Properties

Label 1575.1.cb.a.718.2
Level $1575$
Weight $1$
Character 1575.718
Analytic conductor $0.786$
Analytic rank $0$
Dimension $8$
Projective image $A_{4}$
CM/RM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1575.cb (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.786027394897\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(A_{4}\)
Projective field Galois closure of 4.0.99225.1

Embedding invariants

Embedding label 718.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1575.718
Dual form 1575.1.cb.a.1507.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.500000 + 0.866025i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.500000 + 0.866025i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.258819 - 0.965926i) q^{13} +(0.866025 - 0.500000i) q^{14} +1.00000 q^{16} +(0.258819 + 0.965926i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-0.866025 + 0.500000i) q^{19} +(-0.500000 + 0.866025i) q^{21} +(-0.866025 + 0.500000i) q^{24} +(-0.500000 - 0.866025i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.866025 - 0.500000i) q^{29} -1.00000 q^{31} +(0.866025 + 0.500000i) q^{34} +(0.965926 + 0.258819i) q^{37} +(-0.258819 + 0.965926i) q^{38} +(0.866025 + 0.500000i) q^{39} +(-0.500000 - 0.866025i) q^{41} +(0.258819 + 0.965926i) q^{42} +(0.965926 - 0.258819i) q^{43} +(-0.707107 + 0.707107i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(0.866025 + 0.500000i) q^{49} -1.00000 q^{51} +(0.965926 - 0.258819i) q^{53} -1.00000i q^{54} +(0.500000 + 0.866025i) q^{56} +(-0.258819 - 0.965926i) q^{57} +(-0.965926 + 0.258819i) q^{58} +1.00000i q^{59} +1.00000 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-0.707107 - 0.707107i) q^{63} +1.00000i q^{64} +(0.707107 - 0.707107i) q^{67} -2.00000 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-0.965926 + 0.258819i) q^{73} +(0.866025 - 0.500000i) q^{74} +(0.965926 - 0.258819i) q^{78} -1.00000i q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.965926 - 0.258819i) q^{82} +(-0.965926 + 0.258819i) q^{83} +(0.500000 - 0.866025i) q^{86} +(0.707107 - 0.707107i) q^{87} +(0.866025 - 0.500000i) q^{89} +(0.500000 - 0.866025i) q^{91} +(0.258819 - 0.965926i) q^{93} +1.00000i q^{94} +(-0.258819 - 0.965926i) q^{97} +(0.965926 - 0.258819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{6} + O(q^{10}) \) \( 8q + 4q^{6} + 8q^{16} - 4q^{21} - 4q^{26} - 8q^{31} - 4q^{41} - 8q^{51} + 4q^{56} + 8q^{61} - 16q^{71} + 4q^{81} + 4q^{86} + 4q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(1226\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(3\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(4\) 0 0
\(5\) 0 0
\(6\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(7\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(8\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(9\) −0.866025 0.500000i −0.866025 0.500000i
\(10\) 0 0
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(14\) 0.866025 0.500000i 0.866025 0.500000i
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(19\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(20\) 0 0
\(21\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(22\) 0 0
\(23\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(24\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(25\) 0 0
\(26\) −0.500000 0.866025i −0.500000 0.866025i
\(27\) 0.707107 0.707107i 0.707107 0.707107i
\(28\) 0 0
\(29\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 0 0
\(31\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(38\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(39\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(40\) 0 0
\(41\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(42\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(43\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(48\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(49\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(50\) 0 0
\(51\) −1.00000 −1.00000
\(52\) 0 0
\(53\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) 1.00000i 1.00000i
\(55\) 0 0
\(56\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(57\) −0.258819 0.965926i −0.258819 0.965926i
\(58\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(59\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(63\) −0.707107 0.707107i −0.707107 0.707107i
\(64\) 1.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(72\) −0.258819 0.965926i −0.258819 0.965926i
\(73\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(74\) 0.866025 0.500000i 0.866025 0.500000i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0.965926 0.258819i 0.965926 0.258819i
\(79\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(82\) −0.965926 0.258819i −0.965926 0.258819i
\(83\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.500000 0.866025i 0.500000 0.866025i
\(87\) 0.707107 0.707107i 0.707107 0.707107i
\(88\) 0 0
\(89\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) 0.500000 0.866025i 0.500000 0.866025i
