Properties

Label 1407.1.cz.a.851.1
Level $1407$
Weight $1$
Character 1407.851
Analytic conductor $0.702$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -3
Inner twists $4$

Related objects

Downloads

Learn more

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 851.1
Root \(0.580057 + 0.814576i\) of defining polynomial
Character \(\chi\) \(=\) 1407.851
Dual form 1407.1.cz.a.1283.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.786053 - 0.618159i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.981929 - 0.189251i) q^{7} +(0.235759 + 0.971812i) q^{9} +O(q^{10})\) \(q+(-0.786053 - 0.618159i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.981929 - 0.189251i) q^{7} +(0.235759 + 0.971812i) q^{9} +(-0.327068 - 0.945001i) q^{12} +(0.627639 + 1.81344i) q^{13} +(0.415415 + 0.909632i) q^{16} +(-1.78153 + 0.523103i) q^{19} +(-0.888835 - 0.458227i) q^{21} +(-0.327068 - 0.945001i) q^{25} +(0.415415 - 0.909632i) q^{27} +(0.928368 + 0.371662i) q^{28} +(-0.544078 - 0.627899i) q^{31} +(-0.327068 + 0.945001i) q^{36} +1.96386 q^{37} +(0.627639 - 1.81344i) q^{39} +(-1.10181 + 0.708089i) q^{43} +(0.235759 - 0.971812i) q^{48} +(0.928368 - 0.371662i) q^{49} +(-0.452418 + 1.86489i) q^{52} +(1.72373 + 0.690079i) q^{57} +(0.771316 - 1.68895i) q^{61} +(0.415415 + 0.909632i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.981929 + 0.189251i) q^{67} +(-1.15486 + 0.110276i) q^{73} +(-0.327068 + 0.945001i) q^{75} +(-1.78153 - 0.523103i) q^{76} +(-0.642315 - 1.85585i) q^{79} +(-0.888835 + 0.458227i) q^{81} +(-0.500000 - 0.866025i) q^{84} +(0.959493 + 1.66189i) q^{91} +(0.0395325 + 0.829889i) q^{93} +(0.786053 - 1.36148i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{3} - 2q^{4} + q^{7} + q^{9} + O(q^{10}) \) \( 20q + q^{3} - 2q^{4} + q^{7} + q^{9} + q^{12} + 2q^{13} - 2q^{16} + 2q^{19} + q^{21} + q^{25} - 2q^{27} + q^{28} - 4q^{31} + q^{36} + 2q^{37} + 2q^{39} - 4q^{43} + q^{48} + q^{49} - 9q^{52} + 21q^{57} + 2q^{61} - 2q^{63} - 2q^{64} + q^{67} - 12q^{73} + q^{75} + 2q^{76} - 12q^{79} + q^{81} - 10q^{84} + 2q^{91} + 2q^{93} - q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(337\) \(470\) \(1207\)
\(\chi(n)\) \(e\left(\frac{25}{33}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(3\) −0.786053 0.618159i −0.786053 0.618159i
\(4\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(5\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(6\) 0 0
\(7\) 0.981929 0.189251i 0.981929 0.189251i
\(8\) 0 0
\(9\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(10\) 0 0
\(11\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(12\) −0.327068 0.945001i −0.327068 0.945001i
\(13\) 0.627639 + 1.81344i 0.627639 + 1.81344i 0.580057 + 0.814576i \(0.303030\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(17\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(18\) 0 0
\(19\) −1.78153 + 0.523103i −1.78153 + 0.523103i −0.995472 0.0950560i \(-0.969697\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(20\) 0 0
\(21\) −0.888835 0.458227i −0.888835 0.458227i
\(22\) 0 0
\(23\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(24\) 0 0
\(25\) −0.327068 0.945001i −0.327068 0.945001i
\(26\) 0 0
\(27\) 0.415415 0.909632i 0.415415 0.909632i
\(28\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(37\) 1.96386 1.96386 0.981929 0.189251i \(-0.0606061\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(38\) 0 0
\(39\) 0.627639 1.81344i 0.627639 1.81344i
\(40\) 0 0
\(41\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(42\) 0 0
\(43\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(48\) 0.235759 0.971812i 0.235759 0.971812i
\(49\) 0.928368 0.371662i 0.928368 0.371662i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.452418 + 1.86489i −0.452418 + 1.86489i
\(53\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.72373 + 0.690079i 1.72373 + 0.690079i
\(58\) 0 0
\(59\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(60\) 0 0
\(61\) 0.771316 1.68895i 0.771316 1.68895i 0.0475819 0.998867i \(-0.484848\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(62\) 0 0
\(63\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(64\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(72\) 0 0
\(73\) −1.15486 + 0.110276i −1.15486 + 0.110276i −0.654861 0.755750i \(-0.727273\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(76\) −1.78153 0.523103i −1.78153 0.523103i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.642315 1.85585i −0.642315 1.85585i −0.500000 0.866025i \(-0.666667\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(80\) 0 0
