Properties

Label 116.1.j.a.107.1
Level $116$
Weight $1$
Character 116.107
Analytic conductor $0.058$
Analytic rank $0$
Dimension $6$
Projective image $D_{7}$
CM discriminant -4
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 116 = 2^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 116.j (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.0578915414654\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{14})\)
Defining polynomial: \(x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.38068692544.1

Embedding invariants

Embedding label 107.1
Root \(0.900969 - 0.433884i\) of defining polynomial
Character \(\chi\) \(=\) 116.107
Dual form 116.1.j.a.103.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.900969 + 0.433884i) q^{2} +(0.623490 - 0.781831i) q^{4} +(0.400969 - 0.193096i) q^{5} +(-0.222521 + 0.974928i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})\) \(q+(-0.900969 + 0.433884i) q^{2} +(0.623490 - 0.781831i) q^{4} +(0.400969 - 0.193096i) q^{5} +(-0.222521 + 0.974928i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(-0.277479 + 0.347948i) q^{10} +(-0.277479 - 1.21572i) q^{13} +(-0.222521 - 0.974928i) q^{16} -1.80194 q^{17} +(-0.222521 - 0.974928i) q^{18} +(0.0990311 - 0.433884i) q^{20} +(-0.500000 + 0.626980i) q^{25} +(0.777479 + 0.974928i) q^{26} +(-0.222521 - 0.974928i) q^{29} +(0.623490 + 0.781831i) q^{32} +(1.62349 - 0.781831i) q^{34} +(0.623490 + 0.781831i) q^{36} +(-0.277479 + 1.21572i) q^{37} +(0.0990311 + 0.433884i) q^{40} +1.24698 q^{41} +(0.0990311 + 0.433884i) q^{45} +(-0.222521 + 0.974928i) q^{49} +(0.178448 - 0.781831i) q^{50} +(-1.12349 - 0.541044i) q^{52} +(1.62349 - 0.781831i) q^{53} +(0.623490 + 0.781831i) q^{58} +(-1.12349 - 1.40881i) q^{61} +(-0.900969 - 0.433884i) q^{64} +(-0.346011 - 0.433884i) q^{65} +(-1.12349 + 1.40881i) q^{68} +(-0.900969 - 0.433884i) q^{72} +(1.62349 + 0.781831i) q^{73} +(-0.277479 - 1.21572i) q^{74} +(-0.277479 - 0.347948i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(-1.12349 + 0.541044i) q^{82} +(-0.722521 + 0.347948i) q^{85} +(0.400969 - 0.193096i) q^{89} +(-0.277479 - 0.347948i) q^{90} +(0.777479 - 0.974928i) q^{97} +(-0.222521 - 0.974928i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9} + O(q^{10}) \) \( 6 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9} - 2 q^{10} - 2 q^{13} - q^{16} - 2 q^{17} - q^{18} + 5 q^{20} - 3 q^{25} + 5 q^{26} - q^{29} - q^{32} + 5 q^{34} - q^{36} - 2 q^{37} + 5 q^{40} - 2 q^{41} + 5 q^{45} - q^{49} - 3 q^{50} - 2 q^{52} + 5 q^{53} - q^{58} - 2 q^{61} - q^{64} + 3 q^{65} - 2 q^{68} - q^{72} + 5 q^{73} - 2 q^{74} - 2 q^{80} - q^{81} - 2 q^{82} - 4 q^{85} - 2 q^{89} - 2 q^{90} + 5 q^{97} - q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/116\mathbb{Z}\right)^\times\).

