Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7350,2,Mod(1,7350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7350.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7350.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(58.6900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7350.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.585786 | 0.176621 | 0.0883106 | − | 0.996093i | \(-0.471853\pi\) | ||||
0.0883106 | + | 0.996093i | \(0.471853\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.171573 | 0.0416125 | 0.0208063 | − | 0.999784i | \(-0.493377\pi\) | ||||
0.0208063 | + | 0.999784i | \(0.493377\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.41421 | 0.324443 | 0.162221 | − | 0.986754i | \(-0.448134\pi\) | ||||
0.162221 | + | 0.986754i | \(0.448134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.585786 | 0.124890 | ||||||||
\(23\) | −2.41421 | −0.503398 | −0.251699 | − | 0.967806i | \(-0.580989\pi\) | ||||
−0.251699 | + | 0.967806i | \(0.580989\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.00000 | 0.588348 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.414214 | −0.0743950 | −0.0371975 | − | 0.999308i | \(-0.511843\pi\) | ||||
−0.0371975 | + | 0.999308i | \(0.511843\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.585786 | 0.101972 | ||||||||
\(34\) | 0.171573 | 0.0294245 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.07107 | 1.16248 | 0.581238 | − | 0.813733i | \(-0.302568\pi\) | ||||
0.581238 | + | 0.813733i | \(0.302568\pi\) | |||||||
\(38\) | 1.41421 | 0.229416 | ||||||||
\(39\) | 3.00000 | 0.480384 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.171573 | 0.0267952 | 0.0133976 | − | 0.999910i | \(-0.495735\pi\) | ||||
0.0133976 | + | 0.999910i | \(0.495735\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.41421 | −0.673161 | −0.336581 | − | 0.941655i | \(-0.609270\pi\) | ||||
−0.336581 | + | 0.941655i | \(0.609270\pi\) | |||||||
\(44\) | 0.585786 | 0.0883106 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.41421 | −0.355956 | ||||||||
\(47\) | 9.65685 | 1.40860 | 0.704298 | − | 0.709904i | \(-0.251262\pi\) | ||||
0.704298 | + | 0.709904i | \(0.251262\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.171573 | 0.0240250 | ||||||||
\(52\) | 3.00000 | 0.416025 | ||||||||
\(53\) | −1.34315 | −0.184495 | −0.0922476 | − | 0.995736i | \(-0.529405\pi\) | ||||
−0.0922476 | + | 0.995736i | \(0.529405\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.41421 | 0.187317 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 1.24264 | 0.161778 | 0.0808890 | − | 0.996723i | \(-0.474224\pi\) | ||||
0.0808890 | + | 0.996723i | \(0.474224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.82843 | 0.746254 | 0.373127 | − | 0.927780i | \(-0.378286\pi\) | ||||
0.373127 | + | 0.927780i | \(0.378286\pi\) | |||||||
\(62\) | −0.414214 | −0.0526052 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.585786 | 0.0721053 | ||||||||
\(67\) | −7.31371 | −0.893512 | −0.446756 | − | 0.894656i | \(-0.647421\pi\) | ||||
−0.446756 | + | 0.894656i | \(0.647421\pi\) | |||||||
\(68\) | 0.171573 | 0.0208063 | ||||||||
\(69\) | −2.41421 | −0.290637 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3137 | 1.58005 | 0.790023 | − | 0.613077i | \(-0.210068\pi\) | ||||
0.790023 | + | 0.613077i | \(0.210068\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.928932 | 0.108723 | 0.0543616 | − | 0.998521i | \(-0.482688\pi\) | ||||
0.0543616 | + | 0.998521i | \(0.482688\pi\) | |||||||
\(74\) | 7.07107 | 0.821995 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.41421 | 0.162221 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.00000 | 0.339683 | ||||||||
\(79\) | −13.0711 | −1.47061 | −0.735305 | − | 0.677736i | \(-0.762961\pi\) | ||||
−0.735305 | + | 0.677736i | \(0.762961\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.171573 | 0.0189471 | ||||||||
\(83\) | 14.0711 | 1.54450 | 0.772250 | − | 0.635319i | \(-0.219131\pi\) | ||||
0.772250 | + | 0.635319i | \(0.219131\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.41421 | −0.475997 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0.585786 | 0.0624450 | ||||||||
\(89\) | −4.00000 | −0.423999 | −0.212000 | − | 0.977270i | \(-0.567998\pi\) | ||||
−0.212000 | + | 0.977270i | \(0.567998\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.41421 | −0.251699 | ||||||||
\(93\) | −0.414214 | −0.0429519 | ||||||||
\(94\) | 9.65685 | 0.996028 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.6569 | −1.18357 | −0.591787 | − | 0.806094i | \(-0.701577\pi\) | ||||
−0.591787 | + | 0.806094i | \(0.701577\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.585786 | 0.0588738 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.65685 | 0.562878 | 0.281439 | − | 0.959579i | \(-0.409188\pi\) | ||||
0.281439 | + | 0.959579i | \(0.409188\pi\) | |||||||
\(102\) | 0.171573 | 0.0169882 | ||||||||
\(103\) | 14.0711 | 1.38646 | 0.693232 | − | 0.720715i | \(-0.256186\pi\) | ||||
0.693232 | + | 0.720715i | \(0.256186\pi\) | |||||||
\(104\) | 3.00000 | 0.294174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.34315 | −0.130458 | ||||||||
\(107\) | 10.4853 | 1.01365 | 0.506825 | − | 0.862049i | \(-0.330819\pi\) | ||||
0.506825 | + | 0.862049i | \(0.330819\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 11.3137 | 1.08366 | 0.541828 | − | 0.840489i | \(-0.317732\pi\) | ||||
0.541828 | + | 0.840489i | \(0.317732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.07107 | 0.671156 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.41421 | −0.885615 | −0.442807 | − | 0.896617i | \(-0.646017\pi\) | ||||
−0.442807 | + | 0.896617i | \(0.646017\pi\) | |||||||
\(114\) | 1.41421 | 0.132453 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 3.00000 | 0.277350 | ||||||||
\(118\) | 1.24264 | 0.114394 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | 5.82843 | 0.527681 | ||||||||
\(123\) | 0.171573 | 0.0154702 | ||||||||
\(124\) | −0.414214 | −0.0371975 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.82843 | 0.783396 | 0.391698 | − | 0.920094i | \(-0.371888\pi\) | ||||
0.391698 | + | 0.920094i | \(0.371888\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.41421 | −0.388650 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.1716 | 1.15081 | 0.575403 | − | 0.817870i | \(-0.304845\pi\) | ||||
