Properties

Label 536.1.ba.a.419.1
Level $536$
Weight $1$
Character 536.419
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 419.1
Root \(0.580057 + 0.814576i\) of defining polynomial
Character \(\chi\) \(=\) 536.419
Dual form 536.1.ba.a.339.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.995472 + 0.0950560i) q^{2} +(0.396666 - 0.254922i) q^{3} +(0.981929 - 0.189251i) q^{4} +(-0.370638 + 0.291473i) q^{6} +(-0.959493 + 0.281733i) q^{8} +(-0.323056 + 0.707394i) q^{9} +O(q^{10})\) \(q+(-0.995472 + 0.0950560i) q^{2} +(0.396666 - 0.254922i) q^{3} +(0.981929 - 0.189251i) q^{4} +(-0.370638 + 0.291473i) q^{6} +(-0.959493 + 0.281733i) q^{8} +(-0.323056 + 0.707394i) q^{9} +(1.50842 + 1.18624i) q^{11} +(0.341254 - 0.325385i) q^{12} +(0.928368 - 0.371662i) q^{16} +(-0.642315 - 0.123796i) q^{17} +(0.254351 - 0.734900i) q^{18} +(1.07701 - 1.51245i) q^{19} +(-1.61435 - 1.03748i) q^{22} +(-0.308779 + 0.356349i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(0.119289 + 0.829672i) q^{27} +(-0.888835 + 0.458227i) q^{32} +(0.900739 + 0.0860101i) q^{33} +(0.651174 + 0.0621796i) q^{34} +(-0.183343 + 0.755750i) q^{36} +(-0.928368 + 1.60798i) q^{38} +(-0.271738 - 0.785135i) q^{41} +(1.02951 - 1.18812i) q^{43} +(1.70566 + 0.879330i) q^{44} +(0.273507 - 0.384087i) q^{48} +(-0.327068 + 0.945001i) q^{49} +(0.981929 + 0.189251i) q^{50} +(-0.286343 + 0.114634i) q^{51} +(-0.197614 - 0.814576i) q^{54} +(0.0416572 - 0.874493i) q^{57} +(-1.38884 + 0.407799i) q^{59} +(0.841254 - 0.540641i) q^{64} -0.904836 q^{66} +(-0.142315 + 0.989821i) q^{67} -0.654136 q^{68} +(0.110674 - 0.769755i) q^{72} +(-1.54370 + 1.21398i) q^{73} +(-0.452418 + 0.132842i) q^{75} +(0.771316 - 1.68895i) q^{76} +(-0.250447 - 0.289031i) q^{81} +(0.345139 + 0.755750i) q^{82} +(-0.264241 + 0.105786i) q^{83} +(-0.911911 + 1.28060i) q^{86} +(-1.78153 - 0.713215i) q^{88} +(-1.67489 - 1.07639i) q^{89} +(-0.235759 + 0.408346i) q^{96} +(-0.981929 - 1.70075i) q^{97} +(0.235759 - 0.971812i) q^{98} +(-1.32644 + 0.683830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{32}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(3\) 0.396666 0.254922i 0.396666 0.254922i −0.327068 0.945001i \(-0.606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(4\) 0.981929 0.189251i 0.981929 0.189251i
\(5\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(6\) −0.370638 + 0.291473i −0.370638 + 0.291473i
\(7\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(8\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(9\) −0.323056 + 0.707394i −0.323056 + 0.707394i
\(10\) 0 0
\(11\) 1.50842 + 1.18624i 1.50842 + 1.18624i 0.928368 + 0.371662i \(0.121212\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(12\) 0.341254 0.325385i 0.341254 0.325385i
\(13\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.928368 0.371662i 0.928368 0.371662i
\(17\) −0.642315 0.123796i −0.642315 0.123796i −0.142315 0.989821i \(-0.545455\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 0.254351 0.734900i 0.254351 0.734900i
\(19\) 1.07701 1.51245i 1.07701 1.51245i 0.235759 0.971812i \(-0.424242\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.61435 1.03748i −1.61435 1.03748i
\(23\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(24\) −0.308779 + 0.356349i −0.308779 + 0.356349i
\(25\) −0.959493 0.281733i −0.959493 0.281733i
\(26\) 0 0
\(27\) 0.119289 + 0.829672i 0.119289 + 0.829672i
\(28\) 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 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(32\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(33\) 0.900739 + 0.0860101i 0.900739 + 0.0860101i
\(34\) 0.651174 + 0.0621796i 0.651174 + 0.0621796i
\(35\) 0 0
\(36\) −0.183343 + 0.755750i −0.183343 + 0.755750i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.271738 0.785135i −0.271738 0.785135i −0.995472 0.0950560i \(-0.969697\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(42\) 0 0
