Properties

Label 1407.1.cz.a.473.1
Level $1407$
Weight $1$
Character 1407.473
Analytic conductor $0.702$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -3
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1407 = 3 \cdot 7 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1407.cz (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.702184472775\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
Defining polynomial: \(x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{33}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{33} - \cdots)\)

Embedding invariants

Embedding label 473.1
Root \(-0.786053 - 0.618159i\) of defining polynomial
Character \(\chi\) \(=\) 1407.473
Dual form 1407.1.cz.a.821.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.888835 + 0.458227i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.723734 - 0.690079i) q^{7} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\) \(q+(-0.888835 + 0.458227i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(0.723734 - 0.690079i) q^{7} +(0.580057 - 0.814576i) q^{9} +(0.235759 - 0.971812i) q^{12} +(0.195876 - 0.807410i) q^{13} +(-0.142315 - 0.989821i) q^{16} +(0.0395325 - 0.0865641i) q^{19} +(-0.327068 + 0.945001i) q^{21} +(0.235759 - 0.971812i) q^{25} +(-0.142315 + 0.989821i) q^{27} +(0.0475819 + 0.998867i) q^{28} +(0.273100 + 0.0801894i) q^{31} +(0.235759 + 0.971812i) q^{36} +1.44747 q^{37} +(0.195876 + 0.807410i) q^{39} +(1.25667 + 1.45027i) q^{43} +(0.580057 + 0.814576i) q^{48} +(0.0475819 - 0.998867i) q^{49} +(0.481929 + 0.676774i) q^{52} +(0.00452808 + 0.0950560i) q^{57} +(-0.0135432 + 0.0941952i) q^{61} +(-0.142315 - 0.989821i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.723734 + 0.690079i) q^{67} +(-1.45949 + 0.584293i) q^{73} +(0.235759 + 0.971812i) q^{75} +(0.0395325 + 0.0865641i) q^{76} +(0.341254 - 1.40667i) q^{79} +(-0.327068 - 0.945001i) q^{81} +(-0.500000 - 0.866025i) q^{84} +(-0.415415 - 0.719520i) q^{91} +(-0.279486 + 0.0538665i) q^{93} +(0.888835 - 1.53951i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{3} - 2q^{4} + q^{7} + q^{9} + O(q^{10}) \) \( 20q + q^{3} - 2q^{4} + q^{7} + q^{9} + q^{12} + 2q^{13} - 2q^{16} + 2q^{19} + q^{21} + q^{25} - 2q^{27} + q^{28} - 4q^{31} + q^{36} + 2q^{37} + 2q^{39} - 4q^{43} + q^{48} + q^{49} - 9q^{52} + 21q^{57} + 2q^{61} - 2q^{63} - 2q^{64} + q^{67} - 12q^{73} + q^{75} + 2q^{76} - 12q^{79} + q^{81} - 10q^{84} + 2q^{91} + 2q^{93} - q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1407\mathbb{Z}\right)^\times\).

\(n\) \(337\) \(470\) \(1207\)
\(\chi(n)\) \(e\left(\frac{1}{33}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(3\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(4\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(5\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(6\) 0 0
\(7\) 0.723734 0.690079i 0.723734 0.690079i
\(8\) 0 0
\(9\) 0.580057 0.814576i 0.580057 0.814576i
\(10\) 0 0
\(11\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(12\) 0.235759 0.971812i 0.235759 0.971812i
\(13\) 0.195876 0.807410i 0.195876 0.807410i −0.786053 0.618159i \(-0.787879\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.142315 0.989821i −0.142315 0.989821i
\(17\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(18\) 0 0
\(19\) 0.0395325 0.0865641i 0.0395325 0.0865641i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(20\) 0 0
\(21\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(22\) 0 0
\(23\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(24\) 0 0
\(25\) 0.235759 0.971812i 0.235759 0.971812i
\(26\) 0 0
\(27\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(28\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(37\) 1.44747 1.44747 0.723734 0.690079i \(-0.242424\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(38\) 0 0
\(39\) 0.195876 + 0.807410i 0.195876 + 0.807410i
\(40\) 0 0
\(41\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(42\) 0 0
\(43\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(48\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(49\) 0.0475819 0.998867i 0.0475819 0.998867i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.481929 + 0.676774i 0.481929 + 0.676774i
\(53\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.00452808 + 0.0950560i 0.00452808 + 0.0950560i
\(58\) 0 0
\(59\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(60\) 0 0
\(61\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i −0.995472 0.0950560i \(-0.969697\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(62\) 0 0
\(63\) −0.142315 0.989821i −0.142315 0.989821i