0.575403 | + | 0.817870i | \(0.304845\pi\) | |||||||
\(132\) | 0.585786 | 0.0509862 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.31371 | −0.631808 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.171573 | 0.0147123 | ||||||||
\(137\) | −19.2132 | −1.64149 | −0.820747 | − | 0.571291i | \(-0.806443\pi\) | ||||
−0.820747 | + | 0.571291i | \(0.806443\pi\) | |||||||
\(138\) | −2.41421 | −0.205512 | ||||||||
\(139\) | −15.5563 | −1.31947 | −0.659736 | − | 0.751497i | \(-0.729332\pi\) | ||||
−0.659736 | + | 0.751497i | \(0.729332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.65685 | 0.813254 | ||||||||
\(142\) | 13.3137 | 1.11726 | ||||||||
\(143\) | 1.75736 | 0.146958 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.928932 | 0.0768790 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.07107 | 0.581238 | ||||||||
\(149\) | −6.65685 | −0.545351 | −0.272675 | − | 0.962106i | \(-0.587908\pi\) | ||||
−0.272675 | + | 0.962106i | \(0.587908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.8995 | −0.968367 | −0.484184 | − | 0.874966i | \(-0.660883\pi\) | ||||
−0.484184 | + | 0.874966i | \(0.660883\pi\) | |||||||
\(152\) | 1.41421 | 0.114708 | ||||||||
\(153\) | 0.171573 | 0.0138708 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | 0.240192 | ||||||||
\(157\) | 19.7990 | 1.58013 | 0.790066 | − | 0.613022i | \(-0.210046\pi\) | ||||
0.790066 | + | 0.613022i | \(0.210046\pi\) | |||||||
\(158\) | −13.0711 | −1.03988 | ||||||||
\(159\) | −1.34315 | −0.106518 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 3.24264 | 0.253983 | 0.126992 | − | 0.991904i | \(-0.459468\pi\) | ||||
0.126992 | + | 0.991904i | \(0.459468\pi\) | |||||||
\(164\) | 0.171573 | 0.0133976 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.0711 | 1.09213 | ||||||||
\(167\) | −3.17157 | −0.245424 | −0.122712 | − | 0.992442i | \(-0.539159\pi\) | ||||
−0.122712 | + | 0.992442i | \(0.539159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.41421 | 0.108148 | ||||||||
\(172\) | −4.41421 | −0.336581 | ||||||||
\(173\) | 5.75736 | 0.437724 | 0.218862 | − | 0.975756i | \(-0.429766\pi\) | ||||
0.218862 | + | 0.975756i | \(0.429766\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.585786 | 0.0441553 | ||||||||
\(177\) | 1.24264 | 0.0934026 | ||||||||
\(178\) | −4.00000 | −0.299813 | ||||||||
\(179\) | 9.07107 | 0.678003 | 0.339002 | − | 0.940786i | \(-0.389911\pi\) | ||||
0.339002 | + | 0.940786i | \(0.389911\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.686292 | 0.0510116 | 0.0255058 | − | 0.999675i | \(-0.491880\pi\) | ||||
0.0255058 | + | 0.999675i | \(0.491880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.82843 | 0.430850 | ||||||||
\(184\) | −2.41421 | −0.177978 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.414214 | −0.0303716 | ||||||||
\(187\) | 0.100505 | 0.00734966 | ||||||||
\(188\) | 9.65685 | 0.704298 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.92893 | 0.139573 | 0.0697863 | − | 0.997562i | \(-0.477768\pi\) | ||||
0.0697863 | + | 0.997562i | \(0.477768\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 1.17157 | 0.0843317 | 0.0421658 | − | 0.999111i | \(-0.486574\pi\) | ||||
0.0421658 | + | 0.999111i | \(0.486574\pi\) | |||||||
\(194\) | −11.6569 | −0.836913 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.14214 | 0.366362 | 0.183181 | − | 0.983079i | \(-0.441361\pi\) | ||||
0.183181 | + | 0.983079i | \(0.441361\pi\) | |||||||
\(198\) | 0.585786 | 0.0416300 | ||||||||
\(199\) | −8.34315 | −0.591430 | −0.295715 | − | 0.955276i | \(-0.595558\pi\) | ||||
−0.295715 | + | 0.955276i | \(0.595558\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.31371 | −0.515869 | ||||||||
\(202\) | 5.65685 | 0.398015 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.171573 | 0.0120125 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.0711 | 0.980378 | ||||||||
\(207\) | −2.41421 | −0.167799 | ||||||||
\(208\) | 3.00000 | 0.208013 | ||||||||
\(209\) | 0.828427 | 0.0573035 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.55635 | 0.313672 | 0.156836 | − | 0.987625i | \(-0.449871\pi\) | ||||
0.156836 | + | 0.987625i | \(0.449871\pi\) | |||||||
\(212\) | −1.34315 | −0.0922476 | ||||||||
\(213\) | 13.3137 | 0.912240 | ||||||||
\(214\) | 10.4853 | 0.716759 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 11.3137 | 0.766261 | ||||||||
\(219\) | 0.928932 | 0.0627714 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.514719 | 0.0346237 | ||||||||
\(222\) | 7.07107 | 0.474579 | ||||||||
\(223\) | −6.55635 | −0.439046 | −0.219523 | − | 0.975607i | \(-0.570450\pi\) | ||||
−0.219523 | + | 0.975607i | \(0.570450\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.41421 | −0.626224 | ||||||||
\(227\) | −11.3848 | −0.755634 | −0.377817 | − | 0.925880i | \(-0.623325\pi\) | ||||
−0.377817 | + | 0.925880i | \(0.623325\pi\) | |||||||
\(228\) | 1.41421 | 0.0936586 | ||||||||
\(229\) | −6.68629 | −0.441843 | −0.220921 | − | 0.975292i | \(-0.570906\pi\) | ||||
−0.220921 | + | 0.975292i | \(0.570906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −5.75736 | −0.377177 | −0.188589 | − | 0.982056i | \(-0.560391\pi\) | ||||
−0.188589 | + | 0.982056i | \(0.560391\pi\) | |||||||
\(234\) | 3.00000 | 0.196116 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.24264 | 0.0808890 | ||||||||
\(237\) | −13.0711 | −0.849057 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3137 | 0.731823 | 0.365911 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365911 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | −10.6569 | −0.685049 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.82843 | 0.373127 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.171573 | 0.0109391 | ||||||||
\(247\) | 4.24264 | 0.269953 | ||||||||
\(248\) | −0.414214 | −0.0263026 | ||||||||
\(249\) | 14.0711 | 0.891718 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0711 | 1.01440 | 0.507198 | − | 0.861829i | \(-0.330681\pi\) | ||||
0.507198 | + | 0.861829i | \(0.330681\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.41421 | −0.0889108 | ||||||||
