Properties

Label 536.1.ba.a.371.1
Level $536$
Weight $1$
Character 536.371
Analytic conductor $0.267$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -8
Inner twists $4$

Related objects

Downloads

Learn more

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 371.1
Root \(0.928368 - 0.371662i\) of defining polynomial
Character \(\chi\) \(=\) 536.371
Dual form 536.1.ba.a.523.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.786053 - 0.618159i) q^{2} +(1.30379 + 1.50465i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-0.0947329 - 1.98869i) q^{6} +(0.415415 - 0.909632i) q^{8} +(-0.421801 + 2.93369i) q^{9} +O(q^{10})\) \(q+(-0.786053 - 0.618159i) q^{2} +(1.30379 + 1.50465i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-0.0947329 - 1.98869i) q^{6} +(0.415415 - 0.909632i) q^{8} +(-0.421801 + 2.93369i) q^{9} +(0.0395325 - 0.829889i) q^{11} +(-1.15486 + 1.62177i) q^{12} +(-0.888835 + 0.458227i) q^{16} +(0.341254 - 1.40667i) q^{17} +(2.14504 - 2.04530i) q^{18} +(-1.65033 - 0.660694i) q^{19} +(-0.544078 + 0.627899i) q^{22} +(1.91030 - 0.560914i) q^{24} +(0.415415 + 0.909632i) q^{25} +(-3.28924 + 2.11387i) q^{27} +(0.981929 + 0.189251i) q^{32} +(1.30024 - 1.02252i) q^{33} +(-1.13779 + 0.894765i) q^{34} +(-2.95044 + 0.281733i) q^{36} +(0.888835 + 1.53951i) q^{38} +(-0.205996 - 0.196417i) q^{41} +(-0.0913090 + 0.0268107i) q^{43} +(0.815816 - 0.157236i) q^{44} +(-1.84833 - 0.739959i) q^{48} +(0.723734 - 0.690079i) q^{49} +(0.235759 - 0.971812i) q^{50} +(2.56147 - 1.32053i) q^{51} +(3.89223 + 0.371662i) q^{54} +(-1.15757 - 3.34459i) q^{57} +(0.481929 - 1.05528i) q^{59} +(-0.654861 - 0.755750i) q^{64} -1.65414 q^{66} +(0.841254 + 0.540641i) q^{67} +1.44747 q^{68} +(2.49336 + 1.60238i) q^{72} +(0.0224357 + 0.470984i) q^{73} +(-0.827068 + 1.81103i) q^{75} +(0.252989 - 1.75958i) q^{76} +(-4.62533 - 1.35812i) q^{81} +(0.0405070 + 0.281733i) q^{82} +(-1.49547 + 0.770969i) q^{83} +(0.0883470 + 0.0353688i) q^{86} +(-0.738471 - 0.380708i) q^{88} +(1.02951 - 1.18812i) q^{89} +(0.995472 + 1.72421i) q^{96} +(-0.235759 + 0.408346i) q^{97} +(-0.995472 + 0.0950560i) q^{98} +(2.41796 + 0.466024i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{7}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.786053 0.618159i −0.786053 0.618159i
\(3\) 1.30379 + 1.50465i 1.30379 + 1.50465i 0.723734 + 0.690079i \(0.242424\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(4\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(5\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(6\) −0.0947329 1.98869i −0.0947329 1.98869i
\(7\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(8\) 0.415415 0.909632i 0.415415 0.909632i
\(9\) −0.421801 + 2.93369i −0.421801 + 2.93369i
\(10\) 0 0
\(11\) 0.0395325 0.829889i 0.0395325 0.829889i −0.888835 0.458227i \(-0.848485\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(12\) −1.15486 + 1.62177i −1.15486 + 1.62177i
\(13\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(17\) 0.341254 1.40667i 0.341254 1.40667i −0.500000 0.866025i \(-0.666667\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(18\) 2.14504 2.04530i 2.14504 2.04530i
\(19\) −1.65033 0.660694i −1.65033 0.660694i −0.654861 0.755750i \(-0.727273\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(23\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(24\) 1.91030 0.560914i 1.91030 0.560914i
\(25\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(26\) 0 0
\(27\) −3.28924 + 2.11387i −3.28924 + 2.11387i
\(28\) 0 0
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(32\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(33\) 1.30024 1.02252i 1.30024 1.02252i
\(34\) −1.13779 + 0.894765i −1.13779 + 0.894765i
\(35\) 0 0
