Properties

Label 648.1.bf.a.355.1
Level $648$
Weight $1$
Character 648.355
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 355.1
Root \(0.0581448 + 0.998308i\) of defining polynomial
Character \(\chi\) \(=\) 648.355
Dual form 648.1.bf.a.115.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.396080 + 0.918216i) q^{2} +(0.893633 + 0.448799i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.0581448 + 0.998308i) q^{6} +(-0.939693 - 0.342020i) q^{8} +(0.597159 + 0.802123i) q^{9} +O(q^{10})\) \(q+(0.396080 + 0.918216i) q^{2} +(0.893633 + 0.448799i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.0581448 + 0.998308i) q^{6} +(-0.939693 - 0.342020i) q^{8} +(0.597159 + 0.802123i) q^{9} +(1.14669 - 0.754192i) q^{11} +(-0.939693 + 0.342020i) q^{12} +(-0.0581448 - 0.998308i) q^{16} +(-1.52173 - 1.27688i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.28004 + 1.07408i) q^{19} +(1.14669 + 0.754192i) q^{22} +(-0.686242 - 0.727374i) q^{24} +(-0.993238 - 0.116093i) q^{25} +(0.173648 + 0.984808i) q^{27} +(0.893633 - 0.448799i) q^{32} +(1.36320 - 0.159336i) q^{33} +(0.569728 - 1.90302i) q^{34} +(-0.993238 - 0.116093i) q^{36} +(-1.49324 - 0.749932i) q^{38} +(0.707900 - 1.64110i) q^{41} +(0.707900 + 0.355521i) q^{43} +(-0.238329 + 1.35163i) q^{44} +(0.396080 - 0.918216i) q^{48} +(0.893633 - 0.448799i) q^{49} +(-0.286803 - 0.957990i) q^{50} +(-0.786803 - 1.82401i) q^{51} +(-0.835488 + 0.549509i) q^{54} +(-1.62593 + 0.385353i) q^{57} +(0.0971586 + 0.0639022i) q^{59} +(0.766044 + 0.642788i) q^{64} +(0.686242 + 1.18861i) q^{66} +(1.16212 + 1.56100i) q^{67} +(1.97304 - 0.230616i) q^{68} +(-0.286803 - 0.957990i) q^{72} +(-1.12229 - 0.408481i) q^{73} +(-0.835488 - 0.549509i) q^{75} +(0.0971586 - 1.66815i) q^{76} +(-0.286803 + 0.957990i) q^{81} +1.78727 q^{82} +(0.137557 + 0.318893i) q^{83} +(-0.0460600 + 0.790819i) q^{86} +(-1.33549 + 0.316516i) q^{88} +(-1.43969 - 0.524005i) q^{89} +1.00000 q^{96} +(0.0333522 + 0.572636i) q^{97} +(0.766044 + 0.642788i) q^{98} +(1.28971 + 0.469417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + O(q^{10}) \) \( 18q - 9q^{18} - 9q^{38} - 9q^{51} - 9q^{59} + 18q^{68} - 9q^{76} - 9q^{88} - 9q^{89} + 18q^{96} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{10}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(3\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(4\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(5\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(6\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(7\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(8\) −0.939693 0.342020i −0.939693 0.342020i
\(9\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(10\) 0 0
\(11\) 1.14669 0.754192i 1.14669 0.754192i 0.173648 0.984808i \(-0.444444\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(12\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(13\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.0581448 0.998308i −0.0581448 0.998308i
\(17\) −1.52173 1.27688i −1.52173 1.27688i −0.835488 0.549509i \(-0.814815\pi\)
−0.686242 0.727374i \(-0.740741\pi\)
\(18\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(19\) −1.28004 + 1.07408i −1.28004 + 1.07408i −0.286803 + 0.957990i \(0.592593\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.14669 + 0.754192i 1.14669 + 0.754192i
\(23\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(24\) −0.686242 0.727374i −0.686242 0.727374i
\(25\) −0.993238 0.116093i −0.993238 0.116093i
\(26\) 0 0
\(27\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(28\) 0 0
\(29\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(30\) 0 0
\(31\) 0 0 −0.286803 0.957990i \(-0.592593\pi\)
0.286803 + 0.957990i \(0.407407\pi\)
\(32\) 0.893633 0.448799i 0.893633 0.448799i
\(33\) 1.36320 0.159336i 1.36320 0.159336i
\(34\) 0.569728 1.90302i 0.569728 1.90302i
\(35\) 0 0
\(36\) −0.993238 0.116093i −0.993238 0.116093i
\(37\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(38\) −1.49324 0.749932i −1.49324 0.749932i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.707900 1.64110i 0.707900 1.64110i −0.0581448 0.998308i \(-0.518519\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(42\) 0 0