\(64\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(72\) 0 0
\(73\) −1.45949 + 0.584293i −1.45949 + 0.584293i −0.959493 0.281733i \(-0.909091\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(76\) 0.0395325 + 0.0865641i 0.0395325 + 0.0865641i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.341254 1.40667i 0.341254 1.40667i −0.500000 0.866025i \(-0.666667\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(80\) 0 0
\(81\) −0.327068 0.945001i −0.327068 0.945001i
\(82\) 0 0
\(83\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(84\) −0.500000 0.866025i −0.500000 0.866025i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(90\) 0 0
\(91\) −0.415415 0.719520i −0.415415 0.719520i
\(92\) 0 0
\(93\) −0.279486 + 0.0538665i −0.279486 + 0.0538665i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.888835 1.53951i 0.888835 1.53951i 0.0475819 0.998867i \(-0.484848\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(101\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(102\) 0 0
\(103\) −1.44091 + 1.37391i −1.44091 + 1.37391i −0.654861 + 0.755750i \(0.727273\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(108\) −0.654861 0.755750i −0.654861 0.755750i
\(109\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i −0.995472 0.0950560i \(-0.969697\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(110\) 0 0
\(111\) −1.28656 + 0.663268i −1.28656 + 0.663268i
\(112\) −0.786053 0.618159i −0.786053 0.618159i
\(113\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.544078 0.627899i −0.544078 0.627899i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.273507 0.384087i 0.273507 0.384087i −0.654861 0.755750i \(-0.727273\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(128\) 0 0
\(129\) −1.78153 0.713215i −1.78153 0.713215i
\(130\) 0 0
\(131\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(132\) 0 0
\(133\) −0.0311250 0.0899299i −0.0311250 0.0899299i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(138\) 0 0
\(139\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.888835 0.458227i −0.888835 0.458227i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(148\) −0.947890 + 1.09392i −0.947890 + 1.09392i
\(149\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(150\) 0 0
\(151\) 0.514186 1.48564i 0.514186 1.48564i −0.327068 0.945001i \(-0.606061\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.738471 0.380708i −0.738471 0.380708i
\(157\) 0.0395325 0.829889i 0.0395325 0.829889i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.981929 + 1.70075i −0.981929 + 1.70075i −0.327068 + 0.945001i \(0.606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(168\) 0 0
\(169\) 0.275291 + 0.141923i 0.275291 + 0.141923i
\(170\) 0 0
\(171\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(172\) −1.91899 −1.91899
\(173\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(174\) 0 0
\(175\) −0.500000 0.866025i −0.500000 0.866025i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(180\) 0 0
\(181\) 0.0800569 1.68060i 0.0800569 1.68060i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(182\) 0 0
\(183\) −0.0311250 0.0899299i −0.0311250 0.0899299i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(190\) 0 0
\(191\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(192\) −0.995472 0.0950560i −0.995472 0.0950560i
\(193\) 0.839614 0.800570i 0.839614 0.800570i −0.142315 0.989821i \(-0.545455\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(197\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(198\) 0 0
\(199\) −0.379436 + 0.532843i −0.379436 + 0.532843i −0.959493 0.281733i \(-0.909091\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(200\) 0 0
\(201\) −0.959493 0.281733i −0.959493 0.281733i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.827068 0.0789754i −0.827068 0.0789754i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.0883470 + 1.85463i 0.0883470 + 1.85463i 0.415415 + 0.909632i \(0.363636\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0.252989 0.130425i 0.252989 0.130425i
\(218\) 0 0
\(219\) 1.02951 1.18812i 1.02951 1.18812i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.49547 + 0.961081i −1.49547 + 0.961081i −0.500000 + 0.866025i \(0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(224\) 0 0
\(225\) −0.654861 0.755750i −0.654861 0.755750i
\(226\) 0 0
\(227\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(228\) −0.0748038 0.0588264i −0.0748038 0.0588264i
\(229\) 1.84125 + 0.540641i 1.84125 + 0.540641i 1.00000 \(0\)
0.841254 + 0.540641i \(0.181818\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.341254 + 1.40667i 0.341254 + 1.40667i