\(92\) 0 0
\(93\) 0.258819 0.965926i 0.258819 0.965926i
\(94\) 1.00000i 1.00000i
\(95\) 0 0
\(96\) 0 0
\(97\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(98\) 0.965926 0.258819i 0.965926 0.258819i
\(99\) 0 0
\(100\) 0 0
\(101\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(102\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(103\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(104\) 0.866025 0.500000i 0.866025 0.500000i
\(105\) 0 0
\(106\) 0.500000 0.866025i 0.500000 0.866025i
\(107\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(108\) 0 0
\(109\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(110\) 0 0
\(111\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(112\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(113\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(114\) −0.866025 0.500000i −0.866025 0.500000i
\(115\) 0 0
\(116\) 0 0
\(117\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(118\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(119\) 1.00000i 1.00000i
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.500000 0.866025i
\(122\) 0.707107 0.707107i 0.707107 0.707107i
\(123\) 0.965926 0.258819i 0.965926 0.258819i
\(124\) 0 0
\(125\) 0 0
\(126\) −1.00000 −1.00000
\(127\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(128\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(129\) 1.00000i 1.00000i
\(130\) 0 0
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 0 0
\(133\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(134\) 1.00000i 1.00000i
\(135\) 0 0
\(136\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(137\) −1.93185 0.517638i −1.93185 0.517638i −0.965926 0.258819i \(-0.916667\pi\)
−0.965926 0.258819i \(-0.916667\pi\)
\(138\) 0 0
\(139\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(140\) 0 0
\(141\) −0.500000 0.866025i −0.500000 0.866025i
\(142\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(143\) 0 0
\(144\) −0.866025 0.500000i −0.866025 0.500000i
\(145\) 0 0
\(146\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(147\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(148\) 0 0
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0 0
\(151\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(152\) −0.965926 0.258819i −0.965926 0.258819i
\(153\) 0.258819 0.965926i 0.258819 0.965926i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(158\) −0.707107 0.707107i −0.707107 0.707107i
\(159\) 1.00000i 1.00000i
\(160\) 0 0
\(161\) 0 0
\(162\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(163\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(167\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(168\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(169\) 0 0
\(170\) 0 0
\(171\) 1.00000 1.00000
\(172\) 0 0
\(173\) −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(174\) 1.00000i 1.00000i
\(175\) 0 0
\(176\) 0 0
\(177\) −0.965926 0.258819i −0.965926 0.258819i
\(178\) 0.258819 0.965926i 0.258819 0.965926i
\(179\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) −0.258819 0.965926i −0.258819 0.965926i
\(183\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(184\) 0 0
\(185\) 0 0
\(186\) −0.500000 0.866025i −0.500000 0.866025i
\(187\) 0 0
\(188\) 0 0
\(189\) 0.866025 0.500000i 0.866025 0.500000i
\(190\) 0 0
\(191\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −0.965926 0.258819i −0.965926 0.258819i
\(193\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(194\) −0.866025 0.500000i −0.866025 0.500000i
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 0 0
\(199\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 0 0
\(201\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(202\) −1.93185 0.517638i −1.93185 0.517638i
\(203\) −0.707107 0.707107i −0.707107 0.707107i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0.258819 0.965926i 0.258819 0.965926i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) 0.517638 1.93185i 0.517638 1.93185i
\(214\) 0.866025 0.500000i 0.866025 0.500000i
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) −0.965926 0.258819i −0.965926 0.258819i
\(218\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(219\) 1.00000i 1.00000i
\(220\) 0 0
\(221\) 1.00000 1.00000
\(222\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(223\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.500000 0.866025i −0.500000 0.866025i
\(227\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(228\) 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
\(232\) −0.258819 0.965926i −0.258819 0.965926i
\(233\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(234\) 1.00000i 1.00000i
\(235\) 0 0
\(236\) 0 0
\(237\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(238\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(239\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(240\) 0 0
\(241\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(242\) −0.258819 0.965926i −0.258819 0.965926i
