446i 0.347948 + 1.52446i 0.781831 + 0.623490i \(0.214286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(488\) 0 0
\(489\) −0.656405 + 0.0739590i −0.656405 + 0.0739590i
\(490\) 0 0
\(491\) −1.68280 + 1.05737i −1.68280 + 1.05737i −0.781831 + 0.623490i \(0.785714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(492\) −0.354140 + 0.222521i −0.354140 + 0.222521i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.828660 0.289961i −0.828660 0.289961i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.75676 + 0.400969i −1.75676 + 0.400969i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(500\) 0 0
\(501\) −0.347948 + 0.277479i −0.347948 + 0.277479i
\(502\) 0 0
\(503\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.801938i 0.801938i
\(508\) −0.354140 0.222521i −0.354140 0.222521i
\(509\) 0.678448 0.541044i 0.678448 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.10614 + 0.387055i −1.10614 + 0.387055i
\(513\) 0 0
\(514\) 1.46028 0.164534i 1.46028 0.164534i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 1.21572 0.277479i 1.21572 0.277479i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 1.43388 0.900969i 1.43388 0.900969i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −1.05737 1.68280i −1.05737 1.68280i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.900969 0.433884i 0.900969 0.433884i
\(530\) 0 0
\(531\) 0.781831 + 1.62349i 0.781831 + 1.62349i
\(532\) 0 0
\(533\) 0.0990311 + 0.0111581i 0.0990311 + 0.0111581i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.24698i 1.24698i
\(538\) 0.236435 + 0.296480i 0.236435 + 0.296480i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.623490 1.78183i −0.623490 1.78183i −0.623490 0.781831i \(-0.714286\pi\)
1.00000i \(-0.5\pi\)
\(542\) 1.40881 + 1.12349i 1.40881 + 1.12349i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.12349 + 0.541044i 1.12349 + 0.541044i 0.900969 0.433884i \(-0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 1.24428 0.781831i 1.24428 0.781831i
\(553\) 0 0
\(554\) −0.248917 + 0.711363i −0.248917 + 0.711363i
\(555\) 0 0
\(556\) −3.55057 0.810394i −3.55057 0.810394i
\(557\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(558\) −2.39490 −2.39490
\(559\) 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 \(0.250000\pi\)
\(564\) 1.16453 + 0.407488i 1.16453 + 0.407488i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −2.02611 2.02611i −2.02611 2.02611i
\(569\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(570\) 0 0
\(571\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.974928 0.222521i −0.974928 0.222521i
\(576\) −1.03911 + 0.828660i −1.03911 + 0.828660i
\(577\) 0.656405 1.87590i 0.656405 1.87590i 0.222521 0.974928i \(-0.428571\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(578\) −1.43388 + 0.900969i −1.43388 + 0.900969i
\(579\) −1.00435 1.59842i −1.00435 1.59842i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.874573 0.421172i −0.874573 0.421172i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.678448 1.40881i −0.678448 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(588\) 1.16453 + 1.46028i 1.16453 + 1.46028i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.974928 1.22252i −0.974928 1.22252i −0.974928 0.222521i \(-0.928571\pi\)
1.00000i \(-0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.748917 0.0843826i −0.748917 0.0843826i
\(599\) −1.00435 + 0.351438i −1.00435 + 0.351438i −0.781831 0.623490i \(-0.785714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(600\) −1.46028 0.164534i −1.46028 0.164534i
\(601\) −1.40532 + 0.158342i −1.40532 + 0.158342i −0.781831 0.623490i \(-0.785714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.831235 3.64188i 0.831235 3.64188i
\(605\) 0 0
\(606\) 0.248917 + 1.09057i 0.248917 + 1.09057i
\(607\) −1.05737 1.68280i −1.05737 1.68280i −0.623490 0.781831i \(-0.714286\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.156405 0.248917i −0.156405 0.248917i
\(612\) 0 0
\(613\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(614\) 0.711363 3.11668i 0.711363 3.11668i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(618\) 0 0
\(619\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(620\) 0 0
\(621\) 0.623490 0.781831i 0.623490 0.781831i
\(622\) −2.24211 + 1.78802i −2.24211 + 1.78802i
\(623\) 0 0
\(624\) −0.276277 −0.276277
\(625\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(632\) 0 0