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) −0.370638 0.291473i −0.370638 0.291473i 0.415415 0.909632i \(-0.363636\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(242\) 0 0
\(243\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(244\) −0.0623191 0.0719200i −0.0623191 0.0719200i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.0621493 0.0488747i −0.0621493 0.0488747i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(252\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(257\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(258\) 0 0
\(259\) 1.04758 0.998867i 1.04758 0.998867i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) −0.0947329 + 1.98869i −0.0947329 + 1.98869i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(272\) 0 0
\(273\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.651174 + 0.0621796i 0.651174 + 0.0621796i 0.415415 0.909632i \(-0.363636\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(278\) 0 0
\(279\) 0.223734 0.175946i 0.223734 0.175946i
\(280\) 0 0
\(281\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(282\) 0 0
\(283\) 1.07701 + 1.51245i 1.07701 + 1.51245i 0.841254 + 0.540641i \(0.181818\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.786053 0.618159i −0.786053 0.618159i
\(290\) 0 0
\(291\) −0.0845850 + 1.77566i −0.0845850 + 1.77566i
\(292\) 0.514186 1.48564i 0.514186 1.48564i
\(293\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −0.888835 0.458227i −0.888835 0.458227i
\(301\) 1.91030 + 0.182411i 1.91030 + 0.182411i
\(302\) 0 0
\(303\) 0 0
\(304\) −0.0913090 0.0268107i −0.0913090 0.0268107i
\(305\) 0 0
\(306\) 0 0
\(307\) −0.947890 + 0.903811i −0.947890 + 0.903811i −0.995472 0.0950560i \(-0.969697\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(308\) 0 0
\(309\) 0.651174 1.88144i 0.651174 1.88144i
\(310\) 0 0
\(311\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(312\) 0 0
\(313\) −1.03115 0.531595i −1.03115 0.531595i −0.142315 0.989821i \(-0.545455\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.839614 + 1.17907i 0.839614 + 1.17907i
\(317\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(325\) −0.738471 0.380708i −0.738471 0.380708i
\(326\) 0 0
\(327\) −0.0671040 0.276606i −0.0671040 0.276606i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.550294 1.58997i −0.550294 1.58997i −0.786053 0.618159i \(-0.787879\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(332\) 0 0
\(333\) 0.839614 1.17907i 0.839614 1.17907i
\(334\) 0 0
\(335\) 0 0
\(336\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(337\) −0.469383 0.0448206i −0.469383 0.0448206i −0.142315 0.989821i \(-0.545455\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.654861 0.755750i −0.654861 0.755750i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(348\) 0 0
\(349\) −0.759713 + 0.876756i −0.759713 + 0.876756i −0.995472 0.0950560i \(-0.969697\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(350\) 0 0
\(351\) 0.771316 + 0.308788i 0.771316 + 0.308788i
\(352\) 0 0
\(353\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(360\) 0 0
\(361\) 0.648930 + 0.748905i 0.648930 + 0.748905i
\(362\) 0 0
\(363\) 0.723734 0.690079i 0.723734 0.690079i
\(364\) 0.815816 + 0.157236i 0.815816 + 0.157236i
\(365\) 0 0
\(366\) 0 0
\(367\) 1.56199 1.00383i 1.56199 1.00383i 0.580057 0.814576i \(-0.303030\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0.142315 0.246497i 0.142315 0.246497i
\(373\) −0.415415 + 0.719520i −0.415415 + 0.719520i −0.995472 0.0950560i \(-0.969697\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.03115 + 0.531595i −1.03115 + 0.531595i −0.888835 0.458227i \(-0.848485\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(380\) 0 0
\(381\) −0.0671040 + 0.466718i −0.0671040 + 0.466718i
\(382\) 0 0
\(383\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.91030 0.182411i 1.91030 0.182411i
\(388\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(389\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −1.54370 + 1.21398i −1.54370 + 1.21398i −0.654861 + 0.755750i \(0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(398\) 0 0
\(399\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
\(400\) −0.995472 0.0950560i −0.995472 0.0950560i
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) 0.118239 0.204797i 0.118239 0.204797i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.653077 1.43004i −0.653077 1.43004i −0.888835 0.458227i \(-0.848485\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.0947329 1.98869i −0.0947329 1.98869i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.975950 + 1.37053i 0.975950 + 1.37053i
