Properties

Label 129.1.l.a.11.1
Level $129$
Weight $1$
Character 129.11
Analytic conductor $0.064$
Analytic rank $0$
Dimension $6$
Projective image $D_{7}$
CM discriminant -3
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 129 = 3 \cdot 43 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 129.l (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.0643793866297\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.170676802323.1

Embedding invariants

Embedding label 11.1
Root \(0.900969 + 0.433884i\) of defining polynomial
Character \(\chi\) \(=\) 129.11
Dual form 129.1.l.a.47.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.623490 - 0.781831i) q^{3} +(-0.222521 + 0.974928i) q^{4} -1.80194 q^{7} +(-0.222521 - 0.974928i) q^{9} +O(q^{10})\) \(q+(0.623490 - 0.781831i) q^{3} +(-0.222521 + 0.974928i) q^{4} -1.80194 q^{7} +(-0.222521 - 0.974928i) q^{9} +(0.623490 + 0.781831i) q^{12} +(0.400969 - 0.193096i) q^{13} +(-0.900969 - 0.433884i) q^{16} +(-0.277479 + 1.21572i) q^{19} +(-1.12349 + 1.40881i) q^{21} +(0.623490 - 0.781831i) q^{25} +(-0.900969 - 0.433884i) q^{27} +(0.400969 - 1.75676i) q^{28} +(0.777479 + 0.974928i) q^{31} +1.00000 q^{36} -0.445042 q^{37} +(0.0990311 - 0.433884i) q^{39} +(0.623490 - 0.781831i) q^{43} +(-0.900969 + 0.433884i) q^{48} +2.24698 q^{49} +(0.0990311 + 0.433884i) q^{52} +(0.777479 + 0.974928i) q^{57} +(-0.277479 + 0.347948i) q^{61} +(0.400969 + 1.75676i) q^{63} +(0.623490 - 0.781831i) q^{64} +(0.400969 - 1.75676i) q^{67} +(-1.12349 + 0.541044i) q^{73} +(-0.222521 - 0.974928i) q^{75} +(-1.12349 - 0.541044i) q^{76} -1.80194 q^{79} +(-0.900969 + 0.433884i) q^{81} +(-1.12349 - 1.40881i) q^{84} +(-0.722521 + 0.347948i) q^{91} +1.24698 q^{93} +(0.400969 + 1.75676i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{3} - q^{4} - 2q^{7} - q^{9} + O(q^{10}) \) \( 6q - q^{3} - q^{4} - 2q^{7} - q^{9} - q^{12} - 2q^{13} - q^{16} - 2q^{19} - 2q^{21} - q^{25} - q^{27} - 2q^{28} + 5q^{31} + 6q^{36} - 2q^{37} + 5q^{39} - q^{43} - q^{48} + 4q^{49} + 5q^{52} + 5q^{57} - 2q^{61} - 2q^{63} - q^{64} - 2q^{67} - 2q^{73} - q^{75} - 2q^{76} - 2q^{79} - q^{81} - 2q^{84} - 4q^{91} - 2q^{93} - 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/129\mathbb{Z}\right)^\times\).

\(n\) \(44\) \(46\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{7}\right)\)

