Properties

Label 536.1.ba.a.435.1
Level $536$
Weight $1$
Character 536.435
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 435.1
Root \(-0.888835 - 0.458227i\) of defining polynomial
Character \(\chi\) \(=\) 536.435
Dual form 536.1.ba.a.467.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0475819 + 0.998867i) q^{2} +(1.50842 - 0.442913i) q^{3} +(-0.995472 + 0.0950560i) q^{4} +(0.514186 + 1.48564i) q^{6} +(-0.142315 - 0.989821i) q^{8} +(1.23792 - 0.795563i) q^{9} +O(q^{10})\) \(q+(0.0475819 + 0.998867i) q^{2} +(1.50842 - 0.442913i) q^{3} +(-0.995472 + 0.0950560i) q^{4} +(0.514186 + 1.48564i) q^{6} +(-0.142315 - 0.989821i) q^{8} +(1.23792 - 0.795563i) q^{9} +(0.0930932 - 0.268975i) q^{11} +(-1.45949 + 0.584293i) q^{12} +(0.981929 - 0.189251i) q^{16} +(-1.15486 - 0.110276i) q^{17} +(0.853564 + 1.19866i) q^{18} +(-1.74555 + 0.899892i) q^{19} +(0.273100 + 0.0801894i) q^{22} +(-0.653077 - 1.43004i) q^{24} +(-0.142315 + 0.989821i) q^{25} +(0.485433 - 0.560219i) q^{27} +(0.235759 + 0.971812i) q^{32} +(0.0212914 - 0.446961i) q^{33} +(0.0552004 - 1.15880i) q^{34} +(-1.15669 + 0.909632i) q^{36} +(-0.981929 - 1.70075i) q^{38} +(0.975950 - 1.37053i) q^{41} +(-0.271738 - 0.595023i) q^{43} +(-0.0671040 + 0.276606i) q^{44} +(1.39734 - 0.720381i) q^{48} +(0.580057 + 0.814576i) q^{49} +(-0.995472 - 0.0950560i) q^{50} +(-1.79086 + 0.345161i) q^{51} +(0.582682 + 0.458227i) q^{54} +(-2.23445 + 2.13054i) q^{57} +(-0.264241 - 1.83784i) q^{59} +(-0.959493 + 0.281733i) q^{64} +0.447468 q^{66} +(-0.654861 - 0.755750i) q^{67} +1.16011 q^{68} +(-0.963639 - 1.11210i) q^{72} +(0.651174 + 1.88144i) q^{73} +(0.223734 + 1.55610i) q^{75} +(1.65210 - 1.06174i) q^{76} +(-0.127181 + 0.278487i) q^{81} +(1.41542 + 0.909632i) q^{82} +(-1.28605 + 0.247866i) q^{83} +(0.581419 - 0.299742i) q^{86} +(-0.279486 - 0.0538665i) q^{88} +(-0.0913090 - 0.0268107i) q^{89} +(0.786053 + 1.36148i) q^{96} +(0.995472 - 1.72421i) q^{97} +(-0.786053 + 0.618159i) q^{98} +(-0.0987447 - 0.407031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + O(q^{10}) \) \( 20q + q^{2} + 2q^{3} + q^{4} - q^{6} - 2q^{8} + 2q^{11} - 12q^{12} + q^{16} - 12q^{17} - q^{19} - 4q^{22} + 2q^{24} - 2q^{25} - 2q^{27} + q^{32} - 2q^{33} - q^{34} - q^{38} + 2q^{41} + 2q^{43} + 2q^{44} - q^{48} + q^{49} + q^{50} + q^{51} + 23q^{54} + q^{57} - 9q^{59} - 2q^{64} - 18q^{66} - 2q^{67} + 2q^{68} - q^{73} - 9q^{75} + 2q^{76} + 2q^{81} + 18q^{82} - 9q^{83} - q^{86} + 2q^{88} + 2q^{89} - q^{96} - q^{97} + q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{16}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(3\) 1.50842 0.442913i 1.50842 0.442913i 0.580057 0.814576i \(-0.303030\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(4\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(5\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(6\) 0.514186 + 1.48564i 0.514186 + 1.48564i
\(7\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(8\) −0.142315 0.989821i −0.142315 0.989821i
\(9\) 1.23792 0.795563i 1.23792 0.795563i
\(10\) 0 0
\(11\) 0.0930932 0.268975i 0.0930932 0.268975i −0.888835 0.458227i \(-0.848485\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(12\) −1.45949 + 0.584293i −1.45949 + 0.584293i
\(13\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.981929 0.189251i 0.981929 0.189251i
\(17\) −1.15486 0.110276i −1.15486 0.110276i −0.500000 0.866025i \(-0.666667\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(18\) 0.853564 + 1.19866i 0.853564 + 1.19866i
\(19\) −1.74555 + 0.899892i −1.74555 + 0.899892i −0.786053 + 0.618159i \(0.787879\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(23\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(24\) −0.653077 1.43004i −0.653077 1.43004i
\(25\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(26\) 0 0
\(27\) 0.485433 0.560219i 0.485433 0.560219i
