Properties

Label 536.1.ba.a.307.1
Level $536$
Weight $1$
Character 536.307
Analytic conductor $0.267$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -8
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 536 = 2^{3} \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 536.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.267498846771\)
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: \(\Z[a_1, a_2]\)
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 307.1
Root \(-0.786053 - 0.618159i\) of defining polynomial
Character \(\chi\) \(=\) 536.307
Dual form 536.1.ba.a.323.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.928368 - 0.371662i) q^{2} +(-0.759713 - 0.876756i) q^{3} +(0.723734 - 0.690079i) q^{4} +(-1.03115 - 0.531595i) q^{6} +(0.415415 - 0.909632i) q^{8} +(-0.0492216 + 0.342344i) q^{9} +O(q^{10})\) \(q+(0.928368 - 0.371662i) q^{2} +(-0.759713 - 0.876756i) q^{3} +(0.723734 - 0.690079i) q^{4} +(-1.03115 - 0.531595i) q^{6} +(0.415415 - 0.909632i) q^{8} +(-0.0492216 + 0.342344i) q^{9} +(-0.738471 + 0.380708i) q^{11} +(-1.15486 - 0.110276i) q^{12} +(0.0475819 - 0.998867i) q^{16} +(0.341254 + 0.325385i) q^{17} +(0.0815405 + 0.336115i) q^{18} +(-0.0748038 + 0.0588264i) q^{19} +(-0.544078 + 0.627899i) q^{22} +(-1.11312 + 0.326842i) q^{24} +(0.415415 + 0.909632i) q^{25} +(-0.638404 + 0.410277i) q^{27} +(-0.327068 - 0.945001i) q^{32} +(0.894814 + 0.358230i) q^{33} +(0.437742 + 0.175245i) q^{34} +(0.200621 + 0.281733i) q^{36} +(-0.0475819 + 0.0824143i) q^{38} +(-0.0671040 + 0.276606i) q^{41} +(1.70566 - 0.500828i) q^{43} +(-0.271738 + 0.785135i) q^{44} +(-0.911911 + 0.717135i) q^{48} +(0.235759 + 0.971812i) q^{49} +(0.723734 + 0.690079i) q^{50} +(0.0260280 - 0.546395i) q^{51} +(-0.440189 + 0.618159i) q^{54} +(0.108406 + 0.0208935i) q^{57} +(-0.827068 + 1.81103i) q^{59} +(-0.654861 - 0.755750i) q^{64} +0.963857 q^{66} +(0.841254 + 0.540641i) q^{67} +0.471518 q^{68} +(0.290959 + 0.186988i) q^{72} +(-1.28656 - 0.663268i) q^{73} +(0.481929 - 1.05528i) q^{75} +(-0.0135432 + 0.0941952i) q^{76} +(1.17657 + 0.345472i) q^{81} +(0.0405070 + 0.281733i) q^{82} +(0.0800569 - 1.68060i) q^{83} +(1.39734 - 1.09888i) q^{86} +(0.0395325 + 0.829889i) q^{88} +(-1.21590 + 1.40323i) q^{89} +(-0.580057 + 1.00469i) q^{96} +(-0.723734 - 1.25354i) q^{97} +(0.580057 + 0.814576i) q^{98} +(-0.0939844 - 0.271550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/536\mathbb{Z}\right)^\times\).