\(81\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(82\) 0 0
\(83\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(84\) −0.500000 0.866025i −0.500000 0.866025i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(90\) 0 0
\(91\) 0.959493 + 1.66189i 0.959493 + 1.66189i
\(92\) 0 0
\(93\) 0.0395325 + 0.829889i 0.0395325 + 0.829889i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.786053 1.36148i 0.786053 1.36148i −0.142315 0.989821i \(-0.545455\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.235759 0.971812i 0.235759 0.971812i
\(101\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(102\) 0 0
\(103\) 1.42131 0.273935i 1.42131 0.273935i 0.580057 0.814576i \(-0.303030\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(108\) 0.841254 0.540641i 0.841254 0.540641i
\(109\) −0.271738 0.785135i −0.271738 0.785135i −0.995472 0.0950560i \(-0.969697\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(110\) 0 0
\(111\) −1.54370 1.21398i −1.54370 1.21398i
\(112\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(113\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.118239 0.822373i −0.118239 0.822373i
\(125\) 0 0
\(126\) 0 0
\(127\) −0.154218 0.635697i −0.154218 0.635697i −0.995472 0.0950560i \(-0.969697\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(128\) 0 0
\(129\) 1.30379 + 0.124497i 1.30379 + 0.124497i
\(130\) 0 0
\(131\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(132\) 0 0
\(133\) −1.65033 + 0.850806i −1.65033 + 0.850806i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(138\) 0 0
\(139\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.959493 0.281733i −0.959493 0.281733i
\(148\) 1.65210 + 1.06174i 1.65210 + 1.06174i
\(149\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(150\) 0 0
\(151\) −1.03115 0.531595i −1.03115 0.531595i −0.142315 0.989821i \(-0.545455\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.50842 1.18624i 1.50842 1.18624i
\(157\) −1.78153 + 0.713215i −1.78153 + 0.713215i −0.786053 + 0.618159i \(0.787879\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(168\) 0 0
\(169\) −2.10859 + 1.65822i −2.10859 + 1.65822i
\(170\) 0 0
\(171\) −0.928368 1.60798i −0.928368 1.60798i
\(172\) −1.30972 −1.30972
\(173\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(174\) 0 0
\(175\) −0.500000 0.866025i −0.500000 0.866025i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(180\) 0 0
\(181\) −0.264241 + 0.105786i −0.264241 + 0.105786i −0.500000 0.866025i \(-0.666667\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(182\) 0 0
\(183\) −1.65033 + 0.850806i −1.65033 + 0.850806i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.235759 0.971812i 0.235759 0.971812i
\(190\) 0 0
\(191\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(192\) 0.723734 0.690079i 0.723734 0.690079i
\(193\) 0.462997 0.0892353i 0.462997 0.0892353i 0.0475819 0.998867i \(-0.484848\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(197\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(198\) 0 0
\(199\) −0.419102 1.72756i −0.419102 1.72756i −0.654861 0.755750i \(-0.727273\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(200\) 0 0
\(201\) −0.654861 0.755750i −0.654861 0.755750i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −1.38884 + 1.32425i −1.38884 + 1.32425i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.84833 0.739959i −1.84833 0.739959i −0.959493 0.281733i \(-0.909091\pi\)
−0.888835 0.458227i \(-0.848485\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.653077 0.513585i −0.653077 0.513585i
\(218\) 0 0
\(219\) 0.975950 + 0.627205i 0.975950 + 0.627205i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.223734 + 1.55610i 0.223734 + 1.55610i 0.723734 + 0.690079i \(0.242424\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) 0 0
\(225\) 0.841254 0.540641i 0.841254 0.540641i
\(226\) 0 0
\(227\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(228\) 1.07701 + 1.51245i 1.07701 + 1.51245i
\(229\) 0.857685 + 0.989821i 0.857685 + 0.989821i 1.00000 \(0\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −0.642315 + 1.85585i −0.642315 + 1.85585i
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) −0.379436 0.532843i −0.379436 0.532843i 0.580057 0.814576i \(-0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(242\) 0 0
\(243\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(244\) 1.56199 1.00383i 1.56199 1.00383i