\(43\) 1.02951 1.18812i 1.02951 1.18812i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(44\) 1.70566 + 0.879330i 1.70566 + 0.879330i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(48\) 0.273507 0.384087i 0.273507 0.384087i
\(49\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(50\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(51\) −0.286343 + 0.114634i −0.286343 + 0.114634i
\(52\) 0 0
\(53\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(54\) −0.197614 0.814576i −0.197614 0.814576i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.0416572 0.874493i 0.0416572 0.874493i
\(58\) 0 0
\(59\) −1.38884 + 0.407799i −1.38884 + 0.407799i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.841254 0.540641i 0.841254 0.540641i
\(65\) 0 0
\(66\) −0.904836 −0.904836
\(67\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(68\) −0.654136 −0.654136
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(72\) 0.110674 0.769755i 0.110674 0.769755i
\(73\) −1.54370 + 1.21398i −1.54370 + 1.21398i −0.654861 + 0.755750i \(0.727273\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(74\) 0 0
\(75\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(76\) 0.771316 1.68895i 0.771316 1.68895i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(80\) 0 0
\(81\) −0.250447 0.289031i −0.250447 0.289031i
\(82\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(83\) −0.264241 + 0.105786i −0.264241 + 0.105786i −0.500000 0.866025i \(-0.666667\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.911911 + 1.28060i −0.911911 + 1.28060i
\(87\) 0 0
\(88\) −1.78153 0.713215i −1.78153 0.713215i
\(89\) −1.67489 1.07639i −1.67489 1.07639i −0.888835 0.458227i \(-0.848485\pi\)
−0.786053 0.618159i \(-0.787879\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.235759 + 0.408346i −0.235759 + 0.408346i
\(97\) −0.981929 1.70075i −0.981929 1.70075i −0.654861 0.755750i \(-0.727273\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(98\) 0.235759 0.971812i 0.235759 0.971812i
\(99\) −1.32644 + 0.683830i −1.32644 + 0.683830i
\(100\) −0.995472 0.0950560i −0.995472 0.0950560i
\(101\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(102\) 0.274150 0.141334i 0.274150 0.141334i
\(103\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(108\) 0.274150 + 0.792103i 0.274150 + 0.792103i
\(109\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.34378 + 0.537970i 1.34378 + 0.537970i 0.928368 0.371662i \(-0.121212\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(114\) 0.0416572 + 0.874493i 0.0416572 + 0.874493i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.34378 0.537970i 1.34378 0.537970i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.632425 + 2.60689i 0.632425 + 2.60689i
\(122\) 0 0
\(123\) −0.307937 0.242165i −0.307937 0.242165i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(128\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(129\) 0.105495 0.733731i 0.105495 0.733731i
\(130\) 0 0
\(131\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(132\) 0.900739 0.0860101i 0.900739 0.0860101i
\(133\) 0 0
\(134\) 0.0475819 0.998867i 0.0475819 0.998867i
\(135\) 0 0
\(136\) 0.651174 0.0621796i 0.651174 0.0621796i
\(137\) 0.0800569 0.0514495i 0.0800569 0.0514495i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(138\) 0 0
\(139\) 0.142315 0.989821i 0.142315 0.989821i −0.786053 0.618159i \(-0.787879\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.0370031 + 0.776790i −0.0370031 + 0.776790i
\(145\) 0 0
\(146\) 1.42131 1.35522i 1.42131 1.35522i
\(147\) 0.111165 + 0.458227i 0.111165 + 0.458227i
\(148\) 0 0
\(149\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(150\) 0.437742 0.175245i 0.437742 0.175245i
\(151\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(152\) −0.607279 + 1.75462i −0.607279 + 1.75462i
