Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9904,2,Mod(1,9904)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9904, 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("9904.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9904 = 2^{4} \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9904.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: | \(79.0838381619\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 619) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 9904.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.725873 | 0.419083 | 0.209542 | − | 0.977800i | \(-0.432803\pi\) | ||||
0.209542 | + | 0.977800i | \(0.432803\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.225133 | −0.100683 | −0.0503414 | − | 0.998732i | \(-0.516031\pi\) | ||||
−0.0503414 | + | 0.998732i | \(0.516031\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.47282 | −0.934637 | −0.467319 | − | 0.884089i | \(-0.654780\pi\) | ||||
−0.467319 | + | 0.884089i | \(0.654780\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.47311 | −0.824369 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.06256 | 1.22491 | 0.612455 | − | 0.790506i | \(-0.290182\pi\) | ||||
0.612455 | + | 0.790506i | \(0.290182\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.26536 | 0.628298 | 0.314149 | − | 0.949374i | \(-0.398281\pi\) | ||||
0.314149 | + | 0.949374i | \(0.398281\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.163418 | −0.0421944 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.19086 | 1.74404 | 0.872019 | − | 0.489471i | \(-0.162810\pi\) | ||||
0.872019 | + | 0.489471i | \(0.162810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.47015 | 1.71377 | 0.856885 | − | 0.515507i | \(-0.172397\pi\) | ||||
0.856885 | + | 0.515507i | \(0.172397\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.79495 | −0.391691 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.178059 | 0.0371279 | 0.0185639 | − | 0.999828i | \(-0.494091\pi\) | ||||
0.0185639 | + | 0.999828i | \(0.494091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.94931 | −0.989863 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.97278 | −0.764562 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.5609 | 1.96111 | 0.980557 | − | 0.196232i | \(-0.0628707\pi\) | ||||
0.980557 | + | 0.196232i | \(0.0628707\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.27650 | −0.229266 | −0.114633 | − | 0.993408i | \(-0.536569\pi\) | ||||
−0.114633 | + | 0.993408i | \(0.536569\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.94891 | 0.513339 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.556714 | 0.0941018 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.08508 | 0.342784 | 0.171392 | − | 0.985203i | \(-0.445173\pi\) | ||||
0.171392 | + | 0.985203i | \(0.445173\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.64436 | 0.263309 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.23367 | 0.661188 | 0.330594 | − | 0.943773i | \(-0.392751\pi\) | ||||
0.330594 | + | 0.943773i | \(0.392751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.52011 | −1.29930 | −0.649652 | − | 0.760232i | \(-0.725085\pi\) | ||||
−0.649652 | + | 0.760232i | \(0.725085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.556779 | 0.0829997 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.96677 | −1.45380 | −0.726901 | − | 0.686742i | \(-0.759040\pi\) | ||||
−0.726901 | + | 0.686742i | \(0.759040\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.885174 | −0.126453 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.21965 | 0.730897 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.619984 | 0.0851614 | 0.0425807 | − | 0.999093i | \(-0.486442\pi\) | ||||
0.0425807 | + | 0.999093i | \(0.486442\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.914619 | −0.123327 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.42238 | 0.718212 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.8540 | −1.54326 | −0.771628 | − | 0.636074i | \(-0.780557\pi\) | ||||
−0.771628 | + | 0.636074i | \(0.780557\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.30300 | 0.807017 | 0.403508 | − | 0.914976i | \(-0.367791\pi\) | ||||
0.403508 | + | 0.914976i | \(0.367791\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.11554 | 0.770486 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.510008 | −0.0632587 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5388 | −1.53186 | −0.765928 | − | 0.642927i | \(-0.777720\pi\) | ||||
−0.765928 | + | 0.642927i | \(0.777720\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.129248 | 0.0155597 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.50401 | 1.12792 | 0.563959 | − | 0.825803i | \(-0.309277\pi\) | ||||
0.563959 | + | 0.825803i | \(0.309277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.14906 | 0.602652 | 0.301326 | − | 0.953521i | \(-0.402571\pi\) | ||||
0.301326 | + | 0.953521i | \(0.402571\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.59258 | −0.414835 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.0460 | −1.14485 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.3932 | 1.84438 | 0.922190 | − | 0.386737i | \(-0.126398\pi\) | ||||
0.922190 | + | 0.386737i | \(0.126398\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.53559 | 0.503954 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.79273 | −0.526071 | −0.263035 | − | 0.964786i | \(-0.584724\pi\) | ||||
