Properties

Label 1148.1.bj.a.1075.2
Level $1148$
Weight $1$
Character 1148.1075
Analytic conductor $0.573$
Analytic rank $0$
Dimension $8$
Projective image $S_{4}$
CM/RM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1148.bj (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.572926634503\)
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: \(S_{4}\)
Projective field: Galois closure of 4.2.13508516.2

Embedding invariants

Embedding label 1075.2
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1148.1075
Dual form 1148.1.bj.a.975.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.965926 + 0.258819i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.965926 + 0.258819i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(0.258819 + 0.965926i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-1.00000 - 1.00000i) q^{13} +(-0.965926 + 0.258819i) q^{14} +(0.707107 + 0.707107i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.258819 - 0.965926i) q^{19} -1.00000i q^{20} +1.00000i q^{21} +(-0.707107 - 0.707107i) q^{22} +(-0.965926 + 0.258819i) q^{24} +(1.36603 + 0.366025i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.707107 - 0.707107i) q^{28} +(-0.965926 - 0.258819i) q^{30} +(-1.22474 - 0.707107i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.866025 + 0.500000i) q^{33} +(0.965926 - 0.258819i) q^{35} +(0.258819 + 0.965926i) q^{38} +(0.707107 - 1.22474i) q^{39} +(0.500000 + 0.866025i) q^{40} -1.00000i q^{41} +(-0.500000 - 0.866025i) q^{42} +(0.965926 + 0.258819i) q^{44} +(0.707107 - 0.707107i) q^{48} +(0.866025 + 0.500000i) q^{49} +(-1.36603 + 0.366025i) q^{52} +(-1.36603 + 0.366025i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(0.707107 + 0.707107i) q^{55} +(-0.258819 + 0.965926i) q^{56} +1.00000 q^{57} +(1.22474 + 0.707107i) q^{59} +(0.965926 - 0.258819i) q^{60} +(-0.866025 + 0.500000i) q^{61} +1.41421 q^{62} -1.00000 q^{64} +(-1.36603 - 0.366025i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-1.93185 + 0.517638i) q^{67} +(-0.707107 + 0.707107i) q^{70} +(-0.707107 + 0.707107i) q^{71} +(-0.707107 - 0.707107i) q^{76} +1.00000i q^{77} +1.41421i q^{78} +(-0.965926 - 0.258819i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +1.41421i q^{83} +(0.866025 + 0.500000i) q^{84} +(-0.965926 + 0.258819i) q^{88} +(0.366025 - 1.36603i) q^{89} +(-0.707107 - 1.22474i) q^{91} +(0.366025 - 1.36603i) q^{93} +(-0.258819 - 0.965926i) q^{95} +(-0.258819 + 0.965926i) q^{96} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{10} - 8q^{13} - 4q^{16} + 4q^{26} + 4q^{40} - 4q^{42} - 4q^{52} - 4q^{53} + 8q^{57} - 8q^{64} - 4q^{65} + 4q^{66} - 4q^{81} + 4q^{82} - 4q^{89} - 4q^{93} - 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(3\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(4\) 0.500000 0.866025i 0.500000 0.866025i
\(5\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) −0.707107 0.707107i −0.707107 0.707107i
\(7\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(8\) 1.00000i 1.00000i
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(11\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(12\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(13\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(14\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(15\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(16\) −0.500000 0.866025i −0.500000 0.866025i
\(17\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(18\) 0 0
\(19\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(20\) 1.00000i 1.00000i
\(21\) 1.00000i 1.00000i
\(22\) −0.707107 0.707107i −0.707107 0.707107i
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(25\) 0 0
\(26\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(27\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(28\) 0.707107 0.707107i 0.707107 0.707107i
\(29\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(30\) −0.965926 0.258819i −0.965926 0.258819i
\(31\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(32\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(33\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(34\) 0 0
\(35\) 0.965926 0.258819i 0.965926 0.258819i
\(36\) 0 0
\(37\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(38\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(39\) 0.707107 1.22474i 0.707107 1.22474i
\(40\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(41\) 1.00000i 1.00000i
\(42\) −0.500000 0.866025i −0.500000 0.866025i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(48\) 0.707107 0.707107i 0.707107 0.707107i
\(49\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(53\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) −0.965926 0.258819i −0.965926 0.258819i
\(55\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(56\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(57\) 1.00000 1.00000
\(58\) 0 0
\(59\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(60\) 0.965926 0.258819i 0.965926 0.258819i
\(61\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(62\) 1.41421 1.41421
\(63\) 0 0
\(64\) −1.00000 −1.00000
\(65\) −1.36603 0.366025i −1.36603 0.366025i
\(66\) 0.500000 0.866025i 0.500000 0.866025i
\(67\) −1.93185 + 0.517638i −1.93185 + 0.517638i −0.965926 + 0.258819i \(0.916667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(71\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(72\) 0 0
\(73\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −0.707107 0.707107i −0.707107 0.707107i
\(77\) 1.00000i 1.00000i