\(n\) \(59\) \(89\)
\(\chi(n)\) \(-1\) \(e\left(\frac{6}{7}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(3\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(4\) 0.623490 0.781831i 0.623490 0.781831i
\(5\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(6\) 0 0
\(7\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(8\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(9\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(10\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(11\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(12\) 0 0
\(13\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.222521 0.974928i −0.222521 0.974928i
\(17\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(18\) −0.222521 0.974928i −0.222521 0.974928i
\(19\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(20\) 0.0990311 0.433884i 0.0990311 0.433884i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(26\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.222521 0.974928i −0.222521 0.974928i
\(30\) 0 0
\(31\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(32\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(33\) 0 0
\(34\) 1.62349 0.781831i 1.62349 0.781831i
\(35\) 0 0
\(36\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(37\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(41\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(42\) 0 0
\(43\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(44\) 0 0
\(45\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(46\) 0 0
\(47\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(48\) 0 0
\(49\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(50\) 0.178448 0.781831i 0.178448 0.781831i
\(51\) 0 0
\(52\) −1.12349 0.541044i −1.12349 0.541044i
\(53\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.900969 0.433884i −0.900969 0.433884i
\(65\) −0.346011 0.433884i −0.346011 0.433884i
\(66\) 0 0
\(67\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(68\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(72\) −0.900969 0.433884i −0.900969 0.433884i
\(73\) 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 \(0\)
0.623490 + 0.781831i \(0.285714\pi\)
\(74\) −0.277479 1.21572i −0.277479 1.21572i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(80\) −0.277479 0.347948i −0.277479 0.347948i
\(81\) −0.900969 0.433884i −0.900969 0.433884i
\(82\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(83\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(84\) 0 0
\(85\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(90\) −0.277479 0.347948i −0.277479 0.347948i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i \(-0.571429\pi\)
1.00000 \(0\)
\(98\) −0.222521 0.974928i −0.222521 0.974928i
\(99\) 0 0
\(100\) 0.178448 + 0.781831i 0.178448 + 0.781831i
\(101\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(102\) 0 0
\(103\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(104\) 1.24698 1.24698
\(105\) 0 0
\(106\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(107\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(108\) 0 0
\(109\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.900969 0.433884i −0.900969 0.433884i
\(117\) 1.24698 1.24698
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(122\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(123\) 0 0
\(124\) 0 0
\(125\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(126\) 0 0
\(127\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(131\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.400969 1.75676i 0.400969 1.75676i
\(137\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(138\) 0 0
\(139\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) −0.277479 0.347948i −0.277479 0.347948i
\(146\) −1.80194 −1.80194
\(147\) 0 0
\(148\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(149\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(150\) 0 0
\(151\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(152\) 0 0
\(153\) 0.400969 1.75676i 0.400969 1.75676i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(161\) 0 0
\(162\) 1.00000 1.00000
\(163\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(164\) 0.777479 0.974928i 0.777479 0.974928i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(168\) 0 0
\(169\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(170\) 0.500000 0.626980i 0.500000 0.626980i
\(171\) 0 0
\(172\) 0 0
\(173\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(179\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(180\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(181\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(194\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(195\) 0 0
\(196\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(197\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(198\) 0 0
\(199\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(200\) −0.500000 0.626980i −0.500000 0.626980i
\(201\) 0 0
\(202\) −0.445042 −0.445042
\(203\) 0 0
\(204\) 0 0
\(205\) 0.500000 0.240787i 0.500000 0.240787i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(212\) 0.400969 1.75676i 0.400969 1.75676i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −1.12349 0.541044i −1.12349 0.541044i
\(219\) 0 0
\(220\) 0 0
\(221\) 0.500000 + 2.19064i 0.500000 + 2.19064i
\(222\) 0 0
\(223\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(224\) 0 0
\(225\) −0.500000 0.626980i −0.500000 0.626980i
\(226\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(227\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(228\) 0 0
\(229\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000 1.00000