\(36\) −2.95044 + 0.281733i −2.95044 + 0.281733i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.205996 0.196417i −0.205996 0.196417i 0.580057 0.814576i \(-0.303030\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(42\) 0 0
\(43\) −0.0913090 + 0.0268107i −0.0913090 + 0.0268107i −0.327068 0.945001i \(-0.606061\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(44\) 0.815816 0.157236i 0.815816 0.157236i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(48\) −1.84833 0.739959i −1.84833 0.739959i
\(49\) 0.723734 0.690079i 0.723734 0.690079i
\(50\) 0.235759 0.971812i 0.235759 0.971812i
\(51\) 2.56147 1.32053i 2.56147 1.32053i
\(52\) 0 0
\(53\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(54\) 3.89223 + 0.371662i 3.89223 + 0.371662i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.15757 3.34459i −1.15757 3.34459i
\(58\) 0 0
\(59\) 0.481929 1.05528i 0.481929 1.05528i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(60\) 0 0
\(61\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) −1.65414 −1.65414
\(67\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(68\) 1.44747 1.44747
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(72\) 2.49336 + 1.60238i 2.49336 + 1.60238i
\(73\) 0.0224357 + 0.470984i 0.0224357 + 0.470984i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(74\) 0 0
\(75\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(76\) 0.252989 1.75958i 0.252989 1.75958i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(80\) 0 0
\(81\) −4.62533 1.35812i −4.62533 1.35812i
\(82\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(83\) −1.49547 + 0.770969i −1.49547 + 0.770969i −0.995472 0.0950560i \(-0.969697\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.0883470 + 0.0353688i 0.0883470 + 0.0353688i
\(87\) 0 0
\(88\) −0.738471 0.380708i −0.738471 0.380708i
\(89\) 1.02951 1.18812i 1.02951 1.18812i 0.0475819 0.998867i \(-0.484848\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.995472 + 1.72421i 0.995472 + 1.72421i
\(97\) −0.235759 + 0.408346i −0.235759 + 0.408346i −0.959493 0.281733i \(-0.909091\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(98\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(99\) 2.41796 + 0.466024i 2.41796 + 0.466024i
\(100\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(101\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(102\) −2.82975 0.545389i −2.82975 0.545389i
\(103\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(104\) 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 \(0.545455\pi\)
\(108\) −2.82975 2.69816i −2.82975 2.69816i
\(109\) 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
\(113\) −1.03115 0.531595i −1.03115 0.531595i −0.142315 0.989821i \(-0.545455\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(114\) −1.15757 + 3.34459i −1.15757 + 3.34459i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.03115 + 0.531595i −1.03115 + 0.531595i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.308319 + 0.0294409i 0.308319 + 0.0294409i
\(122\) 0 0
\(123\) 0.0269638 0.566040i 0.0269638 0.566040i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(128\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(129\) −0.159389 0.102433i −0.159389 0.102433i
\(130\) 0 0
\(131\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(132\) 1.30024 + 1.02252i 1.30024 + 1.02252i
\(133\) 0 0
\(134\) −0.327068 0.945001i −0.327068 0.945001i
\(135\) 0 0
\(136\) −1.13779 0.894765i −1.13779 0.894765i
\(137\) 0.428368 + 0.494363i 0.428368 + 0.494363i 0.928368 0.371662i \(-0.121212\pi\)
−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
\(144\) −0.969383 2.80085i −0.969383 2.80085i
\(145\) 0 0
\(146\) 0.273507 0.384087i 0.273507 0.384087i
\(147\) 1.98193 + 0.189251i 1.98193 + 0.189251i
\(148\) 0 0
\(149\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(150\) 1.76962 0.912303i 1.76962 0.912303i