\(243\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.500000 0.866025i 0.500000 0.866025i
\(247\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(248\) −0.707107 0.707107i −0.707107 0.707107i
\(249\) 1.00000i 1.00000i
\(250\) 0 0
\(251\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(258\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(259\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(260\) 0 0
\(261\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(262\) 0 0
\(263\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(267\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(268\) 0 0
\(269\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(270\) 0 0
\(271\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(273\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(274\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(278\) 0.258819 0.965926i 0.258819 0.965926i
\(279\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(280\) 0 0
\(281\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(282\) −0.965926 0.258819i −0.965926 0.258819i
\(283\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.258819 0.965926i −0.258819 0.965926i
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 1.00000 1.00000
\(292\) 0 0
\(293\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(294\) 1.00000i 1.00000i
\(295\) 0 0
\(296\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 1.00000 1.00000
\(302\) 0 0
\(303\) 1.93185 0.517638i 1.93185 0.517638i
\(304\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(305\) 0 0
\(306\) −0.500000 0.866025i −0.500000 0.866025i
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(313\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(314\) 1.00000i 1.00000i
\(315\) 0 0
\(316\) 0 0
\(317\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(318\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(319\) 0 0
\(320\) 0 0
\(321\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(322\) 0 0
\(323\) −0.707107 0.707107i −0.707107 0.707107i
\(324\) 0 0
\(325\) 0 0
\(326\) −0.500000 0.866025i −0.500000 0.866025i
\(327\) 0.707107 0.707107i 0.707107 0.707107i
\(328\) 0.258819 0.965926i 0.258819 0.965926i
\(329\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(330\) 0 0
\(331\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) −0.707107 0.707107i −0.707107 0.707107i
\(334\) 0.866025 0.500000i 0.866025 0.500000i
\(335\) 0 0
\(336\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(337\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(338\) 0 0
\(339\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.707107 0.707107i 0.707107 0.707107i
\(343\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(344\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(345\) 0 0
\(346\) −1.00000 −1.00000
\(347\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(348\) 0 0
\(349\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(350\) 0 0
\(351\) −0.500000 0.866025i −0.500000 0.866025i
\(352\) 0 0
\(353\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(354\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(355\) 0 0
\(356\) 0 0
\(357\) −0.965926 0.258819i −0.965926 0.258819i
\(358\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(359\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(367\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(368\) 0 0
\(369\) 1.00000i 1.00000i
\(370\) 0 0
\(371\) 1.00000 1.00000
\(372\) 0 0
\(373\) −1.93185 + 0.517638i −1.93185 + 0.517638i −0.965926 + 0.258819i \(0.916667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.00000 −1.00000
\(377\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(378\) 0.258819 0.965926i 0.258819 0.965926i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.707107 0.707107i 0.707107 0.707107i
\(383\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(384\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(385\) 0 0
\(386\) 1.00000 1.00000
\(387\) −0.965926 0.258819i −0.965926 0.258819i
\(388\) 0 0
\(389\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(398\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(399\) 1.00000i 1.00000i
\(400\) 0 0
\(401\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(402\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(403\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(404\) 0 0
\(405\) 0 0
\(406\) −1.00000 −1.00000
\(407\) 0 0
\(408\) −0.707107 0.707107i −0.707107 0.707107i
\(409\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(410\) 0 0
\(411\) 1.00000 1.73205i 1.00000 1.73205i
\(412\) 0 0
\(413\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(418\) 0 0
\(419\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(420\) 0 0
\(421\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(422\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(423\) 0.965926 0.258819i 0.965926 0.258819i