\(233\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(234\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(240\) 0 0
\(241\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(242\) 0.623490 0.781831i 0.623490 0.781831i
\(243\) 0 0
\(244\) −1.80194 −1.80194
\(245\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −0.178448 0.781831i −0.178448 0.781831i
\(251\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(257\) 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i \(-0.571429\pi\)
1.00000 \(0\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.554958 −0.554958
\(261\) 1.00000 1.00000
\(262\) 0 0
\(263\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(264\) 0 0
\(265\) 0.500000 0.626980i 0.500000 0.626980i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(270\) 0 0
\(271\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(272\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(273\) 0 0
\(274\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(275\) 0 0
\(276\) 0 0
\(277\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(282\) 0 0
\(283\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(289\) 2.24698 2.24698
\(290\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(291\) 0 0
\(292\) 1.62349 0.781831i 1.62349 0.781831i
\(293\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.12349 0.541044i −1.12349 0.541044i
\(297\) 0 0
\(298\) 0.400969 1.75676i 0.400969 1.75676i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.722521 0.347948i −0.722521 0.347948i
\(306\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(312\) 0 0
\(313\) 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 \(0\)
0.623490 + 0.781831i \(0.285714\pi\)
\(314\) 0.400969 0.193096i 0.400969 0.193096i
\(315\) 0 0
\(316\) 0 0
\(317\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.445042 −0.445042
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(325\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(326\) 0 0
\(327\) 0 0
\(328\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −1.12349 0.541044i −1.12349 0.541044i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(338\) 0.346011 0.433884i 0.346011 0.433884i
\(339\) 0 0
\(340\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 1.62349 0.781831i 1.62349 0.781831i
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.0990311 0.433884i 0.0990311 0.433884i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(360\) −0.445042 −0.445042
\(361\) −0.222521 0.974928i −0.222521 0.974928i
\(362\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(363\) 0 0
\(364\) 0 0
\(365\) 0.801938 0.801938
\(366\) 0 0
\(367\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(368\) 0 0
\(369\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(370\) −0.346011 0.433884i −0.346011 0.433884i
\(371\) 0 0
\(372\) 0 0
\(373\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(378\) 0 0
\(379\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.0990311 0.433884i 0.0990311 0.433884i
\(387\) 0 0
\(388\) −0.277479 1.21572i −0.277479 1.21572i
\(389\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.900969 0.433884i −0.900969 0.433884i
\(393\) 0 0
\(394\) −0.445042 −0.445042
\(395\) 0 0
\(396\) 0 0
\(397\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(401\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.400969 0.193096i 0.400969 0.193096i
\(405\) −0.445042 −0.445042
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(410\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.777479 0.974928i 0.777479 0.974928i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(420\) 0 0
\(421\) −1.80194 0.867767i −1.80194 0.867767i −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(425\) 0.900969 1.12978i 0.900969 1.12978i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(432\) 0 0
\(433\) −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i \(0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.24698 1.24698
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(440\) 0 0
\(441\) −0.900969 0.433884i −0.900969 0.433884i
\(442\) −1.40097 1.75676i −1.40097 1.75676i
\(443\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(444\) 0 0
\(445\) 0.123490 0.154851i 0.123490 0.154851i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 \(0\)
0.623490 + 0.781831i \(0.285714\pi\)
\(450\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(451\) 0 0
\(452\) −0.445042 −0.445042
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(458\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(459\) 0 0
\(460\) 0 0
\(461\) 1.24698 + 1.56366i 1.24698 + 1.56366i 0.623490 + 0.781831i \(0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(465\) 0 0
\(466\) 0.400969 0.193096i 0.400969 0.193096i
\(467\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(468\) 0.777479 0.974928i 0.777479 0.974928i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(478\) 0 0
\(479\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(480\) 0 0
\(481\) 1.55496 1.55496
\(482\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(483\) 0 0
\(484\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(485\) 0.123490 0.541044i 0.123490 0.541044i
\(486\) 0 0
\(487\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(488\) 1.62349 0.781831i 1.62349 0.781831i
\(489\) 0 0
\(490\) −0.277479 0.347948i −0.277479 0.347948i
\(491\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(492\) 0 0
\(493\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(500\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(504\) 0 0
\(505\) 0.198062 0.198062
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.623490 0.781831i 0.623490 0.781831i
\(513\) 0 0
\(514\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.500000 0.240787i 0.500000 0.240787i