\(151\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(152\) −1.28656 + 1.22673i −1.28656 + 1.22673i
\(153\) 3.98278 + 1.59446i 3.98278 + 1.59446i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 2.79622 + 3.92674i 2.79622 + 3.92674i
\(163\) −0.928368 1.60798i −0.928368 1.60798i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(164\) 0.142315 0.246497i 0.142315 0.246497i
\(165\) 0 0
\(166\) 1.65210 + 0.318417i 1.65210 + 0.318417i
\(167\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(168\) 0 0
\(169\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(170\) 0 0
\(171\) 2.63438 4.56288i 2.63438 4.56288i
\(172\) −0.0475819 0.0824143i −0.0475819 0.0824143i
\(173\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(177\) 2.21616 0.650724i 2.21616 0.650724i
\(178\) −1.54370 + 0.297523i −1.54370 + 0.297523i
\(179\) −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 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.15389 0.338812i −1.15389 0.338812i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(192\) 0.283341 1.97068i 0.283341 1.97068i
\(193\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(194\) 0.437742 0.175245i 0.437742 0.175245i
\(195\) 0 0
\(196\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(197\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(198\) −1.61257 1.86100i −1.61257 1.86100i
\(199\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(200\) 1.00000 1.00000
\(201\) 0.283341 + 1.97068i 0.283341 + 1.97068i
\(202\) 0 0
\(203\) 0 0
\(204\) 1.88720 + 2.17794i 1.88720 + 2.17794i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.613544 + 1.34347i −0.613544 + 1.34347i
\(210\) 0 0
\(211\) 0.514186 + 1.48564i 0.514186 + 1.48564i 0.841254 + 0.540641i \(0.181818\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.30379 + 0.124497i 1.30379 + 0.124497i
\(215\) 0 0
\(216\) 0.556441 + 3.87013i 0.556441 + 3.87013i
\(217\) 0 0
\(218\) 0 0
\(219\) −0.679417 + 0.647822i −0.679417 + 0.647822i
\(220\) 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
\(225\) −2.84380 + 0.835015i −2.84380 + 0.835015i
\(226\) 0.481929 + 1.05528i 0.481929 + 1.05528i
\(227\) 1.34378 + 1.28129i 1.34378 + 1.28129i 0.928368 + 0.371662i \(0.121212\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(228\) 2.97740 1.91346i 2.97740 1.91346i
\(229\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.981929 0.189251i −0.981929 0.189251i −0.327068 0.945001i \(-0.606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.13915 + 0.219553i 1.13915 + 0.219553i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(242\) −0.224156 0.213732i −0.224156 0.213732i
\(243\) −2.36271 5.17362i −2.36271 5.17362i
\(244\) 0 0
\(245\) 0 0
\(246\) −0.371098 + 0.428269i −0.371098 + 0.428269i
\(247\) 0 0
\(248\) 0 0
\(249\) −3.10983 1.24499i −3.10983 1.24499i
\(250\) 0 0
\(251\) 0.437742 1.80440i 0.437742 1.80440i −0.142315 0.989821i \(-0.545455\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.580057 0.814576i 0.580057 0.814576i
\(257\) −0.0913090 + 1.91681i −0.0913090 + 1.91681i 0.235759 + 0.971812i \(0.424242\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(258\) 0.0619682 + 0.179045i 0.0619682 + 0.179045i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.0135432 0.284307i −0.0135432 0.284307i
\(263\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(264\) −0.389977 1.60751i −0.389977 1.60751i
\(265\) 0 0
\(266\) 0 0
\(267\) 3.12998 3.12998
\(268\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(269\) 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 + 1.40667i 0.341254 + 1.40667i
\(273\) 0 0
\(274\) −0.0311250 0.653395i −0.0311250 0.653395i
\(275\) 0.771316 0.308788i 0.771316 0.308788i
\(276\) 0 0