\(245\) 0 0
\(246\) 0 0
\(247\) −2.06677 2.90237i −2.06677 2.90237i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(252\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(257\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(258\) 0 0
\(259\) 1.92837 0.371662i 1.92837 0.371662i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(269\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 1.34378 0.537970i 1.34378 0.537970i 0.415415 0.909632i \(-0.363636\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(272\) 0 0
\(273\) 0.273100 1.89945i 0.273100 1.89945i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.28656 + 1.22673i −1.28656 + 1.22673i −0.327068 + 0.945001i \(0.606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(278\) 0 0
\(279\) 0.481929 0.676774i 0.481929 0.676774i
\(280\) 0 0
\(281\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(282\) 0 0
\(283\) −0.469383 + 1.93482i −0.469383 + 1.93482i −0.142315 + 0.989821i \(0.545455\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(290\) 0 0
\(291\) −1.45949 + 0.584293i −1.45949 + 0.584293i
\(292\) −1.03115 0.531595i −1.03115 0.531595i
\(293\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(301\) −0.947890 + 0.903811i −0.947890 + 0.903811i
\(302\) 0 0
\(303\) 0 0
\(304\) −1.21590 1.40323i −1.21590 1.40323i
\(305\) 0 0
\(306\) 0 0
\(307\) 1.65210 0.318417i 1.65210 0.318417i 0.723734 0.690079i \(-0.242424\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(308\) 0 0
\(309\) −1.28656 0.663268i −1.28656 0.663268i
\(310\) 0 0
\(311\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(312\) 0 0
\(313\) −0.370638 + 0.291473i −0.370638 + 0.291473i −0.786053 0.618159i \(-0.787879\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.462997 1.90850i 0.462997 1.90850i
\(317\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.995472 0.0950560i −0.995472 0.0950560i
\(325\) 1.50842 1.18624i 1.50842 1.18624i
\(326\) 0 0
\(327\) −0.271738 + 0.785135i −0.271738 + 0.785135i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.252989 0.130425i 0.252989 0.130425i −0.327068 0.945001i \(-0.606061\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(332\) 0 0
\(333\) 0.462997 + 1.90850i 0.462997 + 1.90850i
\(334\) 0 0
\(335\) 0 0
\(336\) 0.0475819 0.998867i 0.0475819 0.998867i
\(337\) −0.473420 + 0.451405i −0.473420 + 0.451405i −0.888835 0.458227i \(-0.848485\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.841254 0.540641i 0.841254 0.540641i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(348\) 0 0
\(349\) 0.396666 + 0.254922i 0.396666 + 0.254922i 0.723734 0.690079i \(-0.242424\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(350\) 0 0
\(351\) 1.91030 + 0.182411i 1.91030 + 0.182411i
\(352\) 0 0
\(353\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(360\) 0 0
\(361\) 2.05894 1.32320i 2.05894 1.32320i
\(362\) 0 0
\(363\) 0.981929 0.189251i 0.981929 0.189251i
\(364\) −0.0913090 + 1.91681i −0.0913090 + 1.91681i
\(365\) 0 0
\(366\) 0 0
\(367\) 0.283341 + 1.97068i 0.283341 + 1.97068i 0.235759 + 0.971812i \(0.424242\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −0.415415 + 0.719520i −0.415415 + 0.719520i
\(373\) 0.959493 1.66189i 0.959493 1.66189i 0.235759 0.971812i \(-0.424242\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.370638 0.291473i −0.370638 0.291473i 0.415415 0.909632i \(-0.363636\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(380\) 0 0
\(381\) −0.271738 + 0.595023i −0.271738 + 0.595023i
\(382\) 0 0
\(383\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.947890 0.903811i −0.947890 0.903811i
\(388\) 1.39734 0.720381i 1.39734 0.720381i
\(389\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.0552004 0.0775182i 0.0552004 0.0775182i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(398\) 0 0
\(399\) 1.82318 + 0.351390i 1.82318 + 0.351390i
\(400\) 0.723734 0.690079i 0.723734 0.690079i
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) 0.797176 1.38075i 0.797176 1.38075i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.11312 0.326842i −1.11312 0.326842i −0.327068 0.945001i \(-0.606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.34378 + 0.537970i 1.34378 + 0.537970i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i
\(418\) 0 0
\(419\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(420\) 0 0