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{29}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.928368 0.371662i 0.928368 0.371662i
\(3\) −0.759713 0.876756i −0.759713 0.876756i 0.235759 0.971812i \(-0.424242\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(4\) 0.723734 0.690079i 0.723734 0.690079i
\(5\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(6\) −1.03115 0.531595i −1.03115 0.531595i
\(7\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(8\) 0.415415 0.909632i 0.415415 0.909632i
\(9\) −0.0492216 + 0.342344i −0.0492216 + 0.342344i
\(10\) 0 0
\(11\) −0.738471 + 0.380708i −0.738471 + 0.380708i −0.786053 0.618159i \(-0.787879\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(12\) −1.15486 0.110276i −1.15486 0.110276i
\(13\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.0475819 0.998867i 0.0475819 0.998867i
\(17\) 0.341254 + 0.325385i 0.341254 + 0.325385i 0.841254 0.540641i \(-0.181818\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 0.0815405 + 0.336115i 0.0815405 + 0.336115i
\(19\) −0.0748038 + 0.0588264i −0.0748038 + 0.0588264i −0.654861 0.755750i \(-0.727273\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(23\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(24\) −1.11312 + 0.326842i −1.11312 + 0.326842i
\(25\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(26\) 0 0
\(27\) −0.638404 + 0.410277i −0.638404 + 0.410277i
\(28\) 0 0
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(32\) −0.327068 0.945001i −0.327068 0.945001i
\(33\) 0.894814 + 0.358230i 0.894814 + 0.358230i
\(34\) 0.437742 + 0.175245i 0.437742 + 0.175245i
\(35\) 0 0
\(36\) 0.200621 + 0.281733i 0.200621 + 0.281733i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i −0.995472 0.0950560i \(-0.969697\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(42\) 0 0
\(43\) 1.70566 0.500828i 1.70566 0.500828i 0.723734 0.690079i \(-0.242424\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(44\) −0.271738 + 0.785135i −0.271738 + 0.785135i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(48\) −0.911911 + 0.717135i −0.911911 + 0.717135i
\(49\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(50\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(51\) 0.0260280 0.546395i 0.0260280 0.546395i
\(52\) 0 0
\(53\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(54\) −0.440189 + 0.618159i −0.440189 + 0.618159i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.108406 + 0.0208935i 0.108406 + 0.0208935i
\(58\) 0 0
\(59\) −0.827068 + 1.81103i −0.827068 + 1.81103i −0.327068 + 0.945001i \(0.606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) 0.963857 0.963857
\(67\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(68\) 0.471518 0.471518
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(72\) 0.290959 + 0.186988i 0.290959 + 0.186988i
\(73\) −1.28656 0.663268i −1.28656 0.663268i −0.327068 0.945001i \(-0.606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(74\) 0 0
\(75\) 0.481929 1.05528i 0.481929 1.05528i
\(76\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(80\) 0 0
\(81\) 1.17657 + 0.345472i 1.17657 + 0.345472i
\(82\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(83\) 0.0800569 1.68060i 0.0800569 1.68060i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.39734 1.09888i 1.39734 1.09888i
\(87\) 0 0
\(88\) 0.0395325 + 0.829889i 0.0395325 + 0.829889i
\(89\) −1.21590 + 1.40323i −1.21590 + 1.40323i −0.327068 + 0.945001i \(0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.580057 + 1.00469i −0.580057 + 1.00469i
\(97\) −0.723734 1.25354i −0.723734 1.25354i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(98\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(99\) −0.0939844 0.271550i −0.0939844 0.271550i
\(100\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(101\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(102\) −0.178911 0.516929i −0.178911 0.516929i
\(103\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(108\) −0.178911 + 0.737481i −0.178911 + 0.737481i