\(254\) | 8.82843 | 0.553945 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.6569 | 1.53805 | 0.769026 | − | 0.639217i | \(-0.220742\pi\) | ||||
0.769026 | + | 0.639217i | \(0.220742\pi\) | |||||||
\(258\) | −4.41421 | −0.274817 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 13.1716 | 0.813742 | ||||||||
\(263\) | −20.5563 | −1.26756 | −0.633779 | − | 0.773514i | \(-0.718497\pi\) | ||||
−0.633779 | + | 0.773514i | \(0.718497\pi\) | |||||||
\(264\) | 0.585786 | 0.0360527 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.00000 | −0.244796 | ||||||||
\(268\) | −7.31371 | −0.446756 | ||||||||
\(269\) | −31.5563 | −1.92402 | −0.962012 | − | 0.273006i | \(-0.911982\pi\) | ||||
−0.962012 | + | 0.273006i | \(0.911982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.4853 | 1.73036 | 0.865179 | − | 0.501463i | \(-0.167205\pi\) | ||||
0.865179 | + | 0.501463i | \(0.167205\pi\) | |||||||
\(272\) | 0.171573 | 0.0104031 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.2132 | −1.16071 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.41421 | −0.145319 | ||||||||
\(277\) | −24.0416 | −1.44452 | −0.722261 | − | 0.691621i | \(-0.756897\pi\) | ||||
−0.722261 | + | 0.691621i | \(0.756897\pi\) | |||||||
\(278\) | −15.5563 | −0.933008 | ||||||||
\(279\) | −0.414214 | −0.0247983 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000 | 1.19310 | 0.596550 | − | 0.802576i | \(-0.296538\pi\) | ||||
0.596550 | + | 0.802576i | \(0.296538\pi\) | |||||||
\(282\) | 9.65685 | 0.575057 | ||||||||
\(283\) | 8.24264 | 0.489974 | 0.244987 | − | 0.969526i | \(-0.421216\pi\) | ||||
0.244987 | + | 0.969526i | \(0.421216\pi\) | |||||||
\(284\) | 13.3137 | 0.790023 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.75736 | 0.103915 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.9706 | −0.998268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.6569 | −0.683337 | ||||||||
\(292\) | 0.928932 | 0.0543616 | ||||||||
\(293\) | 11.3137 | 0.660954 | 0.330477 | − | 0.943814i | \(-0.392790\pi\) | ||||
0.330477 | + | 0.943814i | \(0.392790\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.07107 | 0.410997 | ||||||||
\(297\) | 0.585786 | 0.0339908 | ||||||||
\(298\) | −6.65685 | −0.385621 | ||||||||
\(299\) | −7.24264 | −0.418853 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.8995 | −0.684739 | ||||||||
\(303\) | 5.65685 | 0.324978 | ||||||||
\(304\) | 1.41421 | 0.0811107 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.171573 | 0.00980817 | ||||||||
\(307\) | 11.4142 | 0.651444 | 0.325722 | − | 0.945466i | \(-0.394393\pi\) | ||||
0.325722 | + | 0.945466i | \(0.394393\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0711 | 0.800475 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.58579 | 0.486855 | 0.243428 | − | 0.969919i | \(-0.421728\pi\) | ||||
0.243428 | + | 0.969919i | \(0.421728\pi\) | |||||||
\(312\) | 3.00000 | 0.169842 | ||||||||
\(313\) | 32.0416 | 1.81110 | 0.905550 | − | 0.424240i | \(-0.139459\pi\) | ||||
0.905550 | + | 0.424240i | \(0.139459\pi\) | |||||||
\(314\) | 19.7990 | 1.11732 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.0711 | −0.735305 | ||||||||
\(317\) | 13.9706 | 0.784665 | 0.392332 | − | 0.919823i | \(-0.371668\pi\) | ||||
0.392332 | + | 0.919823i | \(0.371668\pi\) | |||||||
\(318\) | −1.34315 | −0.0753199 | ||||||||
\(319\) | 0.585786 | 0.0327977 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4853 | 0.585231 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.242641 | 0.0135009 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.24264 | 0.179593 | ||||||||
\(327\) | 11.3137 | 0.625650 | ||||||||
\(328\) | 0.171573 | 0.00947353 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.92893 | −0.545743 | −0.272872 | − | 0.962050i | \(-0.587973\pi\) | ||||
−0.272872 | + | 0.962050i | \(0.587973\pi\) | |||||||
\(332\) | 14.0711 | 0.772250 | ||||||||
\(333\) | 7.07107 | 0.387492 | ||||||||
\(334\) | −3.17157 | −0.173541 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.7990 | 1.89562 | 0.947811 | − | 0.318833i | \(-0.103291\pi\) | ||||
0.947811 | + | 0.318833i | \(0.103291\pi\) | |||||||
\(338\) | −4.00000 | −0.217571 | ||||||||
\(339\) | −9.41421 | −0.511310 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.242641 | −0.0131397 | ||||||||
\(342\) | 1.41421 | 0.0764719 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.41421 | −0.237998 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.75736 | 0.309518 | ||||||||
\(347\) | −29.7990 | −1.59969 | −0.799847 | − | 0.600204i | \(-0.795086\pi\) | ||||
−0.799847 | + | 0.600204i | \(0.795086\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | −13.3431 | −0.714242 | −0.357121 | − | 0.934058i | \(-0.616242\pi\) | ||||
−0.357121 | + | 0.934058i | \(0.616242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.00000 | 0.160128 | ||||||||
\(352\) | 0.585786 | 0.0312225 | ||||||||
\(353\) | 3.51472 | 0.187070 | 0.0935348 | − | 0.995616i | \(-0.470183\pi\) | ||||
0.0935348 | + | 0.995616i | \(0.470183\pi\) | |||||||
\(354\) | 1.24264 | 0.0660456 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.00000 | −0.212000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.07107 | 0.479421 | ||||||||
\(359\) | −19.8701 | −1.04870 | −0.524351 | − | 0.851502i | \(-0.675692\pi\) | ||||
−0.524351 | + | 0.851502i | \(0.675692\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0.686292 | 0.0360707 | ||||||||
\(363\) | −10.6569 | −0.559340 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.82843 | 0.304657 | ||||||||
\(367\) | 9.24264 | 0.482462 | 0.241231 | − | 0.970468i | \(-0.422449\pi\) | ||||
0.241231 | + | 0.970468i | \(0.422449\pi\) | |||||||
\(368\) | −2.41421 | −0.125850 | ||||||||
\(369\) | 0.171573 | 0.00893173 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.414214 | −0.0214760 | ||||||||
\(373\) | −13.6569 | −0.707125 | −0.353563 | − | 0.935411i | \(-0.615030\pi\) | ||||
−0.353563 | + | 0.935411i | \(0.615030\pi\) | |||||||
\(374\) | 0.100505 | 0.00519699 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.65685 | 0.498014 | ||||||||
\(377\) | 3.00000 | 0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.21320 | 0.421884 | 0.210942 | − | 0.977499i | \(-0.432347\pi\) | ||||
