Properties

Label 2009.1.i.a.1844.2
Level 2009
Weight 1
Character 2009.1844
Analytic conductor 1.003
Analytic rank 0
Dimension 6
Projective image \(D_{7}\)
CM discriminant -287
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2009.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00262161038\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.64827.1
Defining polynomial: \(x^{6} - x^{5} + 3 x^{4} + 5 x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 287)
Projective image \(D_{7}\)
Projective field Galois closure of 7.1.23639903.1
Artin image $C_6\times D_7$
Artin field Galois closure of \(\mathbb{Q}[x]/(x^{42} + \cdots)\)

Embedding invariants

Embedding label 1844.2
Root \(0.222521 + 0.385418i\) of defining polynomial
Character \(\chi\) \(=\) 2009.1844
Dual form 2009.1.i.a.901.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.222521 + 0.385418i) q^{2} +(-0.900969 + 1.56052i) q^{3} +(0.400969 - 0.694498i) q^{4} -0.801938 q^{6} +0.801938 q^{8} +(-1.12349 - 1.94594i) q^{9} +O(q^{10})\) \(q+(0.222521 + 0.385418i) q^{2} +(-0.900969 + 1.56052i) q^{3} +(0.400969 - 0.694498i) q^{4} -0.801938 q^{6} +0.801938 q^{8} +(-1.12349 - 1.94594i) q^{9} +(0.722521 + 1.25144i) q^{12} +0.445042 q^{13} +(-0.222521 - 0.385418i) q^{16} +(0.623490 - 1.07992i) q^{17} +(0.500000 - 0.866025i) q^{18} +(0.623490 + 1.07992i) q^{19} +(0.900969 + 1.56052i) q^{23} +(-0.722521 + 1.25144i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.0990311 + 0.171527i) q^{26} +2.24698 q^{27} +(0.500000 - 0.866025i) q^{32} +0.554958 q^{34} -1.80194 q^{36} +(0.222521 + 0.385418i) q^{37} +(-0.277479 + 0.480608i) q^{38} +(-0.400969 + 0.694498i) q^{39} -1.00000 q^{41} +1.24698 q^{43} +(-0.400969 + 0.694498i) q^{46} +(-0.222521 - 0.385418i) q^{47} +0.801938 q^{48} -0.445042 q^{50} +(1.12349 + 1.94594i) q^{51} +(0.178448 - 0.309081i) q^{52} +(0.500000 + 0.866025i) q^{54} -2.24698 q^{57} +(-0.500000 - 0.866025i) q^{68} -3.24698 q^{69} +(-0.900969 - 1.56052i) q^{72} +(-0.0990311 + 0.171527i) q^{74} +(-0.900969 - 1.56052i) q^{75} +1.00000 q^{76} -0.356896 q^{78} +(-0.900969 + 1.56052i) q^{81} +(-0.222521 - 0.385418i) q^{82} +(0.277479 + 0.480608i) q^{86} +(-0.222521 - 0.385418i) q^{89} +1.44504 q^{92} +(0.0990311 - 0.171527i) q^{94} +(0.900969 + 1.56052i) q^{96} +1.80194 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} - q^{3} - 2q^{4} + 4q^{6} - 4q^{8} - 2q^{9} + O(q^{10}) \) \( 6q + q^{2} - q^{3} - 2q^{4} + 4q^{6} - 4q^{8} - 2q^{9} + 4q^{12} + 2q^{13} - q^{16} - q^{17} + 3q^{18} - q^{19} + q^{23} - 4q^{24} - 3q^{25} + 5q^{26} + 4q^{27} + 3q^{32} + 4q^{34} - 2q^{36} + q^{37} - 2q^{38} + 2q^{39} - 6q^{41} - 2q^{43} + 2q^{46} - q^{47} - 4q^{48} - 2q^{50} + 2q^{51} - 3q^{52} + 3q^{54} - 4q^{57} - 3q^{68} - 10q^{69} - q^{72} - 5q^{74} - q^{75} + 6q^{76} + 6q^{78} - q^{81} - q^{82} + 2q^{86} - q^{89} + 8q^{92} + 5q^{94} + q^{96} + 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2009\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(3\) −0.900969 + 1.56052i −0.900969 + 1.56052i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(4\) 0.400969 0.694498i 0.400969 0.694498i
\(5\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(6\) −0.801938 −0.801938
\(7\) 0 0
\(8\) 0.801938 0.801938
\(9\) −1.12349 1.94594i −1.12349 1.94594i
\(10\) 0 0
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0.722521 + 1.25144i 0.722521 + 1.25144i
\(13\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.222521 0.385418i −0.222521 0.385418i
\(17\) 0.623490 1.07992i 0.623490 1.07992i −0.365341 0.930874i \(-0.619048\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(18\) 0.500000 0.866025i 0.500000 0.866025i
\(19\) 0.623490 + 1.07992i 0.623490 + 1.07992i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(24\) −0.722521 + 1.25144i −0.722521 + 1.25144i
\(25\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(26\) 0.0990311 + 0.171527i 0.0990311 + 0.171527i
\(27\) 2.24698 2.24698
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0.500000 0.866025i 0.500000 0.866025i
\(33\) 0 0
\(34\) 0.554958 0.554958
\(35\) 0 0
\(36\) −1.80194 −1.80194
\(37\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(38\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(39\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(40\) 0 0
\(41\) −1.00000 −1.00000
\(42\) 0 0
\(43\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(47\) −0.222521 0.385418i −0.222521 0.385418i 0.733052 0.680173i \(-0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(48\) 0.801938 0.801938