\(153\) 0.295076 0.414377i 0.295076 0.414377i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.276787 + 0.263916i 0.276787 + 0.263916i
\(163\) −0.580057 + 1.00469i −0.580057 + 1.00469i 0.415415 + 0.909632i \(0.363636\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(164\) −0.415415 0.719520i −0.415415 0.719520i
\(165\) 0 0
\(166\) 0.252989 0.130425i 0.252989 0.130425i
\(167\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(168\) 0 0
\(169\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(170\) 0 0
\(171\) 0.721965 + 1.25048i 0.721965 + 1.25048i
\(172\) 0.786053 1.36148i 0.786053 1.36148i
\(173\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(177\) −0.446947 + 0.515804i −0.446947 + 0.515804i
\(178\) 1.76962 + 0.912303i 1.76962 + 0.912303i
\(179\) −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(180\) 0 0
\(181\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.822032 0.948676i −0.822032 0.948676i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(192\) 0.195876 0.428908i 0.195876 0.428908i
\(193\) 1.25667 0.368991i 1.25667 0.368991i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(194\) 1.13915 + 1.59971i 1.13915 + 1.59971i
\(195\) 0 0
\(196\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(197\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(198\) 1.25544 0.806820i 1.25544 0.806820i
\(199\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(200\) 1.00000 1.00000
\(201\) 0.195876 + 0.428908i 0.195876 + 0.428908i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.259474 + 0.166754i −0.259474 + 0.166754i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.41872 1.00383i 3.41872 1.00383i
\(210\) 0 0
\(211\) −0.0947329 + 1.98869i −0.0947329 + 1.98869i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.396666 + 1.63508i 0.396666 + 1.63508i
\(215\) 0 0
\(216\) −0.348202 0.762457i −0.348202 0.762457i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.302863 + 0.875065i −0.302863 + 0.875065i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(224\) 0 0
\(225\) 0.509266 0.587724i 0.509266 0.587724i
\(226\) −1.38884 0.407799i −1.38884 0.407799i
\(227\) −0.379436 1.09631i −0.379436 1.09631i −0.959493 0.281733i \(-0.909091\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(228\) −0.124594 0.866573i −0.124594 0.866573i
\(229\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.888835 0.458227i 0.888835 0.458227i 0.0475819 0.998867i \(-0.484848\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.28656 + 0.663268i −1.28656 + 0.663268i
\(237\) 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
\(241\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(242\) −0.877362 2.53497i −0.877362 2.53497i
\(243\) −0.977275 0.286954i −0.977275 0.286954i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.329562 + 0.211797i 0.329562 + 0.211797i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.0778483 + 0.109323i −0.0778483 + 0.109323i
\(250\) 0 0
\(251\) 1.13915 + 0.219553i 1.13915 + 0.219553i 0.723734 0.690079i \(-0.242424\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.723734 0.690079i 0.723734 0.690079i
\(257\) 1.02951 + 0.809616i 1.02951 + 0.809616i 0.981929 0.189251i \(-0.0606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(258\) −0.0352713 + 0.740437i −0.0352713 + 0.740437i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.653077 + 0.513585i −0.653077 + 0.513585i
\(263\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(264\) −0.888485 + 0.171241i −0.888485 + 0.171241i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.938766 −0.938766
\(268\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(272\) −0.642315 + 0.123796i −0.642315 + 0.123796i
\(273\) 0 0
\(274\) −0.0748038 + 0.0588264i −0.0748038 + 0.0588264i
\(275\) −1.11312 1.56316i −1.11312 1.56316i
\(276\) 0 0