\(421\) −0.308779 + 1.27280i −0.308779 + 1.27280i 0.580057 + 0.814576i \(0.303030\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.437742 1.80440i 0.437742 1.80440i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 1.00000 1.00000
\(433\) 0.213947 0.618159i 0.213947 0.618159i −0.786053 0.618159i \(-0.787879\pi\)
1.00000 \(0\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.195876 0.807410i 0.195876 0.807410i
\(437\) 0 0
\(438\) 0 0
\(439\) 0.0951638 0.0951638 0.0475819 0.998867i \(-0.484848\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(440\) 0 0
\(441\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(442\) 0 0
\(443\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(444\) −0.642315 1.85585i −0.642315 1.85585i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(449\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0.481929 + 1.05528i 0.481929 + 1.05528i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.473420 1.36786i −0.473420 1.36786i −0.888835 0.458227i \(-0.848485\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(462\) 0 0
\(463\) 0.273507 + 0.384087i 0.273507 + 0.384087i 0.928368 0.371662i \(-0.121212\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(468\) −1.91899 −1.91899
\(469\) 1.00000 1.00000
\(470\) 0 0
\(471\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 1.07701 + 1.51245i 1.07701 + 1.51245i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(480\) 0 0
\(481\) 1.23259 + 3.56134i 1.23259 + 3.56134i
\(482\) 0 0
\(483\) 0 0
\(484\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(485\) 0 0
\(486\) 0 0
\(487\) 0.0800569 1.68060i 0.0800569 1.68060i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(488\) 0 0
\(489\) 0.0883470 0.0353688i 0.0883470 0.0353688i
\(490\) 0 0
\(491\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.345139 0.755750i 0.345139 0.755750i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.654136 −0.654136 −0.327068 0.945001i \(-0.606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.68251 2.68251
\(508\) 0.213947 0.618159i 0.213947 0.618159i
\(509\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(510\) 0 0
\(511\) −1.11312 + 0.326842i −1.11312 + 0.326842i
\(512\) 0 0
\(513\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(514\) 0 0
\(515\) 0 0
\(516\) 1.02951 + 0.809616i 1.02951 + 0.809616i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(522\) 0 0
\(523\) −0.308779 + 0.356349i −0.308779 + 0.356349i −0.888835 0.458227i \(-0.848485\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(524\) 0 0
\(525\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.959493 0.281733i −0.959493 0.281733i
\(530\) 0 0
\(531\) 0 0
\(532\) −1.84833 0.176494i −1.84833 0.176494i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.03115 + 1.44805i −1.03115 + 1.44805i −0.142315 + 0.989821i \(0.545455\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(542\) 0 0
\(543\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.0552004 0.0775182i 0.0552004 0.0775182i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(548\) 0 0
\(549\) 1.82318 + 0.351390i 1.82318 + 0.351390i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −0.981929 1.70075i −0.981929 1.70075i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.0405070 0.281733i 0.0405070 0.281733i
\(557\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(558\) 0 0
\(559\) −1.97562 1.55364i −1.97562 1.55364i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(568\) 0 0
\(569\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(570\) 0 0
\(571\) 0.223734 + 1.55610i 0.223734 + 1.55610i 0.723734 + 0.690079i \(0.242424\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(577\) 0.975950 0.627205i 0.975950 0.627205i 0.0475819 0.998867i \(-0.484848\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(578\) 0 0
\(579\) −0.419102 0.216062i −0.419102 0.216062i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(588\) −0.654861 0.755750i −0.654861 0.755750i
\(589\) 1.29774 + 0.834010i 1.29774 + 0.834010i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.815816 + 1.78639i 0.815816 + 1.78639i
\(593\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.738471 + 1.61703i −0.738471 + 1.61703i
\(598\) 0 0
\(599\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(600\) 0 0
\(601\) −1.44091 + 1.37391i −1.44091 + 1.37391i −0.654861 + 0.755750i \(0.727273\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(602\) 0 0
\(603\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(604\) −0.580057 1.00469i −0.580057 1.00469i