\(49\) 0 0
\(50\) −0.445042 −0.445042
\(51\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(52\) 0.178448 0.309081i 0.178448 0.309081i
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(55\) 0 0
\(56\) 0 0
\(57\) −2.24698 −2.24698
\(58\) 0 0
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −0.500000 0.866025i −0.500000 0.866025i
\(69\) −3.24698 −3.24698
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −0.900969 1.56052i −0.900969 1.56052i
\(73\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) −0.0990311 + 0.171527i −0.0990311 + 0.171527i
\(75\) −0.900969 1.56052i −0.900969 1.56052i
\(76\) 1.00000 1.00000
\(77\) 0 0
\(78\) −0.356896 −0.356896
\(79\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(80\) 0 0
\(81\) −0.900969 + 1.56052i −0.900969 + 1.56052i
\(82\) −0.222521 0.385418i −0.222521 0.385418i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(87\) 0 0
\(88\) 0 0
\(89\) −0.222521 0.385418i −0.222521 0.385418i 0.733052 0.680173i \(-0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.44504 1.44504
\(93\) 0 0
\(94\) 0.0990311 0.171527i 0.0990311 0.171527i
\(95\) 0 0
\(96\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(97\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.400969 + 0.694498i 0.400969 + 0.694498i
\(101\) −0.900969 + 1.56052i −0.900969 + 1.56052i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(102\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(103\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) 0.356896 0.356896
\(105\) 0 0
\(106\) 0 0
\(107\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(108\) 0.900969 1.56052i 0.900969 1.56052i
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0 0
\(111\) −0.801938 −0.801938
\(112\) 0 0
\(113\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(114\) −0.500000 0.866025i −0.500000 0.866025i
\(115\) 0 0
\(116\) 0 0
\(117\) −0.500000 0.866025i −0.500000 0.866025i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.500000 0.866025i
\(122\) 0 0
\(123\) 0.900969 1.56052i 0.900969 1.56052i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(128\) −0.500000 0.866025i −0.500000 0.866025i
\(129\) −1.12349 + 1.94594i −1.12349 + 1.94594i
\(130\) 0 0
\(131\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.500000 0.866025i 0.500000 0.866025i
\(137\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) −0.722521 1.25144i −0.722521 1.25144i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0.801938 0.801938
\(142\) 0 0
\(143\) 0 0
\(144\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0.356896 0.356896
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0.400969 0.694498i 0.400969 0.694498i
\(151\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(153\) −2.80194 −2.80194
\(154\) 0 0
\(155\) 0 0
\(156\) 0.321552 + 0.556945i 0.321552 + 0.556945i
\(157\) 0.623490 1.07992i 0.623490 1.07992i −0.365341 0.930874i \(-0.619048\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.801938 −0.801938
\(163\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(164\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(165\) 0 0
\(166\) 0 0
\(167\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(168\) 0 0
\(169\) −0.801938 −0.801938
\(170\) 0 0
\(171\) 1.40097 2.42655i 1.40097 2.42655i
\(172\) 0.500000 0.866025i 0.500000 0.866025i
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0.0990311 0.171527i 0.0990311 0.171527i
\(179\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0 0
\(181\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.722521 + 1.25144i 0.722521 + 1.25144i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.356896 −0.356896
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) 0 0
\(193\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0.400969 + 0.694498i 0.400969 + 0.694498i
\(195\) 0 0
\(196\) 0 0
\(197\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(198\) 0 0
\(199\) −0.222521 + 0.385418i −0.222521 + 0.385418i −0.955573 0.294755i \(-0.904762\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(200\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(201\) 0 0
\(202\) −0.801938 −0.801938
\(203\) 0 0
\(204\) 1.80194 1.80194
\(205\) 0 0
\(206\) 0 0
\(207\) 2.02446 3.50647i 2.02446 3.50647i
\(208\) −0.0990311 0.171527i −0.0990311 0.171527i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.277479 0.480608i 0.277479 0.480608i
