Properties

Label 2001.1.bf.b.896.1
Level $2001$
Weight $1$
Character 2001.896
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 896.1
Root \(0.781831 - 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 2001.896
Dual form 2001.1.bf.b.1034.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.900969 + 0.566116i) q^{2} +(0.623490 - 0.781831i) q^{3} +(0.0573735 + 0.119137i) q^{4} +(1.00435 - 0.351438i) q^{6} +(0.103384 - 0.917554i) q^{8} +(-0.222521 - 0.974928i) q^{9} +O(q^{10})\) \(q+(0.900969 + 0.566116i) q^{2} +(0.623490 - 0.781831i) q^{3} +(0.0573735 + 0.119137i) q^{4} +(1.00435 - 0.351438i) q^{6} +(0.103384 - 0.917554i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(0.128917 + 0.0294245i) q^{12} +(-0.347948 - 0.277479i) q^{13} +(0.695033 - 0.871544i) q^{16} +(0.351438 - 1.00435i) q^{18} +(0.974928 + 0.222521i) q^{23} +(-0.652914 - 0.652914i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(-0.156405 - 0.446979i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-0.433884 - 0.900969i) q^{29} +(-0.752407 + 1.19745i) q^{31} +(0.248055 - 0.0867980i) q^{32} +(0.103384 - 0.0824456i) q^{36} +(-0.433884 + 0.0990311i) q^{39} +(1.40532 + 1.40532i) q^{41} +(0.752407 + 0.752407i) q^{46} +(1.87590 - 0.211363i) q^{47} +(-0.248055 - 1.08680i) q^{48} +(0.623490 + 0.781831i) q^{49} +(-1.05737 - 0.119137i) q^{50} +(0.0130951 - 0.0573735i) q^{52} +(-0.566116 - 0.900969i) q^{54} +(0.119137 - 1.05737i) q^{58} -1.80194i q^{59} +(-1.35579 + 0.652914i) q^{62} +(-0.814171 - 0.185829i) q^{64} +(0.781831 - 0.623490i) q^{69} +(-1.21572 + 1.52446i) q^{71} +(-0.917554 + 0.103384i) q^{72} +(1.00435 + 1.59842i) q^{73} +(-0.222521 + 0.974928i) q^{75} +(-0.446979 - 0.156405i) q^{78} +(-0.900969 + 0.433884i) q^{81} +(0.470575 + 2.06173i) q^{82} +(-0.974928 - 0.222521i) q^{87} +(0.0294245 + 0.128917i) q^{92} +(0.467085 + 1.33485i) q^{93} +(1.80978 + 0.871544i) q^{94} +(0.0867980 - 0.248055i) q^{96} +(0.119137 + 1.05737i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - 2q^{3} - 14q^{4} + 2q^{6} - 2q^{9} + O(q^{10}) \) \( 12q + 2q^{2} - 2q^{3} - 14q^{4} + 2q^{6} - 2q^{9} + 12q^{16} + 2q^{18} - 2q^{25} + 4q^{26} - 2q^{27} + 2q^{31} + 2q^{32} - 2q^{41} - 2q^{46} + 2q^{47} - 2q^{48} - 2q^{49} + 2q^{50} + 10q^{52} - 12q^{54} + 2q^{58} - 4q^{62} - 14q^{64} - 14q^{72} + 2q^{73} - 2q^{75} - 10q^{78} - 2q^{81} + 4q^{82} + 2q^{92} + 2q^{93} - 4q^{94} - 12q^{96} + 2q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(-1\)

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 + 0.566116i 0.900969 + 0.566116i 0.900969 0.433884i \(-0.142857\pi\)
1.00000i \(0.5\pi\)
\(3\) 0.623490 0.781831i 0.623490 0.781831i
\(4\) 0.0573735 + 0.119137i 0.0573735 + 0.119137i
\(5\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(6\) 1.00435 0.351438i 1.00435 0.351438i
\(7\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(8\) 0.103384 0.917554i 0.103384 0.917554i
\(9\) −0.222521 0.974928i −0.222521 0.974928i
\(10\) 0 0
\(11\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(12\) 0.128917 + 0.0294245i 0.128917 + 0.0294245i
\(13\) −0.347948 0.277479i −0.347948 0.277479i 0.433884 0.900969i \(-0.357143\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.695033 0.871544i 0.695033 0.871544i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 0.351438 1.00435i 0.351438 1.00435i
\(19\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(24\) −0.652914 0.652914i −0.652914 0.652914i
\(25\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(26\) −0.156405 0.446979i −0.156405 0.446979i
\(27\) −0.900969 0.433884i −0.900969 0.433884i
\(28\) 0 0
\(29\) −0.433884 0.900969i −0.433884 0.900969i
\(30\) 0 0
\(31\) −0.752407 + 1.19745i −0.752407 + 1.19745i 0.222521 + 0.974928i \(0.428571\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(32\) 0.248055 0.0867980i 0.248055 0.0867980i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.103384 0.0824456i 0.103384 0.0824456i
\(37\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(38\) 0 0
\(39\) −0.433884 + 0.0990311i −0.433884 + 0.0990311i
\(40\) 0 0
\(41\) 1.40532 + 1.40532i 1.40532 + 1.40532i 0.781831 + 0.623490i \(0.214286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(42\) 0 0
\(43\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.752407 + 0.752407i 0.752407 + 0.752407i
