Properties

Label 648.1.bf.a.619.1
Level $648$
Weight $1$
Character 648.619
Analytic conductor $0.323$
Analytic rank $0$
Dimension $18$
Projective image $D_{27}$
CM discriminant -8
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 648.bf (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.323394128186\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\Q(\zeta_{54})\)
Defining polynomial: \(x^{18} - x^{9} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{27}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{27} + \cdots)\)

Embedding invariants

Embedding label 619.1
Root \(0.686242 - 0.727374i\) of defining polynomial
Character \(\chi\) \(=\) 648.619
Dual form 648.1.bf.a.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.835488 - 0.549509i) q^{2} +(0.973045 + 0.230616i) q^{3} +(0.396080 + 0.918216i) q^{4} +(-0.686242 - 0.727374i) q^{6} +(0.173648 - 0.984808i) q^{8} +(0.893633 + 0.448799i) q^{9} +O(q^{10})\) \(q+(-0.835488 - 0.549509i) q^{2} +(0.973045 + 0.230616i) q^{3} +(0.396080 + 0.918216i) q^{4} +(-0.686242 - 0.727374i) q^{6} +(0.173648 - 0.984808i) q^{8} +(0.893633 + 0.448799i) q^{9} +(-0.227194 - 0.758881i) q^{11} +(0.173648 + 0.984808i) q^{12} +(-0.686242 + 0.727374i) q^{16} +(0.109277 + 0.0397734i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.539014 - 0.196185i) q^{19} +(-0.227194 + 0.758881i) q^{22} +(0.396080 - 0.918216i) q^{24} +(-0.0581448 + 0.998308i) q^{25} +(0.766044 + 0.642788i) q^{27} +(0.973045 - 0.230616i) q^{32} +(-0.0460600 - 0.790819i) q^{33} +(-0.0694434 - 0.0932786i) q^{34} +(-0.0581448 + 0.998308i) q^{36} +(-0.558145 - 0.132283i) q^{38} +(-1.62593 + 1.06939i) q^{41} +(-1.62593 - 0.385353i) q^{43} +(0.606829 - 0.509190i) q^{44} +(-0.835488 + 0.549509i) q^{48} +(0.973045 - 0.230616i) q^{49} +(0.597159 - 0.802123i) q^{50} +(0.0971586 + 0.0639022i) q^{51} +(-0.286803 - 0.957990i) q^{54} +(0.569728 - 0.0665916i) q^{57} +(0.393633 - 1.31482i) q^{59} +(-0.939693 - 0.342020i) q^{64} +(-0.396080 + 0.686030i) q^{66} +(-1.77518 - 0.891529i) q^{67} +(0.00676164 + 0.116093i) q^{68} +(0.597159 - 0.802123i) q^{72} +(0.310355 - 1.76011i) q^{73} +(-0.286803 + 0.957990i) q^{75} +(0.393633 + 0.417226i) q^{76} +(0.597159 + 0.802123i) q^{81} +1.94609 q^{82} +(-1.28004 - 0.841897i) q^{83} +(1.14669 + 1.21542i) q^{86} +(-0.786803 + 0.0919641i) q^{88} +(-0.326352 + 1.85083i) q^{89} +1.00000 q^{96} +(-0.819590 + 0.868715i) q^{97} +(-0.939693 - 0.342020i) q^{98} +(0.137557 - 0.780125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + O(q^{10}) \) \( 18q - 9q^{18} - 9q^{38} - 9q^{51} - 9q^{59} + 18q^{68} - 9q^{76} - 9q^{88} - 9q^{89} + 18q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.835488 0.549509i −0.835488 0.549509i
\(3\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(4\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(5\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(6\) −0.686242 0.727374i −0.686242 0.727374i
\(7\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(8\) 0.173648 0.984808i 0.173648 0.984808i
\(9\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(10\) 0 0
\(11\) −0.227194 0.758881i −0.227194 0.758881i −0.993238 0.116093i \(-0.962963\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(12\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(13\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(17\) 0.109277 + 0.0397734i 0.109277 + 0.0397734i 0.396080 0.918216i \(-0.370370\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(18\) −0.500000 0.866025i −0.500000 0.866025i
\(19\) 0.539014 0.196185i 0.539014 0.196185i −0.0581448 0.998308i \(-0.518519\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.227194 + 0.758881i −0.227194 + 0.758881i
\(23\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(24\) 0.396080 0.918216i 0.396080 0.918216i
\(25\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(26\) 0 0
\(27\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(28\) 0 0
\(29\) 0 0 0.893633 0.448799i \(-0.148148\pi\)
−0.893633 + 0.448799i \(0.851852\pi\)
\(30\) 0 0
\(31\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(32\) 0.973045 0.230616i 0.973045 0.230616i