\(28\) 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 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(32\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(33\) 0.0212914 0.446961i 0.0212914 0.446961i
\(34\) 0.0552004 1.15880i 0.0552004 1.15880i
\(35\) 0 0
\(36\) −1.15669 + 0.909632i −1.15669 + 0.909632i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) −0.981929 1.70075i −0.981929 1.70075i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.975950 1.37053i 0.975950 1.37053i 0.0475819 0.998867i \(-0.484848\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(42\) 0 0
\(43\) −0.271738 0.595023i −0.271738 0.595023i 0.723734 0.690079i \(-0.242424\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(44\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(48\) 1.39734 0.720381i 1.39734 0.720381i
\(49\) 0.580057 + 0.814576i 0.580057 + 0.814576i
\(50\) −0.995472 0.0950560i −0.995472 0.0950560i
\(51\) −1.79086 + 0.345161i −1.79086 + 0.345161i
\(52\) 0 0
\(53\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(54\) 0.582682 + 0.458227i 0.582682 + 0.458227i
\(55\) 0 0
\(56\) 0 0
\(57\) −2.23445 + 2.13054i −2.23445 + 2.13054i
\(58\) 0 0
\(59\) −0.264241 1.83784i −0.264241 1.83784i −0.500000 0.866025i \(-0.666667\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(60\) 0 0
\(61\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(65\) 0 0
\(66\) 0.447468 0.447468
\(67\) −0.654861 0.755750i −0.654861 0.755750i
\(68\) 1.16011 1.16011
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(72\) −0.963639 1.11210i −0.963639 1.11210i
\(73\) 0.651174 + 1.88144i 0.651174 + 1.88144i 0.415415 + 0.909632i \(0.363636\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(74\) 0 0
\(75\) 0.223734 + 1.55610i 0.223734 + 1.55610i
\(76\) 1.65210 1.06174i 1.65210 1.06174i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(80\) 0 0
\(81\) −0.127181 + 0.278487i −0.127181 + 0.278487i
\(82\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(83\) −1.28605 + 0.247866i −1.28605 + 0.247866i −0.786053 0.618159i \(-0.787879\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.581419 0.299742i 0.581419 0.299742i
\(87\) 0 0
\(88\) −0.279486 0.0538665i −0.279486 0.0538665i
\(89\) −0.0913090 0.0268107i −0.0913090 0.0268107i 0.235759 0.971812i \(-0.424242\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.786053 + 1.36148i 0.786053 + 1.36148i
\(97\) 0.995472 1.72421i 0.995472 1.72421i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(98\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(99\) −0.0987447 0.407031i −0.0987447 0.407031i
\(100\) 0.0475819 0.998867i 0.0475819 0.998867i
\(101\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(102\) −0.429982 1.77241i −0.429982 1.77241i
\(103\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(108\) −0.429982 + 0.603826i −0.429982 + 0.603826i
\(109\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.82318 + 0.351390i 1.82318 + 0.351390i 0.981929 0.189251i \(-0.0606061\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(114\) −2.23445 2.13054i −2.23445 2.13054i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.82318 0.351390i 1.82318 0.351390i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.722372 + 0.568079i 0.722372 + 0.568079i
\(122\) 0 0
\(123\) 0.865121 2.49960i 0.865121 2.49960i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(128\) −0.327068 0.945001i −0.327068 0.945001i
\(129\) −0.673440 0.777191i −0.673440 0.777191i
\(130\) 0 0
\(131\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(132\) 0.0212914 + 0.446961i 0.0212914 + 0.446961i
\(133\) 0 0
\(134\) 0.723734 0.690079i 0.723734 0.690079i
\(135\) 0 0
\(136\) 0.0552004 + 1.15880i 0.0552004 + 1.15880i
\(137\) −1.38884 + 0.407799i −1.38884 + 0.407799i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) 0.654861 + 0.755750i 0.654861 + 0.755750i 0.981929 0.189251i \(-0.0606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.06499 1.01546i 1.06499 1.01546i
\(145\) 0 0
\(146\) −1.84833 + 0.739959i −1.84833 + 0.739959i
