Properties

Label 1911.1.w.e.1598.3
Level $1911$
Weight $1$
Character 1911.1598
Analytic conductor $0.954$
Analytic rank $0$
Dimension $8$
Projective image $D_{8}$
CM discriminant -39
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1911.w (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.953713239142\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.2
Defining polynomial: \( x^{8} + 4x^{6} + 14x^{4} + 8x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{8}\)
Projective field: Galois closure of 8.2.90724673403.2

Embedding invariants

Embedding label 1598.3
Root \(0.923880 - 1.60021i\) of defining polynomial
Character \(\chi\) \(=\) 1911.1598
Dual form 1911.1.w.e.116.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.382683 - 0.662827i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.207107 + 0.358719i) q^{4} +(0.923880 - 1.60021i) q^{5} -0.765367 q^{6} +1.08239 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.382683 - 0.662827i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.207107 + 0.358719i) q^{4} +(0.923880 - 1.60021i) q^{5} -0.765367 q^{6} +1.08239 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.707107 - 1.22474i) q^{10} +(-0.382683 - 0.662827i) q^{11} +(0.207107 - 0.358719i) q^{12} -1.00000 q^{13} -1.84776 q^{15} +(0.207107 - 0.358719i) q^{16} +(0.382683 + 0.662827i) q^{18} +0.765367 q^{20} -0.585786 q^{22} +(-0.541196 - 0.937379i) q^{24} +(-1.20711 - 2.09077i) q^{25} +(-0.382683 + 0.662827i) q^{26} +1.00000 q^{27} +(-0.707107 + 1.22474i) q^{30} +(0.382683 + 0.662827i) q^{32} +(-0.382683 + 0.662827i) q^{33} -0.414214 q^{36} +(0.500000 + 0.866025i) q^{39} +(1.00000 - 1.73205i) q^{40} +1.84776 q^{41} +(0.158513 - 0.274552i) q^{44} +(0.923880 + 1.60021i) q^{45} +(-0.923880 + 1.60021i) q^{47} -0.414214 q^{48} -1.84776 q^{50} +(-0.207107 - 0.358719i) q^{52} +(0.382683 - 0.662827i) q^{54} -1.41421 q^{55} +(-0.382683 - 0.662827i) q^{59} +(-0.382683 - 0.662827i) q^{60} +1.00000 q^{64} +(-0.923880 + 1.60021i) q^{65} +(0.292893 + 0.507306i) q^{66} +1.84776 q^{71} +(-0.541196 + 0.937379i) q^{72} +(-1.20711 + 2.09077i) q^{75} +0.765367 q^{78} +(-0.707107 + 1.22474i) q^{79} +(-0.382683 - 0.662827i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.707107 - 1.22474i) q^{82} -0.765367 q^{83} +(-0.414214 - 0.717439i) q^{88} +(0.382683 - 0.662827i) q^{89} +1.41421 q^{90} +(0.707107 + 1.22474i) q^{94} +(0.382683 - 0.662827i) q^{96} +0.765367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} - 4 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} - 4 q^{4} - 4 q^{9} - 4 q^{12} - 8 q^{13} - 4 q^{16} - 16 q^{22} - 4 q^{25} + 8 q^{27} + 8 q^{36} + 4 q^{39} + 8 q^{40} + 8 q^{48} + 4 q^{52} + 8 q^{64} + 8 q^{66} - 4 q^{75} - 4 q^{81} + 8 q^{88}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1911\mathbb{Z}\right)^\times\).