\(424\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(425\) 0 0
\(426\) −1.00000 1.73205i −1.00000 1.73205i
\(427\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(432\) 0.707107 0.707107i 0.707107 0.707107i
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.707107 0.707107i −0.707107 0.707107i
\(439\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(440\) 0 0
\(441\) −0.500000 0.866025i −0.500000 0.866025i
\(442\) 0.707107 0.707107i 0.707107 0.707107i
\(443\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(447\) 0 0
\(448\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0.500000 0.866025i 0.500000 0.866025i
\(457\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(458\) 0 0
\(459\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(460\) 0 0
\(461\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(462\) 0 0
\(463\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(464\) −0.866025 0.500000i −0.866025 0.500000i
\(465\) 0 0
\(466\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(467\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(468\) 0 0
\(469\) 0.866025 0.500000i 0.866025 0.500000i
\(470\) 0 0
\(471\) −0.500000 0.866025i −0.500000 0.866025i
\(472\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(473\) 0 0
\(474\) 0.866025 0.500000i 0.866025 0.500000i
\(475\) 0 0
\(476\) 0 0
\(477\) −0.965926 0.258819i −0.965926 0.258819i
\(478\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0 0
\(481\) 0.500000 0.866025i 0.500000 0.866025i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(487\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(488\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(489\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(490\) 0 0
\(491\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 0.258819 0.965926i 0.258819 0.965926i
\(494\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(495\) 0 0
\(496\) −1.00000 −1.00000
\(497\) −1.93185 0.517638i −1.93185 0.517638i
\(498\) −0.707107 0.707107i −0.707107 0.707107i
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(502\) 1.41421 1.41421i 1.41421 1.41421i
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 1.00000i 1.00000i
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) −1.00000 −1.00000
\(512\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(513\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0.965926 0.258819i 0.965926 0.258819i
\(519\) 0.866025 0.500000i 0.866025 0.500000i
\(520\) 0 0
\(521\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(522\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(523\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.258819 0.965926i −0.258819 0.965926i
\(528\) 0 0
\(529\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(530\) 0 0
\(531\) 0.500000 0.866025i 0.500000 0.866025i
\(532\) 0 0
\(533\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(534\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(535\) 0 0
\(536\) 1.00000 1.00000
\(537\) 0.707107 0.707107i 0.707107 0.707107i
\(538\) 0.965926 0.258819i 0.965926 0.258819i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(-1.00000\pi\)
\(542\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 1.00000 1.00000
\(547\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) 0 0
\(549\) −0.866025 0.500000i −0.866025 0.500000i
\(550\) 0 0
\(551\) 1.00000 1.00000
\(552\) 0 0
\(553\) 0.258819 0.965926i 0.258819 0.965926i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 0.965926 0.258819i 0.965926 0.258819i
\(559\) 1.00000i 1.00000i
\(560\) 0 0
\(561\) 0 0
\(562\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(563\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.00000 1.00000
\(567\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(568\) −1.41421 1.41421i −1.41421 1.41421i
\(569\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(570\) 0 0
\(571\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(574\) −0.866025 0.500000i −0.866025 0.500000i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.500000 0.866025i
\(577\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(578\) 0 0
\(579\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(580\) 0 0
\(581\) −1.00000 −1.00000
\(582\) 0.707107 0.707107i 0.707107 0.707107i
\(583\) 0 0
\(584\) −0.866025 0.500000i −0.866025 0.500000i
\(585\) 0 0
\(586\) −0.500000 0.866025i −0.500000 0.866025i
\(587\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 0 0
\(589\) 0.866025 0.500000i 0.866025 0.500000i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(593\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.707107 0.707107i 0.707107 0.707107i
\(598\) 0 0
\(599\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 0 0
\(601\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(602\) 0.707107 0.707107i 0.707107 0.707107i
\(603\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(604\) 0 0
\(605\) 0 0
\(606\) 1.00000 1.73205i 1.00000 1.73205i
