Properties

Label 1407.1.cz.a.1376.1
Level $1407$
Weight $1$
Character 1407.1376
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 1376.1
Root \(0.0475819 + 0.998867i\) of defining polynomial
Character \(\chi\) \(=\) 1407.1376
Dual form 1407.1.cz.a.590.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.981929 - 0.189251i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.580057 + 0.814576i) q^{7} +(0.928368 - 0.371662i) q^{9} +O(q^{10})\) \(q+(0.981929 - 0.189251i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.580057 + 0.814576i) q^{7} +(0.928368 - 0.371662i) q^{9} +(-0.995472 - 0.0950560i) q^{12} +(0.283341 + 0.0270558i) q^{13} +(0.841254 + 0.540641i) q^{16} +(0.0930932 + 0.647478i) q^{19} +(0.723734 + 0.690079i) q^{21} +(-0.995472 - 0.0950560i) q^{25} +(0.841254 - 0.540641i) q^{27} +(-0.327068 - 0.945001i) q^{28} +(0.698939 - 1.53046i) q^{31} +(-0.995472 + 0.0950560i) q^{36} +1.16011 q^{37} +(0.283341 - 0.0270558i) q^{39} +(-0.797176 + 0.234072i) q^{43} +(0.928368 + 0.371662i) q^{48} +(-0.327068 + 0.945001i) q^{49} +(-0.264241 - 0.105786i) q^{52} +(0.213947 + 0.618159i) q^{57} +(-0.550294 + 0.353653i) q^{61} +(0.841254 + 0.540641i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.580057 - 0.814576i) q^{67} +(-0.0845850 - 0.0436066i) q^{73} +(-0.995472 + 0.0950560i) q^{75} +(0.0930932 - 0.647478i) q^{76} +(-1.15486 - 0.110276i) q^{79} +(0.723734 - 0.690079i) q^{81} +(-0.500000 - 0.866025i) q^{84} +(0.142315 + 0.246497i) q^{91} +(0.396666 - 1.63508i) q^{93} +(-0.981929 + 1.70075i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{3} - 2q^{4} + q^{7} + q^{9} + O(q^{10}) \) \( 20q + q^{3} - 2q^{4} + q^{7} + q^{9} + q^{12} + 2q^{13} - 2q^{16} + 2q^{19} + q^{21} + q^{25} - 2q^{27} + q^{28} - 4q^{31} + q^{36} + 2q^{37} + 2q^{39} - 4q^{43} + q^{48} + q^{49} - 9q^{52} + 21q^{57} + 2q^{61} - 2q^{63} - 2q^{64} + q^{67} - 12q^{73} + q^{75} + 2q^{76} - 12q^{79} + q^{81} - 10q^{84} + 2q^{91} + 2q^{93} - q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(337\) \(470\) \(1207\)
\(\chi(n)\) \(e\left(\frac{7}{33}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(3\) 0.981929 0.189251i 0.981929 0.189251i
\(4\) −0.959493 0.281733i −0.959493 0.281733i
\(5\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(6\) 0 0
\(7\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(8\) 0 0
\(9\) 0.928368 0.371662i 0.928368 0.371662i
\(10\) 0 0
\(11\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(12\) −0.995472 0.0950560i −0.995472 0.0950560i
\(13\) 0.283341 + 0.0270558i 0.283341 + 0.0270558i 0.235759 0.971812i \(-0.424242\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(17\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(18\) 0 0
\(19\) 0.0930932 + 0.647478i 0.0930932 + 0.647478i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(20\) 0 0
\(21\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(22\) 0 0
\(23\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(24\) 0 0
\(25\) −0.995472 0.0950560i −0.995472 0.0950560i
\(26\) 0 0
\(27\) 0.841254 0.540641i 0.841254 0.540641i
\(28\) −0.327068 0.945001i −0.327068 0.945001i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(37\) 1.16011 1.16011 0.580057 0.814576i \(-0.303030\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(38\) 0 0
\(39\) 0.283341 0.0270558i 0.283341 0.0270558i
\(40\) 0 0
\(41\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(42\) 0 0
\(43\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(48\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(49\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.264241 0.105786i −0.264241 0.105786i
\(53\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.213947 + 0.618159i 0.213947 + 0.618159i
\(58\) 0 0
\(59\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(60\) 0 0
\(61\) −0.550294 + 0.353653i −0.550294 + 0.353653i −0.786053 0.618159i \(-0.787879\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(62\) 0 0
\(63\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.580057 0.814576i 0.580057 0.814576i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(72\) 0 0
\(73\) −0.0845850 0.0436066i −0.0845850 0.0436066i 0.415415 0.909632i \(-0.363636\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(76\) 0.0930932 0.647478i 0.0930932 0.647478i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.15486 0.110276i −1.15486 0.110276i −0.500000 0.866025i \(-0.666667\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(80\) 0 0