−0.263035 | + | 0.964786i | \(0.584724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.61890 | −0.175595 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.66589 | 0.821870 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.64933 | −0.174829 | −0.0874143 | − | 0.996172i | \(-0.527860\pi\) | ||||
−0.0874143 | + | 0.996172i | \(0.527860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.60182 | −0.587231 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.926577 | −0.0960816 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.68178 | −0.172547 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.34400 | 0.339531 | 0.169766 | − | 0.985484i | \(-0.445699\pi\) | ||||
0.169766 | + | 0.985484i | \(0.445699\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.0472 | −1.00978 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.6806 | −1.26176 | −0.630882 | − | 0.775878i | \(-0.717307\pi\) | ||||
−0.630882 | + | 0.775878i | \(0.717307\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.47808 | 0.441238 | 0.220619 | − | 0.975360i | \(-0.429192\pi\) | ||||
0.220619 | + | 0.975360i | \(0.429192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.404104 | 0.0394365 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.0754 | −1.45740 | −0.728699 | − | 0.684834i | \(-0.759875\pi\) | ||||
−0.728699 | + | 0.684834i | \(0.759875\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.66599 | 0.351138 | 0.175569 | − | 0.984467i | \(-0.443823\pi\) | ||||
0.175569 | + | 0.984467i | \(0.443823\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.51350 | 0.143655 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.54316 | 0.615528 | 0.307764 | − | 0.951463i | \(-0.400419\pi\) | ||||
0.307764 | + | 0.951463i | \(0.400419\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0400870 | −0.00373814 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.60248 | −0.517949 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.7817 | −1.63004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50443 | 0.500403 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.07311 | 0.277093 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.23992 | 0.200345 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.0494 | 1.33542 | 0.667711 | − | 0.744420i | \(-0.267274\pi\) | ||||
0.667711 | + | 0.744420i | \(0.267274\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.18452 | −0.544516 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.57374 | −0.836462 | −0.418231 | − | 0.908341i | \(-0.637350\pi\) | ||||
−0.418231 | + | 0.908341i | \(0.637350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.4723 | −1.60175 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.894406 | 0.0769782 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.15272 | 0.183919 | 0.0919595 | − | 0.995763i | \(-0.470687\pi\) | ||||
0.0919595 | + | 0.995763i | \(0.470687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.62106 | −0.476772 | −0.238386 | − | 0.971171i | \(-0.576618\pi\) | ||||
−0.238386 | + | 0.971171i | \(0.576618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.23461 | −0.609264 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.20317 | 0.769608 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.37762 | −0.197450 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.642524 | −0.0529945 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.1382 | 1.24017 | 0.620086 | − | 0.784534i | \(-0.287098\pi\) | ||||
0.620086 | + | 0.784534i | \(0.287098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.7193 | 1.60474 | 0.802369 | − | 0.596828i | \(-0.203573\pi\) | ||||
0.802369 | + | 0.596828i | \(0.203573\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.7838 | −1.43773 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.287383 | 0.0230831 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7111 | 1.25389 | 0.626943 | − | 0.779065i | \(-0.284306\pi\) | ||||
0.626943 | + | 0.779065i | \(0.284306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.450030 | 0.0356897 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.440308 | −0.0347011 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8717 | 0.929864 | 0.464932 | − | 0.885346i | \(-0.346079\pi\) | ||||
0.464932 | + | 0.885346i | \(0.346079\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.663897 | −0.0516843 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.37936 | 0.416267 | 0.208134 | − | 0.978100i | \(-0.433261\pi\) | ||||
0.208134 | + | 0.978100i | \(0.433261\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.86814 | −0.605242 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.4745 | −1.41278 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.6393 | −1.41712 | −0.708560 | − | 0.705651i | \(-0.750655\pi\) | ||||
−0.708560 | + | 0.705651i | \(0.750655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.2388 | 0.925163 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.60448 | −0.646753 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.6264 | 1.69117 | 0.845587 | − | 0.533837i | \(-0.179250\pi\) | ||||
0.845587 | + | 0.533837i | \(0.179250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.1002 | 0.899398 | 0.449699 | − | 0.893180i | \(-0.351531\pi\) | ||||
0.449699 | + | 0.893180i | \(0.351531\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.57518 | 0.338207 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.469420 | −0.0345124 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.2133 | 2.13629 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.82397 | 0.714588 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.166765 | 0.0120667 | 0.00603336 | − | 0.999982i | \(-0.498080\pi\) | ||||