\(147\) 1.23576 + 0.971812i 1.23576 + 0.971812i
\(148\) 0 0
\(149\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(150\) −1.54370 + 0.297523i −1.54370 + 0.297523i
\(151\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(152\) 1.13915 + 1.59971i 1.13915 + 1.59971i
\(153\) −1.51736 + 0.782251i −1.51736 + 0.782251i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.284223 0.113786i −0.284223 0.113786i
\(163\) 0.888835 + 1.53951i 0.888835 + 1.53951i 0.841254 + 0.540641i \(0.181818\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(164\) −0.841254 + 1.45709i −0.841254 + 1.45709i
\(165\) 0 0
\(166\) −0.308779 1.27280i −0.308779 1.27280i
\(167\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(168\) 0 0
\(169\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(170\) 0 0
\(171\) −1.44493 + 2.50268i −1.44493 + 2.50268i
\(172\) 0.327068 + 0.566498i 0.327068 + 0.566498i
\(173\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.0405070 0.281733i 0.0405070 0.281733i
\(177\) −1.21259 2.65520i −1.21259 2.65520i
\(178\) 0.0224357 0.0924813i 0.0224357 0.0924813i
\(179\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(180\) 0 0
\(181\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.137171 + 0.300363i −0.137171 + 0.300363i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(192\) −1.32254 + 0.849945i −1.32254 + 0.849945i
\(193\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(194\) 1.76962 + 0.912303i 1.76962 + 0.912303i
\(195\) 0 0
\(196\) −0.654861 0.755750i −0.654861 0.755750i
\(197\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(198\) 0.401872 0.118000i 0.401872 0.118000i
\(199\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(200\) 1.00000 1.00000
\(201\) −1.32254 0.849945i −1.32254 0.849945i
\(202\) 0 0
\(203\) 0 0
\(204\) 1.74994 0.513830i 1.74994 0.513830i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.0795500 + 0.553283i 0.0795500 + 0.553283i
\(210\) 0 0
\(211\) 0.0688733 0.0656706i 0.0688733 0.0656706i −0.654861 0.755750i \(-0.727273\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.50842 + 1.18624i 1.50842 + 1.18624i
\(215\) 0 0
\(216\) −0.623601 0.400764i −0.623601 0.400764i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.81556 + 2.54960i 1.81556 + 2.54960i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(224\) 0 0
\(225\) 0.611291 + 1.33854i 0.611291 + 1.33854i
\(226\) −0.264241 + 1.83784i −0.264241 + 1.83784i
\(227\) −1.03115 + 1.44805i −1.03115 + 1.44805i −0.142315 + 0.989821i \(0.545455\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(228\) 2.02181 2.33330i 2.02181 2.33330i
\(229\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.235759 0.971812i −0.235759 0.971812i −0.959493 0.281733i \(-0.909091\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.437742 + 1.80440i 0.437742 + 1.80440i
\(237\) 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
\(241\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(242\) −0.533064 + 0.748584i −0.533064 + 0.748584i
\(243\) −0.173991 + 1.21014i −0.173991 + 1.21014i
\(244\) 0 0
\(245\) 0 0
\(246\) 2.53794 + 0.745205i 2.53794 + 0.745205i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.83013 + 0.943498i −1.83013 + 0.943498i
\(250\) 0 0
\(251\) 1.76962 + 0.168978i 1.76962 + 0.168978i 0.928368 0.371662i \(-0.121212\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.928368 0.371662i 0.928368 0.371662i
\(257\) −0.271738 + 0.785135i −0.271738 + 0.785135i 0.723734 + 0.690079i \(0.242424\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(258\) 0.744267 0.709657i 0.744267 0.709657i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.550294 1.58997i −0.550294 1.58997i
\(263\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(264\) −0.445442 + 0.0425345i −0.445442 + 0.0425345i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.149608 −0.149608
\(268\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(272\) −1.15486 + 0.110276i −1.15486 + 0.110276i