\(521\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(522\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(530\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(531\) 0 0
\(532\) 0 0
\(533\) −0.346011 1.51597i −0.346011 1.51597i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i \(-0.571429\pi\)
1.00000 \(0\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.12349 1.40881i −1.12349 1.40881i
\(545\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(546\) 0 0
\(547\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(548\) −0.277479 0.347948i −0.277479 0.347948i
\(549\) 1.62349 0.781831i 1.62349 0.781831i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −1.12349 1.40881i −1.12349 1.40881i
\(555\) 0 0
\(556\) 0 0
\(557\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.277479 1.21572i −0.277479 1.21572i
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) −0.178448 0.0859360i −0.178448 0.0859360i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(570\) 0 0
\(571\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.623490 0.781831i 0.623490 0.781831i
\(577\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(578\) −2.02446 + 0.974928i −2.02446 + 0.974928i
\(579\) 0 0
\(580\) −0.445042 −0.445042
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(585\) 0.500000 0.240787i 0.500000 0.240787i
\(586\) −1.12349 0.541044i −1.12349 0.541044i
\(587\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.24698 1.24698
\(593\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(600\) 0 0
\(601\) −0.445042 + 1.94986i −0.445042 + 1.94986i −0.222521 + 0.974928i \(0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(606\) 0 0
\(607\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0.801938 0.801938
\(611\) 0 0
\(612\) −1.12349 1.40881i −1.12349 1.40881i
\(613\) 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i \(-0.571429\pi\)
1.00000 \(0\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(618\) 0 0
\(619\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.0990311 0.433884i −0.0990311 0.433884i
\(626\) −1.80194 −1.80194
\(627\) 0 0
\(628\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(629\) 0.500000 2.19064i 0.500000 2.19064i
\(630\) 0 0
\(631\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.24698 1.24698
\(638\) 0 0
\(639\) 0 0
\(640\) 0.400969 0.193096i 0.400969 0.193096i
\(641\) 1.24698 + 1.56366i 1.24698 + 1.56366i 0.623490 + 0.781831i \(0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(642\) 0 0
\(643\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(648\) 0.623490 0.781831i 0.623490 0.781831i
\(649\) 0 0
\(650\) −1.00000 −1.00000
\(651\) 0 0
\(652\) 0 0
\(653\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.277479 1.21572i −0.277479 1.21572i
\(657\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(658\) 0 0
\(659\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(660\) 0 0
\(661\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.24698 1.24698
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(674\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(675\) 0 0
\(676\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(677\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.178448 0.781831i −0.178448 0.781831i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(684\) 0 0
\(685\) −0.0440730 0.193096i −0.0440730 0.193096i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.40097 1.75676i −1.40097 1.75676i
\(690\) 0 0
\(691\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(692\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −2.24698 −2.24698
\(698\) 1.62349 0.781831i 1.62349 0.781831i
\(699\) 0 0
\(700\) 0 0
\(701\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.777479 0.974928i 0.777479 0.974928i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i 1.00000 \(0\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(720\) 0.400969 0.193096i 0.400969 0.193096i
\(721\) 0 0
\(722\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(723\) 0 0
\(724\) −0.445042 −0.445042
\(725\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(726\) 0 0
\(727\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(728\) 0 0
\(729\) 0.623490 0.781831i 0.623490 0.781831i
\(730\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(731\) 0 0
\(732\) 0 0
\(733\) −0.445042 + 1.94986i −0.445042 + 1.94986i −0.222521 + 0.974928i \(0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −0.277479 1.21572i −0.277479 1.21572i
\(739\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(740\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(744\) 0 0
\(745\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(746\) 0.0990311 0.433884i 0.0990311 0.433884i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0.777479 0.974928i 0.777479 0.974928i
\(755\) 0 0
\(756\) 0 0
\(757\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.178448 0.781831i −0.178448 0.781831i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(773\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(777\) 0 0
\(778\) 1.62349 0.781831i 1.62349 0.781831i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) −0.178448 + 0.0859360i −0.178448 + 0.0859360i
\(786\) 0 0
\(787\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(788\) 0.400969 0.193096i 0.400969 0.193096i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −1.40097 + 1.75676i −1.40097 + 1.75676i
\(794\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(795\) 0 0
\(796\) 0 0
\(797\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.801938 −0.801938
\(801\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(802\) 0.777479 0.974928i 0.777479 0.974928i