\(33\) −0.0460600 0.790819i −0.0460600 0.790819i
\(34\) −0.0694434 0.0932786i −0.0694434 0.0932786i
\(35\) 0 0
\(36\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(37\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(38\) −0.558145 0.132283i −0.558145 0.132283i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.62593 + 1.06939i −1.62593 + 1.06939i −0.686242 + 0.727374i \(0.740741\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(42\) 0 0
\(43\) −1.62593 0.385353i −1.62593 0.385353i −0.686242 0.727374i \(-0.740741\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(44\) 0.606829 0.509190i 0.606829 0.509190i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.597159 0.802123i \(-0.703704\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(48\) −0.835488 + 0.549509i −0.835488 + 0.549509i
\(49\) 0.973045 0.230616i 0.973045 0.230616i
\(50\) 0.597159 0.802123i 0.597159 0.802123i
\(51\) 0.0971586 + 0.0639022i 0.0971586 + 0.0639022i
\(52\) 0 0
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −0.286803 0.957990i −0.286803 0.957990i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.569728 0.0665916i 0.569728 0.0665916i
\(58\) 0 0
\(59\) 0.393633 1.31482i 0.393633 1.31482i −0.500000 0.866025i \(-0.666667\pi\)
0.893633 0.448799i \(-0.148148\pi\)
\(60\) 0 0
\(61\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.939693 0.342020i −0.939693 0.342020i
\(65\) 0 0
\(66\) −0.396080 + 0.686030i −0.396080 + 0.686030i
\(67\) −1.77518 0.891529i −1.77518 0.891529i −0.939693 0.342020i \(-0.888889\pi\)
−0.835488 0.549509i \(-0.814815\pi\)
\(68\) 0.00676164 + 0.116093i 0.00676164 + 0.116093i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(72\) 0.597159 0.802123i 0.597159 0.802123i
\(73\) 0.310355 1.76011i 0.310355 1.76011i −0.286803 0.957990i \(-0.592593\pi\)
0.597159 0.802123i \(-0.296296\pi\)
\(74\) 0 0
\(75\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(76\) 0.393633 + 0.417226i 0.393633 + 0.417226i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(80\) 0 0
\(81\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(82\) 1.94609 1.94609
\(83\) −1.28004 0.841897i −1.28004 0.841897i −0.286803 0.957990i \(-0.592593\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.14669 + 1.21542i 1.14669 + 1.21542i
\(87\) 0 0
\(88\) −0.786803 + 0.0919641i −0.786803 + 0.0919641i
\(89\) −0.326352 + 1.85083i −0.326352 + 1.85083i 0.173648 + 0.984808i \(0.444444\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.00000 1.00000
\(97\) −0.819590 + 0.868715i −0.819590 + 0.868715i −0.993238 0.116093i \(-0.962963\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(98\) −0.939693 0.342020i −0.939693 0.342020i
\(99\) 0.137557 0.780125i 0.137557 0.780125i
\(100\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(101\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(102\) −0.0460600 0.106779i −0.0460600 0.106779i
\(103\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.893633 + 1.54782i −0.893633 + 1.54782i −0.0581448 + 0.998308i \(0.518519\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(108\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.337935 0.0800921i 0.337935 0.0800921i −0.0581448 0.998308i \(-0.518519\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(114\) −0.512593 0.257434i −0.512593 0.257434i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.05138 + 0.882215i −1.05138 + 0.882215i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.311205 0.204683i 0.311205 0.204683i
\(122\) 0 0
\(123\) −1.82873 + 0.665602i −1.82873 + 0.665602i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(128\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(129\) −1.49324 0.749932i −1.49324 0.749932i
\(130\) 0 0
\(131\) 0.207391 0.278574i 0.207391 0.278574i −0.686242 0.727374i \(-0.740741\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(132\) 0.707900 0.355521i 0.707900 0.355521i
\(133\) 0 0
\(134\) 0.993238 + 1.72034i 0.993238 + 1.72034i
\(135\) 0 0
\(136\) 0.0581448 0.100710i 0.0581448 0.100710i
\(137\) −0.0694434 + 1.19230i −0.0694434 + 1.19230i 0.766044 + 0.642788i \(0.222222\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(138\) 0 0