\(47\) 1.87590 0.211363i 1.87590 0.211363i 0.900969 0.433884i \(-0.142857\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(48\) −0.248055 1.08680i −0.248055 1.08680i
\(49\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(50\) −1.05737 0.119137i −1.05737 0.119137i
\(51\) 0 0
\(52\) 0.0130951 0.0573735i 0.0130951 0.0573735i
\(53\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(54\) −0.566116 0.900969i −0.566116 0.900969i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.119137 1.05737i 0.119137 1.05737i
\(59\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(60\) 0 0
\(61\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(62\) −1.35579 + 0.652914i −1.35579 + 0.652914i
\(63\) 0 0
\(64\) −0.814171 0.185829i −0.814171 0.185829i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(68\) 0 0
\(69\) 0.781831 0.623490i 0.781831 0.623490i
\(70\) 0 0
\(71\) −1.21572 + 1.52446i −1.21572 + 1.52446i −0.433884 + 0.900969i \(0.642857\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(72\) −0.917554 + 0.103384i −0.917554 + 0.103384i
\(73\) 1.00435 + 1.59842i 1.00435 + 1.59842i 0.781831 + 0.623490i \(0.214286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(74\) 0 0
\(75\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(76\) 0 0
\(77\) 0 0
\(78\) −0.446979 0.156405i −0.446979 0.156405i
\(79\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(80\) 0 0
\(81\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(82\) 0.470575 + 2.06173i 0.470575 + 2.06173i
\(83\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.974928 0.222521i −0.974928 0.222521i
\(88\) 0 0
\(89\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.0294245 + 0.128917i 0.0294245 + 0.128917i
\(93\) 0.467085 + 1.33485i 0.467085 + 1.33485i
\(94\) 1.80978 + 0.871544i 1.80978 + 0.871544i
\(95\) 0 0
\(96\) 0.0867980 0.248055i 0.0867980 0.248055i
\(97\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(98\) 0.119137 + 1.05737i 0.119137 + 1.05737i
\(99\) 0 0
\(100\) −0.103384 0.0824456i −0.103384 0.0824456i
\(101\) −1.00435 1.59842i −1.00435 1.59842i −0.781831 0.623490i \(-0.785714\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(102\) 0 0
\(103\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(104\) −0.290574 + 0.290574i −0.290574 + 0.290574i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(108\) 0.132233i 0.132233i
\(109\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.0824456 0.103384i 0.0824456 0.103384i
\(117\) −0.193096 + 0.400969i −0.193096 + 0.400969i
\(118\) 1.02011 1.62349i 1.02011 1.62349i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(122\) 0 0
\(123\) 1.97493 0.222521i 1.97493 0.222521i
\(124\) −0.185829 0.0209379i −0.185829 0.0209379i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.97493 + 0.222521i −1.97493 + 0.222521i −0.974928 + 0.222521i \(0.928571\pi\)
−1.00000 \(\pi\)
\(128\) −0.814171 0.814171i −0.814171 0.814171i
\(129\) 0 0
\(130\) 0 0
\(131\) 1.43388 0.900969i 1.43388 0.900969i 0.433884 0.900969i \(-0.357143\pi\)
1.00000 \(0\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(138\) 1.05737 0.119137i 1.05737 0.119137i
\(139\) −0.433884 + 1.90097i −0.433884 + 1.90097i 1.00000i \(0.5\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(140\) 0 0
\(141\) 1.00435 1.59842i 1.00435 1.59842i
\(142\) −1.95834 + 0.685254i −1.95834 + 0.685254i
\(143\) 0 0
\(144\) −1.00435 0.483671i −1.00435 0.483671i
\(145\) 0 0
\(146\) 2.00870i 2.00870i
\(147\) 1.00000 1.00000
\(148\) 0 0
\(149\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(150\) −0.752407 + 0.752407i −0.752407 + 0.752407i
\(151\) 1.94986 + 0.445042i 1.94986 + 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.0366918 0.0460100i −0.0366918 0.0460100i
\(157\) 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
\(162\) −1.05737 0.119137i −1.05737 0.119137i
\(163\) 0.211363 + 1.87590i 0.211363 + 1.87590i 0.433884 + 0.900969i \(0.357143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(164\) −0.0867980 + 0.248055i −0.0867980 + 0.248055i
\(165\) 0 0
\(166\) 0 0
\(167\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(168\) 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 \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(174\) −0.752407 0.752407i −0.752407 0.752407i
\(175\) 0 0
\(176\) 0 0
\(177\) −1.40881 1.12349i −1.40881 1.12349i
\(178\) 0 0
\(179\) 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(180\) 0 0