\(43\) 0.707900 + 0.355521i 0.707900 + 0.355521i 0.766044 0.642788i \(-0.222222\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(44\) −0.238329 + 1.35163i −0.238329 + 1.35163i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(48\) 0.396080 0.918216i 0.396080 0.918216i
\(49\) 0.893633 0.448799i 0.893633 0.448799i
\(50\) −0.286803 0.957990i −0.286803 0.957990i
\(51\) −0.786803 1.82401i −0.786803 1.82401i
\(52\) 0 0
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) −0.835488 + 0.549509i −0.835488 + 0.549509i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.62593 + 0.385353i −1.62593 + 0.385353i
\(58\) 0 0
\(59\) 0.0971586 + 0.0639022i 0.0971586 + 0.0639022i 0.597159 0.802123i \(-0.296296\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(65\) 0 0
\(66\) 0.686242 + 1.18861i 0.686242 + 1.18861i
\(67\) 1.16212 + 1.56100i 1.16212 + 1.56100i 0.766044 + 0.642788i \(0.222222\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(68\) 1.97304 0.230616i 1.97304 0.230616i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(72\) −0.286803 0.957990i −0.286803 0.957990i
\(73\) −1.12229 0.408481i −1.12229 0.408481i −0.286803 0.957990i \(-0.592593\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(74\) 0 0
\(75\) −0.835488 0.549509i −0.835488 0.549509i
\(76\) 0.0971586 1.66815i 0.0971586 1.66815i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.396080 0.918216i \(-0.629630\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(80\) 0 0
\(81\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(82\) 1.78727 1.78727
\(83\) 0.137557 + 0.318893i 0.137557 + 0.318893i 0.973045 0.230616i \(-0.0740741\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.0460600 + 0.790819i −0.0460600 + 0.790819i
\(87\) 0 0
\(88\) −1.33549 + 0.316516i −1.33549 + 0.316516i
\(89\) −1.43969 0.524005i −1.43969 0.524005i −0.500000 0.866025i \(-0.666667\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.00000 1.00000
\(97\) 0.0333522 + 0.572636i 0.0333522 + 0.572636i 0.973045 + 0.230616i \(0.0740741\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(98\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(99\) 1.28971 + 0.469417i 1.28971 + 0.469417i
\(100\) 0.766044 0.642788i 0.766044 0.642788i
\(101\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(102\) 1.36320 1.44491i 1.36320 1.44491i
\(103\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.597159 1.03431i −0.597159 1.03431i −0.993238 0.116093i \(-0.962963\pi\)
0.396080 0.918216i \(-0.370370\pi\)
\(108\) −0.835488 0.549509i −0.835488 0.549509i
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.67948 + 0.843467i −1.67948 + 0.843467i −0.686242 + 0.727374i \(0.740741\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(114\) −0.997837 1.34033i −0.997837 1.34033i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.0201935 + 0.114523i −0.0201935 + 0.114523i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.350020 0.811437i 0.350020 0.811437i
\(122\) 0 0
\(123\) 1.36912 1.14883i 1.36912 1.14883i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(128\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(129\) 0.473045 + 0.635410i 0.473045 + 0.635410i
\(130\) 0 0
\(131\) 0.539014 + 1.80043i 0.539014 + 1.80043i 0.597159 + 0.802123i \(0.296296\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(132\) −0.819590 + 1.10090i −0.819590 + 1.10090i
\(133\) 0 0
\(134\) −0.973045 + 1.68536i −0.973045 + 1.68536i
\(135\) 0 0
\(136\) 0.993238 + 1.72034i 0.993238 + 1.72034i
\(137\) 0.569728 + 0.0665916i 0.569728 + 0.0665916i 0.396080 0.918216i \(-0.370370\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(138\) 0 0
\(139\) −0.558145 0.132283i −0.558145 0.132283i −0.0581448 0.998308i \(-0.518519\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.766044 0.642788i 0.766044 0.642788i
\(145\) 0 0
\(146\) −0.0694434 1.19230i −0.0694434 1.19230i
\(147\) 1.00000 1.00000
\(148\) 0 0
\(149\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(150\) 0.173648 0.984808i 0.173648 0.984808i