\(78\) 1.41421i 1.41421i
\(79\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(80\) −0.866025 0.500000i −0.866025 0.500000i
\(81\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(82\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(83\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(84\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(89\) 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i \(-0.666667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(90\) 0 0
\(91\) −0.707107 1.22474i −0.707107 1.22474i
\(92\) 0 0
\(93\) 0.366025 1.36603i 0.366025 1.36603i
\(94\) 0 0
\(95\) −0.258819 0.965926i −0.258819 0.965926i
\(96\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(97\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) −1.00000 −1.00000
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(102\) 0 0
\(103\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(104\) 1.00000 1.00000i 1.00000 1.00000i
\(105\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(106\) 1.00000 1.00000i 1.00000 1.00000i
\(107\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(108\) 0.965926 0.258819i 0.965926 0.258819i
\(109\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(110\) −0.965926 0.258819i −0.965926 0.258819i
\(111\) 0 0
\(112\) −0.258819 0.965926i −0.258819 0.965926i
\(113\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.41421 −1.41421
\(119\) 0 0
\(120\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(121\) 0 0
\(122\) 0.500000 0.866025i 0.500000 0.866025i
\(123\) 0.965926 0.258819i 0.965926 0.258819i
\(124\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(125\) 1.00000i 1.00000i
\(126\) 0 0
\(127\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(128\) 0.866025 0.500000i 0.866025 0.500000i
\(129\) 0 0
\(130\) 1.36603 0.366025i 1.36603 0.366025i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 1.00000i 1.00000i
\(133\) 0.500000 0.866025i 0.500000 0.866025i
\(134\) 1.41421 1.41421i 1.41421 1.41421i
\(135\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(136\) 0 0
\(137\) 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(140\) 0.258819 0.965926i 0.258819 0.965926i
\(141\) 0 0
\(142\) 0.258819 0.965926i 0.258819 0.965926i
\(143\) 0.707107 1.22474i 0.707107 1.22474i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(148\) 0 0
\(149\) −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 0 0
\(151\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(152\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(153\) 0 0
\(154\) −0.500000 0.866025i −0.500000 0.866025i
\(155\) −1.41421 −1.41421
\(156\) −0.707107 1.22474i −0.707107 1.22474i
\(157\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(158\) 0.965926 0.258819i 0.965926 0.258819i
\(159\) −0.707107 1.22474i −0.707107 1.22474i
\(160\) 1.00000 1.00000
\(161\) 0 0
\(162\) 1.00000i 1.00000i
\(163\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(164\) −0.866025 0.500000i −0.866025 0.500000i
\(165\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(166\) −0.707107 1.22474i −0.707107 1.22474i
\(167\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) −1.00000 −1.00000
\(169\) 1.00000i 1.00000i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.707107 0.707107i 0.707107 0.707107i
\(177\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(178\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(179\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(180\) 0 0
\(181\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(182\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(183\) −0.707107 0.707107i −0.707107 0.707107i
\(184\) 0 0
\(185\) 0 0
\(186\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(187\) 0 0
\(188\) 0 0
\(189\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(190\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(191\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(192\) −0.258819 0.965926i −0.258819 0.965926i
\(193\) 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(194\) 0 0
\(195\) 1.41421i 1.41421i
\(196\) 0.866025 0.500000i 0.866025 0.500000i
\(197\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(198\) 0 0
\(199\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(200\) 0 0
\(201\) −1.00000 1.73205i −1.00000 1.73205i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.500000 0.866025i −0.500000 0.866025i
\(206\) −1.22474 0.707107i −1.22474 0.707107i
\(207\) 0 0
\(208\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(209\) 1.00000 1.00000
\(210\) −0.866025 0.500000i −0.866025 0.500000i
\(211\) −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(212\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(213\) −0.866025 0.500000i −0.866025 0.500000i
\(214\) 0.707107 1.22474i 0.707107 1.22474i
\(215\) 0 0
\(216\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(217\) −1.00000 1.00000i −1.00000 1.00000i
\(218\) 0 0
\(219\) 0 0
\(220\) 0.965926 0.258819i 0.965926 0.258819i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(225\) 0 0
\(226\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(227\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(228\) 0.500000 0.866025i 0.500000 0.866025i
\(229\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(230\) 0 0
\(231\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(232\) 0 0
\(233\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.22474 0.707107i 1.22474 0.707107i
\(237\) 1.00000i 1.00000i
\(238\) 0 0