\(277\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(278\) 0.327068 + 0.945001i 0.327068 + 0.945001i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.44091 0.137591i −1.44091 0.137591i −0.654861 0.755750i \(-0.727273\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(282\) 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
\(288\) −0.969383 + 2.80085i −0.969383 + 2.80085i
\(289\) −0.973420 0.501833i −0.973420 0.501833i
\(290\) 0 0
\(291\) −0.921801 + 0.177663i −0.921801 + 0.177663i
\(292\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) −1.44091 1.37391i −1.44091 1.37391i
\(295\) 0 0
\(296\) 0 0
\(297\) 1.62424 + 2.81327i 1.62424 + 2.81327i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.95496 0.376789i −1.95496 0.376789i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.76962 0.168978i 1.76962 0.168978i
\(305\) 0 0
\(306\) −2.14504 3.71533i −2.14504 3.71533i
\(307\) 0.0552004 + 0.0775182i 0.0552004 + 0.0775182i 0.841254 0.540641i \(-0.181818\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(308\) 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
\(313\) 1.16413 1.34347i 1.16413 1.34347i 0.235759 0.971812i \(-0.424242\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −2.50196 0.734641i −2.50196 0.734641i
\(322\) 0 0
\(323\) −1.49256 + 2.09600i −1.49256 + 2.09600i
\(324\) 0.229373 4.81513i 0.229373 4.81513i
\(325\) 0 0
\(326\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(327\) 0 0
\(328\) −0.264241 + 0.105786i −0.264241 + 0.105786i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.419102 1.72756i −0.419102 1.72756i −0.654861 0.755750i \(-0.727273\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(332\) −1.10181 1.27155i −1.10181 1.27155i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.50842 + 1.18624i 1.50842 + 1.18624i 0.928368 + 0.371662i \(0.121212\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(338\) −0.654861 0.755750i −0.654861 0.755750i
\(339\) −0.544537 2.24461i −0.544537 2.24461i
\(340\) 0 0
\(341\) 0 0
\(342\) −4.89135 + 1.95820i −4.89135 + 1.95820i
\(343\) 0 0
\(344\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.580057 + 0.814576i −0.580057 + 0.814576i −0.995472 0.0950560i \(-0.969697\pi\)
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
\(352\) 0.195876 0.807410i 0.195876 0.807410i
\(353\) −0.947890 + 0.903811i −0.947890 + 0.903811i −0.995472 0.0950560i \(-0.969697\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(354\) −2.14427 0.858437i −2.14427 0.858437i
\(355\) 0 0
\(356\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(357\) 0 0
\(358\) 1.65210 0.318417i 1.65210 0.318417i
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) 0 0
\(361\) 1.56335 + 1.49065i 1.56335 + 1.49065i
\(362\) 0 0
\(363\) 0.357685 + 0.502299i 0.357685 + 0.502299i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(368\) 0 0
\(369\) 0.663116 0.521480i 0.663116 0.521480i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0.697576 + 0.979609i 0.697576 + 0.979609i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.279486 + 0.0538665i −0.279486 + 0.0538665i −0.327068 0.945001i \(-0.606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(384\) −1.44091 + 1.37391i −1.44091 + 1.37391i
\(385\) 0 0
\(386\) 1.70566 0.879330i 1.70566 0.879330i
\(387\) −0.0401402 0.279181i −0.0401402 0.279181i
\(388\) −0.452418 0.132842i −0.452418 0.132842i
\(389\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.327068 0.945001i −0.327068 0.945001i
\(393\) −0.0806472 + 0.560914i −0.0806472 + 0.560914i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.117169 + 2.45967i 0.117169 + 2.45967i
\(397\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.786053 0.618159i −0.786053 0.618159i
\(401\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(402\) 0.995472 1.72421i 0.995472 1.72421i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.137123 2.87856i −0.137123 2.87856i