\(151\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(152\) 1.57020 0.571507i 1.57020 0.571507i
\(153\) 0.115503 1.98312i 0.115503 1.98312i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(163\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(164\) 0.707900 + 1.64110i 0.707900 + 1.64110i
\(165\) 0 0
\(166\) −0.238329 + 0.252614i −0.238329 + 0.252614i
\(167\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(168\) 0 0
\(169\) 0.973045 0.230616i 0.973045 0.230616i
\(170\) 0 0
\(171\) −1.62593 0.385353i −1.62593 0.385353i
\(172\) −0.744386 + 0.270935i −0.744386 + 0.270935i
\(173\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.819590 1.10090i −0.819590 1.10090i
\(177\) 0.0581448 + 0.100710i 0.0581448 + 0.100710i
\(178\) −0.0890830 1.52950i −0.0890830 1.52950i
\(179\) 1.17365 + 0.984808i 1.17365 + 0.984808i 1.00000 \(0\)
0.173648 + 0.984808i \(0.444444\pi\)
\(180\) 0 0
\(181\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.70797 0.316516i −2.70797 0.316516i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(192\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(193\) −0.512593 1.71218i −0.512593 1.71218i −0.686242 0.727374i \(-0.740741\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(194\) −0.512593 + 0.257434i −0.512593 + 0.257434i
\(195\) 0 0
\(196\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(197\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(198\) 0.0798028 + 1.37016i 0.0798028 + 1.37016i
\(199\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(200\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(201\) 0.337935 + 1.91652i 0.337935 + 1.91652i
\(202\) 0 0
\(203\) 0 0
\(204\) 1.86668 + 0.679415i 1.86668 + 0.679415i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.657751 + 2.19704i −0.657751 + 2.19704i
\(210\) 0 0
\(211\) 0.310355 0.155866i 0.310355 0.155866i −0.286803 0.957990i \(-0.592593\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.713197 0.957990i 0.713197 0.957990i
\(215\) 0 0
\(216\) 0.173648 0.984808i 0.173648 0.984808i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.819590 0.868715i −0.819590 0.868715i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(224\) 0 0
\(225\) −0.500000 0.866025i −0.500000 0.866025i
\(226\) −1.43969 1.20805i −1.43969 1.20805i
\(227\) −0.0460600 0.790819i −0.0460600 0.790819i −0.939693 0.342020i \(-0.888889\pi\)
0.893633 0.448799i \(-0.148148\pi\)
\(228\) 0.835488 1.44711i 0.835488 1.44711i
\(229\) 0 0 −0.597159 0.802123i \(-0.703704\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.109277 0.0397734i 0.109277 0.0397734i −0.286803 0.957990i \(-0.592593\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.113155 + 0.0268182i −0.113155 + 0.0268182i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.686242 0.727374i \(-0.259259\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(240\) 0 0
\(241\) 0.770807 + 1.78693i 0.770807 + 1.78693i 0.597159 + 0.802123i \(0.296296\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(242\) 0.883710 0.883710
\(243\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.59716 + 0.802123i 1.59716 + 0.802123i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.0201935 + 0.346709i −0.0201935 + 0.346709i
\(250\) 0 0
\(251\) −0.744386 0.270935i −0.744386 0.270935i −0.0581448 0.998308i \(-0.518519\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(257\) 1.16212 + 1.56100i 1.16212 + 1.56100i 0.766044 + 0.642788i \(0.222222\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(258\) −0.396080 + 0.686030i −0.396080 + 0.686030i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −1.43969 + 1.20805i −1.43969 + 1.20805i
\(263\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(264\) −1.33549 0.316516i −1.33549 0.316516i
\(265\) 0 0
\(266\) 0 0
\(267\) −1.05138 1.11440i −1.05138 1.11440i
\(268\) −1.93293 0.225927i −1.93293 0.225927i
\(269\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(270\) 0 0
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) −1.18624 + 1.59340i −1.18624 + 1.59340i
\(273\) 0 0
\(274\) 0.164512 + 0.549509i 0.164512 + 0.549509i