\(239\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(240\) 0.258819 0.965926i 0.258819 0.965926i
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 1.00000i 1.00000i
\(245\) 1.00000 1.00000
\(246\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(247\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(248\) 0.707107 1.22474i 0.707107 1.22474i
\(249\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(250\) −0.500000 0.866025i −0.500000 0.866025i
\(251\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(264\) −0.500000 0.866025i −0.500000 0.866025i
\(265\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(266\) 1.00000i 1.00000i
\(267\) 1.41421 1.41421
\(268\) −0.517638 + 1.93185i −0.517638 + 1.93185i
\(269\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(270\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(271\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0 0
\(273\) 1.00000 1.00000i 1.00000 1.00000i
\(274\) −1.00000 1.00000i −1.00000 1.00000i
\(275\) 0 0
\(276\) 0 0
\(277\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(278\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(279\) 0 0
\(280\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(281\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(282\) 0 0
\(283\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(284\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(285\) 0.866025 0.500000i 0.866025 0.500000i
\(286\) 1.41421i 1.41421i
\(287\) 0.258819 0.965926i 0.258819 0.965926i
\(288\) 0 0
\(289\) 0.866025 0.500000i 0.866025 0.500000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(294\) −0.258819 0.965926i −0.258819 0.965926i
\(295\) 1.41421 1.41421
\(296\) 0 0
\(297\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(298\) 1.36603 0.366025i 1.36603 0.366025i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(305\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(309\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(310\) 1.22474 0.707107i 1.22474 0.707107i
\(311\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(312\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(313\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(317\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(318\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(319\) 0 0
\(320\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(321\) −1.00000 1.00000i −1.00000 1.00000i
\(322\) 0 0
\(323\) 0 0
\(324\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(325\) 0 0
\(326\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(327\) 0 0
\(328\) 1.00000 1.00000
\(329\) 0 0
\(330\) 1.00000i 1.00000i
\(331\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(332\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(333\) 0 0
\(334\) 0 0
\(335\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(336\) 0.866025 0.500000i 0.866025 0.500000i
\(337\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(338\) −0.500000 0.866025i −0.500000 0.866025i
\(339\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(340\) 0 0
\(341\) 0.366025 1.36603i 0.366025 1.36603i
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(344\) 0 0
\(345\) 0 0
\(346\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(347\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 1.41421i 1.41421i
\(352\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(353\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(354\) −0.366025 1.36603i −0.366025 1.36603i
\(355\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(356\) −1.00000 1.00000i −1.00000 1.00000i
\(357\) 0 0
\(358\) 0.707107 0.707107i 0.707107 0.707107i
\(359\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(363\) 0 0
\(364\) −1.41421 −1.41421
\(365\) 0 0
\(366\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(367\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.41421 −1.41421
\(372\) −1.00000 1.00000i −1.00000 1.00000i
\(373\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.866025 0.500000i −0.866025 0.500000i
\(379\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(380\) −0.965926 0.258819i −0.965926 0.258819i
\(381\) 1.36603 0.366025i 1.36603 0.366025i
\(382\) 0 0
\(383\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(384\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(385\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(386\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(387\) 0 0
\(388\) 0 0
\(389\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(390\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(391\) 0 0
\(392\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(393\) 0 0
\(394\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(395\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(396\) 0 0
\(397\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 0 0
\(399\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(400\) 0 0
\(401\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(402\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(403\) 0.517638 + 1.93185i 0.517638 + 1.93185i
\(404\) 0 0
\(405\) 1.00000i 1.00000i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(410\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(411\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(412\) 1.41421 1.41421
\(413\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(414\) 0 0
\(415\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(416\) −0.366025 1.36603i −0.366025 1.36603i