\(409\) −1.21590 + 0.486774i −1.21590 + 0.486774i −0.888835 0.458227i \(-0.848485\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(410\) 0 0
\(411\) −0.185343 + 1.28909i −0.185343 + 1.28909i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.283341 1.97068i −0.283341 1.97068i
\(418\) 1.31276 0.676774i 1.31276 0.676774i
\(419\) 0.111165 0.458227i 0.111165 0.458227i −0.888835 0.458227i \(-0.848485\pi\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(422\) 0.514186 1.48564i 0.514186 1.48564i
\(423\) 0 0
\(424\) 0 0
\(425\) 1.42131 0.273935i 1.42131 0.273935i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.947890 0.903811i −0.947890 0.903811i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 1.95496 3.38610i 1.95496 3.38610i
\(433\) 0.651174 0.0621796i 0.651174 0.0621796i 0.235759 0.971812i \(-0.424242\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.934515 0.0892353i 0.934515 0.0892353i
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 1.71921 + 2.41429i 1.71921 + 2.41429i
\(442\) 0 0
\(443\) 1.04758 + 0.998867i 1.04758 + 0.998867i 1.00000 \(0\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.271738 + 0.785135i −0.271738 + 0.785135i 0.723734 + 0.690079i \(0.242424\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(450\) 2.75155 + 1.10155i 2.75155 + 1.10155i
\(451\) −0.171148 + 0.163189i −0.171148 + 0.163189i
\(452\) 0.273507 1.12741i 0.273507 1.12741i
\(453\) 0 0
\(454\) −0.264241 1.83784i −0.264241 1.83784i
\(455\) 0 0
\(456\) −3.52322 0.336426i −3.52322 0.336426i
\(457\) −0.911911 + 1.28060i −0.911911 + 1.28060i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(458\) 0 0
\(459\) 1.85104 + 5.34823i 1.85104 + 5.34823i
\(460\) 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 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(467\) −0.653077 0.513585i −0.653077 0.513585i 0.235759 0.971812i \(-0.424242\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.759713 0.876756i −0.759713 0.876756i
\(473\) 0.0186403 + 0.0768363i 0.0186403 + 0.0768363i
\(474\) 0 0
\(475\) −0.0845850 1.77566i −0.0845850 1.77566i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.67489 0.159932i −1.67489 0.159932i
\(483\) 0 0
\(484\) 0.0440780 + 0.306569i 0.0440780 + 0.306569i
\(485\) 0 0
\(486\) −1.34090 + 5.52728i −1.34090 + 5.52728i
\(487\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(488\) 0 0
\(489\) 1.20906 3.49334i 1.20906 3.49334i
\(490\) 0 0
\(491\) 0.654861 0.755750i 0.654861 0.755750i −0.327068 0.945001i \(-0.606061\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(492\) 0.556441 0.107245i 0.556441 0.107245i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.67489 + 2.90099i 1.67489 + 2.90099i
\(499\) −0.981929 + 1.70075i −0.981929 + 1.70075i −0.327068 + 0.945001i \(0.606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.45949 + 1.14776i −1.45949 + 1.14776i
\(503\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.995472 + 1.72421i 0.995472 + 1.72421i
\(508\) 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
\(513\) 6.82496 1.31540i 6.82496 1.31540i
\(514\) 1.25667 1.45027i 1.25667 1.45027i
\(515\) 0 0
\(516\) 0.0619682 0.179045i 0.0619682 0.179045i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.279486 1.94387i −0.279486 1.94387i −0.327068 0.945001i \(-0.606061\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(522\) 0 0
\(523\) 0.651174 + 0.0621796i 0.651174 + 0.0621796i 0.415415 0.909632i \(-0.363636\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(524\) −0.165101 + 0.231852i −0.165101 + 0.231852i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.687153 + 1.50465i −0.687153 + 1.50465i
\(529\) 0.928368 0.371662i 0.928368 0.371662i
\(530\) 0 0