0.00603336 | + | 0.999982i | \(0.498080\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.5260 | −1.18956 | −0.594782 | − | 0.803887i | \(-0.702762\pi\) | ||||
−0.594782 | + | 0.803887i | \(0.702762\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.370201 | −0.0265107 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.82274 | 0.699841 | 0.349921 | − | 0.936779i | \(-0.386209\pi\) | ||||
0.349921 | + | 0.936779i | \(0.386209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5691 | −0.820113 | −0.410056 | − | 0.912060i | \(-0.634491\pi\) | ||||
−0.410056 | + | 0.912060i | \(0.634491\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.10156 | −0.641975 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26.1152 | −1.83293 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.953140 | −0.0665702 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.440359 | −0.0306071 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 30.3480 | 2.09921 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2316 | 1.32396 | 0.661978 | − | 0.749523i | \(-0.269717\pi\) | ||||
0.661978 | + | 0.749523i | \(0.269717\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.89871 | 0.472692 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.91816 | 0.130817 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.15655 | 0.214281 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.73757 | 0.252561 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.2899 | 1.09578 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.26463 | 0.151651 | 0.0758255 | − | 0.997121i | \(-0.475841\pi\) | ||||
0.0758255 | + | 0.997121i | \(0.475841\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2402 | 0.816013 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.6616 | −0.840378 | −0.420189 | − | 0.907437i | \(-0.638036\pi\) | ||||
−0.420189 | + | 0.907437i | \(0.638036\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.7524 | 1.83393 | 0.916967 | − | 0.398964i | \(-0.130630\pi\) | ||||
0.916967 | + | 0.398964i | \(0.130630\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.29211 | −0.479786 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.9164 | −0.715157 | −0.357579 | − | 0.933883i | \(-0.616398\pi\) | ||||
−0.357579 | + | 0.933883i | \(0.616398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.24385 | 0.146373 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.8994 | 0.772949 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.41476 | −0.414936 | −0.207468 | − | 0.978242i | \(-0.566522\pi\) | ||||
−0.207468 | + | 0.978242i | \(0.566522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.85126 | 0.634576 | 0.317288 | − | 0.948329i | \(-0.397228\pi\) | ||||
0.317288 | + | 0.948329i | \(0.397228\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2106 | 0.975761 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.199282 | 0.0127317 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.9226 | 1.07676 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.47892 | −0.220467 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.56947 | −0.351542 | −0.175771 | − | 0.984431i | \(-0.556242\pi\) | ||||
−0.175771 | + | 0.984431i | \(0.556242\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.723376 | 0.0454783 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.17512 | −0.0735887 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.0328 | 1.49913 | 0.749564 | − | 0.661932i | \(-0.230263\pi\) | ||||
0.749564 | + | 0.661932i | \(0.230263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.15601 | −0.320379 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.1183 | −1.61668 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.9598 | −0.922463 | −0.461232 | − | 0.887280i | \(-0.652592\pi\) | ||||
−0.461232 | + | 0.887280i | \(0.652592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.139579 | −0.00857428 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.19720 | −0.0732677 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4385 | 0.819357 | 0.409679 | − | 0.912230i | \(-0.365641\pi\) | ||||
0.409679 | + | 0.912230i | \(0.365641\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.72605 | −0.347833 | −0.173916 | − | 0.984760i | \(-0.555642\pi\) | ||||
−0.173916 | + | 0.984760i | \(0.555642\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.06621 | −0.246098 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.1069 | −1.21249 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0981 | 0.726905 | 0.363452 | − | 0.931613i | \(-0.381598\pi\) | ||||
0.363452 | + | 0.931613i | \(0.381598\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.15692 | 0.189000 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.21778 | −0.370921 | −0.185461 | − | 0.982652i | \(-0.559378\pi\) | ||||
−0.185461 | + | 0.982652i | \(0.559378\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9505 | −0.769826 | −0.384913 | − | 0.922953i | \(-0.625769\pi\) | ||||
−0.384913 | + | 0.922953i | \(0.625769\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.22076 | −0.0723116 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.4691 | −0.617971 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.7084 | 2.04167 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.42732 | 0.142292 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.3490 | 0.838279 | 0.419139 | − | 0.907922i | \(-0.362332\pi\) | ||||