\(139\) −1.18624 0.138652i −1.18624 0.138652i −0.500000 0.866025i \(-0.666667\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(145\) 0 0
\(146\) −1.22650 + 1.30001i −1.22650 + 1.30001i
\(147\) 1.00000 1.00000
\(148\) 0 0
\(149\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(150\) 0.766044 0.642788i 0.766044 0.642788i
\(151\) 0 0 −0.286803 0.957990i \(-0.592593\pi\)
0.286803 + 0.957990i \(0.407407\pi\)
\(152\) −0.0996057 0.564892i −0.0996057 0.564892i
\(153\) 0.0798028 + 0.0845860i 0.0798028 + 0.0845860i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.0581448 0.998308i −0.0581448 0.998308i
\(163\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(164\) −1.62593 1.06939i −1.62593 1.06939i
\(165\) 0 0
\(166\) 0.606829 + 1.40679i 0.606829 + 1.40679i
\(167\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(168\) 0 0
\(169\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(170\) 0 0
\(171\) 0.569728 + 0.0665916i 0.569728 + 0.0665916i
\(172\) −0.290162 1.64559i −0.290162 1.64559i
\(173\) 0 0 −0.286803 0.957990i \(-0.592593\pi\)
0.286803 + 0.957990i \(0.407407\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.707900 + 0.355521i 0.707900 + 0.355521i
\(177\) 0.686242 1.18861i 0.686242 1.18861i
\(178\) 1.28971 1.36702i 1.28971 1.36702i
\(179\) 1.76604 + 0.642788i 1.76604 + 0.642788i 1.00000 \(0\)
0.766044 + 0.642788i \(0.222222\pi\)
\(180\) 0 0
\(181\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.00535630 0.0919641i 0.00535630 0.0919641i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.893633 0.448799i \(-0.148148\pi\)
−0.893633 + 0.448799i \(0.851852\pi\)
\(192\) −0.835488 0.549509i −0.835488 0.549509i
\(193\) 1.16212 1.56100i 1.16212 1.56100i 0.396080 0.918216i \(-0.370370\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(194\) 1.16212 0.275428i 1.16212 0.275428i
\(195\) 0 0
\(196\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(197\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(198\) −0.543613 + 0.576196i −0.543613 + 0.576196i
\(199\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(200\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(201\) −1.52173 1.27688i −1.52173 1.27688i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.0201935 + 0.114523i −0.0201935 + 0.114523i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.271342 0.364475i −0.271342 0.364475i
\(210\) 0 0
\(211\) 1.49079 0.353324i 1.49079 0.353324i 0.597159 0.802123i \(-0.296296\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.59716 0.802123i 1.59716 0.802123i
\(215\) 0 0
\(216\) 0.766044 0.642788i 0.766044 0.642788i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.707900 1.64110i 0.707900 1.64110i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(224\) 0 0
\(225\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(226\) −0.326352 0.118782i −0.326352 0.118782i
\(227\) 1.14669 1.21542i 1.14669 1.21542i 0.173648 0.984808i \(-0.444444\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(228\) 0.286803 + 0.496758i 0.286803 + 0.496758i
\(229\) 0 0 −0.893633 0.448799i \(-0.851852\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.238329 1.35163i −0.238329 1.35163i −0.835488 0.549509i \(-0.814815\pi\)
0.597159 0.802123i \(-0.296296\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.36320 0.159336i 1.36320 0.159336i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.396080 0.918216i \(-0.629630\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(240\) 0 0
\(241\) 1.65968 + 1.09159i 1.65968 + 1.09159i 0.893633 + 0.448799i \(0.148148\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(242\) −0.372483 −0.372483
\(243\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.89363 + 0.448799i 1.89363 + 0.448799i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.05138 1.11440i −1.05138 1.11440i
\(250\) 0 0
\(251\) −0.290162 + 1.64559i −0.290162 + 1.64559i 0.396080 + 0.918216i \(0.370370\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.0581448 0.998308i −0.0581448 0.998308i
\(257\) −1.77518 0.891529i −1.77518 0.891529i −0.939693 0.342020i \(-0.888889\pi\)
−0.835488 0.549509i \(-0.814815\pi\)