\(109\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.0947329 1.98869i −0.0947329 1.98869i −0.142315 0.989821i \(-0.545455\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(114\) 0.108406 0.0208935i 0.108406 0.0208935i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.0947329 + 1.98869i −0.0947329 + 1.98869i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.179656 + 0.252292i −0.179656 + 0.252292i
\(122\) 0 0
\(123\) 0.293496 0.151308i 0.293496 0.151308i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(128\) −0.888835 0.458227i −0.888835 0.458227i
\(129\) −1.73492 1.11496i −1.73492 1.11496i
\(130\) 0 0
\(131\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(132\) 0.894814 0.358230i 0.894814 0.358230i
\(133\) 0 0
\(134\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(135\) 0 0
\(136\) 0.437742 0.175245i 0.437742 0.175245i
\(137\) −1.28605 1.48418i −1.28605 1.48418i −0.786053 0.618159i \(-0.787879\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(138\) 0 0
\(139\) −0.841254 0.540641i −0.841254 0.540641i 0.0475819 0.998867i \(-0.484848\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.339614 + 0.0654552i 0.339614 + 0.0654552i
\(145\) 0 0
\(146\) −1.44091 0.137591i −1.44091 0.137591i
\(147\) 0.672932 0.945001i 0.672932 0.945001i
\(148\) 0 0
\(149\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(150\) 0.0552004 1.15880i 0.0552004 1.15880i
\(151\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(152\) 0.0224357 + 0.0924813i 0.0224357 + 0.0924813i
\(153\) −0.128190 + 0.100810i −0.128190 + 0.100810i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.22069 0.116562i 1.22069 0.116562i
\(163\) 0.786053 1.36148i 0.786053 1.36148i −0.142315 0.989821i \(-0.545455\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(164\) 0.142315 + 0.246497i 0.142315 + 0.246497i
\(165\) 0 0
\(166\) −0.550294 1.58997i −0.550294 1.58997i
\(167\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(168\) 0 0
\(169\) −0.327068 0.945001i −0.327068 0.945001i
\(170\) 0 0
\(171\) −0.0164569 0.0285041i −0.0164569 0.0285041i
\(172\) 0.888835 1.53951i 0.888835 1.53951i
\(173\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(177\) 2.21616 0.650724i 2.21616 0.650724i
\(178\) −0.607279 + 1.75462i −0.607279 + 1.75462i
\(179\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(180\) 0 0
\(181\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.375883 0.110369i −0.375883 0.110369i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(192\) −0.165101 + 1.14831i −0.165101 + 1.14831i
\(193\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(194\) −1.13779 0.894765i −1.13779 0.894765i
\(195\) 0 0
\(196\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(197\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(198\) −0.188177 0.217168i −0.188177 0.217168i
\(199\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(200\) 1.00000 1.00000
\(201\) −0.165101 1.14831i −0.165101 1.14831i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.358218 0.413406i −0.358218 0.413406i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.0328448 0.0719200i 0.0328448 0.0719200i
\(210\) 0 0
\(211\) 1.82318 + 0.351390i 1.82318 + 0.351390i 0.981929 0.189251i \(-0.0606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.759713 + 1.06687i −0.759713 + 1.06687i
\(215\) 0 0
\(216\) 0.107999 + 0.751148i 0.107999 + 0.751148i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.395893 + 1.63189i 0.395893 + 1.63189i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(224\) 0 0
\(225\) −0.331854 + 0.0974412i −0.331854 + 0.0974412i
\(226\) −0.827068 1.81103i −0.827068 1.81103i
\(227\) −0.370638 + 1.52779i −0.370638 + 1.52779i 0.415415 + 0.909632i \(0.363636\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(228\) 0.0928751 0.0596872i 0.0928751 0.0596872i
\(229\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.327068 + 0.945001i 0.327068 + 0.945001i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.651174 + 1.88144i 0.651174 + 1.88144i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 0 0
\(241\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(242\) −0.0730196 + 0.300991i −0.0730196 + 0.300991i
\(243\) −0.275714 0.603730i −0.275714 0.603730i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.216237 0.249551i 0.216237 0.249551i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.53430 + 1.20658i −1.53430 + 1.20658i