0.419139 | + | 0.907922i | \(0.362332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.66873 | 0.155379 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.1397 | −0.936520 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.403368 | 0.0233274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.0687 | 1.21438 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.20450 | −0.528784 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.41902 | −0.0812526 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.7422 | 1.64040 | 0.820202 | − | 0.572075i | \(-0.193861\pi\) | ||||
0.820202 | + | 0.572075i | \(0.193861\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.25052 | 0.184916 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.9677 | 1.69931 | 0.849655 | − | 0.527339i | \(-0.176810\pi\) | ||||
0.849655 | + | 0.527339i | \(0.176810\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.6402 | −0.770990 | −0.385495 | − | 0.922710i | \(-0.625969\pi\) | ||||
−0.385495 | + | 0.922710i | \(0.625969\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.37681 | −0.0775746 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.9433 | 0.726967 | 0.363484 | − | 0.931601i | \(-0.381587\pi\) | ||||
0.363484 | + | 0.931601i | \(0.381587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.9044 | 2.40219 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.9429 | −0.610771 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 53.7168 | 2.98888 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.2120 | −0.621929 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.66104 | 0.147156 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.6460 | 1.35878 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.48346 | −0.466293 | −0.233147 | − | 0.972442i | \(-0.574902\pi\) | ||||
−0.233147 | + | 0.972442i | \(0.574902\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.15662 | −0.282581 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.82290 | 0.154231 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.4431 | −1.54939 | −0.774697 | − | 0.632332i | \(-0.782098\pi\) | ||||
−0.774697 | + | 0.632332i | \(0.782098\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.74950 | 0.257958 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.18586 | −0.280830 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4986 | 1.05283 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0290981 | −0.00156659 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.37057 | −0.341990 | −0.170995 | − | 0.985272i | \(-0.554698\pi\) | ||||
−0.170995 | + | 0.985272i | \(0.554698\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7281 | −0.681317 | −0.340659 | − | 0.940187i | \(-0.610650\pi\) | ||||
−0.340659 | + | 0.940187i | \(0.610650\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.99978 | −0.480373 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.48049 | 0.0787984 | 0.0393992 | − | 0.999224i | \(-0.487456\pi\) | ||||
0.0393992 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.13967 | −0.113562 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.9072 | −0.683124 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.5753 | 1.45537 | 0.727685 | − | 0.685911i | \(-0.240596\pi\) | ||||
0.727685 | + | 0.685911i | \(0.240596\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.8032 | 1.93701 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.99552 | 0.209710 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.15923 | −0.0606766 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.08957 | −0.317873 | −0.158936 | − | 0.987289i | \(-0.550807\pi\) | ||||
−0.158936 | + | 0.987289i | \(0.550807\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.4703 | −0.545063 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.53311 | −0.0795950 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.4949 | 1.16474 | 0.582371 | − | 0.812923i | \(-0.302125\pi\) | ||||
0.582371 | + | 0.812923i | \(0.302125\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.62590 | 0.0839611 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.9243 | 1.23216 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1157 | 0.725075 | 0.362538 | − | 0.931969i | \(-0.381910\pi\) | ||||
0.362538 | + | 0.931969i | \(0.381910\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.9240 | 0.559653 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.3617 | −1.24482 | −0.622412 | − | 0.782690i | \(-0.713847\pi\) | ||||
−0.622412 | + | 0.782690i | \(0.713847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.26169 | 0.115266 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.0711 | 1.07111 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.7319 | −0.848341 | −0.424170 | − | 0.905582i | \(-0.639434\pi\) | ||||
−0.424170 | + | 0.905582i | \(0.639434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.28040 | 0.0647525 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.94932 | −0.350547 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.69066 | −0.185697 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.7689 | −1.09255 | −0.546274 | − | 0.837607i | \(-0.683954\pi\) | ||||
−0.546274 | + | 0.837607i | \(0.683954\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.4086 | −0.671268 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.2269 | 1.01008 | 0.505041 | − | 0.863095i | \(-0.331477\pi\) | ||||