\(n\) \(638\) \(1471\) \(1522\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.382683 0.662827i 0.382683 0.662827i −0.608761 0.793353i \(-0.708333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(3\) −0.500000 0.866025i −0.500000 0.866025i
\(4\) 0.207107 + 0.358719i 0.207107 + 0.358719i
\(5\) 0.923880 1.60021i 0.923880 1.60021i 0.130526 0.991445i \(-0.458333\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(6\) −0.765367 −0.765367
\(7\) 0 0
\(8\) 1.08239 1.08239
\(9\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(10\) −0.707107 1.22474i −0.707107 1.22474i
\(11\) −0.382683 0.662827i −0.382683 0.662827i 0.608761 0.793353i \(-0.291667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(12\) 0.207107 0.358719i 0.207107 0.358719i
\(13\) −1.00000 −1.00000
\(14\) 0 0
\(15\) −1.84776 −1.84776
\(16\) 0.207107 0.358719i 0.207107 0.358719i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 0.765367 0.765367
\(21\) 0 0
\(22\) −0.585786 −0.585786
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) −0.541196 0.937379i −0.541196 0.937379i
\(25\) −1.20711 2.09077i −1.20711 2.09077i
\(26\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(27\) 1.00000 1.00000
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(31\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(33\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.414214 −0.414214
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(40\) 1.00000 1.73205i 1.00000 1.73205i
\(41\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0.158513 0.274552i 0.158513 0.274552i
\(45\) 0.923880 + 1.60021i 0.923880 + 1.60021i
\(46\) 0 0
\(47\) −0.923880 + 1.60021i −0.923880 + 1.60021i −0.130526 + 0.991445i \(0.541667\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(48\) −0.414214 −0.414214
\(49\) 0 0
\(50\) −1.84776 −1.84776
\(51\) 0 0
\(52\) −0.207107 0.358719i −0.207107 0.358719i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0.382683 0.662827i 0.382683 0.662827i
\(55\) −1.41421 −1.41421
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.382683 0.662827i −0.382683 0.662827i 0.608761 0.793353i \(-0.291667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(60\) −0.382683 0.662827i −0.382683 0.662827i
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) −0.923880 + 1.60021i −0.923880 + 1.60021i
\(66\) 0.292893 + 0.507306i 0.292893 + 0.507306i
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.84776 1.84776 0.923880 0.382683i \(-0.125000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(72\) −0.541196 + 0.937379i −0.541196 + 0.937379i
\(73\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 0 0
\(75\) −1.20711 + 2.09077i −1.20711 + 2.09077i
\(76\) 0 0
\(77\) 0 0
\(78\) 0.765367 0.765367
\(79\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(80\) −0.382683 0.662827i −0.382683 0.662827i
\(81\) −0.500000 0.866025i −0.500000 0.866025i
\(82\) 0.707107 1.22474i 0.707107 1.22474i
\(83\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.414214 0.717439i −0.414214 0.717439i
\(89\) 0.382683 0.662827i 0.382683 0.662827i −0.608761 0.793353i \(-0.708333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(90\) 1.41421 1.41421
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(95\) 0 0
\(96\) 0.382683 0.662827i 0.382683 0.662827i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0.765367 0.765367
\(100\) 0.500000 0.866025i 0.500000 0.866025i
\(101\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 0 0
\(103\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(104\) −1.08239 −1.08239
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0.207107 + 0.358719i 0.207107 + 0.358719i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) −0.541196 + 0.937379i −0.541196 + 0.937379i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.500000 0.866025i 0.500000 0.866025i
\(118\) −0.585786 −0.585786
\(119\) 0 0
\(120\) −2.00000 −2.00000
\(121\) 0.207107 0.358719i 0.207107 0.358719i
\(122\) 0 0
\(123\) −0.923880 1.60021i −0.923880 1.60021i
\(124\) 0 0
\(125\) −2.61313 −2.61313
\(126\) 0 0
\(127\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(131\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) −0.317025 −0.317025
\(133\) 0 0
\(134\) 0 0
\(135\) 0.923880 1.60021i 0.923880 1.60021i
\(136\) 0 0
\(137\) 0.923880 + 1.60021i 0.923880 + 1.60021i 0.793353 + 0.608761i \(0.208333\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(138\) 0 0
\(139\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(140\) 0 0
\(141\) 1.84776 1.84776
\(142\) 0.707107 1.22474i 0.707107 1.22474i
\(143\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(144\) 0.207107 + 0.358719i 0.207107 + 0.358719i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.923880 1.60021i 0.923880 1.60021i 0.130526 0.991445i \(-0.458333\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(150\) 0.923880 + 1.60021i 0.923880 + 1.60021i
\(151\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.207107 + 0.358719i −0.207107 + 0.358719i
\(157\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(158\) 0.541196 + 0.937379i 0.541196 + 0.937379i