\(181\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.304967 0.871544i 0.304967 0.871544i
\(185\) 0 0
\(186\) −0.334853 + 1.46709i −0.334853 + 1.46709i
\(187\) 0 0
\(188\) 0.132808 + 0.211363i 0.132808 + 0.211363i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −0.652914 + 0.520682i −0.652914 + 0.520682i
\(193\) −0.623490 0.218169i −0.623490 0.218169i 1.00000i \(-0.5\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.0573735 + 0.119137i −0.0573735 + 0.119137i
\(197\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(198\) 0 0
\(199\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(200\) 0.304967 + 0.871544i 0.304967 + 0.871544i
\(201\) 0 0
\(202\) 2.00870i 2.00870i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.00000i 1.00000i
\(208\) −0.483671 + 0.110395i −0.483671 + 0.110395i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.40532 0.158342i −1.40532 0.158342i −0.623490 0.781831i \(-0.714286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(212\) 0 0
\(213\) 0.433884 + 1.90097i 0.433884 + 1.90097i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.491257 + 0.781831i −0.491257 + 0.781831i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.87590 + 0.211363i 1.87590 + 0.211363i
\(220\) 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
\(225\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(226\) 0 0
\(227\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(228\) 0 0
\(229\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.871544 + 0.304967i −0.871544 + 0.304967i
\(233\) 1.24698i 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(234\) −0.400969 + 0.251945i −0.400969 + 0.251945i
\(235\) 0 0
\(236\) 0.214678 0.103384i 0.214678 0.103384i
\(237\) 0 0
\(238\) 0 0
\(239\) −0.678448 + 1.40881i −0.678448 + 1.40881i 0.222521 + 0.974928i \(0.428571\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(240\) 0 0
\(241\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(242\) −1.00435 0.351438i −1.00435 0.351438i
\(243\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.90532 + 0.917554i 1.90532 + 0.917554i
\(247\) 0 0
\(248\) 1.02094 + 0.814171i 1.02094 + 0.814171i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.90532 0.917554i −1.90532 0.917554i
\(255\) 0 0
\(256\) −0.0867980 0.380287i −0.0867980 0.380287i
\(257\) 0.376510 + 0.781831i 0.376510 + 0.781831i 1.00000 \(0\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(262\) 1.80194 1.80194
\(263\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.222521 1.97493i 0.222521 1.97493i 1.00000i \(-0.5\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(270\) 0 0
\(271\) 0.559311 1.59842i 0.559311 1.59842i −0.222521 0.974928i \(-0.571429\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0.119137 + 0.0573735i 0.119137 + 0.0573735i
\(277\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(278\) −1.46709 + 1.46709i −1.46709 + 1.46709i
\(279\) 1.33485 + 0.467085i 1.33485 + 0.467085i
\(280\) 0 0
\(281\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(282\) 1.80978 0.871544i 1.80978 0.871544i
\(283\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(284\) −0.251370 0.0573735i −0.251370 0.0573735i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.139819 0.222521i −0.139819 0.222521i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.132808 + 0.211363i −0.132808 + 0.211363i
\(293\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(294\) 0.900969 + 0.566116i 0.900969 + 0.566116i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.277479 0.347948i −0.277479 0.347948i
\(300\) −0.128917 + 0.0294245i −0.128917 + 0.0294245i
\(301\) 0 0
\(302\) 1.50481 + 1.50481i 1.50481 + 1.50481i
\(303\) −1.87590 0.211363i −1.87590 0.211363i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.467085 + 0.467085i 0.467085 + 0.467085i 0.900969 0.433884i \(-0.142857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.05737 + 0.119137i 1.05737 + 0.119137i 0.623490 0.781831i \(-0.285714\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(312\) 0.0460100 + 0.408350i 0.0460100 + 0.408350i
\(313\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −0.566116 + 0.900969i −0.566116 + 0.900969i 0.433884 + 0.900969i \(0.357143\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.103384 0.0824456i −0.103384 0.0824456i
\(325\) 0.433884 + 0.0990311i 0.433884 + 0.0990311i
\(326\) −0.871544 + 1.80978i −0.871544 + 1.80978i
\(327\) 0 0