\(258\) 0.835488 + 1.44711i 0.835488 + 1.44711i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.326352 + 0.118782i −0.326352 + 0.118782i
\(263\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(264\) −0.786803 0.0919641i −0.786803 0.0919641i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.744386 + 1.72568i −0.744386 + 1.72568i
\(268\) 0.115503 1.98312i 0.115503 1.98312i
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) −0.103920 + 0.0521907i −0.103920 + 0.0521907i
\(273\) 0 0
\(274\) 0.713197 0.957990i 0.713197 0.957990i
\(275\) 0.770807 0.182685i 0.770807 0.182685i
\(276\) 0 0
\(277\) 0 0 −0.597159 0.802123i \(-0.703704\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(278\) 0.914900 + 0.767692i 0.914900 + 0.767692i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.49079 + 0.353324i 1.49079 + 0.353324i 0.893633 0.448799i \(-0.148148\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(282\) 0 0
\(283\) −1.28004 + 0.841897i −1.28004 + 0.841897i −0.993238 0.116093i \(-0.962963\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(289\) −0.755685 0.634095i −0.755685 0.634095i
\(290\) 0 0
\(291\) −0.997837 + 0.656288i −0.997837 + 0.656288i
\(292\) 1.73909 0.412172i 1.73909 0.412172i
\(293\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(294\) −0.835488 0.549509i −0.835488 0.549509i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.313758 0.727374i 0.313758 0.727374i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.227194 + 0.526695i −0.227194 + 0.526695i
\(305\) 0 0
\(306\) −0.0201935 0.114523i −0.0201935 0.114523i
\(307\) 1.28971 + 0.469417i 1.28971 + 0.469417i 0.893633 0.448799i \(-0.148148\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(312\) 0 0
\(313\) −0.558145 1.86433i −0.558145 1.86433i −0.500000 0.866025i \(-0.666667\pi\)
−0.0581448 0.998308i \(-0.518519\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −1.22650 + 1.30001i −1.22650 + 1.30001i
\(322\) 0 0
\(323\) 0.0667045 0.0667045
\(324\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(325\) 0 0
\(326\) −0.290162 0.190842i −0.290162 0.190842i
\(327\) 0 0
\(328\) 0.770807 + 1.78693i 0.770807 + 1.78693i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.86668 0.218183i 1.86668 0.218183i 0.893633 0.448799i \(-0.148148\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(332\) 0.266044 1.50881i 0.266044 1.50881i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.0971586 + 1.66815i 0.0971586 + 1.66815i 0.597159 + 0.802123i \(0.296296\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(339\) 0.347296 0.347296
\(340\) 0 0
\(341\) 0 0
\(342\) −0.439408 0.368707i −0.439408 0.368707i
\(343\) 0 0
\(344\) −0.661840 + 1.53432i −0.661840 + 1.53432i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.569728 + 0.0665916i 0.569728 + 0.0665916i 0.396080 0.918216i \(-0.370370\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(348\) 0 0
\(349\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.396080 0.686030i −0.396080 0.686030i
\(353\) 1.59716 0.802123i 1.59716 0.802123i 0.597159 0.802123i \(-0.296296\pi\)
1.00000 \(0\)
\(354\) −1.22650 + 0.615969i −1.22650 + 0.615969i
\(355\) 0 0
\(356\) −1.82873 + 0.433416i −1.82873 + 0.433416i
\(357\) 0 0
\(358\) −1.12229 1.50750i −1.12229 1.50750i
\(359\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(360\) 0 0
\(361\) −0.513997 + 0.431295i −0.513997 + 0.431295i
\(362\) 0 0
\(363\) 0.350020 0.127397i 0.350020 0.127397i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(368\) 0 0
\(369\) −1.93293 + 0.225927i −1.93293 + 0.225927i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(374\) −0.0550102 + 0.0738916i −0.0550102 + 0.0738916i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.973045 + 1.68536i −0.973045 + 1.68536i −0.286803 + 0.957990i \(0.592593\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(384\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(385\) 0 0
\(386\) −1.82873 + 0.665602i −1.82873 + 0.665602i
\(387\) −1.28004 1.07408i −1.28004 1.07408i
\(388\) −1.12229 0.408481i −1.12229 0.408481i
\(389\) 0 0 0.686242 0.727374i \(-0.259259\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.0581448 0.998308i −0.0581448 0.998308i