\(277\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(278\) −0.0475819 + 0.998867i −0.0475819 + 0.998867i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.154218 0.635697i −0.154218 0.635697i −0.995472 0.0950560i \(-0.969697\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(282\) 0 0
\(283\) −0.415415 0.909632i −0.415415 0.909632i −0.995472 0.0950560i \(-0.969697\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.0370031 0.776790i −0.0370031 0.776790i
\(289\) −0.531125 0.212630i −0.531125 0.212630i
\(290\) 0 0
\(291\) −0.823056 0.424315i −0.823056 0.424315i
\(292\) −1.28605 + 1.48418i −1.28605 + 1.48418i
\(293\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(294\) −0.154218 0.445585i −0.154218 0.445585i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.804250 + 1.39300i −0.804250 + 1.39300i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.419102 + 0.216062i −0.419102 + 0.216062i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.437742 1.80440i 0.437742 1.80440i
\(305\) 0 0
\(306\) −0.254351 + 0.440549i −0.254351 + 0.440549i
\(307\) −1.13779 1.08488i −1.13779 1.08488i −0.995472 0.0950560i \(-0.969697\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(312\) 0 0
\(313\) 1.56199 + 1.00383i 1.56199 + 1.00383i 0.981929 + 0.189251i \(0.0606061\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.519522 0.599560i −0.519522 0.599560i
\(322\) 0 0
\(323\) −0.879017 + 0.838141i −0.879017 + 0.838141i
\(324\) −0.300620 0.236411i −0.300620 0.236411i
\(325\) 0 0
\(326\) 0.481929 1.05528i 0.481929 1.05528i
\(327\) 0 0
\(328\) 0.481929 + 0.676774i 0.481929 + 0.676774i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.82318 0.351390i 1.82318 0.351390i 0.841254 0.540641i \(-0.181818\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(332\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.30379 0.124497i 1.30379 0.124497i 0.580057 0.814576i \(-0.303030\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(338\) 0.841254 0.540641i 0.841254 0.540641i
\(339\) 0.670173 0.129165i 0.670173 0.129165i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.837561 1.17619i −0.837561 1.17619i
\(343\) 0 0
\(344\) −0.653077 + 1.43004i −0.653077 + 1.43004i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.723734 + 0.690079i −0.723734 + 0.690079i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(348\) 0 0
\(349\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.88431 0.363170i −1.88431 0.363170i
\(353\) −0.550294 + 1.58997i −0.550294 + 1.58997i 0.235759 + 0.971812i \(0.424242\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(354\) 0.395893 0.555954i 0.395893 0.555954i
\(355\) 0 0
\(356\) −1.84833 0.739959i −1.84833 0.739959i
\(357\) 0 0
\(358\) 0.252989 + 0.130425i 0.252989 + 0.130425i
\(359\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(360\) 0 0
\(361\) −0.800488 2.31286i −0.800488 2.31286i
\(362\) 0 0
\(363\) 0.915415 + 0.872846i 0.915415 + 0.872846i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(368\) 0 0
\(369\) 0.643187 + 0.0614169i 0.643187 + 0.0614169i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0.908487 + 0.866241i 0.908487 + 0.866241i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.738471 0.380708i −0.738471 0.380708i 0.0475819 0.998867i \(-0.484848\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(384\) −0.154218 + 0.445585i −0.154218 + 0.445585i
\(385\) 0 0
\(386\) −1.21590 + 0.486774i −1.21590 + 0.486774i
\(387\) 0.507879 + 1.11210i 0.507879 + 1.11210i
\(388\) −1.28605 1.48418i −1.28605 1.48418i
\(389\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.0475819 0.998867i 0.0475819 0.998867i
\(393\) 0.162739 0.356349i 0.162739 0.356349i
\(394\) 0 0
\(395\) 0 0
\(396\) −1.17306 + 0.922503i −1.17306 + 0.922503i
\(397\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(401\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(402\) −0.235759 0.408346i −0.235759 0.408346i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.242448 0.190663i 0.242448 0.190663i