\(275\) −1.22650 + 0.615969i −1.22650 + 0.615969i
\(276\) 0 0
\(277\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(278\) −0.0996057 0.564892i −0.0996057 0.564892i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.310355 + 0.155866i 0.310355 + 0.155866i 0.597159 0.802123i \(-0.296296\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(282\) 0 0
\(283\) 0.137557 0.318893i 0.137557 0.318893i −0.835488 0.549509i \(-0.814815\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(289\) 0.511583 + 2.90133i 0.511583 + 2.90133i
\(290\) 0 0
\(291\) −0.227194 + 0.526695i −0.227194 + 0.526695i
\(292\) 1.06728 0.536009i 1.06728 0.536009i
\(293\) 0 0 −0.286803 0.957990i \(-0.592593\pi\)
0.286803 + 0.957990i \(0.407407\pi\)
\(294\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.941855 + 0.998308i 0.941855 + 0.998308i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.973045 0.230616i 0.973045 0.230616i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.14669 + 1.21542i 1.14669 + 1.21542i
\(305\) 0 0
\(306\) 1.86668 0.679415i 1.86668 0.679415i
\(307\) −0.0890830 0.0747496i −0.0890830 0.0747496i 0.597159 0.802123i \(-0.296296\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(312\) 0 0
\(313\) −1.49324 + 0.982118i −1.49324 + 0.982118i −0.500000 + 0.866025i \(0.666667\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.0694434 1.19230i −0.0694434 1.19230i
\(322\) 0 0
\(323\) 3.31935 3.31935
\(324\) −0.500000 0.866025i −0.500000 0.866025i
\(325\) 0 0
\(326\) −0.744386 1.72568i −0.744386 1.72568i
\(327\) 0 0
\(328\) −1.22650 + 1.30001i −1.22650 + 1.30001i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.49079 0.353324i 1.49079 0.353324i 0.597159 0.802123i \(-0.296296\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(332\) −0.326352 0.118782i −0.326352 0.118782i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.786803 + 0.0919641i −0.786803 + 0.0919641i −0.500000 0.866025i \(-0.666667\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(338\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(339\) −1.87939 −1.87939
\(340\) 0 0
\(341\) 0 0
\(342\) −0.290162 1.64559i −0.290162 1.64559i
\(343\) 0 0
\(344\) −0.543613 0.576196i −0.543613 0.576196i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.62593 0.385353i −1.62593 0.385353i −0.686242 0.727374i \(-0.740741\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(348\) 0 0
\(349\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.686242 1.18861i 0.686242 1.18861i
\(353\) 0.713197 0.957990i 0.713197 0.957990i −0.286803 0.957990i \(-0.592593\pi\)
1.00000 \(0\)
\(354\) −0.0694434 + 0.0932786i −0.0694434 + 0.0932786i
\(355\) 0 0
\(356\) 1.36912 0.687600i 1.36912 0.687600i
\(357\) 0 0
\(358\) −0.439408 + 1.46773i −0.439408 + 1.46773i
\(359\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(360\) 0 0
\(361\) 0.311205 1.76493i 0.311205 1.76493i
\(362\) 0 0
\(363\) 0.676961 0.568038i 0.676961 0.568038i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.893633 0.448799i \(-0.851852\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(368\) 0 0
\(369\) 1.73909 0.412172i 1.73909 0.412172i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.893633 0.448799i \(-0.148148\pi\)
−0.893633 + 0.448799i \(0.851852\pi\)
\(374\) −0.781942 2.61187i −0.781942 2.61187i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.893633 1.54782i −0.893633 1.54782i −0.835488 0.549509i \(-0.814815\pi\)
−0.0581448 0.998308i \(-0.518519\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(384\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(385\) 0 0
\(386\) 1.36912 1.14883i 1.36912 1.14883i
\(387\) 0.137557 + 0.780125i 0.137557 + 0.780125i
\(388\) −0.439408 0.368707i −0.439408 0.368707i
\(389\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(393\) −0.326352 + 1.85083i −0.326352 + 1.85083i
\(394\) 0 0
\(395\) 0 0
\(396\) −1.22650 + 0.615969i −1.22650 + 0.615969i
\(397\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(401\) 1.14669 1.21542i 1.14669 1.21542i 0.173648 0.984808i \(-0.444444\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(402\) −1.62593 + 1.06939i −1.62593 + 1.06939i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.115503 + 1.98312i 0.115503 + 1.98312i