0.210942 | + | 0.977499i | \(0.432347\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.82843 | 0.452294 | ||||||||
\(382\) | 1.92893 | 0.0986928 | ||||||||
\(383\) | −3.55635 | −0.181721 | −0.0908605 | − | 0.995864i | \(-0.528962\pi\) | ||||
−0.0908605 | + | 0.995864i | \(0.528962\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.17157 | 0.0596315 | ||||||||
\(387\) | −4.41421 | −0.224387 | ||||||||
\(388\) | −11.6569 | −0.591787 | ||||||||
\(389\) | −21.6569 | −1.09805 | −0.549023 | − | 0.835807i | \(-0.685000\pi\) | ||||
−0.549023 | + | 0.835807i | \(0.685000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.414214 | −0.0209477 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.1716 | 0.664418 | ||||||||
\(394\) | 5.14214 | 0.259057 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.585786 | 0.0294369 | ||||||||
\(397\) | 7.68629 | 0.385764 | 0.192882 | − | 0.981222i | \(-0.438217\pi\) | ||||
0.192882 | + | 0.981222i | \(0.438217\pi\) | |||||||
\(398\) | −8.34315 | −0.418204 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.8995 | 1.59298 | 0.796492 | − | 0.604649i | \(-0.206686\pi\) | ||||
0.796492 | + | 0.604649i | \(0.206686\pi\) | |||||||
\(402\) | −7.31371 | −0.364775 | ||||||||
\(403\) | −1.24264 | −0.0619003 | ||||||||
\(404\) | 5.65685 | 0.281439 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.14214 | 0.205318 | ||||||||
\(408\) | 0.171573 | 0.00849412 | ||||||||
\(409\) | −25.4142 | −1.25665 | −0.628326 | − | 0.777950i | \(-0.716260\pi\) | ||||
−0.628326 | + | 0.777950i | \(0.716260\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.2132 | −0.947717 | ||||||||
\(412\) | 14.0711 | 0.693232 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.41421 | −0.118652 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.00000 | 0.147087 | ||||||||
\(417\) | −15.5563 | −0.761798 | ||||||||
\(418\) | 0.828427 | 0.0405197 | ||||||||
\(419\) | 6.55635 | 0.320299 | 0.160149 | − | 0.987093i | \(-0.448802\pi\) | ||||
0.160149 | + | 0.987093i | \(0.448802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.3431 | −1.18641 | −0.593206 | − | 0.805051i | \(-0.702138\pi\) | ||||
−0.593206 | + | 0.805051i | \(0.702138\pi\) | |||||||
\(422\) | 4.55635 | 0.221800 | ||||||||
\(423\) | 9.65685 | 0.469532 | ||||||||
\(424\) | −1.34315 | −0.0652289 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13.3137 | 0.645051 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.4853 | 0.506825 | ||||||||
\(429\) | 1.75736 | 0.0848461 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.0416 | −0.724530 | −0.362265 | − | 0.932075i | \(-0.617996\pi\) | ||||
−0.362265 | + | 0.932075i | \(0.617996\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −16.6274 | −0.799063 | −0.399531 | − | 0.916720i | \(-0.630827\pi\) | ||||
−0.399531 | + | 0.916720i | \(0.630827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.3137 | 0.541828 | ||||||||
\(437\) | −3.41421 | −0.163324 | ||||||||
\(438\) | 0.928932 | 0.0443861 | ||||||||
\(439\) | −4.41421 | −0.210679 | −0.105339 | − | 0.994436i | \(-0.533593\pi\) | ||||
−0.105339 | + | 0.994436i | \(0.533593\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.514719 | 0.0244827 | ||||||||
\(443\) | 25.6569 | 1.21899 | 0.609497 | − | 0.792788i | \(-0.291371\pi\) | ||||
0.609497 | + | 0.792788i | \(0.291371\pi\) | |||||||
\(444\) | 7.07107 | 0.335578 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.55635 | −0.310452 | ||||||||
\(447\) | −6.65685 | −0.314858 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.9289 | −0.515768 | −0.257884 | − | 0.966176i | \(-0.583025\pi\) | ||||
−0.257884 | + | 0.966176i | \(0.583025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.100505 | 0.00473260 | ||||||||
\(452\) | −9.41421 | −0.442807 | ||||||||
\(453\) | −11.8995 | −0.559087 | ||||||||
\(454\) | −11.3848 | −0.534314 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.41421 | 0.0662266 | ||||||||
\(457\) | −1.82843 | −0.0855302 | −0.0427651 | − | 0.999085i | \(-0.513617\pi\) | ||||
−0.0427651 | + | 0.999085i | \(0.513617\pi\) | |||||||
\(458\) | −6.68629 | −0.312430 | ||||||||
\(459\) | 0.171573 | 0.00800834 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.0000 | −0.931493 | −0.465746 | − | 0.884918i | \(-0.654214\pi\) | ||||
−0.465746 | + | 0.884918i | \(0.654214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.1005 | −0.469410 | −0.234705 | − | 0.972067i | \(-0.575412\pi\) | ||||
−0.234705 | + | 0.972067i | \(0.575412\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.75736 | −0.266705 | ||||||||
\(467\) | 7.24264 | 0.335149 | 0.167575 | − | 0.985859i | \(-0.446406\pi\) | ||||
0.167575 | + | 0.985859i | \(0.446406\pi\) | |||||||
\(468\) | 3.00000 | 0.138675 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.7990 | 0.912289 | ||||||||
\(472\) | 1.24264 | 0.0571972 | ||||||||
\(473\) | −2.58579 | −0.118895 | ||||||||
\(474\) | −13.0711 | −0.600374 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.34315 | −0.0614984 | ||||||||
\(478\) | 11.3137 | 0.517477 | ||||||||
\(479\) | −11.7574 | −0.537207 | −0.268604 | − | 0.963251i | \(-0.586562\pi\) | ||||
−0.268604 | + | 0.963251i | \(0.586562\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.2132 | 0.967239 | ||||||||
\(482\) | 6.00000 | 0.273293 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.6569 | −0.484402 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −22.4853 | −1.01891 | −0.509453 | − | 0.860499i | \(-0.670152\pi\) | ||||
−0.509453 | + | 0.860499i | \(0.670152\pi\) | |||||||
\(488\) | 5.82843 | 0.263840 | ||||||||
\(489\) | 3.24264 | 0.146637 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.1421 | 1.27004 | 0.635018 | − | 0.772497i | \(-0.280993\pi\) | ||||
0.635018 | + | 0.772497i | \(0.280993\pi\) | |||||||
\(492\) | 0.171573 | 0.00773510 | ||||||||
\(493\) | 0.171573 | 0.00772725 | ||||||||
\(494\) | 4.24264 | 0.190885 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.414214 | −0.0185987 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.0711 | 0.630540 | ||||||||
\(499\) | −11.9289 | −0.534012 | −0.267006 | − | 0.963695i | \(-0.586034\pi\) | ||||
−0.267006 | + | 0.963695i | \(0.586034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.17157 | −0.141695 | ||||||||