\(328\) 1.43475 1.14417i 1.43475 1.14417i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.158342 + 0.158342i −0.158342 + 0.158342i −0.781831 0.623490i \(-0.785714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.251945 + 0.400969i 0.251945 + 0.400969i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(338\) 0.281831 0.805428i 0.281831 0.805428i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −1.12349 0.705935i −1.12349 0.705935i
\(347\) 1.56366 1.56366 0.781831 0.623490i \(-0.214286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(348\) −0.0294245 0.128917i −0.0294245 0.128917i
\(349\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(350\) 0 0
\(351\) 0.193096 + 0.400969i 0.193096 + 0.400969i
\(352\) 0 0
\(353\) −0.347948 1.52446i −0.347948 1.52446i −0.781831 0.623490i \(-0.785714\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(354\) −0.633270 1.80978i −0.633270 1.80978i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.438236 + 1.25241i −0.438236 + 1.25241i
\(359\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(360\) 0 0
\(361\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(362\) 0 0
\(363\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(368\) 0.871544 0.695033i 0.871544 0.695033i
\(369\) 1.05737 1.68280i 1.05737 1.68280i
\(370\) 0 0
\(371\) 0 0
\(372\) −0.132233 + 0.132233i −0.132233 + 0.132233i
\(373\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.74309i 1.74309i
\(377\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(378\) 0 0
\(379\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(380\) 0 0
\(381\) −1.05737 + 1.68280i −1.05737 + 1.68280i
\(382\) 0 0
\(383\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(384\) −1.14417 + 0.128917i −1.14417 + 0.128917i
\(385\) 0 0
\(386\) −0.438236 0.549531i −0.438236 0.549531i
\(387\) 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 0.491257i 0.781831 0.491257i
\(393\) 0.189606 1.68280i 0.189606 1.68280i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −0.974928 1.22252i −0.974928 1.22252i −0.974928 0.222521i \(-0.928571\pi\)
1.00000i \(-0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.248055 + 1.08680i −0.248055 + 1.08680i
\(401\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(402\) 0 0
\(403\) 0.594065 0.207872i 0.594065 0.207872i
\(404\) 0.132808 0.211363i 0.132808 0.211363i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.656405 1.87590i −0.656405 1.87590i −0.433884 0.900969i \(-0.642857\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.566116 0.900969i 0.566116 0.900969i
\(415\) 0 0
\(416\) −0.110395 0.0386288i −0.110395 0.0386288i
\(417\) 1.21572 + 1.52446i 1.21572 + 1.52446i
\(418\) 0 0
\(419\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(420\) 0 0
\(421\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(422\) −1.17651 0.938236i −1.17651 0.938236i
\(423\) −0.623490 1.78183i −0.623490 1.78183i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.685254 + 1.95834i −0.685254 + 1.95834i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(432\) −1.00435 + 0.483671i −1.00435 + 0.483671i
\(433\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.57047 + 1.25241i 1.57047 + 1.25241i
\(439\) −0.678448 1.40881i −0.678448 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(440\) 0 0
\(441\) 0.623490 0.781831i 0.623490 0.781831i
\(442\) 0 0
\(443\) 0.0739590 0.656405i 0.0739590 0.656405i −0.900969 0.433884i \(-0.857143\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.148562 1.31852i −0.148562 1.31852i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.900969 1.43388i −0.900969 1.43388i −0.900969 0.433884i \(-0.857143\pi\)
1.00000i \(-0.5\pi\)
\(450\) 0.119137 + 1.05737i 0.119137 + 1.05737i
\(451\) 0 0
\(452\) 0 0
\(453\) 1.56366 1.24698i 1.56366 1.24698i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −0.0739590 0.211363i −0.0739590 0.211363i 0.900969 0.433884i \(-0.142857\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(462\) 0 0
\(463\) 0.445042i 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(464\) −1.08680 0.248055i −1.08680 0.248055i
\(465\) 0 0
\(466\) 0.705935 1.12349i 0.705935 1.12349i
\(467\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(468\) −0.0588490 −0.0588490
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.65338 0.186291i −1.65338 0.186291i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −1.40881 + 0.885215i −1.40881 + 0.885215i