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 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(3\) 0.623490 0.781831i 0.623490 0.781831i
\(4\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(5\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(6\) 0 0
\(7\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(8\) 0 0
\(9\) −0.222521 0.974928i −0.222521 0.974928i
\(10\) 0 0
\(11\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(12\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(13\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.900969 0.433884i −0.900969 0.433884i
\(17\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(18\) 0 0
\(19\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(20\) 0 0
\(21\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(22\) 0 0
\(23\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(24\) 0 0
\(25\) 0.623490 0.781831i 0.623490 0.781831i
\(26\) 0 0
\(27\) −0.900969 0.433884i −0.900969 0.433884i
\(28\) 0.400969 1.75676i 0.400969 1.75676i
\(29\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(30\) 0 0
\(31\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(38\) 0 0
\(39\) 0.0990311 0.433884i 0.0990311 0.433884i
\(40\) 0 0
\(41\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(42\) 0 0
\(43\) 0.623490 0.781831i 0.623490 0.781831i
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(48\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(49\) 2.24698 2.24698
\(50\) 0 0
\(51\) 0 0
\(52\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(53\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(58\) 0 0
\(59\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(60\) 0 0
\(61\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(62\) 0 0
\(63\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(64\) 0.623490 0.781831i 0.623490 0.781831i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(72\) 0 0
\(73\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(74\) 0 0
\(75\) −0.222521 0.974928i −0.222521 0.974928i
\(76\) −1.12349 0.541044i −1.12349 0.541044i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(80\) 0 0
\(81\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(82\) 0 0
\(83\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(84\) −1.12349 1.40881i −1.12349 1.40881i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(90\) 0 0
\(91\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(92\) 0 0
\(93\) 1.24698 1.24698
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(101\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(102\) 0 0
\(103\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(108\) 0.623490 0.781831i 0.623490 0.781831i
\(109\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i 1.00000 \(0\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(110\) 0 0
\(111\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(112\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(113\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.277479 0.347948i −0.277479 0.347948i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(128\) 0 0
\(129\) −0.222521 0.974928i −0.222521 0.974928i
\(130\) 0 0
\(131\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(132\) 0 0
\(133\) 0.500000 2.19064i 0.500000 2.19064i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(138\) 0 0
\(139\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.40097 1.75676i 1.40097 1.75676i
\(148\) 0.0990311 0.433884i 0.0990311 0.433884i
\(149\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(150\) 0 0
\(151\) 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i \(-0.571429\pi\)
1.00000 \(0\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(157\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i 1.00000 \(0\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(168\) 0 0
\(169\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(170\) 0 0
\(171\) 1.24698 1.24698
\(172\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(182\) 0 0
\(183\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(190\) 0 0
\(191\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(192\) −0.222521 0.974928i −0.222521 0.974928i
\(193\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.500000 + 2.19064i −0.500000 + 2.19064i
\(197\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(198\) 0 0
\(199\) 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 \(0\)
0.623490 + 0.781831i \(0.285714\pi\)
\(200\) 0 0
\(201\) −1.12349 1.40881i −1.12349 1.40881i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.445042 −0.445042
\(209\) 0 0
\(210\) 0 0
\(211\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.40097 1.75676i −1.40097 1.75676i
\(218\) 0 0
\(219\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(224\) 0 0
\(225\) −0.900969 0.433884i −0.900969 0.433884i
\(226\) 0 0
\(227\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(228\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(229\) −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
\(232\) 0 0
\(233\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(238\) 0 0
\(239\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(240\) 0 0
\(241\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(242\) 0 0
\(243\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(244\) −0.277479 0.347948i −0.277479 0.347948i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −1.80194 −1.80194
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0.801938 0.801938
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(269\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(270\) 0 0
\(271\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(272\) 0 0
\(273\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(278\) 0 0
\(279\) 0.777479 0.974928i 0.777479 0.974928i
\(280\) 0 0
\(281\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(282\) 0 0
\(283\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(290\) 0 0
\(291\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(292\) −0.277479 1.21572i −0.277479 1.21572i
\(293\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 1.00000 1.00000
\(301\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(302\) 0 0
\(303\) 0 0
\(304\) 0.777479 0.974928i 0.777479 0.974928i
\(305\) 0 0
\(306\) 0 0
\(307\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(308\) 0 0
\(309\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(310\) 0 0
\(311\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(312\) 0 0
\(313\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.400969 1.75676i 0.400969 1.75676i
\(317\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.222521 0.974928i −0.222521 0.974928i
\(325\) 0.0990311 0.433884i 0.0990311 0.433884i
\(326\) 0 0
\(327\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(332\) 0 0
\(333\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(334\) 0 0
\(335\) 0 0
\(336\) 1.62349 0.781831i 1.62349 0.781831i
\(337\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −2.24698 −2.24698
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(348\) 0 0
\(349\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(350\) 0 0
\(351\) −0.445042 −0.445042
\(352\) 0 0
\(353\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(360\) 0 0
\(361\) −0.500000 0.240787i −0.500000 0.240787i
\(362\) 0 0
\(363\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(364\) −0.178448 0.781831i −0.178448 0.781831i