\(409\) 1.36320 1.44491i 1.36320 1.44491i 0.597159 0.802123i \(-0.296296\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(410\) 0 0
\(411\) 0.479241 + 0.315202i 0.479241 + 0.315202i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.439408 0.368707i −0.439408 0.368707i
\(418\) −2.27788 + 0.266246i −2.27788 + 0.266246i
\(419\) −1.12229 1.50750i −1.12229 1.50750i −0.835488 0.549509i \(-0.814815\pi\)
−0.286803 0.957990i \(-0.592593\pi\)
\(420\) 0 0
\(421\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(422\) 0.266044 + 0.223238i 0.266044 + 0.223238i
\(423\) 0 0
\(424\) 0 0
\(425\) 1.36320 + 1.44491i 1.36320 + 1.44491i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.16212 + 0.275428i 1.16212 + 0.275428i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 0.973045 0.230616i 0.973045 0.230616i
\(433\) 0.993238 1.72034i 0.993238 1.72034i 0.396080 0.918216i \(-0.370370\pi\)
0.597159 0.802123i \(-0.296296\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.473045 1.09664i 0.473045 1.09664i
\(439\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(440\) 0 0
\(441\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(442\) 0 0
\(443\) 1.59716 + 0.802123i 1.59716 + 0.802123i 1.00000 \(0\)
0.597159 + 0.802123i \(0.296296\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.0996057 + 0.564892i −0.0996057 + 0.564892i 0.893633 + 0.448799i \(0.148148\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(450\) 0.597159 0.802123i 0.597159 0.802123i
\(451\) −0.425958 2.41573i −0.425958 2.41573i
\(452\) 0.539014 1.80043i 0.539014 1.80043i
\(453\) 0 0
\(454\) 0.707900 0.355521i 0.707900 0.355521i
\(455\) 0 0
\(456\) 1.65968 + 0.193988i 1.65968 + 0.193988i
\(457\) −0.0694434 + 0.0932786i −0.0694434 + 0.0932786i −0.835488 0.549509i \(-0.814815\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(458\) 0 0
\(459\) 0.993238 1.72034i 0.993238 1.72034i
\(460\) 0 0
\(461\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(462\) 0 0
\(463\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.0798028 + 0.0845860i 0.0798028 + 0.0845860i
\(467\) −1.28004 + 1.07408i −1.28004 + 1.07408i −0.286803 + 0.957990i \(0.592593\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.0694434 0.0932786i −0.0694434 0.0932786i
\(473\) 1.07987 0.126219i 1.07987 0.126219i
\(474\) 0 0
\(475\) 1.39608 0.918216i 1.39608 0.918216i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.33549 + 1.41553i −1.33549 + 1.41553i
\(483\) 0 0
\(484\) 0.350020 + 0.811437i 0.350020 + 0.811437i
\(485\) 0 0
\(486\) −0.939693 0.342020i −0.939693 0.342020i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −1.67948 0.843467i −1.67948 0.843467i
\(490\) 0 0
\(491\) −0.0694434 + 1.19230i −0.0694434 + 1.19230i 0.766044 + 0.642788i \(0.222222\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(492\) −0.103920 + 1.78424i −0.103920 + 1.78424i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.326352 + 0.118782i −0.326352 + 0.118782i
\(499\) 1.97304 0.230616i 1.97304 0.230616i 0.973045 0.230616i \(-0.0740741\pi\)
1.00000 \(0\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.0460600 0.790819i −0.0460600 0.790819i
\(503\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(508\) 0 0
\(509\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.500000 0.866025i −0.500000 0.866025i
\(513\) −1.28004 1.07408i −1.28004 1.07408i
\(514\) −0.973045 + 1.68536i −0.973045 + 1.68536i
\(515\) 0 0
\(516\) −0.786803 0.0919641i −0.786803 0.0919641i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.137557 + 0.780125i 0.137557 + 0.780125i 0.973045 + 0.230616i \(0.0740741\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(522\) 0 0
\(523\) −0.326352 + 1.85083i −0.326352 + 1.85083i 0.173648 + 0.984808i \(0.444444\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) −1.67948 0.843467i −1.67948 0.843467i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.238329 1.35163i −0.238329 1.35163i