\(159\) 0 0
\(160\) 1.41421 1.41421
\(161\) 0 0
\(162\) −0.765367 −0.765367
\(163\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(165\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(166\) −0.292893 + 0.507306i −0.292893 + 0.507306i
\(167\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.317025 −0.317025
\(177\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(178\) −0.292893 0.507306i −0.292893 0.507306i
\(179\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(181\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.765367 −0.765367
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) −0.500000 0.866025i −0.500000 0.866025i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) 1.84776 1.84776
\(196\) 0 0
\(197\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(198\) 0.292893 0.507306i 0.292893 0.507306i
\(199\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(200\) −1.30656 2.26303i −1.30656 2.26303i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1.70711 2.95680i 1.70711 2.95680i
\(206\) 0.541196 + 0.937379i 0.541196 + 0.937379i
\(207\) 0 0
\(208\) −0.207107 + 0.358719i −0.207107 + 0.358719i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(212\) 0 0
\(213\) −0.923880 1.60021i −0.923880 1.60021i
\(214\) 0 0
\(215\) 0 0
\(216\) 1.08239 1.08239
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.292893 0.507306i −0.292893 0.507306i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 2.41421 2.41421
\(226\) 0 0
\(227\) −0.923880 1.60021i −0.923880 1.60021i −0.793353 0.608761i \(-0.791667\pi\)
−0.130526 0.991445i \(-0.541667\pi\)
\(228\) 0 0
\(229\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) −0.382683 0.662827i −0.382683 0.662827i
\(235\) 1.70711 + 2.95680i 1.70711 + 2.95680i
\(236\) 0.158513 0.274552i 0.158513 0.274552i
\(237\) 1.41421 1.41421
\(238\) 0 0
\(239\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(240\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) −0.158513 0.274552i −0.158513 0.274552i
\(243\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(244\) 0 0
\(245\) 0 0
\(246\) −1.41421 −1.41421
\(247\) 0 0
\(248\) 0 0
\(249\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(250\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.541196 + 0.937379i −0.541196 + 0.937379i
\(255\) 0 0
\(256\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.765367 −0.765367
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) −0.414214 + 0.717439i −0.414214 + 0.717439i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.765367 −0.765367
\(268\) 0 0
\(269\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(270\) −0.707107 1.22474i −0.707107 1.22474i
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 1.41421 1.41421
\(275\) −0.923880 + 1.60021i −0.923880 + 1.60021i
\(276\) 0 0
\(277\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(278\) −0.541196 + 0.937379i −0.541196 + 0.937379i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.84776 −1.84776 −0.923880 0.382683i \(-0.875000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(282\) 0.707107 1.22474i 0.707107 1.22474i
\(283\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(285\) 0 0
\(286\) 0.585786 0.585786
\(287\) 0 0
\(288\) −0.765367 −0.765367
\(289\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(294\) 0 0
\(295\) −1.41421 −1.41421
\(296\) 0 0
\(297\) −0.382683 0.662827i −0.382683 0.662827i
\(298\) −0.707107 1.22474i −0.707107 1.22474i
\(299\) 0 0
\(300\) −1.00000 −1.00000
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 1.41421 1.41421
\(310\) 0 0
\(311\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(312\) 0.541196 + 0.937379i 0.541196 + 0.937379i
\(313\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(314\) 1.08239 1.08239
\(315\) 0 0
\(316\) −0.585786 −0.585786
\(317\) 0.382683 0.662827i 0.382683 0.662827i −0.608761 0.793353i \(-0.708333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.923880 1.60021i 0.923880 1.60021i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.207107 0.358719i 0.207107 0.358719i
\(325\) 1.20711 + 2.09077i 1.20711 + 2.09077i
\(326\) 0 0
\(327\) 0 0
\(328\) 2.00000 2.00000
\(329\) 0 0
\(330\) 1.08239 1.08239
\(331\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) −0.158513 0.274552i −0.158513 0.274552i
\(333\) 0 0
\(334\) 0.292893 0.507306i 0.292893 0.507306i
\(335\) 0 0
\(336\) 0 0
\(337\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(338\) 0.382683 0.662827i 0.382683 0.662827i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −1.00000 −1.00000
\(352\) 0.292893 0.507306i 0.292893 0.507306i
\(353\) 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i \(-0.0416667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(354\) 0.292893 + 0.507306i 0.292893 + 0.507306i
\(355\) 1.70711 2.95680i 1.70711 2.95680i
\(356\) 0.317025 0.317025
\(357\) 0 0
\(358\) 0 0
\(359\) 0.382683 0.662827i 0.382683 0.662827i −0.608761 0.793353i \(-0.708333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(360\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(361\) −0.500000 0.866025i −0.500000 0.866025i