\(215\) 0 0
\(216\) 1.80194 1.80194
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.277479 0.480608i 0.277479 0.480608i
\(222\) −0.178448 0.309081i −0.178448 0.309081i
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 2.24698 2.24698
\(226\) −0.400969 0.694498i −0.400969 0.694498i
\(227\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(228\) −0.900969 + 1.56052i −0.900969 + 1.56052i
\(229\) −0.900969 1.56052i −0.900969 1.56052i −0.826239 0.563320i \(-0.809524\pi\)
−0.0747301 0.997204i \(-0.523810\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0.222521 0.385418i 0.222521 0.385418i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0.222521 0.385418i 0.222521 0.385418i
\(243\) −0.500000 0.866025i −0.500000 0.866025i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.801938 0.801938
\(247\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.0990311 0.171527i −0.0990311 0.171527i
\(255\) 0 0
\(256\) 0.222521 0.385418i 0.222521 0.385418i
\(257\) −0.900969 1.56052i −0.900969 1.56052i −0.826239 0.563320i \(-0.809524\pi\)
−0.0747301 0.997204i \(-0.523810\pi\)
\(258\) −1.00000 −1.00000
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.801938 0.801938
\(268\) 0 0
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) −0.554958 −0.554958
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.30194 + 2.25502i −1.30194 + 2.25502i
\(277\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0.178448 + 0.309081i 0.178448 + 0.309081i
\(283\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −2.24698 −2.24698
\(289\) −0.277479 0.480608i −0.277479 0.480608i
\(290\) 0 0
\(291\) −1.62349 + 2.81197i −1.62349 + 2.81197i
\(292\) 0 0
\(293\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.178448 + 0.309081i 0.178448 + 0.309081i
\(297\) 0 0
\(298\) 0 0
\(299\) 0.400969 + 0.694498i 0.400969 + 0.694498i
\(300\) −1.44504 −1.44504
\(301\) 0 0
\(302\) 0 0
\(303\) −1.62349 2.81197i −1.62349 2.81197i
\(304\) 0.277479 0.480608i 0.277479 0.480608i
\(305\) 0 0
\(306\) −0.623490 1.07992i −0.623490 1.07992i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0.623490 1.07992i 0.623490 1.07992i −0.365341 0.930874i \(-0.619048\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(312\) −0.321552 + 0.556945i −0.321552 + 0.556945i
\(313\) 0.623490 + 1.07992i 0.623490 + 1.07992i 0.988831 + 0.149042i \(0.0476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(314\) 0.554958 0.554958
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 2.24698 2.24698
\(322\) 0 0
\(323\) 1.55496 1.55496
\(324\) 0.722521 + 1.25144i 0.722521 + 1.25144i
\(325\) −0.222521 + 0.385418i −0.222521 + 0.385418i
\(326\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(327\) 0 0
\(328\) −0.801938 −0.801938
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 0 0
\(333\) 0.500000 0.866025i 0.500000 0.866025i
\(334\) −0.277479 0.480608i −0.277479 0.480608i
\(335\) 0 0
\(336\) 0 0
\(337\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(338\) −0.178448 0.309081i −0.178448 0.309081i
\(339\) 1.62349 2.81197i 1.62349 2.81197i
\(340\) 0 0
\(341\) 0 0
\(342\) 1.24698 1.24698
\(343\) 0 0
\(344\) 1.00000 1.00000
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 1.00000 1.00000
\(352\) 0 0
\(353\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.356896 −0.356896
\(357\) 0 0
\(358\) 0 0
\(359\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(360\) 0 0
\(361\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(362\) 0.400969 + 0.694498i 0.400969 + 0.694498i
\(363\) 1.80194 1.80194
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 0.400969 0.694498i 0.400969 0.694498i
\(369\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −0.178448 0.309081i −0.178448 0.309081i
\(377\) 0 0
\(378\) 0 0
\(379\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(380\) 0 0
\(381\) 0.400969 0.694498i 0.400969 0.694498i
\(382\) 0 0
\(383\) −0.900969 1.56052i −0.900969 1.56052i −0.826239 0.563320i \(-0.809524\pi\)
−0.0747301 0.997204i \(-0.523810\pi\)
\(384\) 1.80194 1.80194
\(385\) 0 0
\(386\) 0 0
\(387\) −1.40097 2.42655i −1.40097 2.42655i
\(388\) 0.722521 1.25144i 0.722521 1.25144i
\(389\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(390\) 0 0
\(391\) 2.24698 2.24698
\(392\) 0 0
\(393\) 0 0
\(394\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(395\) 0 0
\(396\) 0 0
\(397\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(398\) −0.198062 −0.198062