\(250\) 0 0
\(251\) −1.13779 1.08488i −1.13779 1.08488i −0.995472 0.0950560i \(-0.969697\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.995472 0.0950560i −0.995472 0.0950560i
\(257\) 1.70566 0.879330i 1.70566 0.879330i 0.723734 0.690079i \(-0.242424\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(258\) −2.02503 0.390293i −2.02503 0.390293i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.252989 + 0.130425i 0.252989 + 0.130425i
\(263\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(264\) 0.697576 0.665138i 0.697576 0.665138i
\(265\) 0 0
\(266\) 0 0
\(267\) 2.15402 2.15402
\(268\) 0.981929 0.189251i 0.981929 0.189251i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(272\) 0.341254 0.325385i 0.341254 0.325385i
\(273\) 0 0
\(274\) −1.74555 0.899892i −1.74555 0.899892i
\(275\) −0.653077 0.513585i −0.653077 0.513585i
\(276\) 0 0
\(277\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(278\) −0.981929 0.189251i −0.981929 0.189251i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.273507 0.384087i 0.273507 0.384087i −0.654861 0.755750i \(-0.727273\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(282\) 0 0
\(283\) 0.142315 + 0.989821i 0.142315 + 0.989821i 0.928368 + 0.371662i \(0.121212\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.339614 0.0654552i 0.339614 0.0654552i
\(289\) −0.0370031 0.776790i −0.0370031 0.776790i
\(290\) 0 0
\(291\) −0.549222 + 1.58687i −0.549222 + 1.58687i
\(292\) −1.38884 + 0.407799i −1.38884 + 0.407799i
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) 0.273507 1.12741i 0.273507 1.12741i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.315247 0.546024i 0.315247 0.546024i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.379436 1.09631i −0.379436 1.09631i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.0552004 + 0.0775182i 0.0552004 + 0.0775182i
\(305\) 0 0
\(306\) −0.0815405 + 0.141232i −0.0815405 + 0.141232i
\(307\) 1.76962 0.168978i 1.76962 0.168978i 0.841254 0.540641i \(-0.181818\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(312\) 0 0
\(313\) −0.0623191 + 0.0719200i −0.0623191 + 0.0719200i −0.786053 0.618159i \(-0.787879\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 1.45788 + 0.428072i 1.45788 + 0.428072i
\(322\) 0 0
\(323\) −0.0446683 0.00426530i −0.0446683 0.00426530i
\(324\) 1.08993 0.561897i 1.08993 0.561897i
\(325\) 0 0
\(326\) 0.223734 1.55610i 0.223734 1.55610i
\(327\) 0 0
\(328\) 0.223734 + 0.175946i 0.223734 + 0.175946i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.0688733 0.0656706i 0.0688733 0.0656706i −0.654861 0.755750i \(-0.727273\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(332\) −1.10181 1.27155i −1.10181 1.27155i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.78153 + 0.713215i −1.78153 + 0.713215i −0.786053 + 0.618159i \(0.787879\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(338\) −0.654861 0.755750i −0.654861 0.755750i
\(339\) −1.67162 + 1.59389i −1.67162 + 1.59389i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.0258720 0.0203459i −0.0258720 0.0203459i
\(343\) 0 0
\(344\) 0.252989 1.75958i 0.252989 1.75958i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.995472 + 0.0950560i 0.995472 + 0.0950560i 0.580057 0.814576i \(-0.303030\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(348\) 0 0
\(349\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.601300 + 0.573338i 0.601300 + 0.573338i
\(353\) −0.308779 1.27280i −0.308779 1.27280i −0.888835 0.458227i \(-0.848485\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(354\) 1.81556 1.42778i 1.81556 1.42778i
\(355\) 0 0
\(356\) 0.0883470 + 1.85463i 0.0883470 + 1.85463i
\(357\) 0 0
\(358\) −0.550294 + 1.58997i −0.550294 + 1.58997i
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) 0 0
\(361\) −0.233624 + 0.963011i −0.233624 + 0.963011i
\(362\) 0 0
\(363\) 0.357685 0.0341548i 0.357685 0.0341548i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(368\) 0 0