\(362\) 0.541196 0.937379i 0.541196 0.937379i
\(363\) −0.414214 −0.414214
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(368\) 0 0
\(369\) −0.923880 + 1.60021i −0.923880 + 1.60021i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(374\) 0 0
\(375\) 1.30656 + 2.26303i 1.30656 + 2.26303i
\(376\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(382\) 0 0
\(383\) 0.923880 1.60021i 0.923880 1.60021i 0.130526 0.991445i \(-0.458333\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) 0.707107 1.22474i 0.707107 1.22474i
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0.292893 0.507306i 0.292893 0.507306i
\(395\) 1.30656 + 2.26303i 1.30656 + 2.26303i
\(396\) 0.158513 + 0.274552i 0.158513 + 0.274552i
\(397\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 1.53073 1.53073
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) −0.382683 + 0.662827i −0.382683 + 0.662827i −0.991445 0.130526i \(-0.958333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.84776 −1.84776
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(410\) −1.30656 2.26303i −1.30656 2.26303i
\(411\) 0.923880 1.60021i 0.923880 1.60021i
\(412\) −0.585786 −0.585786
\(413\) 0 0
\(414\) 0 0
\(415\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(416\) −0.382683 0.662827i −0.382683 0.662827i
\(417\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0.541196 0.937379i 0.541196 0.937379i
\(423\) −0.923880 1.60021i −0.923880 1.60021i
\(424\) 0 0
\(425\) 0 0
\(426\) −1.41421 −1.41421
\(427\) 0 0
\(428\) 0 0
\(429\) 0.382683 0.662827i 0.382683 0.662827i
\(430\) 0 0
\(431\) −0.923880 1.60021i −0.923880 1.60021i −0.793353 0.608761i \(-0.791667\pi\)
−0.130526 0.991445i \(-0.541667\pi\)
\(432\) 0.207107 0.358719i 0.207107 0.358719i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(440\) −1.53073 −1.53073
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 0 0
\(445\) −0.707107 1.22474i −0.707107 1.22474i
\(446\) 0 0
\(447\) −1.84776 −1.84776
\(448\) 0 0
\(449\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(450\) 0.923880 1.60021i 0.923880 1.60021i
\(451\) −0.707107 1.22474i −0.707107 1.22474i
\(452\) 0 0
\(453\) 0 0
\(454\) −1.41421 −1.41421
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(462\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 0.414214 0.414214
\(469\) 0 0
\(470\) 2.61313 2.61313
\(471\) 0.707107 1.22474i 0.707107 1.22474i
\(472\) −0.414214 0.717439i −0.414214 0.717439i
\(473\) 0 0
\(474\) 0.541196 0.937379i 0.541196 0.937379i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.292893 + 0.507306i −0.292893 + 0.507306i
\(479\) 0.923880 + 1.60021i 0.923880 + 1.60021i 0.793353 + 0.608761i \(0.208333\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(480\) −0.707107 1.22474i −0.707107 1.22474i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.171573 0.171573
\(485\) 0 0
\(486\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(487\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0.382683 0.662827i 0.382683 0.662827i
\(493\) 0 0
\(494\) 0 0
\(495\) 0.707107 1.22474i 0.707107 1.22474i
\(496\) 0 0
\(497\) 0 0
\(498\) 0.585786 0.585786
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −0.541196 0.937379i −0.541196 0.937379i
\(501\) −0.382683 0.662827i −0.382683 0.662827i
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.500000 0.866025i −0.500000 0.866025i
\(508\) −0.292893 0.507306i −0.292893 0.507306i
\(509\) −0.923880 + 1.60021i −0.923880 + 1.60021i −0.130526 + 0.991445i \(0.541667\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.765367 0.765367
\(513\) 0 0
\(514\) 0 0
\(515\) 1.30656 + 2.26303i 1.30656 + 2.26303i
\(516\) 0 0
\(517\) 1.41421 1.41421
\(518\) 0 0
\(519\) 0 0
\(520\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(521\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0 0
\(523\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.158513 + 0.274552i 0.158513 + 0.274552i
\(529\) −0.500000 0.866025i −0.500000 0.866025i
\(530\) 0 0
\(531\) 0.765367 0.765367
\(532\) 0 0
\(533\) −1.84776 −1.84776
\(534\) −0.292893 + 0.507306i −0.292893 + 0.507306i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0.765367 0.765367
\(541\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) −0.707107 1.22474i −0.707107 1.22474i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(548\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(549\) 0 0
\(550\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.292893 0.507306i −0.292893 0.507306i
\(557\) −0.923880 1.60021i −0.923880 1.60021i −0.793353 0.608761i \(-0.791667\pi\)
−0.130526 0.991445i \(-0.541667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(563\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(564\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 2.00000 2.00000
\(569\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(572\) −0.158513 + 0.274552i −0.158513 + 0.274552i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(577\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(578\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −0.923880 1.60021i −0.923880 1.60021i