\(393\) 0.266044 0.223238i 0.266044 0.223238i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.770807 0.182685i 0.770807 0.182685i
\(397\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.686242 0.727374i −0.686242 0.727374i
\(401\) −0.227194 0.526695i −0.227194 0.526695i 0.766044 0.642788i \(-0.222222\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(402\) 0.569728 + 1.90302i 0.569728 + 1.90302i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.0798028 0.0845860i 0.0798028 0.0845860i
\(409\) −0.0460600 0.106779i −0.0460600 0.106779i 0.893633 0.448799i \(-0.148148\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(410\) 0 0
\(411\) −0.342534 + 1.14414i −0.342534 + 1.14414i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.12229 0.408481i −1.12229 0.408481i
\(418\) 0.0264203 + 0.453619i 0.0264203 + 0.453619i
\(419\) 0.310355 + 0.155866i 0.310355 + 0.155866i 0.597159 0.802123i \(-0.296296\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(420\) 0 0
\(421\) 0 0 0.686242 0.727374i \(-0.259259\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(422\) −1.43969 0.524005i −1.43969 0.524005i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.0460600 + 0.106779i −0.0460600 + 0.106779i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.77518 0.207489i −1.77518 0.207489i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(433\) 0.0581448 + 0.100710i 0.0581448 + 0.100710i 0.893633 0.448799i \(-0.148148\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −1.49324 + 0.982118i −1.49324 + 0.982118i
\(439\) 0 0 −0.597159 0.802123i \(-0.703704\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(440\) 0 0
\(441\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(442\) 0 0
\(443\) 1.89363 + 0.448799i 1.89363 + 0.448799i 1.00000 \(0\)
0.893633 + 0.448799i \(0.148148\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.914900 0.767692i 0.914900 0.767692i −0.0581448 0.998308i \(-0.518519\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(450\) 0.893633 0.448799i 0.893633 0.448799i
\(451\) 1.18094 + 0.990930i 1.18094 + 0.990930i
\(452\) 0.207391 + 0.278574i 0.207391 + 0.278574i
\(453\) 0 0
\(454\) −1.62593 + 0.385353i −1.62593 + 0.385353i
\(455\) 0 0
\(456\) 0.0333522 0.572636i 0.0333522 0.572636i
\(457\) −1.22650 + 0.615969i −1.22650 + 0.615969i −0.939693 0.342020i \(-0.888889\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(458\) 0 0
\(459\) 0.0581448 + 0.100710i 0.0581448 + 0.100710i
\(460\) 0 0
\(461\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(462\) 0 0
\(463\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.543613 + 1.26024i −0.543613 + 1.26024i
\(467\) 0.539014 0.196185i 0.539014 0.196185i −0.0581448 0.998308i \(-0.518519\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.22650 0.615969i −1.22650 0.615969i
\(473\) 0.0769651 + 1.32144i 0.0769651 + 1.32144i
\(474\) 0 0
\(475\) 0.164512 + 0.549509i 0.164512 + 0.549509i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.786803 1.82401i −0.786803 1.82401i
\(483\) 0 0
\(484\) 0.311205 + 0.204683i 0.311205 + 0.204683i
\(485\) 0 0
\(486\) 0.173648 0.984808i 0.173648 0.984808i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0.337935 + 0.0800921i 0.337935 + 0.0800921i
\(490\) 0 0
\(491\) −1.22650 1.30001i −1.22650 1.30001i −0.939693 0.342020i \(-0.888889\pi\)
−0.286803 0.957990i \(-0.592593\pi\)
\(492\) −1.33549 1.41553i −1.33549 1.41553i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.266044 + 1.50881i 0.266044 + 1.50881i
\(499\) 0.00676164 + 0.116093i 0.00676164 + 0.116093i 1.00000 \(0\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.14669 1.21542i 1.14669 1.21542i
\(503\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.993238 0.116093i −0.993238 0.116093i
\(508\) 0 0
\(509\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(513\) 0.539014 + 0.196185i 0.539014 + 0.196185i
\(514\) 0.993238 + 1.72034i 0.993238 + 1.72034i
\(515\) 0 0
\(516\) 0.0971586 1.66815i 0.0971586 1.66815i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.28004 1.07408i −1.28004 1.07408i −0.993238 0.116093i \(-0.962963\pi\)
−0.286803 0.957990i \(-0.592593\pi\)