\(273\) 0 0
\(274\) −0.473420 1.36786i −0.473420 1.36786i
\(275\) 0.252989 + 0.130425i 0.252989 + 0.130425i
\(276\) 0 0
\(277\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(278\) −0.723734 + 0.690079i −0.723734 + 0.690079i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.911911 0.717135i −0.911911 0.717135i 0.0475819 0.998867i \(-0.484848\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(282\) 0 0
\(283\) −0.841254 0.540641i −0.841254 0.540641i 0.0475819 0.998867i \(-0.484848\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.06499 + 1.01546i 1.06499 + 1.01546i
\(289\) 0.339614 + 0.0654552i 0.339614 + 0.0654552i
\(290\) 0 0
\(291\) 0.737920 3.04175i 0.737920 3.04175i
\(292\) −0.827068 1.81103i −0.827068 1.81103i
\(293\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(294\) −0.911911 + 1.28060i −0.911911 + 1.28060i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.105495 0.182722i −0.105495 0.182722i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.370638 1.52779i −0.370638 1.52779i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.54370 + 1.21398i −1.54370 + 1.21398i
\(305\) 0 0
\(306\) −0.853564 1.47842i −0.853564 1.47842i
\(307\) −0.607279 0.243118i −0.607279 0.243118i 0.0475819 0.998867i \(-0.484848\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(312\) 0 0
\(313\) −1.88431 0.553283i −1.88431 0.553283i −0.995472 0.0950560i \(-0.969697\pi\)
−0.888835 0.458227i \(-0.848485\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 1.25324 2.74422i 1.25324 2.74422i
\(322\) 0 0
\(323\) 2.11510 0.846758i 2.11510 0.846758i
\(324\) 0.100133 0.289315i 0.100133 0.289315i
\(325\) 0 0
\(326\) −1.49547 + 0.961081i −1.49547 + 0.961081i
\(327\) 0 0
\(328\) −1.49547 0.770969i −1.49547 0.770969i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.95496 + 0.186677i −1.95496 + 0.186677i −0.995472 0.0950560i \(-0.969697\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(332\) 1.25667 0.368991i 1.25667 0.368991i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.0395325 + 0.829889i 0.0395325 + 0.829889i 0.928368 + 0.371662i \(0.121212\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(338\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(339\) 2.90577 0.277467i 2.90577 0.277467i
\(340\) 0 0
\(341\) 0 0
\(342\) −2.56860 1.32421i −2.56860 1.32421i
\(343\) 0 0
\(344\) −0.550294 + 0.353653i −0.550294 + 0.353653i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.928368 + 0.371662i −0.928368 + 0.371662i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(348\) 0 0
\(349\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.283341 + 0.0270558i 0.283341 + 0.0270558i
\(353\) −1.11312 1.56316i −1.11312 1.56316i −0.786053 0.618159i \(-0.787879\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(354\) 2.59450 1.33756i 2.59450 1.33756i
\(355\) 0 0
\(356\) 0.0934441 + 0.0180099i 0.0934441 + 0.0180099i
\(357\) 0 0
\(358\) −0.308779 + 1.27280i −0.308779 + 1.27280i
\(359\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(360\) 0 0
\(361\) 1.65707 2.32703i 1.65707 2.32703i
\(362\) 0 0
\(363\) 1.34125 + 0.536957i 1.34125 + 0.536957i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(368\) 0 0
\(369\) 0.117805 2.47303i 0.117805 2.47303i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) −0.306550 0.122724i −0.306550 0.122724i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.396666 1.63508i 0.396666 1.63508i −0.327068 0.945001i \(-0.606061\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(384\) −0.911911 1.28060i −0.911911 1.28060i
\(385\) 0 0
\(386\) 0.815816 0.157236i 0.815816 0.157236i
\(387\) −0.809768 0.520406i −0.809768 0.520406i
\(388\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(389\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.723734 0.690079i 0.723734 0.690079i
\(393\) −2.22518 + 1.43004i −2.22518 + 1.43004i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.136988 + 0.395802i 0.136988 + 0.395802i