\(418\) 0 0
\(419\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(420\) 0 0
\(421\) −1.11312 1.56316i −1.11312 1.56316i −0.786053 0.618159i \(-0.787879\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.0552004 + 0.0775182i 0.0552004 + 0.0775182i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 1.00000 1.00000
\(433\) 0.111165 + 0.458227i 0.111165 + 0.458227i 1.00000 \(0\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.165101 0.231852i −0.165101 0.231852i
\(437\) 0 0
\(438\) 0 0
\(439\) 1.96386 1.96386 0.981929 0.189251i \(-0.0606061\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(440\) 0 0
\(441\) −0.786053 0.618159i −0.786053 0.618159i
\(442\) 0 0
\(443\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(444\) 0.341254 1.40667i 0.341254 1.40667i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.981929 0.189251i 0.981929 0.189251i
\(449\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0.223734 + 1.55610i 0.223734 + 1.55610i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.469383 + 1.93482i −0.469383 + 1.93482i −0.142315 + 0.989821i \(0.545455\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(462\) 0 0
\(463\) −0.911911 0.717135i −0.911911 0.717135i 0.0475819 0.998867i \(-0.484848\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(468\) 0.830830 0.830830
\(469\) 1.00000 1.00000
\(470\) 0 0
\(471\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.0748038 0.0588264i −0.0748038 0.0588264i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(480\) 0 0
\(481\) 0.283524 1.16870i 0.283524 1.16870i
\(482\) 0 0
\(483\) 0 0
\(484\) 0.415415 0.909632i 0.415415 0.909632i
\(485\) 0 0
\(486\) 0 0
\(487\) −1.28605 0.247866i −1.28605 0.247866i −0.500000 0.866025i \(-0.666667\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(488\) 0 0
\(489\) 0.0934441 1.96163i 0.0934441 1.96163i
\(490\) 0 0
\(491\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.0405070 0.281733i 0.0405070 0.281733i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.471518 0.471518 0.235759 0.971812i \(-0.424242\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.309721 −0.309721
\(508\) 0.111165 + 0.458227i 0.111165 + 0.458227i
\(509\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(510\) 0 0
\(511\) −0.653077 + 1.43004i −0.653077 + 1.43004i
\(512\) 0 0
\(513\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i
\(514\) 0 0
\(515\) 0 0
\(516\) 1.70566 0.879330i 1.70566 0.879330i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(522\) 0 0
\(523\) −1.11312 + 0.326842i −1.11312 + 0.326842i −0.786053 0.618159i \(-0.787879\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(524\) 0 0
\(525\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(530\) 0 0
\(531\) 0 0
\(532\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0.514186 0.404360i 0.514186 0.404360i −0.327068 0.945001i \(-0.606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(542\) 0 0
\(543\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.54370 + 1.21398i −1.54370 + 1.21398i −0.654861 + 0.755750i \(0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(548\) 0 0
\(549\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −0.723734 1.25354i −0.723734 1.25354i
\(554\) 0 0
\(555\) 0 0
\(556\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(557\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(558\) 0 0
\(559\) 1.41712 0.730574i 1.41712 0.730574i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.888835 0.458227i −0.888835 0.458227i
\(568\) 0 0
\(569\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(570\) 0 0
\(571\) −1.49547 + 0.961081i −1.49547 + 0.961081i −0.500000 + 0.866025i \(0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.928368 0.371662i 0.928368 0.371662i
\(577\) 1.02951 + 1.18812i 1.02951 + 1.18812i 0.981929 + 0.189251i \(0.0606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(578\) 0 0
\(579\) −0.379436 + 1.09631i −0.379436 + 1.09631i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(588\) −0.959493 0.281733i −0.959493 0.281733i
\(589\) 0.0177379 0.0204706i 0.0177379 0.0204706i
\(590\) 0 0
\(591\) 0 0
\(592\) −0.205996 1.43273i −0.205996 1.43273i
\(593\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.0930932 0.647478i 0.0930932 0.647478i
\(598\) 0 0
\(599\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(600\) 0 0
\(601\) −1.84833 0.176494i −1.84833 0.176494i −0.888835 0.458227i \(-0.848485\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(602\) 0 0
\(603\) 0.981929 0.189251i 0.981929 0.189251i
\(604\) 0.786053 + 1.36148i 0.786053 + 1.36148i
\(605\) 0 0