\(633\) 0.467085 + 1.33485i 0.467085 + 1.33485i
\(634\) −2.58377 1.24428i −2.58377 1.24428i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.445042i 0.445042i
\(638\) 0 0
\(639\) −1.75676 0.846011i −1.75676 0.846011i
\(640\) 0 0
\(641\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(642\) 0 0
\(643\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.541044 + 0.678448i −0.541044 + 0.678448i −0.974928 0.222521i \(-0.928571\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(648\) 0.781831 1.24428i 0.781831 1.24428i
\(649\) 0 0
\(650\) 0.532915 + 0.532915i 0.532915 + 0.532915i
\(651\) 0 0
\(652\) 0.656405 1.04466i 0.656405 1.04466i
\(653\) −0.752407 + 1.19745i −0.752407 + 1.19745i 0.222521 + 0.974928i \(0.428571\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.0155644 0.138138i 0.0155644 0.138138i
\(657\) −0.656405 0.0739590i −0.656405 0.0739590i
\(658\) 0 0
\(659\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(660\) 0 0
\(661\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(662\) −3.28122 0.748917i −3.28122 0.748917i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(668\) 0.831235i 0.831235i
\(669\) −0.541044 + 1.12349i −0.541044 + 1.12349i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.52446 + 0.347948i −1.52446 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(674\) 0 0
\(675\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(676\) −1.17105 0.933884i −1.17105 0.933884i
\(677\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.678448 + 0.541044i −0.678448 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
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
\(691\) −0.433884 + 1.90097i −0.433884 + 1.90097i 1.00000i \(0.5\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(692\) −1.01054 + 2.09842i −1.01054 + 2.09842i
\(693\) 0 0
\(694\) −1.40881 2.24211i −1.40881 2.24211i
\(695\) 0 0
\(696\) −0.164534 + 1.46028i −0.164534 + 1.46028i
\(697\) 0 0
\(698\) 1.62349 + 2.58377i 1.62349 + 2.58377i
\(699\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(700\) 0 0
\(701\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(702\) −0.711363 + 0.248917i −0.711363 + 0.248917i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 2.49939 0.874573i 2.49939 0.874573i
\(707\) 0 0
\(708\) −3.28122 0.748917i −3.28122 0.748917i
\(709\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.00000 1.00000i 1.00000 1.00000i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.82094 1.45215i −1.82094 1.45215i
\(717\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(718\) 0 0
\(719\) −1.90097 + 0.433884i −1.90097 + 0.433884i −0.900969 + 0.433884i \(0.857143\pi\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.59842 + 0.559311i 1.59842 + 0.559311i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.781831 0.623490i 0.781831 0.623490i
\(726\) −0.900969 1.43388i −0.900969 1.43388i
\(727\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(728\) 0 0
\(729\) 0.222521 0.974928i 0.222521 0.974928i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.0468288 0.415617i 0.0468288 0.415617i
\(737\) 0 0
\(738\) −0.0843826 0.369704i −0.0843826 0.369704i
\(739\) 0.119137 0.189606i 0.119137 0.189606i −0.781831 0.623490i \(-0.785714\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(744\) 1.29575 1.62481i 1.29575 1.62481i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(752\) −0.347213 + 0.218169i −0.347213 + 0.218169i
\(753\) 0 0
\(754\) 0.532915 0.532915i 0.532915 0.532915i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.193096 + 0.400969i 0.193096 + 0.400969i 0.974928 0.222521i \(-0.0714286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(762\) 0.296480 0.236435i 0.296480 0.236435i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(768\) 1.77411i 1.77411i
\(769\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(770\) 0 0
\(771\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(772\) 3.50374 + 0.394777i 3.50374 + 0.394777i
\(773\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(774\) 0 0
\(775\) −1.40532 + 0.158342i −1.40532 + 0.158342i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(784\) −0.620788 −0.620788
\(785\) 0 0
\(786\) 1.75676 0.400969i 1.75676 0.400969i
\(787\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −2.63133 0.296480i −2.63133 0.296480i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(798\) 0 0