\(397\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(401\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(402\) 0.786053 1.36148i 0.786053 1.36148i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.596514 + 1.72351i 0.596514 + 1.72351i
\(409\) 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i \(0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(410\) 0 0
\(411\) −1.91433 + 1.23027i −1.91433 + 1.23027i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.32254 + 0.849945i 1.32254 + 0.849945i
\(418\) −0.548871 + 0.105786i −0.548871 + 0.105786i
\(419\) 1.98193 + 0.189251i 1.98193 + 0.189251i 1.00000 \(0\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(420\) 0 0
\(421\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(422\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.273507 1.12741i 0.273507 1.12741i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.11312 + 1.56316i −1.11312 + 1.56316i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 0.370638 0.641964i 0.370638 0.641964i
\(433\) −1.13779 + 0.894765i −1.13779 + 0.894765i −0.995472 0.0950560i \(-0.969697\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −2.46033 + 1.93482i −2.46033 + 1.93482i
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 1.36611 + 0.546908i 1.36611 + 0.546908i
\(442\) 0 0
\(443\) 0.672932 0.945001i 0.672932 0.945001i −0.327068 0.945001i \(-0.606061\pi\)
1.00000 \(0\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.205996 0.196417i −0.205996 0.196417i 0.580057 0.814576i \(-0.303030\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(450\) −1.30794 + 0.674289i −1.30794 + 0.674289i
\(451\) −0.277784 0.390093i −0.277784 0.390093i
\(452\) −1.84833 0.176494i −1.84833 0.176494i
\(453\) 0 0
\(454\) −1.49547 0.961081i −1.49547 0.961081i
\(455\) 0 0
\(456\) 2.42685 + 1.90850i 2.42685 + 1.90850i
\(457\) 0.0883470 0.0353688i 0.0883470 0.0353688i −0.327068 0.945001i \(-0.606061\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(458\) 0 0
\(459\) −0.622386 + 0.593444i −0.622386 + 0.593444i
\(460\) 0 0
\(461\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(462\) 0 0
\(463\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.959493 0.281733i 0.959493 0.281733i
\(467\) −0.0135432 0.284307i −0.0135432 0.284307i −0.995472 0.0950560i \(-0.969697\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.78153 + 0.523103i −1.78153 + 0.523103i
\(473\) −0.185343 + 0.0176982i −0.185343 + 0.0176982i
\(474\) 0 0
\(475\) −0.642315 1.85585i −0.642315 1.85585i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.02951 + 0.809616i 1.02951 + 0.809616i
\(483\) 0 0
\(484\) −0.773100 0.496841i −0.773100 0.496841i
\(485\) 0 0
\(486\) −1.21705 0.116214i −1.21705 0.116214i
\(487\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(488\) 0 0
\(489\) 2.02261 + 1.92856i 2.02261 + 1.92856i
\(490\) 0 0
\(491\) 0.959493 + 0.281733i 0.959493 + 0.281733i 0.723734 0.690079i \(-0.242424\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(492\) −0.623601 + 2.57052i −0.623601 + 2.57052i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.02951 1.78316i −1.02951 1.78316i
\(499\) −0.235759 + 0.408346i −0.235759 + 0.408346i −0.959493 0.281733i \(-0.909091\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.0845850 + 1.77566i −0.0845850 + 1.77566i
\(503\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.786053 + 1.36148i 0.786053 + 1.36148i
\(508\) 0 0
\(509\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(513\) −0.343209 + 1.41473i −0.343209 + 1.41473i
\(514\) −0.797176 0.234072i −0.797176 0.234072i
\(515\) 0 0
\(516\) 0.744267 + 0.709657i 0.744267 + 0.709657i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.396666 + 0.254922i 0.396666 + 0.254922i 0.723734 0.690079i \(-0.242424\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(522\) 0 0