\(417\) 1.36603 0.366025i 1.36603 0.366025i
\(418\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 1.00000 1.00000
\(421\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(422\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(423\) 0 0
\(424\) −0.366025 1.36603i −0.366025 1.36603i
\(425\) 0 0
\(426\) 1.00000 1.00000
\(427\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(428\) 1.41421i 1.41421i
\(429\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(430\) 0 0
\(431\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 0.258819 0.965926i 0.258819 0.965926i
\(433\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(434\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(440\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(444\) 0 0
\(445\) −0.366025 1.36603i −0.366025 1.36603i
\(446\) 0 0
\(447\) 1.41421i 1.41421i
\(448\) −0.965926 0.258819i −0.965926 0.258819i
\(449\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(450\) 0 0
\(451\) 0.965926 0.258819i 0.965926 0.258819i
\(452\) 0.500000 0.866025i 0.500000 0.866025i
\(453\) 0 0
\(454\) 0.707107 0.707107i 0.707107 0.707107i
\(455\) −1.22474 0.707107i −1.22474 0.707107i
\(456\) 1.00000i 1.00000i
\(457\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) 0.707107 0.707107i 0.707107 0.707107i
\(463\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(464\) 0 0
\(465\) −0.366025 1.36603i −0.366025 1.36603i
\(466\) −0.366025 1.36603i −0.366025 1.36603i
\(467\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 0 0
\(469\) −2.00000 −2.00000
\(470\) 0 0
\(471\) 0 0
\(472\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(473\) 0 0
\(474\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(479\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(480\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(488\) −0.500000 0.866025i −0.500000 0.866025i
\(489\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(490\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(491\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(492\) 0.258819 0.965926i 0.258819 0.965926i
\(493\) 0 0
\(494\) 0.707107 1.22474i 0.707107 1.22474i
\(495\) 0 0
\(496\) 1.41421i 1.41421i
\(497\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(498\) 1.00000 1.00000i 1.00000 1.00000i
\(499\) 1.93185 + 0.517638i 1.93185 + 0.517638i 0.965926 + 0.258819i \(0.0833333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(500\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(501\) 0 0
\(502\) 1.22474 0.707107i 1.22474 0.707107i
\(503\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(508\) −1.22474 0.707107i −1.22474 0.707107i
\(509\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) 0.866025 0.500000i 0.866025 0.500000i
\(514\) 0 0
\(515\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(520\) 0.366025 1.36603i 0.366025 1.36603i
\(521\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 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
\(528\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(529\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(530\) 0.366025 1.36603i 0.366025 1.36603i
\(531\) 0 0
\(532\) −0.500000 0.866025i −0.500000 0.866025i
\(533\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(534\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(535\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(536\) −0.517638 1.93185i −0.517638 1.93185i
\(537\) −0.500000 0.866025i −0.500000 0.866025i
\(538\) 1.00000i 1.00000i
\(539\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(540\) 0.707107 0.707107i 0.707107 0.707107i
\(541\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) 0 0
\(543\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(544\) 0 0
\(545\) 0 0
\(546\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(547\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −0.866025 0.500000i −0.866025 0.500000i
\(554\) 1.00000i 1.00000i
\(555\) 0 0
\(556\) −1.22474 0.707107i −1.22474 0.707107i
\(557\) −0.366025 1.36603i −0.366025 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.707107 0.707107i −0.707107 0.707107i
\(561\) 0 0
\(562\) 0 0
\(563\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(564\) 0 0
\(565\) 0.866025 0.500000i 0.866025 0.500000i
\(566\) 1.41421 1.41421
\(567\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(568\) −0.707107 0.707107i −0.707107 0.707107i
\(569\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(571\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(572\) −0.707107 1.22474i −0.707107 1.22474i
\(573\) 0 0
\(574\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(575\) 0 0
\(576\) 0 0
\(577\) 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(578\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(579\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(580\) 0 0
\(581\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(582\) 0 0
\(583\) −0.707107 1.22474i −0.707107 1.22474i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(588\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(589\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(590\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(591\) 0.965926 0.258819i 0.965926 0.258819i
\(592\) 0 0
\(593\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(594\) 1.00000i 1.00000i
\(595\) 0 0
\(596\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(608\) 0.707107 0.707107i 0.707107 0.707107i
\(609\) 0 0
\(610\) 1.00000i 1.00000i
\(611\) 0 0
\(612\) 0 0