\(531\) 2.89258 + 1.85895i 2.89258 + 1.85895i
\(532\) 0 0
\(533\) 0 0
\(534\) −2.46033 1.93482i −2.46033 1.93482i
\(535\) 0 0
\(536\) 0.841254 0.540641i 0.841254 0.540641i
\(537\) −3.34978 −3.34978
\(538\) 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
\(544\) 0.601300 1.31666i 0.601300 1.31666i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.0800569 1.68060i 0.0800569 1.68060i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(548\) −0.379436 + 0.532843i −0.379436 + 0.532843i
\(549\) 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
\(556\) 0.327068 0.945001i 0.327068 0.945001i
\(557\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.994632 2.17794i −0.994632 2.17794i
\(562\) 1.04758 + 0.998867i 1.04758 + 0.998867i
\(563\) 1.65210 1.06174i 1.65210 1.06174i 0.723734 0.690079i \(-0.242424\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.500000 0.866025i 0.500000 0.866025i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.370638 + 0.291473i −0.370638 + 0.291473i −0.786053 0.618159i \(-0.787879\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(570\) 0 0
\(571\) 1.42131 + 0.273935i 1.42131 + 0.273935i 0.841254 0.540641i \(-0.181818\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 2.49336 1.60238i 2.49336 1.60238i
\(577\) −1.13779 1.08488i −1.13779 1.08488i −0.995472 0.0950560i \(-0.969697\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(578\) 0.454947 + 0.996196i 0.454947 + 0.996196i
\(579\) −3.66583 + 1.07639i −3.66583 + 1.07639i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.834408 + 0.430167i 0.834408 + 0.430167i
\(583\) 0 0
\(584\) 0.437742 + 0.175245i 0.437742 + 0.175245i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.419102 + 0.216062i −0.419102 + 0.216062i −0.654861 0.755750i \(-0.727273\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(588\) 0.283341 + 1.97068i 0.283341 + 1.97068i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.154218 0.445585i −0.154218 0.445585i 0.841254 0.540641i \(-0.181818\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(594\) 0.462308 3.21542i 0.462308 3.21542i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(600\) 1.30379 + 1.50465i 1.30379 + 1.50465i
\(601\) −1.45949 1.14776i −1.45949 1.14776i −0.959493 0.281733i \(-0.909091\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(602\) 0 0
\(603\) −1.94091 + 2.23993i −1.94091 + 2.23993i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(608\) −1.49547 0.961081i −1.49547 0.961081i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.610543 + 4.24642i −0.610543 + 4.24642i
\(613\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(614\) 0.00452808 0.0950560i 0.00452808 0.0950560i
\(615\) 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
\(619\) 0.581419 0.299742i 0.581419 0.299742i −0.142315 0.989821i \(-0.545455\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(626\) −1.74555 + 0.336426i −1.74555 + 0.336426i
\(627\) −2.82140 + 0.828437i −2.82140 + 0.828437i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(632\) 0 0
\(633\) −1.56499 + 2.71064i −1.56499 + 2.71064i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.928368 1.60798i −0.928368 1.60798i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(642\) 1.51255 + 2.12407i 1.51255 + 2.12407i
\(643\) 0.975950 0.627205i 0.975950 0.627205i 0.0475819 0.998867i \(-0.484848\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.46889 0.724932i 2.46889 0.724932i
\(647\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(648\) −3.15682 + 3.64316i −3.15682 + 3.64316i
\(649\) −0.856711 0.441665i −0.856711 0.441665i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.34378 1.28129i 1.34378 1.28129i
\(653\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(657\) −1.39118 0.132842i −1.39118 0.132842i