\(529\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(530\) 0 0
\(531\) 0.00676164 + 0.116093i 0.00676164 + 0.116093i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.606829 1.40679i 0.606829 1.40679i
\(535\) 0 0
\(536\) −0.558145 1.86433i −0.558145 1.86433i
\(537\) 0.606829 + 1.40679i 0.606829 + 1.40679i
\(538\) 0 0
\(539\) 0.686242 1.18861i 0.686242 1.18861i
\(540\) 0 0
\(541\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.93293 0.458113i −1.93293 0.458113i
\(545\) 0 0
\(546\) 0 0
\(547\) 1.36320 + 1.44491i 1.36320 + 1.44491i 0.766044 + 0.642788i \(0.222222\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(548\) −0.439408 + 0.368707i −0.439408 + 0.368707i
\(549\) 0 0
\(550\) −1.05138 0.882215i −1.05138 0.882215i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.479241 0.315202i 0.479241 0.315202i
\(557\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −2.27788 1.49818i −2.27788 1.49818i
\(562\) −0.0201935 + 0.346709i −0.0201935 + 0.346709i
\(563\) 0.393633 0.417226i 0.393633 0.417226i −0.500000 0.866025i \(-0.666667\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.347296 0.347296
\(567\) 0 0
\(568\) 0 0
\(569\) −0.0460600 0.106779i −0.0460600 0.106779i 0.893633 0.448799i \(-0.148148\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(570\) 0 0
\(571\) −0.819590 + 0.868715i −0.819590 + 0.868715i −0.993238 0.116093i \(-0.962963\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(577\) 0.539014 0.196185i 0.539014 0.196185i −0.0581448 0.998308i \(-0.518519\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(578\) −2.46142 + 1.61890i −2.46142 + 1.61890i
\(579\) 0.310355 1.76011i 0.310355 1.76011i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.573606 −0.573606
\(583\) 0 0
\(584\) 0.914900 + 0.767692i 0.914900 + 0.767692i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.33549 1.41553i −1.33549 1.41553i −0.835488 0.549509i \(-0.814815\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(588\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i \(-0.888889\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(594\) −0.543613 + 1.26024i −0.543613 + 1.26024i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.893633 0.448799i \(-0.148148\pi\)
−0.893633 + 0.448799i \(0.851852\pi\)
\(600\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(601\) 0.393633 1.31482i 0.393633 1.31482i −0.500000 0.866025i \(-0.666667\pi\)
0.893633 0.448799i \(-0.148148\pi\)
\(602\) 0 0
\(603\) −0.558145 + 1.86433i −0.558145 + 1.86433i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(608\) −0.661840 + 1.53432i −0.661840 + 1.53432i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.36320 + 1.44491i 1.36320 + 1.44491i
\(613\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(614\) 0.0333522 0.111404i 0.0333522 0.111404i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.164512 + 0.549509i 0.164512 + 0.549509i 1.00000 \(0\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(618\) 0 0
\(619\) 1.06728 1.43361i 1.06728 1.43361i 0.173648 0.984808i \(-0.444444\pi\)
0.893633 0.448799i \(-0.148148\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(626\) −1.49324 0.982118i −1.49324 0.982118i
\(627\) −1.57382 + 1.66815i −1.57382 + 1.66815i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(632\) 0 0
\(633\) 0.347296 0.347296
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.62593 + 0.385353i −1.62593 + 0.385353i −0.939693 0.342020i \(-0.888889\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(642\) 1.06728 0.536009i 1.06728 0.536009i
\(643\) 0.0798028 1.37016i 0.0798028 1.37016i −0.686242 0.727374i \(-0.740741\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.31473 + 3.04788i 1.31473 + 3.04788i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.597159 0.802123i 0.597159 0.802123i
\(649\) 0.159606 0.159606
\(650\) 0 0
\(651\) 0 0
\(652\) 1.28971 1.36702i 1.28971 1.36702i
\(653\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.67948 0.611281i −1.67948 0.611281i
\(657\) −0.342534 1.14414i −0.342534 1.14414i
\(658\) 0 0