\(369\) −0.0913915 0.0365876i −0.0913915 0.0365876i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) −0.389977 + 0.0372383i −0.389977 + 0.0372383i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.0930932 0.268975i 0.0930932 0.268975i −0.888835 0.458227i \(-0.848485\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(384\) 0.273507 + 1.12741i 0.273507 + 1.12741i
\(385\) 0 0
\(386\) −0.0913090 + 1.91681i −0.0913090 + 1.91681i
\(387\) 0.0874998 + 0.608574i 0.0874998 + 0.608574i
\(388\) −1.38884 0.407799i −1.38884 0.407799i
\(389\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(393\) 0.0469928 0.326842i 0.0469928 0.326842i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.255411 0.131673i −0.255411 0.131673i
\(397\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.928368 0.371662i 0.928368 0.371662i
\(401\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(402\) −0.580057 1.00469i −0.580057 1.00469i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.486206 0.250657i −0.486206 0.250657i
\(409\) 1.02951 + 0.809616i 1.02951 + 0.809616i 0.981929 0.189251i \(-0.0606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(410\) 0 0
\(411\) −0.324236 + 2.25511i −0.324236 + 2.25511i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.165101 + 1.14831i 0.165101 + 1.14831i
\(418\) 0.00376206 0.0789754i 0.00376206 0.0789754i
\(419\) 1.04758 + 0.998867i 1.04758 + 0.998867i 1.00000 \(0\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(420\) 0 0
\(421\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(422\) 1.82318 0.351390i 1.82318 0.351390i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.154218 + 0.445585i −0.154218 + 0.445585i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.308779 + 1.27280i −0.308779 + 1.27280i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0.379436 + 0.657203i 0.379436 + 0.657203i
\(433\) 1.13915 + 1.59971i 1.13915 + 1.59971i 0.723734 + 0.690079i \(0.242424\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.974048 + 1.36786i 0.974048 + 1.36786i
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) −0.344298 + 0.0328765i −0.344298 + 0.0328765i
\(442\) 0 0
\(443\) 0.111165 0.458227i 0.111165 0.458227i −0.888835 0.458227i \(-0.848485\pi\)
1.00000 \(0\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.815816 0.157236i 0.815816 0.157236i 0.235759 0.971812i \(-0.424242\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(450\) −0.271868 + 0.213799i −0.271868 + 0.213799i
\(451\) −0.0557520 0.229813i −0.0557520 0.229813i
\(452\) −1.44091 1.37391i −1.44091 1.37391i
\(453\) 0 0
\(454\) 0.223734 + 1.55610i 0.223734 + 1.55610i
\(455\) 0 0
\(456\) 0.0640388 0.0899299i 0.0640388 0.0899299i
\(457\) −1.84833 0.176494i −1.84833 0.176494i −0.888835 0.458227i \(-0.848485\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(458\) 0 0
\(459\) −0.351355 0.0677182i −0.351355 0.0677182i
\(460\) 0 0
\(461\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(462\) 0 0
\(463\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(467\) 0.771316 0.308788i 0.771316 0.308788i 0.0475819 0.998867i \(-0.484848\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.30379 + 1.50465i 1.30379 + 1.50465i
\(473\) −1.06891 + 1.01921i −1.06891 + 1.01921i
\(474\) 0 0
\(475\) −0.0845850 0.0436066i −0.0845850 0.0436066i
\(476\) 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 0
\(482\) 0.975950 1.37053i 0.975950 1.37053i
\(483\) 0 0
\(484\) 0.0440780 + 0.306569i 0.0440780 + 0.306569i
\(485\) 0 0
\(486\) −0.480348 0.458011i −0.480348 0.458011i
\(487\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(488\) 0 0
\(489\) −1.79086 + 0.345161i −1.79086 + 0.345161i
\(490\) 0 0
\(491\) 0.654861 0.755750i 0.654861 0.755750i −0.327068 0.945001i \(-0.606061\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(492\) 0.107999 0.312042i 0.107999 0.312042i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.975950 + 1.69039i −0.975950 + 1.69039i
\(499\) 0.327068 + 0.566498i 0.327068 + 0.566498i 0.981929 0.189251i \(-0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.45949 0.584293i −1.45949 0.584293i
\(503\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.580057 + 1.00469i −0.580057 + 1.00469i
\(508\) 0 0
\(509\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(513\) 0.0236199 0.0682453i 0.0236199 0.0682453i