\(658\) 0 0
\(659\) −0.0475819 + 0.998867i −0.0475819 + 0.998867i 0.841254 + 0.540641i \(0.181818\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(660\) 0 0
\(661\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(662\) −0.738471 + 1.61703i −0.738471 + 1.61703i
\(663\) 0 0
\(664\) 0.0800569 + 1.68060i 0.0800569 + 1.68060i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.28605 1.48418i −1.28605 1.48418i −0.786053 0.618159i \(-0.787879\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(674\) −0.452418 1.86489i −0.452418 1.86489i
\(675\) −3.28924 2.11387i −3.28924 2.11387i
\(676\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(677\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(678\) −0.959493 + 2.10100i −0.959493 + 2.10100i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.175894 + 3.69247i −0.175894 + 3.69247i
\(682\) 0 0
\(683\) 0.651174 + 0.0621796i 0.651174 + 0.0621796i 0.415415 0.909632i \(-0.363636\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(684\) 5.05534 + 1.48438i 5.05534 + 1.48438i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.0688733 0.0656706i 0.0688733 0.0656706i
\(689\) 0 0
\(690\) 0 0
\(691\) 1.16413 + 0.600149i 1.16413 + 0.600149i 0.928368 0.371662i \(-0.121212\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.959493 0.281733i 0.959493 0.281733i
\(695\) 0 0
\(696\) 0 0
\(697\) −0.346590 + 0.222740i −0.346590 + 0.222740i
\(698\) 0 0
\(699\) −0.995472 1.72421i −0.995472 1.72421i
\(700\) 0 0
\(701\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.653077 + 0.513585i −0.653077 + 0.513585i
\(705\) 0 0
\(706\) 1.30379 0.124497i 1.30379 0.124497i
\(707\) 0 0
\(708\) 1.15486 + 2.00028i 1.15486 + 2.00028i
\(709\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.653077 1.43004i −0.653077 1.43004i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.49547 0.770969i −1.49547 0.770969i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.307416 2.13813i −0.307416 2.13813i
\(723\) 3.21409 + 0.943741i 3.21409 + 0.943741i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.0293408 0.615940i 0.0293408 0.615940i
\(727\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(728\) 0 0
\(729\) 2.70149 5.91543i 2.70149 5.91543i
\(730\) 0 0
\(731\) 0.00655425 + 0.137591i 0.00655425 + 0.137591i
\(732\) 0 0
\(733\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.481929 0.676774i 0.481929 0.676774i
\(738\) −0.843602 −0.843602
\(739\) −0.911911 0.717135i −0.911911 0.717135i 0.0475819 0.998867i \(-0.484848\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.63099 4.71245i −1.63099 4.71245i
\(748\) 0.0572220 1.20124i 0.0572220 1.20124i
\(749\) 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
\(753\) 3.28572 1.69391i 3.28572 1.69391i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(758\) 0.252989 + 0.130425i 0.252989 + 0.130425i
\(759\) 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
\(768\) 1.98193 0.189251i 1.98193 0.189251i
\(769\) 1.82318 + 0.351390i 1.82318 + 0.351390i 0.981929 0.189251i \(-0.0606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(770\) 0 0
\(771\) −3.00319 + 2.36173i −3.00319 + 2.36173i
\(772\) −1.88431 0.363170i −1.88431 0.363170i
\(773\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(774\) −0.141026 + 0.244264i −0.141026 + 0.244264i
\(775\) 0 0
\(776\) 0.273507 + 0.384087i 0.273507 + 0.384087i
\(777\) 0 0
\(778\) 0 0
\(779\) 0.210191 + 0.460254i 0.210191 + 0.460254i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(785\) 0 0
\(786\) 0.410127 0.391055i 0.410127 0.391055i
\(787\) −0.308779 + 1.27280i −0.308779 + 1.27280i 0.580057 + 0.814576i \(0.303030\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.42837 2.00586i 1.42837 2.00586i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)