\(522\) 0 0
\(523\) 0.266044 0.223238i 0.266044 0.223238i −0.500000 0.866025i \(-0.666667\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(524\) 0.337935 + 0.0800921i 0.337935 + 0.0800921i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.606829 + 0.509190i 0.606829 + 0.509190i
\(529\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(530\) 0 0
\(531\) 0.941855 0.998308i 0.941855 0.998308i
\(532\) 0 0
\(533\) 0 0
\(534\) 1.57020 1.03274i 1.57020 1.03274i
\(535\) 0 0
\(536\) −1.18624 + 1.59340i −1.18624 + 1.59340i
\(537\) 1.57020 + 1.03274i 1.57020 + 1.03274i
\(538\) 0 0
\(539\) −0.396080 0.686030i −0.396080 0.686030i
\(540\) 0 0
\(541\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.115503 + 0.0135004i 0.115503 + 0.0135004i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.0460600 + 0.106779i −0.0460600 + 0.106779i −0.939693 0.342020i \(-0.888889\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(548\) −1.12229 + 0.408481i −1.12229 + 0.408481i
\(549\) 0 0
\(550\) −0.744386 0.270935i −0.744386 0.270935i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.342534 1.14414i −0.342534 1.14414i
\(557\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.0264203 0.0882500i 0.0264203 0.0882500i
\(562\) −1.05138 1.11440i −1.05138 1.11440i
\(563\) 0.473045 + 1.09664i 0.473045 + 1.09664i 0.973045 + 0.230616i \(0.0740741\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.53209 1.53209
\(567\) 0 0
\(568\) 0 0
\(569\) 1.14669 + 0.754192i 1.14669 + 0.754192i 0.973045 0.230616i \(-0.0740741\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(570\) 0 0
\(571\) 0.707900 + 1.64110i 0.707900 + 1.64110i 0.766044 + 0.642788i \(0.222222\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.686242 0.727374i −0.686242 0.727374i
\(577\) 0.207391 + 1.17617i 0.207391 + 1.17617i 0.893633 + 0.448799i \(0.148148\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(578\) 0.282925 + 0.945034i 0.282925 + 0.945034i
\(579\) 1.49079 1.25092i 1.49079 1.25092i
\(580\) 0 0
\(581\) 0 0
\(582\) 1.19432 1.19432
\(583\) 0 0
\(584\) −1.67948 0.611281i −1.67948 0.611281i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.786803 + 1.82401i −0.786803 + 1.82401i −0.286803 + 0.957990i \(0.592593\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i \(-0.444444\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(594\) −0.661840 + 0.435299i −0.661840 + 0.435299i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(600\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(601\) 0.473045 + 0.635410i 0.473045 + 0.635410i 0.973045 0.230616i \(-0.0740741\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) −1.18624 1.59340i −1.18624 1.59340i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(608\) 0.479241 0.315202i 0.479241 0.315202i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.0460600 + 0.106779i −0.0460600 + 0.106779i
\(613\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(614\) −0.819590 1.10090i −0.819590 1.10090i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.713197 0.957990i 0.713197 0.957990i −0.286803 0.957990i \(-0.592593\pi\)
1.00000 \(0\)
\(618\) 0 0
\(619\) 1.73909 0.873403i 1.73909 0.873403i 0.766044 0.642788i \(-0.222222\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.993238 0.116093i −0.993238 0.116093i
\(626\) −0.558145 + 1.86433i −0.558145 + 1.86433i
\(627\) −0.179974 0.417226i −0.179974 0.417226i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(632\) 0 0
\(633\) 1.53209 1.53209
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.569728 0.0665916i 0.569728 0.0665916i 0.173648 0.984808i \(-0.444444\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(642\) 1.73909 0.412172i 1.73909 0.412172i
\(643\) −0.543613 0.576196i −0.543613 0.576196i 0.396080 0.918216i \(-0.370370\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.0557308 0.0366547i −0.0557308 0.0366547i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.893633 0.448799i 0.893633 0.448799i
\(649\) −1.08723 −1.08723
\(650\) 0 0
\(651\) 0 0
\(652\) 0.137557 + 0.318893i 0.137557 + 0.318893i
\(653\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.337935 1.91652i 0.337935 1.91652i