0.505041 | + | 0.863095i | \(0.331477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.89173 | −0.144047 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.02111 | −0.0507395 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.47075 | 0.419880 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5461 | 1.41151 | 0.705757 | − | 0.708454i | \(-0.250607\pi\) | ||||
0.705757 | + | 0.708454i | \(0.250607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.56260 | 0.0770773 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.3127 | 1.44238 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.07900 | 0.0529662 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.08018 | −0.199807 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.3207 | 1.77438 | 0.887192 | − | 0.461400i | \(-0.152653\pi\) | ||||
0.887192 | + | 0.461400i | \(0.152653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.8986 | −1.01853 | −0.509267 | − | 0.860609i | \(-0.670083\pi\) | ||||
−0.509267 | + | 0.860609i | \(0.670083\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.6489 | 1.19847 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −35.5898 | −1.72636 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.5862 | −0.754268 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.68034 | 0.322530 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.65795 | −0.272534 | −0.136267 | − | 0.990672i | \(-0.543510\pi\) | ||||
−0.136267 | + | 0.990672i | \(0.543510\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.797593 | −0.0383299 | −0.0191649 | − | 0.999816i | \(-0.506101\pi\) | ||||
−0.0191649 | + | 0.999816i | \(0.506101\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.72585 | −0.0827481 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.33013 | 0.0636286 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.2826 | 0.872581 | 0.436290 | − | 0.899806i | \(-0.356292\pi\) | ||||
0.436290 | + | 0.899806i | \(0.356292\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.18913 | 0.104244 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.4038 | 0.874391 | 0.437195 | − | 0.899367i | \(-0.355972\pi\) | ||||
0.437195 | + | 0.899367i | \(0.355972\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.371319 | 0.0176022 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.9884 | 0.519735 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.95767 | 0.139581 | 0.0697905 | − | 0.997562i | \(-0.477767\pi\) | ||||
0.0697905 | + | 0.997562i | \(0.477767\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.1996 | 0.809896 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.3138 | 0.672519 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.26116 | 0.0591240 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.1383 | 0.848472 | 0.424236 | − | 0.905552i | \(-0.360543\pi\) | ||||
0.424236 | + | 0.905552i | \(0.360543\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28.5677 | −1.33343 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.5572 | −0.771145 | −0.385573 | − | 0.922677i | \(-0.625996\pi\) | ||||
−0.385573 | + | 0.922677i | \(0.625996\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.01151 | −0.186430 | −0.0932152 | − | 0.995646i | \(-0.529714\pi\) | ||||
−0.0932152 | + | 0.995646i | \(0.529714\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.208603 | 0.00967376 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.61263 | 0.213447 | 0.106724 | − | 0.994289i | \(-0.465964\pi\) | ||||
0.106724 | + | 0.994289i | \(0.465964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.0061 | 1.43173 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.4043 | 0.525482 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.6135 | −1.59153 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.9721 | −1.69640 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.53329 | −0.0702044 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.2886 | 1.70376 | 0.851879 | − | 0.523739i | \(-0.175463\pi\) | ||||
0.851879 | + | 0.523739i | \(0.175463\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.72345 | 0.215371 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.319607 | −0.0145426 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.752845 | −0.0341849 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.0176 | −1.13366 | −0.566828 | − | 0.823836i | \(-0.691830\pi\) | ||||
−0.566828 | + | 0.823836i | \(0.691830\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.61736 | 0.389690 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.7021 | 1.06966 | 0.534830 | − | 0.844960i | \(-0.320376\pi\) | ||||
0.534830 | + | 0.844960i | \(0.320376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 75.9421 | 3.42026 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.26195 | 0.101667 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.5017 | −1.05419 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.1748 | −1.21651 | −0.608255 | − | 0.793742i | \(-0.708130\pi\) | ||||
−0.608255 | + | 0.793742i | \(0.708130\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.90473 | 0.174451 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0746 | −0.538381 | −0.269191 | − | 0.963087i | \(-0.586756\pi\) | ||||
−0.269191 | + | 0.963087i | \(0.586756\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.85482 | 0.127038 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.71128 | −0.253647 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.7176 | −1.93775 | −0.968873 | − | 0.247557i | \(-0.920372\pi\) | ||||