\(605\) 0 0
\(606\) 0 0
\(607\) −0.419102 + 0.216062i −0.419102 + 0.216062i −0.654861 0.755750i \(-0.727273\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.39734 1.09888i 1.39734 1.09888i 0.415415 0.909632i \(-0.363636\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(618\) 0 0
\(619\) 0.481929 0.676774i 0.481929 0.676774i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.91030 0.182411i 1.91030 0.182411i
\(625\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(626\) 0 0
\(627\) 0 0
\(628\) −1.88431 0.363170i −1.88431 0.363170i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.279486 + 0.0538665i −0.279486 + 0.0538665i −0.327068 0.945001i \(-0.606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(632\) 0 0
\(633\) 0.995472 + 1.72421i 0.995472 + 1.72421i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0.0395325 0.0865641i 0.0395325 0.0865641i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0.195876 + 0.807410i 0.195876 + 0.807410i
\(652\) −0.0845850 + 0.0436066i −0.0845850 + 0.0436066i
\(653\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.379436 1.09631i −0.379436 1.09631i
\(658\) 0 0
\(659\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(660\) 0 0
\(661\) 1.21769 1.16106i 1.21769 1.16106i 0.235759 0.971812i \(-0.424242\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0.786053 1.36148i 0.786053 1.36148i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.283341 1.97068i 0.283341 1.97068i 0.0475819 0.998867i \(-0.484848\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(674\) 0 0
\(675\) −0.995472 0.0950560i −0.995472 0.0950560i
\(676\) −2.67036 + 0.254989i −2.67036 + 0.254989i
\(677\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(678\) 0 0
\(679\) 0.514186 1.48564i 0.514186 1.48564i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(684\) 0.0883470 1.85463i 0.0883470 1.85463i
\(685\) 0 0
\(686\) 0 0
\(687\) −0.0623191 1.30824i −0.0623191 1.30824i
\(688\) −1.10181 0.708089i −1.10181 0.708089i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.379436 0.532843i −0.379436 0.532843i 0.580057 0.814576i \(-0.303030\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.0475819 0.998867i 0.0475819 0.998867i
\(701\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(702\) 0 0
\(703\) −3.49866 + 1.02730i −3.49866 + 1.02730i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(710\) 0 0
\(711\) 1.65210 1.06174i 1.65210 1.06174i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(720\) 0 0
\(721\) 1.34378 0.537970i 1.34378 0.537970i
\(722\) 0 0
\(723\) −0.0311250 + 0.653395i −0.0311250 + 0.653395i
\(724\) −0.279486 0.0538665i −0.279486 0.0538665i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i 0.415415 0.909632i \(-0.363636\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(728\) 0 0
\(729\) −0.654861 0.755750i −0.654861 0.755750i
\(730\) 0 0
\(731\) 0 0
\(732\) −1.84833 0.176494i −1.84833 0.176494i
\(733\) −1.28656 + 0.663268i −1.28656 + 0.663268i −0.959493 0.281733i \(-0.909091\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.396666 + 1.63508i 0.396666 + 1.63508i 0.723734 + 0.690079i \(0.242424\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(740\) 0 0
\(741\) −0.169537 + 3.55901i −0.169537 + 3.55901i
\(742\) 0 0
\(743\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.0845850 + 1.77566i −0.0845850 + 1.77566i 0.415415 + 0.909632i \(0.363636\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.723734 0.690079i 0.723734 0.690079i
\(757\) 1.07701 0.431171i 1.07701 0.431171i 0.235759 0.971812i \(-0.424242\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(762\) 0 0
\(763\) −0.415415 0.719520i −0.415415 0.719520i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.981929 0.189251i 0.981929 0.189251i
\(769\) 1.02951 0.809616i 1.02951 0.809616i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.437742 + 0.175245i 0.437742 + 0.175245i
\(773\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(774\) 0 0
\(775\) −0.415415 + 0.719520i −0.415415 + 0.719520i
\(776\) 0 0
\(777\) −1.74555 0.899892i −1.74555 0.899892i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(785\) 0 0
\(786\) 0 0
\(787\) 1.16413 + 0.600149i 1.16413 + 0.600149i 0.928368 0.371662i \(-0.121212\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 3.54692 + 0.338689i 3.54692 + 0.338689i
\(794\) 0 0
\(795\) 0 0
\(796\) 0.581419 1.67990i 0.581419 1.67990i
\(797\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0