\(81\) 0.723734 0.690079i 0.723734 0.690079i
\(82\) 0 0
\(83\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(84\) −0.500000 0.866025i −0.500000 0.866025i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(90\) 0 0
\(91\) 0.142315 + 0.246497i 0.142315 + 0.246497i
\(92\) 0 0
\(93\) 0.396666 1.63508i 0.396666 1.63508i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.981929 + 1.70075i −0.981929 + 1.70075i −0.327068 + 0.945001i \(0.606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(101\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(102\) 0 0
\(103\) −0.911911 1.28060i −0.911911 1.28060i −0.959493 0.281733i \(-0.909091\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(108\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(109\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(110\) 0 0
\(111\) 1.13915 0.219553i 1.13915 0.219553i
\(112\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(113\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.273100 0.0801894i 0.273100 0.0801894i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.84833 + 0.739959i −1.84833 + 0.739959i −0.888835 + 0.458227i \(0.848485\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(128\) 0 0
\(129\) −0.738471 + 0.380708i −0.738471 + 0.380708i
\(130\) 0 0
\(131\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(132\) 0 0
\(133\) −0.473420 + 0.451405i −0.473420 + 0.451405i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(138\) 0 0
\(139\) −1.10181 0.708089i −1.10181 0.708089i −0.142315 0.989821i \(-0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(148\) −1.11312 0.326842i −1.11312 0.326842i
\(149\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(150\) 0 0
\(151\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i 0.723734 0.690079i \(-0.242424\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.279486 0.0538665i −0.279486 0.0538665i
\(157\) 0.0930932 0.268975i 0.0930932 0.268975i −0.888835 0.458227i \(-0.848485\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.235759 + 0.408346i −0.235759 + 0.408346i −0.959493 0.281733i \(-0.909091\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(168\) 0 0
\(169\) −0.902379 0.173919i −0.902379 0.173919i
\(170\) 0 0
\(171\) 0.327068 + 0.566498i 0.327068 + 0.566498i
\(172\) 0.830830 0.830830
\(173\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(174\) 0 0
\(175\) −0.500000 0.866025i −0.500000 0.866025i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(180\) 0 0
\(181\) 0.428368 1.23769i 0.428368 1.23769i −0.500000 0.866025i \(-0.666667\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(182\) 0 0
\(183\) −0.473420 + 0.451405i −0.473420 + 0.451405i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(190\) 0 0
\(191\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(192\) −0.786053 0.618159i −0.786053 0.618159i
\(193\) 1.07701 + 1.51245i 1.07701 + 1.51245i 0.841254 + 0.540641i \(0.181818\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.580057 0.814576i 0.580057 0.814576i
\(197\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(198\) 0 0
\(199\) 1.34378 0.537970i 1.34378 0.537970i 0.415415 0.909632i \(-0.363636\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(200\) 0 0
\(201\) 0.415415 0.909632i 0.415415 0.909632i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0.223734 + 0.175946i 0.223734 + 0.175946i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.581419 + 1.67990i 0.581419 + 1.67990i 0.723734 + 0.690079i \(0.242424\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1.65210 0.318417i 1.65210 0.318417i
\(218\) 0 0
\(219\) −0.0913090 0.0268107i −0.0913090 0.0268107i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.28605 + 1.48418i −1.28605 + 1.48418i −0.500000 + 0.866025i \(0.666667\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(224\) 0 0
\(225\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(226\) 0 0
\(227\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(228\) −0.0311250 0.653395i −0.0311250 0.653395i
\(229\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.15486 + 0.110276i −1.15486 + 0.110276i
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) −0.0947329 1.98869i −0.0947329 1.98869i −0.142315 0.989821i \(-0.545455\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(242\) 0 0
\(243\) 0.580057 0.814576i 0.580057 0.814576i