\(523\) −1.13779 0.894765i −1.13779 0.894765i −0.142315 0.989821i \(-0.545455\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(524\) 1.56199 0.625325i 1.56199 0.625325i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.0636813 0.442913i −0.0636813 0.442913i
\(529\) −0.888835 0.458227i −0.888835 0.458227i
\(530\) 0 0
\(531\) −1.78922 2.06487i −1.78922 2.06487i
\(532\) 0 0
\(533\) 0 0
\(534\) −0.00711862 0.149438i −0.00711862 0.149438i
\(535\) 0 0
\(536\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(537\) 2.05902 2.05902
\(538\) 0 0
\(539\) 0.273100 0.0801894i 0.273100 0.0801894i
\(540\) 0 0
\(541\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.165101 1.14831i −0.165101 1.14831i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.428368 1.23769i 0.428368 1.23769i −0.500000 0.866025i \(-0.666667\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(548\) 1.34378 0.537970i 1.34378 0.537970i
\(549\) 0 0
\(550\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.723734 0.690079i −0.723734 0.690079i
\(557\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.0738776 + 0.513830i −0.0738776 + 0.513830i
\(562\) 0.672932 0.945001i 0.672932 0.945001i
\(563\) −0.308779 + 0.356349i −0.308779 + 0.356349i −0.888835 0.458227i \(-0.848485\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.500000 0.866025i 0.500000 0.866025i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.0947329 + 1.98869i −0.0947329 + 1.98869i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(570\) 0 0
\(571\) 0.273507 + 1.12741i 0.273507 + 1.12741i 0.928368 + 0.371662i \(0.121212\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.963639 + 1.11210i −0.963639 + 1.11210i
\(577\) 0.0552004 0.0775182i 0.0552004 0.0775182i −0.786053 0.618159i \(-0.787879\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(578\) −0.0492216 + 0.342344i −0.0492216 + 0.342344i
\(579\) −0.542596 1.18812i −0.542596 1.18812i
\(580\) 0 0
\(581\) 0 0
\(582\) 3.07341 + 0.592352i 3.07341 + 0.592352i
\(583\) 0 0
\(584\) 1.76962 0.912303i 1.76962 0.912303i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.95496 + 0.376789i −1.95496 + 0.376789i −0.959493 + 0.281733i \(0.909091\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(588\) −1.32254 0.849945i −1.32254 0.849945i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.44091 + 1.37391i −1.44091 + 1.37391i −0.654861 + 0.755750i \(0.727273\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(594\) 0.177495 0.114069i 0.177495 0.114069i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(600\) 1.50842 0.442913i 1.50842 0.442913i
\(601\) −0.0845850 1.77566i −0.0845850 1.77566i −0.500000 0.866025i \(-0.666667\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(602\) 0 0
\(603\) −1.41191 0.414574i −1.41191 0.414574i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(608\) −1.28605 1.48418i −1.28605 1.48418i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.43613 0.922943i 1.43613 0.922943i
\(613\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(614\) 0.213947 0.618159i 0.213947 0.618159i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(618\) 0 0
\(619\) 1.42131 0.273935i 1.42131 0.273935i 0.580057 0.814576i \(-0.303030\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.959493 0.281733i −0.959493 0.281733i
\(626\) 0.462997 1.90850i 0.462997 1.90850i
\(627\) 0.365052 + 0.799351i 0.365052 + 0.799351i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(632\) 0 0
\(633\) 0.0748038 0.129564i 0.0748038 0.129564i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.888835 + 1.53951i 0.888835 + 1.53951i 0.841254 + 0.540641i \(0.181818\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(642\) 2.80075 + 1.12125i 2.80075 + 1.12125i
\(643\) −1.21590 + 1.40323i −1.21590 + 1.40323i −0.327068 + 0.945001i \(0.606061\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.946439 + 2.07241i 0.946439 + 2.07241i
\(647\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(648\) 0.293752 + 0.0862533i 0.293752 + 0.0862533i