\(502\) | 16.0711 | 0.717287 | ||||||||
\(503\) | 28.8701 | 1.28725 | 0.643626 | − | 0.765340i | \(-0.277429\pi\) | ||||
0.643626 | + | 0.765340i | \(0.277429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.41421 | −0.0628695 | ||||||||
\(507\) | −4.00000 | −0.177646 | ||||||||
\(508\) | 8.82843 | 0.391698 | ||||||||
\(509\) | −42.0416 | −1.86346 | −0.931731 | − | 0.363149i | \(-0.881702\pi\) | ||||
−0.931731 | + | 0.363149i | \(0.881702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.41421 | 0.0624391 | ||||||||
\(514\) | 24.6569 | 1.08757 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.41421 | −0.194325 | ||||||||
\(517\) | 5.65685 | 0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.75736 | 0.252720 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.656854 | −0.0287773 | −0.0143887 | − | 0.999896i | \(-0.504580\pi\) | ||||
−0.0143887 | + | 0.999896i | \(0.504580\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | 32.2843 | 1.41169 | 0.705846 | − | 0.708365i | \(-0.250567\pi\) | ||||
0.705846 | + | 0.708365i | \(0.250567\pi\) | |||||||
\(524\) | 13.1716 | 0.575403 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.5563 | −0.896299 | ||||||||
\(527\) | −0.0710678 | −0.00309576 | ||||||||
\(528\) | 0.585786 | 0.0254931 | ||||||||
\(529\) | −17.1716 | −0.746590 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.24264 | 0.0539260 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.514719 | 0.0222949 | ||||||||
\(534\) | −4.00000 | −0.173097 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.31371 | −0.315904 | ||||||||
\(537\) | 9.07107 | 0.391445 | ||||||||
\(538\) | −31.5563 | −1.36049 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.7574 | −1.10740 | −0.553698 | − | 0.832718i | \(-0.686784\pi\) | ||||
−0.553698 | + | 0.832718i | \(0.686784\pi\) | |||||||
\(542\) | 28.4853 | 1.22355 | ||||||||
\(543\) | 0.686292 | 0.0294516 | ||||||||
\(544\) | 0.171573 | 0.00735613 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.8701 | 0.849582 | 0.424791 | − | 0.905291i | \(-0.360348\pi\) | ||||
0.424791 | + | 0.905291i | \(0.360348\pi\) | |||||||
\(548\) | −19.2132 | −0.820747 | ||||||||
\(549\) | 5.82843 | 0.248751 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.41421 | 0.0602475 | ||||||||
\(552\) | −2.41421 | −0.102756 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −24.0416 | −1.02143 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.5563 | −0.659736 | ||||||||
\(557\) | −3.31371 | −0.140406 | −0.0702032 | − | 0.997533i | \(-0.522365\pi\) | ||||
−0.0702032 | + | 0.997533i | \(0.522365\pi\) | |||||||
\(558\) | −0.414214 | −0.0175351 | ||||||||
\(559\) | −13.2426 | −0.560104 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.100505 | 0.00424333 | ||||||||
\(562\) | 20.0000 | 0.843649 | ||||||||
\(563\) | −9.38478 | −0.395521 | −0.197761 | − | 0.980250i | \(-0.563367\pi\) | ||||
−0.197761 | + | 0.980250i | \(0.563367\pi\) | |||||||
\(564\) | 9.65685 | 0.406627 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.24264 | 0.346464 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.3137 | 0.558631 | ||||||||
\(569\) | −19.7574 | −0.828272 | −0.414136 | − | 0.910215i | \(-0.635916\pi\) | ||||
−0.414136 | + | 0.910215i | \(0.635916\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.0122 | −1.92555 | −0.962775 | − | 0.270303i | \(-0.912876\pi\) | ||||
−0.962775 | + | 0.270303i | \(0.912876\pi\) | |||||||
\(572\) | 1.75736 | 0.0734789 | ||||||||
\(573\) | 1.92893 | 0.0805823 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 8.34315 | 0.347330 | 0.173665 | − | 0.984805i | \(-0.444439\pi\) | ||||
0.173665 | + | 0.984805i | \(0.444439\pi\) | |||||||
\(578\) | −16.9706 | −0.705882 | ||||||||
\(579\) | 1.17157 | 0.0486889 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.6569 | −0.483192 | ||||||||
\(583\) | −0.786797 | −0.0325858 | ||||||||
\(584\) | 0.928932 | 0.0384395 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.3137 | 0.467365 | ||||||||
\(587\) | 23.5269 | 0.971060 | 0.485530 | − | 0.874220i | \(-0.338627\pi\) | ||||
0.485530 | + | 0.874220i | \(0.338627\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.585786 | −0.0241369 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.14214 | 0.211519 | ||||||||
\(592\) | 7.07107 | 0.290619 | ||||||||
\(593\) | −26.0000 | −1.06769 | −0.533846 | − | 0.845582i | \(-0.679254\pi\) | ||||
−0.533846 | + | 0.845582i | \(0.679254\pi\) | |||||||
\(594\) | 0.585786 | 0.0240351 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.65685 | −0.272675 | ||||||||
\(597\) | −8.34315 | −0.341462 | ||||||||
\(598\) | −7.24264 | −0.296174 | ||||||||
\(599\) | −27.5858 | −1.12712 | −0.563562 | − | 0.826074i | \(-0.690570\pi\) | ||||
−0.563562 | + | 0.826074i | \(0.690570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.7279 | −1.09025 | −0.545127 | − | 0.838353i | \(-0.683519\pi\) | ||||
−0.545127 | + | 0.838353i | \(0.683519\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.31371 | −0.297837 | ||||||||
\(604\) | −11.8995 | −0.484184 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.65685 | 0.229794 | ||||||||
\(607\) | −27.9411 | −1.13410 | −0.567048 | − | 0.823685i | \(-0.691914\pi\) | ||||
−0.567048 | + | 0.823685i | \(0.691914\pi\) | |||||||
\(608\) | 1.41421 | 0.0573539 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.9706 | 1.17202 | ||||||||
\(612\) | 0.171573 | 0.00693542 | ||||||||
\(613\) | 22.0000 | 0.888572 | 0.444286 | − | 0.895885i | \(-0.353457\pi\) | ||||
0.444286 | + | 0.895885i | \(0.353457\pi\) | |||||||
\(614\) | 11.4142 | 0.460640 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3848 | 0.579109 | 0.289555 | − | 0.957161i | \(-0.406493\pi\) | ||||
0.289555 | + | 0.957161i | \(0.406493\pi\) | |||||||
\(618\) | 14.0711 | 0.566021 | ||||||||
\(619\) | −16.1421 | −0.648807 | −0.324404 | − | 0.945919i | \(-0.605164\pi\) | ||||
−0.324404 | + | 0.945919i | \(0.605164\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.41421 | −0.0968791 | ||||||||
\(622\) | 8.58579 | 0.344259 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.00000 | 0.120096 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32.0416 | 1.28064 | ||||||||
\(627\) | 0.828427 | 0.0330842 | ||||||||