\(657\) 1.06728 1.43361i 1.06728 1.43361i
\(658\) 0 0
\(659\) −0.439408 1.46773i −0.439408 1.46773i −0.835488 0.549509i \(-0.814815\pi\)
0.396080 0.918216i \(-0.370370\pi\)
\(660\) 0 0
\(661\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(662\) −1.67948 0.843467i −1.67948 0.843467i
\(663\) 0 0
\(664\) −1.05138 + 1.11440i −1.05138 + 1.11440i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.0890830 + 1.52950i −0.0890830 + 1.52950i 0.597159 + 0.802123i \(0.296296\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(674\) 0.835488 1.44711i 0.835488 1.44711i
\(675\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(676\) −0.500000 0.866025i −0.500000 0.866025i
\(677\) 0 0 0.893633 0.448799i \(-0.148148\pi\)
−0.893633 + 0.448799i \(0.851852\pi\)
\(678\) −0.290162 0.190842i −0.290162 0.190842i
\(679\) 0 0
\(680\) 0 0
\(681\) 1.39608 0.918216i 1.39608 0.918216i
\(682\) 0 0
\(683\) −1.52173 1.27688i −1.52173 1.27688i −0.835488 0.549509i \(-0.814815\pi\)
−0.686242 0.727374i \(-0.740741\pi\)
\(684\) 0.164512 + 0.549509i 0.164512 + 0.549509i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.39608 0.918216i 1.39608 0.918216i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.82873 0.433416i −1.82873 0.433416i −0.835488 0.549509i \(-0.814815\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.439408 0.368707i −0.439408 0.368707i
\(695\) 0 0
\(696\) 0 0
\(697\) −0.220210 + 0.0521907i −0.220210 + 0.0521907i
\(698\) 0 0
\(699\) 0.0798028 1.37016i 0.0798028 1.37016i
\(700\) 0 0
\(701\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.0460600 + 0.790819i −0.0460600 + 0.790819i
\(705\) 0 0
\(706\) −1.77518 0.207489i −1.77518 0.207489i
\(707\) 0 0
\(708\) 1.36320 + 0.159336i 1.36320 + 0.159336i
\(709\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.76604 + 0.642788i 1.76604 + 0.642788i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.109277 + 1.87621i 0.109277 + 1.87621i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.666439 0.0778955i 0.666439 0.0778955i
\(723\) 1.36320 + 1.44491i 1.36320 + 1.44491i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.362443 0.0859006i −0.362443 0.0859006i
\(727\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(728\) 0 0
\(729\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(730\) 0 0
\(731\) −0.162350 0.106779i −0.162350 0.106779i
\(732\) 0 0
\(733\) 0 0 −0.396080 0.918216i \(-0.629630\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.273254 + 1.54970i −0.273254 + 1.54970i
\(738\) 1.73909 + 0.873403i 1.73909 + 0.873403i
\(739\) 0.137557 + 0.780125i 0.137557 + 0.780125i 0.973045 + 0.230616i \(0.0740741\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.893633 0.448799i \(-0.851852\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.766044 1.32683i −0.766044 1.32683i
\(748\) 0.0865644 0.0315069i 0.0865644 0.0315069i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(752\) 0 0
\(753\) −0.661840 + 1.53432i −0.661840 + 1.53432i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(758\) 1.73909 0.873403i 1.73909 0.873403i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.973045 + 0.230616i −0.973045 + 0.230616i −0.686242 0.727374i \(-0.740741\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.173648 0.984808i 0.173648 0.984808i
\(769\) −0.290162 + 0.190842i −0.290162 + 0.190842i −0.686242 0.727374i \(-0.740741\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(770\) 0 0
\(771\) −1.52173 1.27688i −1.52173 1.27688i
\(772\) 1.89363 + 0.448799i 1.89363 + 0.448799i
\(773\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(774\) 0.479241 + 1.60078i 0.479241 + 1.60078i
\(775\) 0 0
\(776\) 0.713197 + 0.957990i 0.713197 + 0.957990i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.666602 + 0.895402i −0.666602 + 0.895402i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(785\) 0 0
\(786\) −0.344948 + 0.0403186i −0.344948 + 0.0403186i
\(787\) −1.52173 0.177865i −1.52173 0.177865i −0.686242 0.727374i \(-0.740741\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.744386 0.270935i −0.744386 0.270935i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(798\) 0 0
\(799\) 0 0