\(613\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(614\) 0 0
\(615\) 0.707107 0.707107i 0.707107 0.707107i
\(616\) −1.00000 −1.00000
\(617\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(618\) 0.366025 1.36603i 0.366025 1.36603i
\(619\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(620\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(621\) 0 0
\(622\) 0 0
\(623\) 0.707107 1.22474i 0.707107 1.22474i
\(624\) −1.41421 −1.41421
\(625\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(626\) 0 0
\(627\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(632\) 0.258819 0.965926i 0.258819 0.965926i
\(633\) 0.500000 0.866025i 0.500000 0.866025i
\(634\) 0 0
\(635\) −0.707107 1.22474i −0.707107 1.22474i
\(636\) −1.41421 −1.41421
\(637\) −0.366025 1.36603i −0.366025 1.36603i
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.500000 0.866025i
\(641\) 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(643\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(648\) −0.866025 0.500000i −0.866025 0.500000i
\(649\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(650\) 0 0
\(651\) 0.707107 1.22474i 0.707107 1.22474i
\(652\) 1.41421i 1.41421i
\(653\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(660\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(661\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.41421 −1.41421
\(665\) 1.00000i 1.00000i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0.517638 1.93185i 0.517638 1.93185i
\(671\) −0.707107 0.707107i −0.707107 0.707107i
\(672\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(673\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(674\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(675\) 0 0
\(676\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(677\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(678\) −0.707107 0.707107i −0.707107 0.707107i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.500000 0.866025i −0.500000 0.866025i
\(682\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(683\) 1.93185 0.517638i 1.93185 0.517638i 0.965926 0.258819i \(-0.0833333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(684\) 0 0
\(685\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(686\) −0.965926 0.258819i −0.965926 0.258819i
\(687\) 0 0
\(688\) 0 0
\(689\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(690\) 0 0
\(691\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(692\) 1.00000i 1.00000i
\(693\) 0 0
\(694\) 0.707107 0.707107i 0.707107 0.707107i
\(695\) −0.707107 1.22474i −0.707107 1.22474i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −1.41421 −1.41421
\(700\) 0 0
\(701\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(702\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(703\) 0 0
\(704\) −0.258819 0.965926i −0.258819 0.965926i
\(705\) 0 0
\(706\) 1.00000i 1.00000i
\(707\) 0 0
\(708\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(709\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(710\) −0.258819 0.965926i −0.258819 0.965926i
\(711\) 0 0
\(712\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(713\) 0 0
\(714\) 0 0
\(715\) 1.41421i 1.41421i
\(716\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(717\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(718\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(719\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(720\) 0 0
\(721\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(722\) 0 0
\(723\) 0 0
\(724\) −0.366025 1.36603i −0.366025 1.36603i
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) 1.22474 0.707107i 1.22474 0.707107i
\(729\) 1.00000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(733\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(734\) 1.41421i 1.41421i
\(735\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(736\) 0 0
\(737\) −1.00000 1.73205i −1.00000 1.73205i
\(738\) 0 0
\(739\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(740\) 0 0
\(741\) −1.00000 1.00000i −1.00000 1.00000i
\(742\) 1.22474 0.707107i 1.22474 0.707107i
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(745\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(746\) −0.866025 0.500000i −0.866025 0.500000i
\(747\) 0 0
\(748\) 0 0
\(749\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(750\) 0.707107 0.707107i 0.707107 0.707107i
\(751\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(752\) 0 0
\(753\) −0.366025 1.36603i −0.366025 1.36603i
\(754\) 0 0
\(755\) 0 0
\(756\) 1.00000 1.00000
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) −0.707107 1.22474i −0.707107 1.22474i
\(759\) 0 0
\(760\) 0.965926 0.258819i 0.965926 0.258819i
\(761\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(767\) −0.517638 1.93185i −0.517638 1.93185i
\(768\) −0.965926 0.258819i −0.965926 0.258819i
\(769\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) −0.866025 0.500000i −0.866025 0.500000i
\(771\) 0 0
\(772\) 0.366025 1.36603i 0.366025 1.36603i
\(773\) 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −1.00000 −1.00000
\(779\) −0.965926 0.258819i −0.965926 0.258819i
\(780\) −1.22474 0.707107i −1.22474 0.707107i
\(781\) −0.866025 0.500000i −0.866025 0.500000i
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000i 1.00000i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(788\) −0.866025 0.500000i −0.866025 0.500000i
\(789\) 0 0
\(790\) 0.707107 0.707107i 0.707107 0.707107i
\(791\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(792\) 0 0