−0.968873 | + | 0.247557i | \(0.920372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7327 | −0.563261 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.6773 | −1.31028 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.00817 | −0.0444251 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.4906 | −1.78078 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.5298 | −0.593891 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.3638 | −1.54932 | −0.774659 | − | 0.632379i | \(-0.782078\pi\) | ||||
−0.774659 | + | 0.632379i | \(0.782078\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.8938 | −0.869897 | −0.434949 | − | 0.900455i | \(-0.643233\pi\) | ||||
−0.434949 | + | 0.900455i | \(0.643233\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.88378 | 0.387720 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.17913 | −0.399849 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9683 | −0.998622 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.3162 | 1.27221 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.59079 | 0.415423 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.39399 | 0.146735 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.4239 | 0.708743 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.59608 | −0.154894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.3119 | −0.658311 | −0.329156 | − | 0.944276i | \(-0.606764\pi\) | ||||
−0.329156 | + | 0.944276i | \(0.606764\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.78319 | 0.376923 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.825337 | −0.0353535 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.3037 | −1.80878 | −0.904388 | − | 0.426711i | \(-0.859672\pi\) | ||||
−0.904388 | + | 0.426711i | \(0.859672\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.5880 | −0.665280 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 78.8917 | 3.36090 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.5374 | −1.72383 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.340739 | −0.0144636 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.44351 | 0.315392 | 0.157696 | − | 0.987488i | \(-0.449593\pi\) | ||||
0.157696 | + | 0.987488i | \(0.449593\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.3011 | −0.816350 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.2052 | 0.895283 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.6551 | 1.29196 | 0.645978 | − | 0.763356i | \(-0.276450\pi\) | ||||
0.645978 | + | 0.763356i | \(0.276450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.47308 | −0.0619731 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.2157 | −0.471014 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.0445 | 1.88836 | 0.944182 | − | 0.329425i | \(-0.106855\pi\) | ||||
0.944182 | + | 0.329425i | \(0.106855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.5533 | 0.860127 | 0.430063 | − | 0.902799i | \(-0.358491\pi\) | ||||
0.430063 | + | 0.902799i | \(0.358491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.121051 | 0.00505696 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.881270 | −0.0367515 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.43980 | 0.101570 | 0.0507851 | − | 0.998710i | \(-0.483828\pi\) | ||||
0.0507851 | + | 0.998710i | \(0.483828\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.9957 | −0.498526 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.8516 | 0.491685 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.51873 | 0.104315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.26131 | 0.0521486 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.0624 | −1.15826 | −0.579129 | − | 0.815236i | \(-0.696607\pi\) | ||||
−0.579129 | + | 0.815236i | \(0.696607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.53565 | −0.392910 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.13007 | 0.293292 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.1600 | −0.827873 | −0.413937 | − | 0.910306i | \(-0.635847\pi\) | ||||
−0.413937 | + | 0.910306i | \(0.635847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00325 | 0.164117 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.39771 | −0.343696 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.5060 | −0.960427 | −0.480214 | − | 0.877152i | \(-0.659441\pi\) | ||||
−0.480214 | + | 0.877152i | \(0.659441\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.9839 | −0.855952 | −0.427976 | − | 0.903790i | \(-0.640773\pi\) | ||||
−0.427976 | + | 0.903790i | \(0.640773\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.0097 | 1.26281 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.23923 | −0.0503819 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.2511 | −1.30903 | −0.654516 | − | 0.756048i | \(-0.727128\pi\) | ||||
−0.654516 | + | 0.756048i | \(0.727128\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.9564 | −0.768150 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.5783 | −0.913421 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.2120 | −1.50298 | −0.751489 | − | 0.659746i | \(-0.770664\pi\) | ||||
−0.751489 | + | 0.659746i | \(0.770664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.691859 | −0.0278985 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.3479 | 1.54383 | 0.771915 | − | 0.635726i | \(-0.219299\pi\) | ||||
0.771915 | + | 0.635726i | \(0.219299\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.707390 | −0.0283866 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.07849 | 0.163401 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2423 | 0.969692 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22.0288 | 0.879745 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.9935 | 0.597829 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.9829 | −1.55188 | −0.775942 | − | 0.630804i | \(-0.782725\pi\) | ||||