\(628\) | 19.7990 | 0.790066 | ||||||||
\(629\) | 1.21320 | 0.0483736 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.1716 | −1.40016 | −0.700079 | − | 0.714065i | \(-0.746852\pi\) | ||||
−0.700079 | + | 0.714065i | \(0.746852\pi\) | |||||||
\(632\) | −13.0711 | −0.519939 | ||||||||
\(633\) | 4.55635 | 0.181099 | ||||||||
\(634\) | 13.9706 | 0.554842 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.34315 | −0.0532592 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.585786 | 0.0231915 | ||||||||
\(639\) | 13.3137 | 0.526682 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.2426 | 1.58949 | 0.794744 | − | 0.606944i | \(-0.207605\pi\) | ||||
0.794744 | + | 0.606944i | \(0.207605\pi\) | |||||||
\(642\) | 10.4853 | 0.413821 | ||||||||
\(643\) | −22.2426 | −0.877164 | −0.438582 | − | 0.898691i | \(-0.644519\pi\) | ||||
−0.438582 | + | 0.898691i | \(0.644519\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.242641 | 0.00954657 | ||||||||
\(647\) | −48.8701 | −1.92128 | −0.960640 | − | 0.277796i | \(-0.910396\pi\) | ||||
−0.960640 | + | 0.277796i | \(0.910396\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0.727922 | 0.0285734 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.24264 | 0.126992 | ||||||||
\(653\) | 35.3137 | 1.38193 | 0.690966 | − | 0.722887i | \(-0.257185\pi\) | ||||
0.690966 | + | 0.722887i | \(0.257185\pi\) | |||||||
\(654\) | 11.3137 | 0.442401 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.171573 | 0.00669880 | ||||||||
\(657\) | 0.928932 | 0.0362411 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.82843 | 0.343907 | 0.171953 | − | 0.985105i | \(-0.444992\pi\) | ||||
0.171953 | + | 0.985105i | \(0.444992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.6569 | −1.77585 | −0.887923 | − | 0.459992i | \(-0.847852\pi\) | ||||
−0.887923 | + | 0.459992i | \(0.847852\pi\) | |||||||
\(662\) | −9.92893 | −0.385899 | ||||||||
\(663\) | 0.514719 | 0.0199900 | ||||||||
\(664\) | 14.0711 | 0.546063 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.07107 | 0.273998 | ||||||||
\(667\) | −2.41421 | −0.0934787 | ||||||||
\(668\) | −3.17157 | −0.122712 | ||||||||
\(669\) | −6.55635 | −0.253483 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.41421 | 0.131804 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.7990 | −1.49559 | −0.747796 | − | 0.663929i | \(-0.768888\pi\) | ||||
−0.747796 | + | 0.663929i | \(0.768888\pi\) | |||||||
\(674\) | 34.7990 | 1.34041 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | 32.3848 | 1.24465 | 0.622324 | − | 0.782760i | \(-0.286189\pi\) | ||||
0.622324 | + | 0.782760i | \(0.286189\pi\) | |||||||
\(678\) | −9.41421 | −0.361551 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3848 | −0.436266 | ||||||||
\(682\) | −0.242641 | −0.00929119 | ||||||||
\(683\) | −10.9289 | −0.418184 | −0.209092 | − | 0.977896i | \(-0.567051\pi\) | ||||
−0.209092 | + | 0.977896i | \(0.567051\pi\) | |||||||
\(684\) | 1.41421 | 0.0540738 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.68629 | −0.255098 | ||||||||
\(688\) | −4.41421 | −0.168290 | ||||||||
\(689\) | −4.02944 | −0.153509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.1127 | 1.10750 | 0.553750 | − | 0.832683i | \(-0.313196\pi\) | ||||
0.553750 | + | 0.832683i | \(0.313196\pi\) | |||||||
\(692\) | 5.75736 | 0.218862 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.7990 | −1.13115 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | 0.0294373 | 0.00111502 | ||||||||
\(698\) | −13.3431 | −0.505046 | ||||||||
\(699\) | −5.75736 | −0.217763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.6863 | 0.516924 | 0.258462 | − | 0.966021i | \(-0.416784\pi\) | ||||
0.258462 | + | 0.966021i | \(0.416784\pi\) | |||||||
\(702\) | 3.00000 | 0.113228 | ||||||||
\(703\) | 10.0000 | 0.377157 | ||||||||
\(704\) | 0.585786 | 0.0220777 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.51472 | 0.132278 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.24264 | 0.0467013 | ||||||||
\(709\) | 0.100505 | 0.00377455 | 0.00188727 | − | 0.999998i | \(-0.499399\pi\) | ||||
0.00188727 | + | 0.999998i | \(0.499399\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.0711 | −0.490203 | ||||||||
\(712\) | −4.00000 | −0.149906 | ||||||||
\(713\) | 1.00000 | 0.0374503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.07107 | 0.339002 | ||||||||
\(717\) | 11.3137 | 0.422518 | ||||||||
\(718\) | −19.8701 | −0.741544 | ||||||||
\(719\) | −33.0711 | −1.23334 | −0.616671 | − | 0.787221i | \(-0.711519\pi\) | ||||
−0.616671 | + | 0.787221i | \(0.711519\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.0000 | −0.632674 | ||||||||
\(723\) | 6.00000 | 0.223142 | ||||||||
\(724\) | 0.686292 | 0.0255058 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.6569 | −0.395513 | ||||||||
\(727\) | 15.8701 | 0.588588 | 0.294294 | − | 0.955715i | \(-0.404916\pi\) | ||||
0.294294 | + | 0.955715i | \(0.404916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.757359 | −0.0280119 | ||||||||
\(732\) | 5.82843 | 0.215425 | ||||||||
\(733\) | −17.4853 | −0.645834 | −0.322917 | − | 0.946427i | \(-0.604663\pi\) | ||||
−0.322917 | + | 0.946427i | \(0.604663\pi\) | |||||||
\(734\) | 9.24264 | 0.341152 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.41421 | −0.0889891 | ||||||||
\(737\) | −4.28427 | −0.157813 | ||||||||
\(738\) | 0.171573 | 0.00631568 | ||||||||
\(739\) | 0.129942 | 0.00478001 | 0.00239000 | − | 0.999997i | \(-0.499239\pi\) | ||||
0.00239000 | + | 0.999997i | \(0.499239\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.24264 | 0.155857 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.44365 | 0.199708 | 0.0998541 | − | 0.995002i | \(-0.468162\pi\) | ||||
0.0998541 | + | 0.995002i | \(0.468162\pi\) | |||||||
\(744\) | −0.414214 | −0.0151858 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.6569 | −0.500013 | ||||||||
\(747\) | 14.0711 | 0.514833 | ||||||||
\(748\) | 0.100505 | 0.00367483 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.9706 | 0.765227 | 0.382613 | − | 0.923909i | \(-0.375024\pi\) | ||||
0.382613 | + | 0.923909i | \(0.375024\pi\) | |||||||
\(752\) | 9.65685 | 0.352149 | ||||||||
\(753\) | 16.0711 | 0.585662 | ||||||||