\(514\) 1.25667 1.45027i 1.25667 1.45027i
\(515\) 0 0
\(516\) −2.02503 + 0.390293i −2.02503 + 0.390293i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.0930932 + 0.647478i 0.0930932 + 0.647478i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(522\) 0 0
\(523\) 1.13915 1.59971i 1.13915 1.59971i 0.415415 0.909632i \(-0.363636\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(524\) 0.283341 + 0.0270558i 0.283341 + 0.0270558i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.400401 0.876756i 0.400401 0.876756i
\(529\) −0.786053 0.618159i −0.786053 0.618159i
\(530\) 0 0
\(531\) −0.579284 0.372283i −0.579284 0.372283i
\(532\) 0 0
\(533\) 0 0
\(534\) 1.99973 0.800570i 1.99973 0.800570i
\(535\) 0 0
\(536\) 0.841254 0.540641i 0.841254 0.540641i
\(537\) 1.95190 1.95190
\(538\) 0 0
\(539\) −0.544078 0.627899i −0.544078 0.627899i
\(540\) 0 0
\(541\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.195876 0.428908i 0.195876 0.428908i
\(545\) 0 0
\(546\) 0 0
\(547\) −1.49547 + 0.770969i −1.49547 + 0.770969i −0.995472 0.0950560i \(-0.969697\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) −1.95496 0.186677i −1.95496 0.186677i
\(549\) 0 0
\(550\) −0.797176 0.234072i −0.797176 0.234072i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.981929 + 0.189251i −0.981929 + 0.189251i
\(557\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.188796 + 0.413406i 0.188796 + 0.413406i
\(562\) 0.111165 0.458227i 0.111165 0.458227i
\(563\) −0.550294 + 0.353653i −0.550294 + 0.353653i −0.786053 0.618159i \(-0.787879\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.34378 + 0.537970i 1.34378 + 0.537970i 0.928368 0.371662i \(-0.121212\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(570\) 0 0
\(571\) −0.154218 0.445585i −0.154218 0.445585i 0.841254 0.540641i \(-0.181818\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.290959 0.186988i 0.290959 0.186988i
\(577\) 0.437742 1.80440i 0.437742 1.80440i −0.142315 0.989821i \(-0.545455\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(578\) −0.323056 0.707394i −0.323056 0.707394i
\(579\) 2.13606 0.627205i 2.13606 0.627205i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.0799009 + 1.67733i 0.0799009 + 1.67733i
\(583\) 0 0
\(584\) −1.13779 + 0.894765i −1.13779 + 0.894765i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.0688733 1.44583i 0.0688733 1.44583i −0.654861 0.755750i \(-0.727273\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(588\) −0.165101 1.14831i −0.165101 1.14831i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.42131 + 0.273935i 1.42131 + 0.273935i 0.841254 0.540641i \(-0.181818\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(594\) 0.0897286 0.624076i 0.0897286 0.624076i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(600\) −0.759713 0.876756i −0.759713 0.876756i
\(601\) −1.45949 + 0.584293i −1.45949 + 0.584293i −0.959493 0.281733i \(-0.909091\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) −0.226493 + 0.261387i −0.226493 + 0.261387i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(608\) 0.0800569 + 0.0514495i 0.0800569 + 0.0514495i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.0232089 + 0.161421i −0.0232089 + 0.161421i
\(613\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(614\) 1.58006 0.814576i 1.58006 0.814576i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(618\) 0 0
\(619\) 0.0934441 1.96163i 0.0934441 1.96163i −0.142315 0.989821i \(-0.545455\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(626\) −0.0311250 + 0.0899299i −0.0311250 + 0.0899299i
\(627\) −0.0880089 + 0.0258417i −0.0880089 + 0.0258417i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(632\) 0 0
\(633\) −1.07701 1.86544i −1.07701 1.86544i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.786053 1.36148i 0.786053 1.36148i −0.142315 0.989821i \(-0.545455\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(642\) 1.51255 0.144431i 1.51255 0.144431i
\(643\) −1.67489 + 1.07639i −1.67489 + 1.07639i −0.786053 + 0.618159i \(0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.0430538 + 0.0126417i −0.0430538 + 0.0126417i