\(586\) 0.292893 0.507306i 0.292893 0.507306i
\(587\) −1.84776 −1.84776 −0.923880 0.382683i \(-0.875000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −0.541196 + 0.937379i −0.541196 + 0.937379i
\(591\) −0.382683 0.662827i −0.382683 0.662827i
\(592\) 0 0
\(593\) 0.382683 0.662827i 0.382683 0.662827i −0.608761 0.793353i \(-0.708333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(594\) −0.585786 −0.585786
\(595\) 0 0
\(596\) 0.765367 0.765367
\(597\) 1.00000 1.73205i 1.00000 1.73205i
\(598\) 0 0
\(599\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) −1.30656 + 2.26303i −1.30656 + 2.26303i
\(601\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.382683 0.662827i −0.382683 0.662827i
\(606\) 0 0
\(607\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.923880 1.60021i 0.923880 1.60021i
\(612\) 0 0
\(613\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(614\) 0 0
\(615\) −3.41421 −3.41421
\(616\) 0 0
\(617\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(618\) 0.541196 0.937379i 0.541196 0.937379i
\(619\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0.414214 0.414214
\(625\) −1.20711 + 2.09077i −1.20711 + 2.09077i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.292893 + 0.507306i −0.292893 + 0.507306i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) −0.765367 + 1.32565i −0.765367 + 1.32565i
\(633\) −0.707107 1.22474i −0.707107 1.22474i
\(634\) −0.292893 0.507306i −0.292893 0.507306i
\(635\) −1.30656 + 2.26303i −1.30656 + 2.26303i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −0.923880 + 1.60021i −0.923880 + 1.60021i
\(640\) 0 0
\(641\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) −0.541196 0.937379i −0.541196 0.937379i
\(649\) −0.292893 + 0.507306i −0.292893 + 0.507306i
\(650\) 1.84776 1.84776
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.382683 0.662827i 0.382683 0.662827i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −0.292893 + 0.507306i −0.292893 + 0.507306i
\(661\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.828427 −0.828427
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.158513 + 0.274552i 0.158513 + 0.274552i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(674\) −0.541196 + 0.937379i −0.541196 + 0.937379i
\(675\) −1.20711 2.09077i −1.20711 2.09077i
\(676\) 0.207107 + 0.358719i 0.207107 + 0.358719i
\(677\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.923880 + 1.60021i −0.923880 + 1.60021i
\(682\) 0 0
\(683\) 0.923880 + 1.60021i 0.923880 + 1.60021i 0.793353 + 0.608761i \(0.208333\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(684\) 0 0
\(685\) 3.41421 3.41421
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.30656 + 2.26303i −1.30656 + 2.26303i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(703\) 0 0
\(704\) −0.382683 0.662827i −0.382683 0.662827i
\(705\) 1.70711 2.95680i 1.70711 2.95680i
\(706\) 0.585786 0.585786
\(707\) 0 0
\(708\) −0.317025 −0.317025
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) −1.30656 2.26303i −1.30656 2.26303i
\(711\) −0.707107 1.22474i −0.707107 1.22474i
\(712\) 0.414214 0.717439i 0.414214 0.717439i
\(713\) 0 0
\(714\) 0 0
\(715\) 1.41421 1.41421
\(716\) 0 0
\(717\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(718\) −0.292893 0.507306i −0.292893 0.507306i
\(719\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 0.765367 0.765367
\(721\) 0 0
\(722\) −0.765367 −0.765367
\(723\) 0 0
\(724\) 0.292893 + 0.507306i 0.292893 + 0.507306i
\(725\) 0 0
\(726\) −0.158513 + 0.274552i −0.158513 + 0.274552i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) −1.08239 −1.08239
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(744\) 0 0
\(745\) −1.70711 2.95680i −1.70711 2.95680i
\(746\) 0.541196 + 0.937379i 0.541196 + 0.937379i
\(747\) 0.382683 0.662827i 0.382683 0.662827i
\(748\) 0 0
\(749\) 0 0
\(750\) 2.00000 2.00000
\(751\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(752\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.923880 + 1.60021i −0.923880 + 1.60021i −0.130526 + 0.991445i \(0.541667\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(762\) 1.08239 1.08239
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.707107 1.22474i −0.707107 1.22474i
\(767\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(768\) 0.500000 0.866025i 0.500000 0.866025i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i \(-0.0416667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(781\) −0.707107 1.22474i −0.707107 1.22474i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.61313 2.61313
\(786\) 0 0
\(787\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(788\) 0.158513 + 0.274552i 0.158513 + 0.274552i
\(789\) 0 0
\(790\) 2.00000 2.00000
\(791\) 0 0
\(792\) 0.828427 0.828427
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −0.414214 + 0.717439i −0.414214 + 0.717439i
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.923880 1.60021i 0.923880 1.60021i