\(244\) 0.627639 0.184291i 0.627639 0.184291i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.00885911 + 0.185976i 0.00885911 + 0.185976i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(252\) −0.654861 0.755750i −0.654861 0.755750i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(257\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(258\) 0 0
\(259\) 0.672932 + 0.945001i 0.672932 + 0.945001i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 0.514186 1.48564i 0.514186 1.48564i −0.327068 0.945001i \(-0.606061\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(272\) 0 0
\(273\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.13779 0.894765i −1.13779 0.894765i −0.142315 0.989821i \(-0.545455\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(278\) 0 0
\(279\) 0.0800569 1.68060i 0.0800569 1.68060i
\(280\) 0 0
\(281\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(282\) 0 0
\(283\) −1.65033 0.660694i −1.65033 0.660694i −0.654861 0.755750i \(-0.727273\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(290\) 0 0
\(291\) −0.642315 + 1.85585i −0.642315 + 1.85585i
\(292\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(301\) −0.653077 0.513585i −0.653077 0.513585i
\(302\) 0 0
\(303\) 0 0
\(304\) −0.271738 + 0.595023i −0.271738 + 0.595023i
\(305\) 0 0
\(306\) 0 0
\(307\) −1.11312 1.56316i −1.11312 1.56316i −0.786053 0.618159i \(-0.787879\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(308\) 0 0
\(309\) −1.13779 1.08488i −1.13779 1.08488i
\(310\) 0 0
\(311\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(312\) 0 0
\(313\) 1.82318 + 0.351390i 1.82318 + 0.351390i 0.981929 0.189251i \(-0.0606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.07701 + 0.431171i 1.07701 + 0.431171i
\(317\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(325\) −0.279486 0.0538665i −0.279486 0.0538665i
\(326\) 0 0
\(327\) −1.67489 + 0.159932i −1.67489 + 0.159932i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.947890 + 0.903811i −0.947890 + 0.903811i −0.995472 0.0950560i \(-0.969697\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(332\) 0 0
\(333\) 1.07701 0.431171i 1.07701 0.431171i
\(334\) 0 0
\(335\) 0 0
\(336\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(337\) 1.56499 + 1.23072i 1.56499 + 1.23072i 0.841254 + 0.540641i \(0.181818\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(348\) 0 0
\(349\) −1.78153 0.523103i −1.78153 0.523103i −0.786053 0.618159i \(-0.787879\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(350\) 0 0
\(351\) 0.252989 0.130425i 0.252989 0.130425i
\(352\) 0 0
\(353\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(360\) 0 0
\(361\) 0.548932 0.161181i 0.548932 0.161181i
\(362\) 0 0
\(363\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(364\) −0.0671040 0.276606i −0.0671040 0.276606i
\(365\) 0 0
\(366\) 0 0
\(367\) 1.16413 1.34347i 1.16413 1.34347i 0.235759 0.971812i \(-0.424242\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −0.841254 + 1.45709i −0.841254 + 1.45709i
\(373\) 0.142315 0.246497i 0.142315 0.246497i −0.786053 0.618159i \(-0.787879\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.82318 0.351390i 1.82318 0.351390i 0.841254 0.540641i \(-0.181818\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(380\) 0 0
\(381\) −1.67489 + 1.07639i −1.67489 + 1.07639i
\(382\) 0 0
\(383\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.653077 + 0.513585i −0.653077 + 0.513585i
\(388\) 1.42131 1.35522i 1.42131 1.35522i
\(389\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.0224357 0.470984i 0.0224357 0.470984i −0.959493 0.281733i \(-0.909091\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(398\) 0 0
\(399\) −0.379436 + 0.532843i −0.379436 + 0.532843i
\(400\) −0.786053 0.618159i −0.786053 0.618159i
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) 0.239446 0.414732i 0.239446 0.414732i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i −0.995472 0.0950560i \(-0.969697\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.514186 + 1.48564i 0.514186 + 1.48564i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.21590 0.486774i −1.21590 0.486774i
\(418\) 0 0
\(419\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(420\) 0 0
\(421\) 0.771316 + 0.308788i 0.771316 + 0.308788i 0.723734 0.690079i \(-0.242424\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.607279 0.243118i −0.607279 0.243118i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 1.00000 1.00000