\(754\) | 3.00000 | 0.109254 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.7574 | 1.29962 | 0.649812 | − | 0.760095i | \(-0.274848\pi\) | ||||
0.649812 | + | 0.760095i | \(0.274848\pi\) | |||||||
\(758\) | 8.21320 | 0.298317 | ||||||||
\(759\) | −1.41421 | −0.0513327 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.9706 | −1.77518 | −0.887591 | − | 0.460633i | \(-0.847622\pi\) | ||||
−0.887591 | + | 0.460633i | \(0.847622\pi\) | |||||||
\(762\) | 8.82843 | 0.319820 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.92893 | 0.0697863 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.55635 | −0.128496 | ||||||||
\(767\) | 3.72792 | 0.134607 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −7.31371 | −0.263739 | −0.131870 | − | 0.991267i | \(-0.542098\pi\) | ||||
−0.131870 | + | 0.991267i | \(0.542098\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.6569 | 0.887995 | ||||||||
\(772\) | 1.17157 | 0.0421658 | ||||||||
\(773\) | 3.31371 | 0.119186 | 0.0595929 | − | 0.998223i | \(-0.481020\pi\) | ||||
0.0595929 | + | 0.998223i | \(0.481020\pi\) | |||||||
\(774\) | −4.41421 | −0.158666 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.6569 | −0.418457 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.6569 | −0.776436 | ||||||||
\(779\) | 0.242641 | 0.00869350 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.79899 | 0.279070 | ||||||||
\(782\) | −0.414214 | −0.0148122 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.1716 | 0.469814 | ||||||||
\(787\) | 7.45584 | 0.265772 | 0.132886 | − | 0.991131i | \(-0.457576\pi\) | ||||
0.132886 | + | 0.991131i | \(0.457576\pi\) | |||||||
\(788\) | 5.14214 | 0.183181 | ||||||||
\(789\) | −20.5563 | −0.731825 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.585786 | 0.0208150 | ||||||||
\(793\) | 17.4853 | 0.620921 | ||||||||
\(794\) | 7.68629 | 0.272776 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.34315 | −0.295715 | ||||||||
\(797\) | 7.75736 | 0.274780 | 0.137390 | − | 0.990517i | \(-0.456129\pi\) | ||||
0.137390 | + | 0.990517i | \(0.456129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.65685 | 0.0586153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.00000 | −0.141333 | ||||||||
\(802\) | 31.8995 | 1.12641 | ||||||||
\(803\) | 0.544156 | 0.0192028 | ||||||||
\(804\) | −7.31371 | −0.257935 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.24264 | −0.0437702 | ||||||||
\(807\) | −31.5563 | −1.11084 | ||||||||
\(808\) | 5.65685 | 0.199007 | ||||||||
\(809\) | 10.6274 | 0.373640 | 0.186820 | − | 0.982394i | \(-0.440182\pi\) | ||||
0.186820 | + | 0.982394i | \(0.440182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.2426 | −1.48334 | −0.741670 | − | 0.670765i | \(-0.765966\pi\) | ||||
−0.741670 | + | 0.670765i | \(0.765966\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.4853 | 0.999022 | ||||||||
\(814\) | 4.14214 | 0.145182 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.171573 | 0.00600625 | ||||||||
\(817\) | −6.24264 | −0.218402 | ||||||||
\(818\) | −25.4142 | −0.888587 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.8284 | 0.657117 | 0.328558 | − | 0.944484i | \(-0.393437\pi\) | ||||
0.328558 | + | 0.944484i | \(0.393437\pi\) | |||||||
\(822\) | −19.2132 | −0.670137 | ||||||||
\(823\) | −31.4142 | −1.09503 | −0.547515 | − | 0.836796i | \(-0.684426\pi\) | ||||
−0.547515 | + | 0.836796i | \(0.684426\pi\) | |||||||
\(824\) | 14.0711 | 0.490189 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.89949 | −0.274692 | −0.137346 | − | 0.990523i | \(-0.543857\pi\) | ||||
−0.137346 | + | 0.990523i | \(0.543857\pi\) | |||||||
\(828\) | −2.41421 | −0.0838997 | ||||||||
\(829\) | −38.7990 | −1.34754 | −0.673772 | − | 0.738939i | \(-0.735327\pi\) | ||||
−0.673772 | + | 0.738939i | \(0.735327\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.0416 | −0.833995 | ||||||||
\(832\) | 3.00000 | 0.104006 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −15.5563 | −0.538672 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.828427 | 0.0286518 | ||||||||
\(837\) | −0.414214 | −0.0143173 | ||||||||
\(838\) | 6.55635 | 0.226485 | ||||||||
\(839\) | −14.5858 | −0.503557 | −0.251779 | − | 0.967785i | \(-0.581015\pi\) | ||||
−0.251779 | + | 0.967785i | \(0.581015\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −24.3431 | −0.838920 | ||||||||
\(843\) | 20.0000 | 0.688837 | ||||||||
\(844\) | 4.55635 | 0.156836 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.65685 | 0.332009 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.34315 | −0.0461238 | ||||||||
\(849\) | 8.24264 | 0.282887 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.0711 | −0.585189 | ||||||||
\(852\) | 13.3137 | 0.456120 | ||||||||
\(853\) | −8.31371 | −0.284656 | −0.142328 | − | 0.989820i | \(-0.545459\pi\) | ||||
−0.142328 | + | 0.989820i | \(0.545459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.4853 | 0.358380 | ||||||||
\(857\) | −21.4558 | −0.732918 | −0.366459 | − | 0.930434i | \(-0.619430\pi\) | ||||
−0.366459 | + | 0.930434i | \(0.619430\pi\) | |||||||
\(858\) | 1.75736 | 0.0599953 | ||||||||
\(859\) | 45.9411 | 1.56749 | 0.783745 | − | 0.621082i | \(-0.213307\pi\) | ||||
0.783745 | + | 0.621082i | \(0.213307\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.0416 | −0.512320 | ||||||||
\(863\) | 8.97056 | 0.305362 | 0.152681 | − | 0.988276i | \(-0.451209\pi\) | ||||
0.152681 | + | 0.988276i | \(0.451209\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.6274 | −0.565023 | ||||||||
\(867\) | −16.9706 | −0.576351 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.65685 | −0.259741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.9411 | −0.743447 | ||||||||
\(872\) | 11.3137 | 0.383131 | ||||||||
\(873\) | −11.6569 | −0.394525 | ||||||||
\(874\) | −3.41421 | −0.115487 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.928932 | 0.0313857 | ||||||||
\(877\) | 37.6569 | 1.27158 | 0.635791 | − | 0.771861i | \(-0.280674\pi\) | ||||
0.635791 | + | 0.771861i | \(0.280674\pi\) | |||||||
\(878\) | −4.41421 | −0.148972 | ||||||||
\(879\) | 11.3137 | 0.381602 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.62742 | 0.122211 | 0.0611054 | − | 0.998131i | \(-0.480537\pi\) | ||||