\(647\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(648\) 0.803018 0.926732i 0.803018 0.926732i
\(649\) −0.0787070 1.65226i −0.0787070 1.65226i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.370638 1.52779i −0.370638 1.52779i
\(653\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(657\) 0.290392 0.407799i 0.290392 0.407799i
\(658\) 0 0
\(659\) 0.888835 0.458227i 0.888835 0.458227i 0.0475819 0.998867i \(-0.484848\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(660\) 0 0
\(661\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(662\) 0.0395325 0.0865641i 0.0395325 0.0865641i
\(663\) 0 0
\(664\) −1.49547 0.770969i −1.49547 0.770969i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.428368 + 0.494363i 0.428368 + 0.494363i 0.928368 0.371662i \(-0.121212\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) −1.38884 + 1.32425i −1.38884 + 1.32425i
\(675\) −0.638404 0.410277i −0.638404 0.410277i
\(676\) −0.888835 0.458227i −0.888835 0.458227i
\(677\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(678\) −0.959493 + 2.10100i −0.959493 + 2.10100i
\(679\) 0 0
\(680\) 0 0
\(681\) 1.62108 0.835724i 1.62108 0.835724i
\(682\) 0 0
\(683\) 1.13915 1.59971i 1.13915 1.59971i 0.415415 0.909632i \(-0.363636\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(684\) −0.0315805 0.00927288i −0.0315805 0.00927288i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.419102 1.72756i −0.419102 1.72756i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.0623191 1.30824i −0.0623191 1.30824i −0.786053 0.618159i \(-0.787879\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.959493 0.281733i 0.959493 0.281733i
\(695\) 0 0
\(696\) 0 0
\(697\) −0.112903 + 0.0725583i −0.112903 + 0.0725583i
\(698\) 0 0
\(699\) 0.580057 1.00469i 0.580057 1.00469i
\(700\) 0 0
\(701\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.771316 + 0.308788i 0.771316 + 0.308788i
\(705\) 0 0
\(706\) −0.759713 1.06687i −0.759713 1.06687i
\(707\) 0 0
\(708\) 1.15486 2.00028i 1.15486 2.00028i
\(709\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.771316 + 1.68895i 0.771316 + 1.68895i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.0800569 + 1.68060i 0.0800569 + 1.68060i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.141026 + 0.980857i 0.141026 + 0.980857i
\(723\) −1.87283 0.549914i −1.87283 0.549914i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.319369 0.164646i 0.319369 0.164646i
\(727\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(728\) 0 0
\(729\) 0.189539 0.415033i 0.189539 0.415033i
\(730\) 0 0
\(731\) 0.745025 + 0.384087i 0.745025 + 0.384087i
\(732\) 0 0
\(733\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.827068 0.0789754i −0.827068 0.0789754i
\(738\) −0.0984432 −0.0984432
\(739\) −1.84833 + 0.739959i −1.84833 + 0.739959i −0.888835 + 0.458227i \(0.848485\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.571403 + 0.110129i 0.571403 + 0.110129i
\(748\) −0.348202 + 0.179511i −0.348202 + 0.179511i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(752\) 0 0
\(753\) −0.0867810 + 1.82176i −0.0867810 + 1.82176i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(758\) −0.0135432 0.284307i −0.0135432 0.284307i
\(759\) 0 0
\(760\) 0 0
\(761\) 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.672932 + 0.945001i 0.672932 + 0.945001i
\(769\) 0.514186 + 1.48564i 0.514186 + 1.48564i 0.841254 + 0.540641i \(0.181818\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(770\) 0 0
\(771\) −2.06677 0.827411i −2.06677 0.827411i
\(772\) 0.627639 + 1.81344i 0.627639 + 1.81344i
\(773\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(774\) 0.307416 + 0.532461i 0.307416 + 0.532461i
\(775\) 0 0
\(776\) −1.44091 + 0.137591i −1.44091 + 0.137591i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.0112521 0.0246387i −0.0112521 0.0246387i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.981929 0.189251i 0.981929 0.189251i
\(785\) 0 0
\(786\) −0.0778483 0.320895i −0.0778483 0.320895i
\(787\) −0.947890 0.903811i −0.947890 0.903811i 0.0475819 0.998867i \(-0.484848\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.286053 0.0273148i −0.286053 0.0273148i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)