\(433\) 1.98193 0.189251i 1.98193 0.189251i 0.981929 0.189251i \(-0.0606061\pi\)
1.00000 \(0\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.56199 + 0.625325i 1.56199 + 0.625325i
\(437\) 0 0
\(438\) 0 0
\(439\) 0.471518 0.471518 0.235759 0.971812i \(-0.424242\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(440\) 0 0
\(441\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(442\) 0 0
\(443\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(444\) −1.15486 0.110276i −1.15486 0.110276i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.235759 0.971812i 0.235759 0.971812i
\(449\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.56499 + 0.149438i 1.56499 + 0.149438i 0.841254 0.540641i \(-0.181818\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(462\) 0 0
\(463\) 0.0883470 + 1.85463i 0.0883470 + 1.85463i 0.415415 + 0.909632i \(0.363636\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(468\) −0.284630 −0.284630
\(469\) 1.00000 1.00000
\(470\) 0 0
\(471\) 0.0405070 0.281733i 0.0405070 0.281733i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.0311250 0.653395i −0.0311250 0.653395i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(480\) 0 0
\(481\) 0.328708 + 0.0313878i 0.328708 + 0.0313878i
\(482\) 0 0
\(483\) 0 0
\(484\) −0.142315 0.989821i −0.142315 0.989821i
\(485\) 0 0
\(486\) 0 0
\(487\) −0.452418 1.86489i −0.452418 1.86489i −0.500000 0.866025i \(-0.666667\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(488\) 0 0
\(489\) −0.154218 + 0.445585i −0.154218 + 0.445585i
\(490\) 0 0
\(491\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.41542 0.909632i 1.41542 0.909632i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.99094 −1.99094 −0.995472 0.0950560i \(-0.969697\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.918986 −0.918986
\(508\) 1.98193 0.189251i 1.98193 0.189251i
\(509\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(510\) 0 0
\(511\) −0.0135432 0.0941952i −0.0135432 0.0941952i
\(512\) 0 0
\(513\) 0.428368 + 0.494363i 0.428368 + 0.494363i
\(514\) 0 0
\(515\) 0 0
\(516\) 0.815816 0.157236i 0.815816 0.157236i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(522\) 0 0
\(523\) 0.771316 + 1.68895i 0.771316 + 1.68895i 0.723734 + 0.690079i \(0.242424\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(524\) 0 0
\(525\) −0.654861 0.755750i −0.654861 0.755750i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(530\) 0 0
\(531\) 0 0
\(532\) 0.581419 0.299742i 0.581419 0.299742i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0.0688733 1.44583i 0.0688733 1.44583i −0.654861 0.755750i \(-0.727273\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(542\) 0 0
\(543\) 0.186393 1.29639i 0.186393 1.29639i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.0224357 0.470984i 0.0224357 0.470984i −0.959493 0.281733i \(-0.909091\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(548\) 0 0
\(549\) −0.379436 + 0.532843i −0.379436 + 0.532843i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −0.580057 1.00469i −0.580057 1.00469i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(557\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(558\) 0 0
\(559\) −0.232205 + 0.0447539i −0.232205 + 0.0447539i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(568\) 0 0
\(569\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(570\) 0 0
\(571\) −1.28605 + 1.48418i −1.28605 + 1.48418i −0.500000 + 0.866025i \(0.666667\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.888835 0.458227i −0.888835 0.458227i
\(577\) −0.0913090 + 0.0268107i −0.0913090 + 0.0268107i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(578\) 0 0
\(579\) 1.34378 + 1.28129i 1.34378 + 1.28129i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(588\) 0.415415 0.909632i 0.415415 0.909632i
\(589\) 1.05601 + 0.310072i 1.05601 + 0.310072i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.975950 + 0.627205i 0.975950 + 0.627205i
\(593\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.21769 0.782560i 1.21769 0.782560i
\(598\) 0 0
\(599\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(600\) 0 0
\(601\) 1.39734 + 1.09888i 1.39734 + 1.09888i 0.981929 + 0.189251i \(0.0606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(602\) 0 0
\(603\) 0.235759 0.971812i 0.235759 0.971812i
\(604\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(605\) 0 0