\(659\) −0.290162 + 0.190842i −0.290162 + 0.190842i −0.686242 0.727374i \(-0.740741\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(660\) 0 0
\(661\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(662\) 0.914900 + 1.22892i 0.914900 + 1.22892i
\(663\) 0 0
\(664\) −0.0201935 0.346709i −0.0201935 0.346709i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.344948 0.0403186i −0.344948 0.0403186i −0.0581448 0.998308i \(-0.518519\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(674\) −0.396080 0.686030i −0.396080 0.686030i
\(675\) −0.0581448 0.998308i −0.0581448 0.998308i
\(676\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(677\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(678\) −0.744386 1.72568i −0.744386 1.72568i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.313758 0.727374i 0.313758 0.727374i
\(682\) 0 0
\(683\) 0.337935 + 1.91652i 0.337935 + 1.91652i 0.396080 + 0.918216i \(0.370370\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(684\) 1.39608 0.918216i 1.39608 0.918216i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.313758 0.727374i 0.313758 0.727374i
\(689\) 0 0
\(690\) 0 0
\(691\) 1.36912 + 0.687600i 1.36912 + 0.687600i 0.973045 0.230616i \(-0.0740741\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.290162 1.64559i −0.290162 1.64559i
\(695\) 0 0
\(696\) 0 0
\(697\) −3.17272 + 1.59340i −3.17272 + 1.59340i
\(698\) 0 0
\(699\) 0.115503 + 0.0135004i 0.115503 + 0.0135004i
\(700\) 0 0
\(701\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.36320 + 0.159336i 1.36320 + 0.159336i
\(705\) 0 0
\(706\) 1.16212 + 0.275428i 1.16212 + 0.275428i
\(707\) 0 0
\(708\) −0.113155 0.0268182i −0.113155 0.0268182i
\(709\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.17365 + 0.984808i 1.17365 + 0.984808i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.52173 + 0.177865i −1.52173 + 0.177865i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.74385 0.413300i 1.74385 0.413300i
\(723\) −0.113155 + 1.94280i −0.113155 + 1.94280i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.789712 + 0.396608i 0.789712 + 0.396608i
\(727\) 0 0 −0.396080 0.918216i \(-0.629630\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(728\) 0 0
\(729\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(730\) 0 0
\(731\) −0.623274 1.44491i −0.623274 1.44491i
\(732\) 0 0
\(733\) 0 0 0.686242 0.727374i \(-0.259259\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.50990 + 0.913527i 2.50990 + 0.913527i
\(738\) 1.06728 + 1.43361i 1.06728 + 1.43361i
\(739\) 1.28971 0.469417i 1.28971 0.469417i 0.396080 0.918216i \(-0.370370\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.597159 0.802123i \(-0.703704\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.173648 + 0.300767i −0.173648 + 0.300767i
\(748\) 2.08855 1.75250i 2.08855 1.75250i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(752\) 0 0
\(753\) −0.543613 0.576196i −0.543613 0.576196i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(758\) 1.06728 1.43361i 1.06728 1.43361i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.893633 + 0.448799i −0.893633 + 0.448799i −0.835488 0.549509i \(-0.814815\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.939693 0.342020i −0.939693 0.342020i
\(769\) −0.744386 + 1.72568i −0.744386 + 1.72568i −0.0581448 + 0.998308i \(0.518519\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(770\) 0 0
\(771\) 0.337935 + 1.91652i 0.337935 + 1.91652i
\(772\) 1.59716 + 0.802123i 1.59716 + 0.802123i
\(773\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(774\) −0.661840 + 0.435299i −0.661840 + 0.435299i
\(775\) 0 0
\(776\) 0.164512 0.549509i 0.164512 0.549509i
\(777\) 0 0
\(778\) 0 0
\(779\) 0.856531 + 2.86101i 0.856531 + 2.86101i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.500000 0.866025i −0.500000 0.866025i
\(785\) 0 0
\(786\) −1.82873 + 0.433416i −1.82873 + 0.433416i
\(787\) 0.337935 + 0.0800921i 0.337935 + 0.0800921i 0.396080 0.918216i \(-0.370370\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −1.05138 0.882215i −1.05138 0.882215i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(798\) 0 0
\(799\) 0 0
\(800