\(409\) 0.975950 + 1.37053i 0.975950 + 1.37053i 0.928368 + 0.371662i \(0.121212\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(410\) 0 0
\(411\) 0.0186403 0.0408165i 0.0186403 0.0408165i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.195876 0.428908i −0.195876 0.428908i
\(418\) −3.30782 + 1.32425i −3.30782 + 1.32425i
\(419\) 1.92837 + 0.371662i 1.92837 + 0.371662i 1.00000 \(0\)
0.928368 + 0.371662i \(0.121212\pi\)
\(420\) 0 0
\(421\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(422\) −0.0947329 1.98869i −0.0947329 1.98869i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.581419 + 0.299742i 0.581419 + 0.299742i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.550294 1.58997i −0.550294 1.58997i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0.419102 + 0.725906i 0.419102 + 0.725906i
\(433\) 0.0224357 0.0924813i 0.0224357 0.0924813i −0.959493 0.281733i \(-0.909091\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.218311 0.899892i 0.218311 0.899892i
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) −0.562827 0.536654i −0.562827 0.536654i
\(442\) 0 0
\(443\) 0.213947 + 0.618159i 0.213947 + 0.618159i 1.00000 \(0\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.0913090 1.91681i −0.0913090 1.91681i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(450\) −0.451093 + 0.633472i −0.451093 + 0.633472i
\(451\) 0.521461 1.50666i 0.521461 1.50666i
\(452\) 1.42131 + 0.273935i 1.42131 + 0.273935i
\(453\) 0 0
\(454\) 0.481929 + 1.05528i 0.481929 + 1.05528i
\(455\) 0 0
\(456\) 0.206403 + 0.850806i 0.206403 + 0.850806i
\(457\) −1.44091 + 1.37391i −1.44091 + 1.37391i −0.654861 + 0.755750i \(0.727273\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(458\) 0 0
\(459\) 0.0260891 0.547678i 0.0260891 0.547678i
\(460\) 0 0
\(461\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(462\) 0 0
\(463\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(467\) 1.91030 0.182411i 1.91030 0.182411i 0.928368 0.371662i \(-0.121212\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.21769 0.782560i 1.21769 0.782560i
\(473\) 2.96233 0.570943i 2.96233 0.570943i
\(474\) 0 0
\(475\) −1.45949 + 1.14776i −1.45949 + 1.14776i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.0671040 0.276606i −0.0671040 0.276606i
\(483\) 0 0
\(484\) 1.11435 + 2.44009i 1.11435 + 2.44009i
\(485\) 0 0
\(486\) 1.00013 + 0.192758i 1.00013 + 0.192758i
\(487\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(488\) 0 0
\(489\) 0.0260280 + 0.546395i 0.0260280 + 0.546395i
\(490\) 0 0
\(491\) −0.841254 0.540641i −0.841254 0.540641i 0.0475819 0.998867i \(-0.484848\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(492\) −0.348202 0.179511i −0.348202 0.179511i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.0671040 0.116228i 0.0671040 0.116228i
\(499\) 0.888835 + 1.53951i 0.888835 + 1.53951i 0.841254 + 0.540641i \(0.181818\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.15486 0.110276i −1.15486 0.110276i
\(503\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.235759 + 0.408346i −0.235759 + 0.408346i
\(508\) 0 0
\(509\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(513\) 1.38331 + 0.713148i 1.38331 + 0.713148i
\(514\) −1.10181 0.708089i −1.10181 0.708089i
\(515\) 0 0
\(516\) −0.0352713 0.740437i −0.0352713 0.740437i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.738471 1.61703i −0.738471 1.61703i −0.786053 0.618159i \(-0.787879\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(522\) 0 0
\(523\) 0.0224357 + 0.0924813i 0.0224357 + 0.0924813i 0.981929 0.189251i \(-0.0606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(524\) 0.601300 0.573338i 0.601300 0.573338i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.868184 0.254922i 0.868184 0.254922i
\(529\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(530\) 0 0