\(607\) −0.517638 1.93185i −0.517638 1.93185i −0.258819 0.965926i \(-0.583333\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(608\) 0 0
\(609\) 0.866025 0.500000i 0.866025 0.500000i
\(610\) 0 0
\(611\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(612\) 0 0
\(613\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(618\) 0 0
\(619\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(623\) 0.965926 0.258819i 0.965926 0.258819i
\(624\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(625\) 0 0
\(626\) 1.00000 1.00000
\(627\) 0 0
\(628\) 0 0
\(629\) 1.00000i 1.00000i
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0.707107 0.707107i 0.707107 0.707107i
\(633\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(634\) 1.00000i 1.00000i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.707107 0.707107i 0.707107 0.707107i
\(638\) 0 0
\(639\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(640\) 0 0
\(641\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(642\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(643\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.00000 −1.00000
\(647\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(649\) 0 0
\(650\) 0 0
\(651\) 0.500000 0.866025i 0.500000 0.866025i
\(652\) 0 0
\(653\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(654\) 1.00000i 1.00000i
\(655\) 0 0
\(656\) −0.500000 0.866025i −0.500000 0.866025i
\(657\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(658\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(659\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) 0 0
\(661\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(663\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(664\) −0.866025 0.500000i −0.866025 0.500000i
\(665\) 0 0
\(666\) −1.00000 −1.00000
\(667\) 0 0
\(668\) 0 0
\(669\) 1.00000i 1.00000i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(674\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(675\) 0 0
\(676\) 0 0
\(677\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(678\) 0.965926 0.258819i 0.965926 0.258819i
\(679\) 1.00000i 1.00000i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 1.00000
\(687\) 0 0
\(688\) 0.965926 0.258819i 0.965926 0.258819i
\(689\) 1.00000i 1.00000i
\(690\) 0 0
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.00000i 1.00000i
\(695\) 0 0
\(696\) 1.00000 1.00000
\(697\) 0.707107 0.707107i 0.707107 0.707107i
\(698\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(699\) −0.866025 0.500000i −0.866025 0.500000i
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −0.965926 0.258819i −0.965926 0.258819i
\(703\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.517638 1.93185i −0.517638 1.93185i
\(708\) 0 0
\(709\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(710\) 0 0
\(711\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(712\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(713\) 0 0
\(714\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(715\) 0 0
\(716\) 0 0
\(717\) −0.258819 0.965926i −0.258819 0.965926i
\(718\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(719\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 1.00000 1.00000
\(727\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(728\) 0.965926 0.258819i 0.965926 0.258819i
\(729\) 1.00000i 1.00000i
\(730\) 0 0
\(731\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(732\) 0 0
\(733\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(739\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.500000\pi\)
\(740\) 0 0
\(741\) −1.00000 −1.00000
\(742\) 0.707107 0.707107i 0.707107 0.707107i
\(743\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(744\) 0.866025 0.500000i 0.866025 0.500000i
\(745\) 0 0
\(746\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(747\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(748\) 0 0
\(749\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(750\) 0 0
\(751\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(752\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(753\) −0.517638 + 1.93185i −0.517638 + 1.93185i
\(754\) 1.00000i 1.00000i
\(755\) 0 0
\(756\) 0 0
\(757\) −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i \(0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) 0 0
\(763\) −0.707107 0.707107i −0.707107 0.707107i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(768\) 0 0
\(769\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(774\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(775\) 0 0
\(776\) 0.500000 0.866025i 0.500000 0.866025i
\(777\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(778\) 0 0
\(779\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(784\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0.500000 0.866025i 0.500000 0.866025i
\(792\) 0 0
\(793\) 0.258819 0.965926i 0.258819 0.965926i
\(794\) 0.866025 0.500000i 0.866025 0.500000i
\(795\) 0 0
\(796\) 0 0
\(797\) −0.965926 0.258819i −0.965926