\(479\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.0824456 0.103384i −0.0824456 0.103384i
\(485\) 0 0
\(486\) −0.752407 + 0.752407i −0.752407 + 0.752407i
\(487\) −0.347948 + 1.52446i −0.347948 + 1.52446i 0.433884 + 0.900969i \(0.357143\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(488\) 0 0
\(489\) 1.59842 + 1.00435i 1.59842 + 1.00435i
\(490\) 0 0
\(491\) 0.119137 0.189606i 0.119137 0.189606i −0.781831 0.623490i \(-0.785714\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(492\) 0.139819 + 0.222521i 0.139819 + 0.222521i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.520682 + 1.48802i 0.520682 + 1.48802i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.75676 + 0.400969i 1.75676 + 0.400969i 0.974928 0.222521i \(-0.0714286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(500\) 0 0
\(501\) 0.400969 0.193096i 0.400969 0.193096i
\(502\) 0 0
\(503\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.722521 0.347948i −0.722521 0.347948i
\(508\) −0.139819 0.222521i −0.139819 0.222521i
\(509\) −0.678448 0.541044i −0.678448 0.541044i 0.222521 0.974928i \(-0.428571\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.243203 + 0.695033i −0.243203 + 0.695033i
\(513\) 0 0
\(514\) −0.103384 + 0.917554i −0.103384 + 0.917554i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −1.05737 + 0.119137i −1.05737 + 0.119137i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0.189606 + 0.119137i 0.189606 + 0.119137i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(530\) 0 0
\(531\) −1.75676 + 0.400969i −1.75676 + 0.400969i
\(532\) 0 0
\(533\) −0.0990311 0.878926i −0.0990311 0.878926i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(538\) 1.31852 1.65338i 1.31852 1.65338i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.623490 0.218169i −0.623490 0.218169i 1.00000i \(-0.5\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(542\) 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 0.222521 0.974928i \(-0.428571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.491257 0.781831i −0.491257 0.781831i
\(553\) 0 0
\(554\) −0.446979 + 0.156405i −0.446979 + 0.156405i
\(555\) 0 0
\(556\) −0.251370 + 0.0573735i −0.251370 + 0.0573735i
\(557\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(558\) 0.938236 + 1.17651i 0.938236 + 1.17651i
\(559\) 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 \(0.250000\pi\)
\(564\) 0.248055 + 0.0279490i 0.248055 + 0.0279490i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 1.27309 + 1.27309i 1.27309 + 1.27309i
\(569\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(570\) 0 0
\(571\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(576\) 0.835109i 0.835109i
\(577\) −0.211363 + 0.0739590i −0.211363 + 0.0739590i −0.433884 0.900969i \(-0.642857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(578\) 0.566116 0.900969i 0.566116 0.900969i
\(579\) −0.559311 + 0.351438i −0.559311 + 0.351438i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 1.57047 0.756298i 1.57047 0.756298i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.678448 1.40881i 0.678448 1.40881i −0.222521 0.974928i \(-0.571429\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(588\) 0.0573735 + 0.119137i 0.0573735 + 0.119137i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.974928 + 1.22252i −0.974928 + 1.22252i 1.00000i \(0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.0530211 0.470575i −0.0530211 0.470575i
\(599\) −0.559311 + 1.59842i −0.559311 + 1.59842i 0.222521 + 0.974928i \(0.428571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(600\) 0.871544 + 0.304967i 0.871544 + 0.304967i
\(601\) 0.158342 1.40532i 0.158342 1.40532i −0.623490 0.781831i \(-0.714286\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.0588490 + 0.257834i 0.0588490 + 0.257834i
\(605\) 0 0
\(606\) −1.57047 1.25241i −1.57047 1.25241i
\(607\) −0.189606 0.119137i −0.189606 0.119137i 0.433884 0.900969i \(-0.357143\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.711363 0.446979i −0.711363 0.446979i
\(612\) 0 0
\(613\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(614\) 0.156405 + 0.685254i 0.156405 + 0.685254i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(618\) 0 0
\(619\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(620\) 0 0
\(621\) −0.781831 0.623490i −0.781831 0.623490i