\(531\) 0.160197 1.11420i 0.160197 1.11420i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.934515 0.0892353i 0.934515 0.0892353i
\(535\) 0 0
\(536\) −0.142315 0.989821i −0.142315 0.989821i
\(537\) −0.134208 −0.134208
\(538\) 0 0
\(539\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(540\) 0 0
\(541\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.627639 0.184291i 0.627639 0.184291i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.223734 + 0.175946i 0.223734 + 0.175946i 0.723734 0.690079i \(-0.242424\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) 0.0688733 0.0656706i 0.0688733 0.0656706i
\(549\) 0 0
\(550\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.0475819 0.998867i −0.0475819 0.998867i
\(557\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.567910 0.166754i −0.567910 0.166754i
\(562\) 0.213947 + 0.618159i 0.213947 + 0.618159i
\(563\) 0.252989 + 1.75958i 0.252989 + 1.75958i 0.580057 + 0.814576i \(0.303030\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(567\) 0 0
\(568\) 0 0
\(569\) −1.95496 0.186677i −1.95496 0.186677i −0.959493 0.281733i \(-0.909091\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(570\) 0 0
\(571\) 0.581419 0.299742i 0.581419 0.299742i −0.142315 0.989821i \(-0.545455\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.110674 + 0.769755i 0.110674 + 0.769755i
\(577\) 0.651174 + 1.88144i 0.651174 + 1.88144i 0.415415 + 0.909632i \(0.363636\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(578\) 0.548932 + 0.161181i 0.548932 + 0.161181i
\(579\) 0.404414 0.466718i 0.404414 0.466718i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.859663 + 0.344157i 0.859663 + 0.344157i
\(583\) 0 0
\(584\) 1.13915 1.59971i 1.13915 1.59971i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.82318 0.729892i 1.82318 0.729892i 0.841254 0.540641i \(-0.181818\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(588\) 0.195876 + 0.428908i 0.195876 + 0.428908i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.0934441 1.96163i 0.0934441 1.96163i −0.142315 0.989821i \(-0.545455\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(594\) 0.668195 1.46314i 0.668195 1.46314i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(600\) 0.396666 0.254922i 0.396666 0.254922i
\(601\) −1.15486 + 0.110276i −1.15486 + 0.110276i −0.654861 0.755750i \(-0.727273\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) −0.654218 0.420441i −0.654218 0.420441i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(608\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.211323 0.462732i 0.211323 0.462732i
\(613\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(614\) 1.23576 + 0.971812i 1.23576 + 0.971812i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(618\) 0 0
\(619\) 0.0883470 0.0353688i 0.0883470 0.0353688i −0.327068 0.945001i \(-0.606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(626\) −1.65033 0.850806i −1.65033 0.850806i
\(627\) 1.10019 1.26969i 1.10019 1.26969i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(632\) 0 0
\(633\) 0.469383 + 0.812995i 0.469383 + 0.812995i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.580057 + 1.00469i −0.580057 + 1.00469i 0.415415 + 0.909632i \(0.363636\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(642\) 0.574161 + 0.547462i 0.574161 + 0.547462i
\(643\) −0.205996 1.43273i −0.205996 1.43273i −0.786053 0.618159i \(-0.787879\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.795366 0.917901i 0.795366 0.917901i
\(647\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(648\) 0.321731 + 0.206764i 0.321731 + 0.206764i
\(649\) −2.57870 1.03236i −2.57870 1.03236i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.379436 + 1.09631i −0.379436 + 1.09631i
\(653\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.544078 0.627899i −0.544078 0.627899i