\(649\) −0.518932 0.100016i −0.518932 0.100016i
\(650\) 0 0
\(651\) 0 0
\(652\) −1.03115 1.44805i −1.03115 1.44805i
\(653\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.698939 1.53046i 0.698939 1.53046i
\(657\) 2.30291 + 1.81103i 2.30291 + 1.81103i
\(658\) 0 0
\(659\) 0.327068 0.945001i 0.327068 0.945001i −0.654861 0.755750i \(-0.727273\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(660\) 0 0
\(661\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(662\) −0.279486 1.94387i −0.279486 1.94387i
\(663\) 0 0
\(664\) 0.428368 + 1.23769i 0.428368 + 1.23769i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.452418 + 0.132842i −0.452418 + 0.132842i −0.500000 0.866025i \(-0.666667\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(674\) −0.827068 + 0.0789754i −0.827068 + 0.0789754i
\(675\) 0.485433 + 0.560219i 0.485433 + 0.560219i
\(676\) −0.327068 0.945001i −0.327068 0.945001i
\(677\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(678\) 0.415415 + 2.88927i 0.415415 + 2.88927i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.914053 + 2.64098i −0.914053 + 2.64098i
\(682\) 0 0
\(683\) −1.13779 0.894765i −1.13779 0.894765i −0.142315 0.989821i \(-0.545455\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(684\) 1.20049 2.62870i 1.20049 2.62870i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.379436 0.532843i −0.379436 0.532843i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.88431 0.363170i −1.88431 0.363170i −0.888835 0.458227i \(-0.848485\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.415415 0.909632i −0.415415 0.909632i
\(695\) 0 0
\(696\) 0 0
\(697\) −1.27822 + 1.47515i −1.27822 + 1.47515i
\(698\) 0 0
\(699\) −0.786053 1.36148i −0.786053 1.36148i
\(700\) 0 0
\(701\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.0135432 + 0.284307i −0.0135432 + 0.284307i
\(705\) 0 0
\(706\) 1.50842 1.18624i 1.50842 1.18624i
\(707\) 0 0
\(708\) 1.45949 + 2.52792i 1.45949 + 2.52792i
\(709\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.28605 0.247866i −1.28605 0.247866i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.40324 + 1.54447i 2.40324 + 1.54447i
\(723\) 0.855348 1.87295i 0.855348 1.87295i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.472529 + 1.36528i −0.472529 + 1.36528i
\(727\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(728\) 0 0
\(729\) 0.229963 + 1.59943i 0.229963 + 1.59943i
\(730\) 0 0
\(731\) 0.248203 + 0.717135i 0.248203 + 0.717135i
\(732\) 0 0
\(733\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.264241 + 0.105786i −0.264241 + 0.105786i
\(738\) 2.47584 2.47584
\(739\) 0.0883470 + 1.85463i 0.0883470 + 1.85463i 0.415415 + 0.909632i \(0.363636\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.39484 + 1.32997i −1.39484 + 1.32997i
\(748\) 0.107999 0.312042i 0.107999 0.312042i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(752\) 0 0
\(753\) 2.74418 0.528898i 2.74418 0.528898i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(758\) 1.65210 + 0.318417i 1.65210 + 0.318417i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.23576 0.971812i 1.23576 0.971812i
\(769\) −0.419102 1.72756i −0.419102 1.72756i −0.654861 0.755750i \(-0.727273\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(770\) 0 0
\(771\) −0.0621493 + 1.30467i −0.0621493 + 1.30467i
\(772\) 0.195876 + 0.807410i 0.195876 + 0.807410i
\(773\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(774\) 0.481286 0.833612i 0.481286 0.833612i
\(775\) 0 0
\(776\) −1.84833 0.739959i −1.84833 0.739959i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.470237 + 3.27057i −0.470237 + 3.27057i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(785\) 0 0
\(786\) −1.53430 2.15462i −1.53430 2.15462i
\(787\) 1.91030 + 0.182411i 1.91030 + 0.182411i 0.981929 0.189251i \(-0.0606061\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.388835 + 0.155666i −0.388835 + 0.155666i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i<