\(606\) 0 0
\(607\) −0.379436 1.09631i −0.379436 1.09631i −0.959493 0.281733i \(-0.909091\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.581419 + 0.299742i 0.581419 + 0.299742i 0.723734 0.690079i \(-0.242424\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(618\) 0 0
\(619\) 0.223734 0.175946i 0.223734 0.175946i −0.500000 0.866025i \(-0.666667\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0.771316 0.308788i 0.771316 0.308788i
\(625\) −0.888835 0.458227i −0.888835 0.458227i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.601300 + 0.573338i 0.601300 + 0.573338i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.21769 1.16106i 1.21769 1.16106i 0.235759 0.971812i \(-0.424242\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(632\) 0 0
\(633\) −0.928368 1.60798i −0.928368 1.60798i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.797176 0.234072i −0.797176 0.234072i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) −0.279486 + 1.94387i −0.279486 + 1.94387i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −0.165101 + 0.231852i −0.165101 + 0.231852i
\(652\) −0.642315 1.85585i −0.642315 1.85585i
\(653\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.370638 + 1.52779i −0.370638 + 1.52779i
\(658\) 0 0
\(659\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(660\) 0 0
\(661\) 1.30379 + 0.124497i 1.30379 + 0.124497i 0.723734 0.690079i \(-0.242424\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0.888835 1.53951i 0.888835 1.53951i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.56199 + 1.00383i 1.56199 + 1.00383i 0.981929 + 0.189251i \(0.0606061\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(674\) 0 0
\(675\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(676\) −0.287535 + 0.115112i −0.287535 + 0.115112i
\(677\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(678\) 0 0
\(679\) −0.419102 1.72756i −0.419102 1.72756i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(684\) 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i
\(685\) 0 0
\(686\) 0 0
\(687\) −1.88431 + 0.363170i −1.88431 + 0.363170i
\(688\) 1.25667 1.45027i 1.25667 1.45027i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.370638 0.291473i −0.370638 0.291473i 0.415415 0.909632i \(-0.363636\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(701\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(702\) 0 0
\(703\) 0.0572220 0.125299i 0.0572220 0.125299i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(710\) 0 0
\(711\) −0.947890 1.09392i −0.947890 1.09392i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(720\) 0 0
\(721\) −0.0947329 + 1.98869i −0.0947329 + 1.98869i
\(722\) 0 0
\(723\) 0.462997 + 0.0892353i 0.462997 + 0.0892353i
\(724\) 1.21769 + 1.16106i 1.21769 + 1.16106i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.0934441 + 1.96163i 0.0934441 + 1.96163i 0.235759 + 0.971812i \(0.424242\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(728\) 0 0
\(729\) −0.959493 0.281733i −0.959493 0.281733i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i
\(733\) 0.651174 + 1.88144i 0.651174 + 1.88144i 0.415415 + 0.909632i \(0.363636\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −0.759713 + 1.06687i −0.759713 + 1.06687i 0.235759 + 0.971812i \(0.424242\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(740\) 0 0
\(741\) 0.0776362 + 0.0149631i 0.0776362 + 0.0149631i
\(742\) 0 0
\(743\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.642315 0.123796i −0.642315 0.123796i −0.142315 0.989821i \(-0.545455\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.995472 0.0950560i −0.995472 0.0950560i
\(757\) −0.0748038 + 1.57033i −0.0748038 + 1.57033i 0.580057 + 0.814576i \(0.303030\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(762\) 0 0
\(763\) 0.142315 + 0.246497i 0.142315 + 0.246497i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.723734 0.690079i 0.723734 0.690079i
\(769\) 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i \(0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.0552004 + 1.15880i 0.0552004 + 1.15880i
\(773\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(774\) 0 0
\(775\) 0.142315 0.246497i 0.142315 0.246497i
\(776\) 0 0
\(777\) −0.473420 + 1.36786i −0.473420 + 1.36786i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.627639 1.81344i 0.627639 1.81344i 0.0475819 0.998867i \(-0.484848\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.0734014 + 0.0293855i 0.0734014 + 0.0293855i
\(794\) 0 0
\(795\) 0 0
\(796\) −0.154218 0.635697i −0.154218 0.635697i
\(797\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0