\(606\) 0 0
\(607\) 1.34378 1.28129i 1.34378 1.28129i 0.415415 0.909632i \(-0.363636\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.42131 + 0.273935i 1.42131 + 0.273935i 0.841254 0.540641i \(-0.181818\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(618\) 0 0
\(619\) 0.0800569 1.68060i 0.0800569 1.68060i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0.252989 + 0.130425i 0.252989 + 0.130425i
\(625\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.165101 + 0.231852i −0.165101 + 0.231852i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.759713 1.06687i −0.759713 1.06687i −0.995472 0.0950560i \(-0.969697\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(632\) 0 0
\(633\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0.396666 0.254922i 0.396666 0.254922i −0.327068 0.945001i \(-0.606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 1.56199 0.625325i 1.56199 0.625325i
\(652\) 0.341254 0.325385i 0.341254 0.325385i
\(653\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.0947329 0.00904590i −0.0947329 0.00904590i
\(658\) 0 0
\(659\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(660\) 0 0
\(661\) 1.50842 + 1.18624i 1.50842 + 1.18624i 0.928368 + 0.371662i \(0.121212\pi\)
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
\(669\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.16413 + 1.34347i 1.16413 + 1.34347i 0.928368 + 0.371662i \(0.121212\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(674\) 0 0
\(675\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(676\) 0.816827 + 0.421104i 0.816827 + 0.421104i
\(677\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(678\) 0 0
\(679\) −1.95496 + 0.186677i −1.95496 + 0.186677i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(684\) −0.154218 0.635697i −0.154218 0.635697i
\(685\) 0 0
\(686\) 0 0
\(687\) 0.195876 0.807410i 0.195876 0.807410i
\(688\) −0.797176 0.234072i −0.797176 0.234072i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.0947329 1.98869i −0.0947329 1.98869i −0.142315 0.989821i \(-0.545455\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(701\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(702\) 0 0
\(703\) 0.107999 + 0.751148i 0.107999 + 0.751148i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(710\) 0 0
\(711\) −1.11312 + 0.326842i −1.11312 + 0.326842i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(720\) 0 0
\(721\) 0.514186 1.48564i 0.514186 1.48564i
\(722\) 0 0
\(723\) −0.469383 1.93482i −0.469383 1.93482i
\(724\) −0.759713 + 1.06687i −0.759713 + 1.06687i
\(725\) 0 0
\(726\) 0 0
\(727\) −0.154218 0.445585i −0.154218 0.445585i 0.841254 0.540641i \(-0.181818\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(728\) 0 0
\(729\) 0.415415 0.909632i 0.415415 0.909632i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.581419 0.299742i 0.581419 0.299742i
\(733\) −1.13779 + 1.08488i −1.13779 + 1.08488i −0.142315 + 0.989821i \(0.545455\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.78153 + 0.713215i −1.78153 + 0.713215i −0.786053 + 0.618159i \(0.787879\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(740\) 0 0
\(741\) 0.0438951 + 0.180938i 0.0438951 + 0.180938i
\(742\) 0 0
\(743\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.341254 + 1.40667i 0.341254 + 1.40667i 0.841254 + 0.540641i \(0.181818\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.786053 0.618159i −0.786053 0.618159i
\(757\) −0.0311250 + 0.0899299i −0.0311250 + 0.0899299i −0.959493 0.281733i \(-0.909091\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(762\) 0 0
\(763\) −0.841254 1.45709i −0.841254 1.45709i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(769\) 0.815816 + 0.157236i 0.815816 + 0.157236i 0.580057 0.814576i \(-0.303030\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.607279 1.75462i −0.607279 1.75462i
\(773\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(774\) 0 0
\(775\) −0.841254 + 1.45709i −0.841254 + 1.45709i
\(776\) 0 0
\(777\) 0.839614 + 0.800570i 0.839614 + 0.800570i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.601300 + 0.573338i 0.601300 + 0.573338i 0.928368 0.371662i \(-0.121212\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.165489 + 0.0853156i −0.165489 + 0.0853156i
\(794\) 0 0
\(795\) 0 0
\(796\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(797\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0