\(399\) 0 0
\(400\) 0.445042 0.445042
\(401\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.722521 + 1.25144i 0.722521 + 1.25144i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(409\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 1.80194 1.80194
\(415\) 0 0
\(416\) 0.222521 0.385418i 0.222521 0.385418i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(424\) 0 0
\(425\) 0.623490 + 1.07992i 0.623490 + 1.07992i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.00000 −1.00000
\(429\) 0 0
\(430\) 0 0
\(431\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −0.500000 0.866025i −0.500000 0.866025i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.12349 + 1.94594i −1.12349 + 1.94594i
\(438\) 0 0
\(439\) −0.900969 1.56052i −0.900969 1.56052i −0.826239 0.563320i \(-0.809524\pi\)
−0.0747301 0.997204i \(-0.523810\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0.246980 0.246980
\(443\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(444\) −0.321552 + 0.556945i −0.321552 + 0.556945i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(450\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(451\) 0 0
\(452\) −0.722521 + 1.25144i −0.722521 + 1.25144i
\(453\) 0 0
\(454\) 0.890084 0.890084
\(455\) 0 0
\(456\) −1.80194 −1.80194
\(457\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(458\) 0.400969 0.694498i 0.400969 0.694498i
\(459\) 1.40097 2.42655i 1.40097 2.42655i
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) −0.801938 −0.801938
\(469\) 0 0
\(470\) 0 0
\(471\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.24698 −1.24698
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.900969 + 1.56052i −0.900969 + 1.56052i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(480\) 0 0
\(481\) 0.0990311 + 0.171527i 0.0990311 + 0.171527i
\(482\) 0 0
\(483\) 0 0
\(484\) −0.801938 −0.801938
\(485\) 0 0
\(486\) 0.222521 0.385418i 0.222521 0.385418i
\(487\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(488\) 0 0
\(489\) −3.24698 −3.24698
\(490\) 0 0
\(491\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(492\) −0.722521 1.25144i −0.722521 1.25144i
\(493\) 0 0
\(494\) −0.123490 + 0.213891i −0.123490 + 0.213891i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(500\) 0 0
\(501\) 1.12349 1.94594i 1.12349 1.94594i
\(502\) 0 0
\(503\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.722521 1.25144i 0.722521 1.25144i
\(508\) −0.178448 + 0.309081i −0.178448 + 0.309081i
\(509\) −0.222521 0.385418i −0.222521 0.385418i 0.733052 0.680173i \(-0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.801938 −0.801938
\(513\) 1.40097 + 2.42655i 1.40097 + 2.42655i
\(514\) 0.400969 0.694498i 0.400969 0.694498i
\(515\) 0 0
\(516\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.222521 + 0.385418i −0.222521 + 0.385418i −0.955573 0.294755i \(-0.904762\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(522\) 0 0
\(523\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.12349 + 1.94594i −1.12349 + 1.94594i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.445042 −0.445042
\(534\) 0.178448 + 0.309081i 0.178448 + 0.309081i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(542\) 0 0
\(543\) −1.62349 + 2.81197i −1.62349 + 2.81197i
\(544\) −0.623490 1.07992i −0.623490 1.07992i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −2.60388 −2.60388
\(553\) 0 0
\(554\) 0.801938 0.801938
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 0.554958 0.554958
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −0.222521 + 0.385418i −0.222521 + 0.385418i −0.955573 0.294755i \(-0.904762\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(564\) 0.321552 0.556945i 0.321552 0.556945i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(570\) 0 0
\(571\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.80194 −1.80194
\(576\) 0 0
\(577\) −0.900969 + 1.56052i −0.900969 + 1.56052i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(578\) 0.123490 0.213891i 0.123490 0.213891i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) −1.44504 −1.44504
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −0.445042 0.770835i −0.445042 0.770835i
\(587\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −1.12349 + 1.94594i −1.12349 + 1.94594i
\(592\) 0.0990311 0.171527i 0.0990311 0.171527i
\(593\) −0.222521 0.385418i −0.222521 0.385418i 0.733052 0.680173i \(-0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.400969 0.694498i −0.400969 0.694498i