\(622\) 0.885215 + 0.705935i 0.885215 + 0.705935i
\(623\) 0 0
\(624\) −0.215254 + 0.446979i −0.215254 + 0.446979i
\(625\) 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 \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(632\) 0 0
\(633\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(634\) −1.02011 + 0.491257i −1.02011 + 0.491257i
\(635\) 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 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(642\) 0 0
\(643\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.541044 0.678448i −0.541044 0.678448i 0.433884 0.900969i \(-0.357143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(648\) 0.304967 + 0.871544i 0.304967 + 0.871544i
\(649\) 0 0
\(650\) 0.334853 + 0.334853i 0.334853 + 0.334853i
\(651\) 0 0
\(652\) −0.211363 + 0.132808i −0.211363 + 0.132808i
\(653\) −1.19745 + 0.752407i −1.19745 + 0.752407i −0.974928 0.222521i \(-0.928571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 2.20155 0.248055i 2.20155 0.248055i
\(657\) 1.33485 1.33485i 1.33485 1.33485i
\(658\) 0 0
\(659\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(660\) 0 0
\(661\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(662\) −0.232301 + 0.0530211i −0.232301 + 0.0530211i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.222521 0.974928i −0.222521 0.974928i
\(668\) 0.0588490i 0.0588490i
\(669\) −1.24698 −1.24698
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.52446 0.347948i −1.52446 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) 0.0829072 0.0661163i 0.0829072 0.0661163i
\(677\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(678\) 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 \(-0.142857\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(684\) 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 0.433884 + 0.900969i \(0.357143\pi\)
1.00000i \(0.500000\pi\)
\(692\) −0.0715436 0.148562i −0.0715436 0.148562i
\(693\) 0 0
\(694\) 1.40881 + 0.885215i 1.40881 + 0.885215i
\(695\) 0 0
\(696\) −0.304967 + 0.871544i −0.304967 + 0.871544i
\(697\) 0 0
\(698\) −1.62349 1.02011i −1.62349 1.02011i
\(699\) −0.974928 0.777479i −0.974928 0.777479i
\(700\) 0 0
\(701\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(702\) −0.0530211 + 0.470575i −0.0530211 + 0.470575i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.549531 1.57047i 0.549531 1.57047i
\(707\) 0 0
\(708\) 0.0530211 0.232301i 0.0530211 0.232301i
\(709\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(714\) 0 0
\(715\) 0 0
\(716\) −0.128917 + 0.102808i −0.128917 + 0.102808i
\(717\) 0.678448 + 1.40881i 0.678448 + 1.40881i
\(718\) 0 0
\(719\) 1.90097 + 0.433884i 1.90097 + 0.433884i 1.00000 \(0\)
0.900969 + 0.433884i \(0.142857\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.351438 + 1.00435i 0.351438 + 1.00435i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(726\) −0.900969 + 0.566116i −0.900969 + 0.566116i
\(727\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(728\) 0 0
\(729\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.261150 0.0294245i 0.261150 0.0294245i
\(737\) 0 0
\(738\) 1.90532 0.917554i 1.90532 0.917554i
\(739\) 1.68280 1.05737i 1.68280 1.05737i 0.781831 0.623490i \(-0.214286\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(744\) 1.27309 0.290574i 1.27309 0.290574i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(752\) 1.11960 1.78183i 1.11960 1.78183i
\(753\) 0 0
\(754\) −0.334853 + 0.334853i −0.334853 + 0.334853i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.193096 0.400969i 0.193096 0.400969i −0.781831 0.623490i \(-0.785714\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(762\) −1.90532 + 0.917554i −1.90532 + 0.917554i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(768\) −0.351438 0.169244i −0.351438 0.169244i
\(769\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(770\) 0 0
\(771\) 0.846011 + 0.193096i 0.846011 + 0.193096i
\(772\) −0.00977979 0.0867980i −0.00977979 0.0867980i
\(773\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(774\) 0 0
\(775\) 0.158342 1.40532i 0.158342 1.40532i
\(776\) 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
\(784\) 1.11475 1.11475
\(785\) 0 0
\(786\) 1.12349 1.40881i 1.12349 1.40881i
\(787\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −0.186291 1.65338i −0.186291 1.65338i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(798\)