\(365\) 0 0
\(366\) 0 0
\(367\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(373\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(380\) 0 0
\(381\) 1.24698 1.24698
\(382\) 0 0
\(383\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.900969 0.433884i −0.900969 0.433884i
\(388\) −1.80194 −1.80194
\(389\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(398\) 0 0
\(399\) −1.40097 1.75676i −1.40097 1.75676i
\(400\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(401\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(402\) 0 0
\(403\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.777479 0.974928i 0.777479 0.974928i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.400969 0.193096i 0.400969 0.193096i
\(418\) 0 0
\(419\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(420\) 0 0
\(421\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.500000 0.626980i 0.500000 0.626980i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(433\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.445042 −0.445042
\(437\) 0 0
\(438\) 0 0
\(439\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(440\) 0 0
\(441\) −0.500000 2.19064i −0.500000 2.19064i
\(442\) 0 0
\(443\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(444\) −0.277479 0.347948i −0.277479 0.347948i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(449\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −0.277479 1.21572i −0.277479 1.21572i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(462\) 0 0
\(463\) −1.80194 0.867767i −1.80194 0.867767i −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0.400969 0.193096i 0.400969 0.193096i
\(469\) −0.722521 + 3.16557i −0.722521 + 3.16557i
\(470\) 0 0
\(471\) −0.277479 0.347948i −0.277479 0.347948i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −0.178448 + 0.0859360i −0.178448 + 0.0859360i
\(482\) 0 0
\(483\) 0 0
\(484\) −0.222521 0.974928i −0.222521 0.974928i
\(485\) 0 0
\(486\) 0 0
\(487\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(488\) 0 0
\(489\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(490\) 0 0
\(491\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.277479 1.21572i −0.277479 1.21572i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.80194 0.867767i −1.80194 0.867767i −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.178448 + 0.781831i 0.178448 + 0.781831i
\(508\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 2.02446 0.974928i 2.02446 0.974928i
\(512\) 0 0
\(513\) 0.777479 0.974928i 0.777479 0.974928i
\(514\) 0 0
\(515\) 0 0
\(516\) 1.00000 1.00000
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(522\) 0 0
\(523\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(524\) 0 0
\(525\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.02446 + 0.974928i 2.02446 + 0.974928i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 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
\(543\) −1.12349 0.541044i −1.12349 0.541044i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(548\) 0 0
\(549\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 3.24698 3.24698
\(554\) 0 0
\(555\) 0 0
\(556\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(557\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(558\) 0 0
\(559\) 0.0990311 0.433884i 0.0990311 0.433884i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.62349 0.781831i 1.62349 0.781831i
\(568\) 0 0
\(569\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(570\) 0 0
\(571\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.900969 0.433884i −0.900969 0.433884i
\(577\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(578\) 0 0
\(579\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(588\) 1.40097 + 1.75676i 1.40097 + 1.75676i
\(589\) −1.40097 + 0.674671i −1.40097 + 0.674671i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(593\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.62349 0.781831i 1.62349 0.781831i
\(598\) 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 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(602\) 0 0
\(603\) −1.80194 −1.80194
\(604\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(605\) 0 0
\(606\) 0 0
\(607\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(618\) 0 0
\(619\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(625\) −0.222521 0.974928i −0.222521 0.974928i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.24698 + 1.56366i 1.24698 + 1.56366i 0.623490 + 0.781831i \(0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(632\) 0 0
\(633\) −1.12349 1.40881i −1.12349 1.40881i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0.900969 0.433884i 0.900969 0.433884i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(642\) 0 0
\(643\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −2.24698 −2.24698
\(652\) −0.445042 −0.445042
\(653\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(658\) 0 0
\(659\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(660\) 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
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0.0990311 0.433884i 0.0990311 0.433884i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(674\) 0 0
\(675\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(676\) −0.500000 0.626980i −0.500000 0.626980i
\(677\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(678\) 0 0
\(679\) −0.722521 3.16557i −0.722521 3.16557i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(684\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(685\) 0 0
\(686\) 0 0
\(687\) −1.80194 −1.80194
\(688\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.12349 1.40881i −1.12349 1.40881i
\(701\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(702\) 0 0
\(703\) 0.123490 0.541044i 0.123490 0.541044i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i \(-0.571429\pi\)
1.00000 \(0\)
\(710\) 0 0
\(711\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(720\) 0 0
\(721\) 2.02446 + 0.974928i 2.02446 + 0.974928i
\(722\) 0 0
\(723\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(724\) 1.24698 1.24698
\(725\) 0 0
\(726\) 0 0
\(727\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(728\) 0 0
\(729\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.445042 −0.445042
\(733\) 1.24698 + 1.56366i 1.24698 + 1.56366i 0.623490 + 0.781831i \(0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(740\) 0 0
\(741\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(742\) 0 0
\(743\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(757\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(762\) 0 0
\(763\) −0.178448 0.781831i −0.178448 0.781831i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.00000 1.00000
\(769\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.277479 0.347948i −0.277479 0.347948i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 1.24698 1.24698
\(776\) 0 0
\(777\) 0.500000 0.626980i 0.500000 0.626980i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −2.02446 0.974928i −2.02446 0.974928i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.0440730 + 0.193096i −0.0440730 + 0.193096i
\(794\) 0 0
\(795\) 0 0
\(796\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(797\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 1.62349 0.781831i 1.62349 0.781831i
\(805\) 0 0
\(806\) 0 0