0.0611054 | + | 0.998131i | \(0.480537\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.5269 | −1.12827 | −0.564135 | − | 0.825682i | \(-0.690790\pi\) | ||||
−0.564135 | + | 0.825682i | \(0.690790\pi\) | |||||||
\(884\) | 0.514719 | 0.0173119 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.6569 | 0.861959 | ||||||||
\(887\) | −34.2426 | −1.14976 | −0.574878 | − | 0.818239i | \(-0.694950\pi\) | ||||
−0.574878 | + | 0.818239i | \(0.694950\pi\) | |||||||
\(888\) | 7.07107 | 0.237289 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.585786 | 0.0196246 | ||||||||
\(892\) | −6.55635 | −0.219523 | ||||||||
\(893\) | 13.6569 | 0.457009 | ||||||||
\(894\) | −6.65685 | −0.222639 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.24264 | −0.241825 | ||||||||
\(898\) | −10.9289 | −0.364703 | ||||||||
\(899\) | −0.414214 | −0.0138148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.230447 | −0.00767732 | ||||||||
\(902\) | 0.100505 | 0.00334645 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.41421 | −0.313112 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.8995 | −0.395334 | ||||||||
\(907\) | 18.6985 | 0.620873 | 0.310436 | − | 0.950594i | \(-0.399525\pi\) | ||||
0.310436 | + | 0.950594i | \(0.399525\pi\) | |||||||
\(908\) | −11.3848 | −0.377817 | ||||||||
\(909\) | 5.65685 | 0.187626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.92893 | 0.262697 | 0.131349 | − | 0.991336i | \(-0.458069\pi\) | ||||
0.131349 | + | 0.991336i | \(0.458069\pi\) | |||||||
\(912\) | 1.41421 | 0.0468293 | ||||||||
\(913\) | 8.24264 | 0.272792 | ||||||||
\(914\) | −1.82843 | −0.0604790 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.68629 | −0.220921 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.171573 | 0.00566275 | ||||||||
\(919\) | 35.5563 | 1.17290 | 0.586448 | − | 0.809987i | \(-0.300526\pi\) | ||||
0.586448 | + | 0.809987i | \(0.300526\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.4142 | 0.376111 | ||||||||
\(922\) | −20.0000 | −0.658665 | ||||||||
\(923\) | 39.9411 | 1.31468 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.1005 | −0.331923 | ||||||||
\(927\) | 14.0711 | 0.462155 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −2.65685 | −0.0871686 | −0.0435843 | − | 0.999050i | \(-0.513878\pi\) | ||||
−0.0435843 | + | 0.999050i | \(0.513878\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.75736 | −0.188589 | ||||||||
\(933\) | 8.58579 | 0.281086 | ||||||||
\(934\) | 7.24264 | 0.236986 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.00000 | 0.0980581 | ||||||||
\(937\) | −8.24264 | −0.269275 | −0.134638 | − | 0.990895i | \(-0.542987\pi\) | ||||
−0.134638 | + | 0.990895i | \(0.542987\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.0416 | 1.04564 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.6863 | −0.935146 | −0.467573 | − | 0.883954i | \(-0.654872\pi\) | ||||
−0.467573 | + | 0.883954i | \(0.654872\pi\) | |||||||
\(942\) | 19.7990 | 0.645086 | ||||||||
\(943\) | −0.414214 | −0.0134886 | ||||||||
\(944\) | 1.24264 | 0.0404445 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.58579 | −0.0840712 | ||||||||
\(947\) | −17.2132 | −0.559354 | −0.279677 | − | 0.960094i | \(-0.590227\pi\) | ||||
−0.279677 | + | 0.960094i | \(0.590227\pi\) | |||||||
\(948\) | −13.0711 | −0.424529 | ||||||||
\(949\) | 2.78680 | 0.0904632 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.9706 | 0.453027 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.5980 | −1.54185 | −0.770925 | − | 0.636926i | \(-0.780206\pi\) | ||||
−0.770925 | + | 0.636926i | \(0.780206\pi\) | |||||||
\(954\) | −1.34315 | −0.0434859 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.3137 | 0.365911 | ||||||||
\(957\) | 0.585786 | 0.0189358 | ||||||||
\(958\) | −11.7574 | −0.379863 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8284 | −0.994465 | ||||||||
\(962\) | 21.2132 | 0.683941 | ||||||||
\(963\) | 10.4853 | 0.337883 | ||||||||
\(964\) | 6.00000 | 0.193247 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.04163 | −0.129970 | −0.0649850 | − | 0.997886i | \(-0.520700\pi\) | ||||
−0.0649850 | + | 0.997886i | \(0.520700\pi\) | |||||||
\(968\) | −10.6569 | −0.342524 | ||||||||
\(969\) | 0.242641 | 0.00779474 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.0294 | 0.353951 | 0.176976 | − | 0.984215i | \(-0.443369\pi\) | ||||
0.176976 | + | 0.984215i | \(0.443369\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.4853 | −0.720475 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.82843 | 0.186563 | ||||||||
\(977\) | 39.5563 | 1.26552 | 0.632760 | − | 0.774348i | \(-0.281922\pi\) | ||||
0.632760 | + | 0.774348i | \(0.281922\pi\) | |||||||
\(978\) | 3.24264 | 0.103688 | ||||||||
\(979\) | −2.34315 | −0.0748873 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3137 | 0.361219 | ||||||||
\(982\) | 28.1421 | 0.898052 | ||||||||
\(983\) | 51.3137 | 1.63665 | 0.818327 | − | 0.574754i | \(-0.194902\pi\) | ||||
0.818327 | + | 0.574754i | \(0.194902\pi\) | |||||||
\(984\) | 0.171573 | 0.00546954 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.171573 | 0.00546399 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.24264 | 0.134976 | ||||||||
\(989\) | 10.6569 | 0.338868 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6569 | −0.942081 | −0.471041 | − | 0.882112i | \(-0.656121\pi\) | ||||
−0.471041 | + | 0.882112i | \(0.656121\pi\) | |||||||
\(992\) | −0.414214 | −0.0131513 | ||||||||
\(993\) | −9.92893 | −0.315085 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.0711 | 0.445859 | ||||||||
\(997\) | −2.68629 | −0.0850757 | −0.0425379 | − | 0.999095i | \(-0.513544\pi\) | ||||
−0.0425379 | + | 0.999095i | \(0.513544\pi\) | |||||||
\(998\) | −11.9289 | −0.377604 | ||||||||
\(999\) | 7.07107 | 0.223719 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7350.2.a.dm.1.1 | yes | 2 | |
5.4 | even | 2 | 7350.2.a.dc.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 7350.2.a.dj.1.1 | yes | 2 | ||
35.34 | odd | 2 | 7350.2.a.dg.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7350.2.a.dc.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
7350.2.a.dg.1.1 | yes | 2 | 35.34 | odd | 2 | ||
7350.2.a.dj.1.1 | yes | 2 | 7.6 | odd | 2 | ||
7350.2.a.dm.1.1 | yes | 2 | 1.1 | even | 1 | trivial |