\(657\) −0.360059 1.48418i −0.360059 1.48418i
\(658\) 0 0
\(659\) 0.786053 + 0.618159i 0.786053 + 0.618159i 0.928368 0.371662i \(-0.121212\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(660\) 0 0
\(661\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(662\) −1.78153 + 0.523103i −1.78153 + 0.523103i
\(663\) 0 0
\(664\) 0.223734 0.175946i 0.223734 0.175946i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.49547 + 0.961081i −1.49547 + 0.961081i −0.500000 + 0.866025i \(0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(674\) −1.28605 + 0.247866i −1.28605 + 0.247866i
\(675\) 0.119289 0.829672i 0.119289 0.829672i
\(676\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(677\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(678\) −0.654861 + 0.192284i −0.654861 + 0.192284i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.429982 0.338142i −0.429982 0.338142i
\(682\) 0 0
\(683\) 0.0224357 + 0.0924813i 0.0224357 + 0.0924813i 0.981929 0.189251i \(-0.0606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(684\) 0.945573 + 1.09125i 0.945573 + 1.09125i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.514186 1.48564i 0.514186 1.48564i
\(689\) 0 0
\(690\) 0 0
\(691\) 1.56199 + 0.625325i 1.56199 + 0.625325i 0.981929 0.189251i \(-0.0606061\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.654861 0.755750i 0.654861 0.755750i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.0773447 + 0.537944i 0.0773447 + 0.537944i
\(698\) 0 0
\(699\) 0.235759 0.408346i 0.235759 0.408346i
\(700\) 0 0
\(701\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.91030 + 0.182411i 1.91030 + 0.182411i
\(705\) 0 0
\(706\) 0.396666 1.63508i 0.396666 1.63508i
\(707\) 0 0
\(708\) −0.341254 + 0.591068i −0.341254 + 0.591068i
\(709\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.91030 + 0.560914i 1.91030 + 0.560914i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.264241 0.105786i −0.264241 0.105786i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.01671 + 2.22630i 1.01671 + 2.22630i
\(723\) 0.0878875 + 0.101428i 0.0878875 + 0.101428i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.994239 0.781878i −0.994239 0.781878i
\(727\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(728\) 0 0
\(729\) −0.0938511 + 0.0275572i −0.0938511 + 0.0275572i
\(730\) 0 0
\(731\) −0.808354 + 0.635697i −0.808354 + 0.635697i
\(732\) 0 0
\(733\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.38884 + 1.32425i −1.38884 + 1.32425i
\(738\) −0.646112 −0.646112
\(739\) −1.44091 + 0.137591i −1.44091 + 0.137591i −0.786053 0.618159i \(-0.787879\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.0105322 0.221098i 0.0105322 0.221098i
\(748\) −0.986715 0.775961i −0.986715 0.775961i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(752\) 0 0
\(753\) 0.507831 0.203305i 0.507831 0.203305i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(758\) 0.771316 + 0.308788i 0.771316 + 0.308788i
\(759\) 0 0
\(760\) 0 0
\(761\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.111165 0.458227i 0.111165 0.458227i
\(769\) −1.03115 + 0.531595i −1.03115 + 0.531595i −0.888835 0.458227i \(-0.848485\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(770\) 0 0
\(771\) 0.614761 + 0.0587025i 0.614761 + 0.0587025i
\(772\) 1.16413 0.600149i 1.16413 0.600149i
\(773\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(774\) −0.611291 1.05879i −0.611291 1.05879i
\(775\) 0 0
\(776\) 1.42131 + 1.35522i 1.42131 + 1.35522i
\(777\) 0 0
\(778\) 0 0
\(779\) −1.48014 0.434610i −1.48014 0.434610i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(785\) 0 0
\(786\) −0.128129 + 0.370205i −0.128129 + 0.370205i
\(787\) 1.65210 + 0.318417i 1.65210 + 0.318417i 0.928368 0.371662i \(-0.121212\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.08006 1.02983i 1.08006 1.02983i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057