\(598\) −0.178448 + 0.309081i −0.178448 + 0.309081i
\(599\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(600\) −0.722521 1.25144i −0.722521 1.25144i
\(601\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0.722521 1.25144i 0.722521 1.25144i
\(607\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) 1.24698 1.24698
\(609\) 0 0
\(610\) 0 0
\(611\) −0.0990311 0.171527i −0.0990311 0.171527i
\(612\) −1.12349 + 1.94594i −1.12349 + 1.94594i
\(613\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(618\) 0 0
\(619\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) 2.02446 + 3.50647i 2.02446 + 3.50647i
\(622\) 0.554958 0.554958
\(623\) 0 0
\(624\) 0.356896 0.356896
\(625\) −0.500000 0.866025i −0.500000 0.866025i
\(626\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(627\) 0 0
\(628\) −0.500000 0.866025i −0.500000 0.866025i
\(629\) 0.554958 0.554958
\(630\) 0 0
\(631\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(643\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.346011 + 0.599308i 0.346011 + 0.599308i
\(647\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) −0.722521 + 1.25144i −0.722521 + 1.25144i
\(649\) 0 0
\(650\) −0.198062 −0.198062
\(651\) 0 0
\(652\) 1.44504 1.44504
\(653\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(664\) 0 0
\(665\) 0 0
\(666\) 0.445042 0.445042
\(667\) 0 0
\(668\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) −0.400969 0.694498i −0.400969 0.694498i
\(675\) −1.12349 + 1.94594i −1.12349 + 1.94594i
\(676\) −0.321552 + 0.556945i −0.321552 + 0.556945i
\(677\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(678\) 1.44504 1.44504
\(679\) 0 0
\(680\) 0 0
\(681\) 1.80194 + 3.12105i 1.80194 + 3.12105i
\(682\) 0 0
\(683\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) −1.12349 1.94594i −1.12349 1.94594i
\(685\) 0 0
\(686\) 0 0
\(687\) 3.24698 3.24698
\(688\) −0.277479 0.480608i −0.277479 0.480608i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.222521 0.385418i −0.222521 0.385418i 0.733052 0.680173i \(-0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(702\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(703\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.178448 0.309081i −0.178448 0.309081i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −0.0990311 + 0.171527i −0.0990311 + 0.171527i
\(719\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.246980 −0.246980
\(723\) 0 0
\(724\) 0.722521 1.25144i 0.722521 1.25144i
\(725\) 0 0
\(726\) 0.400969 + 0.694498i 0.400969 + 0.694498i
\(727\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.777479 1.34663i 0.777479 1.34663i
\(732\) 0 0
\(733\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1.80194 1.80194
\(737\) 0 0
\(738\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(739\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(740\) 0 0
\(741\) −1.00000 −1.00000
\(742\) 0 0
\(743\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.277479 0.480608i 0.277479 0.480608i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) −0.0990311 + 0.171527i −0.0990311 + 0.171527i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −0.400969 0.694498i −0.400969 0.694498i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0.356896 0.356896
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.400969 0.694498i 0.400969 0.694498i
\(767\) 0 0
\(768\) 0.400969 + 0.694498i 0.400969 + 0.694498i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 3.24698 3.24698
\(772\) 0 0
\(773\) 0.623490 1.07992i 0.623490 1.07992i −0.365341 0.930874i \(-0.619048\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(774\) 0.623490 1.07992i 0.623490 1.07992i
\(775\) 0 0
\(776\) 1.44504 1.44504
\(777\) 0 0
\(778\) 0.198062 0.198062
\(779\) −0.623490 1.07992i −0.623490 1.07992i
\(780\) 0 0
\(781\) 0 0
\(782\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(788\) 0.500000 0.866025i 0.500000 0.866025i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −0.445042 + 0.770835i −0.445042 + 0.770835i
\(795\) 0 0
\(796\) 0.178448 + 0.309081i 0.178448 + 0.309081i
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) −0.554958 −0.554958
\(800\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(801\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(802\) −0.0990311 + 0.171527i −0.0990311 + 0.171527i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\)