−0.775942 | + | 0.630804i | \(0.782725\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.9597 | 0.554848 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.38813 | −0.134454 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.00524 | −0.0794504 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.5044 | −0.929822 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.319675 | −0.0126264 | −0.00631321 | − | 0.999980i | \(-0.502010\pi\) | ||||
−0.00631321 | + | 0.999980i | \(0.502010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.159017 | −0.00627101 | −0.00313550 | − | 0.999995i | \(-0.500998\pi\) | ||||
−0.00313550 | + | 0.999995i | \(0.500998\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.39234 | 0.0548234 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.6688 | −0.969829 | −0.484915 | − | 0.874562i | \(-0.661149\pi\) | ||||
−0.484915 | + | 0.874562i | \(0.661149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.1575 | −1.89035 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.29126 | 0.0898014 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.3461 | −1.10927 | −0.554635 | − | 0.832094i | \(-0.687142\pi\) | ||||
−0.554635 | + | 0.832094i | \(0.687142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.15537 | 0.0842172 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.7342 | −0.496808 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.5061 | −1.53894 | −0.769470 | − | 0.638683i | \(-0.779479\pi\) | ||||
−0.769470 | + | 0.638683i | \(0.779479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.7041 | −0.610818 | −0.305409 | − | 0.952221i | \(-0.598793\pi\) | ||||
−0.305409 | + | 0.952221i | \(0.598793\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.8244 | 0.459221 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.15874 | 0.161269 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.88047 | 0.0728120 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.64384 | 0.0635544 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.6064 | 0.988523 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.0243 | −0.887522 | −0.443761 | − | 0.896145i | \(-0.646356\pi\) | ||||
−0.443761 | + | 0.896145i | \(0.646356\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.6626 | 0.756812 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.63096 | 0.293282 | 0.146641 | − | 0.989190i | \(-0.453154\pi\) | ||||
0.146641 | + | 0.989190i | \(0.453154\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.26909 | −0.317339 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.19070 | −0.352188 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.644724 | −0.0246697 | −0.0123348 | − | 0.999924i | \(-0.503926\pi\) | ||||
−0.0123348 | + | 0.999924i | \(0.503926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.484648 | −0.0185175 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.1448 | 0.768571 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.40449 | 0.0535067 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.5024 | 1.12232 | 0.561162 | − | 0.827706i | \(-0.310354\pi\) | ||||
0.561162 | + | 0.827706i | \(0.310354\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.8448 | 0.943776 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.26549 | 0.0480027 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.4437 | 1.15314 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.92393 | −0.299710 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.4332 | −1.14944 | −0.574722 | − | 0.818348i | \(-0.694890\pi\) | ||||
−0.574722 | + | 0.818348i | \(0.694890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.5758 | 0.587453 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.62875 | 0.0613424 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.3568 | 1.17929 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.4754 | 0.393413 | 0.196707 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196707 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.5422 | −1.52045 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.227292 | −0.00851217 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.07194 | −0.0774862 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.65630 | −0.173893 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.815327 | −0.0304066 | −0.0152033 | − | 0.999884i | \(-0.504840\pi\) | ||||
−0.0152033 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.0735 | −0.412398 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.15077 | 0.265940 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −52.2694 | −1.94123 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.58478 | −0.207128 | −0.103564 | − | 0.994623i | \(-0.533025\pi\) | ||||
−0.103564 | + | 0.994623i | \(0.533025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.56578 | −0.0950290 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −61.2669 | −2.26604 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.7414 | 1.02465 | 0.512327 | − | 0.858791i | \(-0.328784\pi\) | ||||
0.512327 | + | 0.858791i | \(0.328784\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.144654 | 0.00533563 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.9396 | −1.87638 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.9980 | 0.404569 | 0.202285 | − | 0.979327i | \(-0.435163\pi\) | ||||
0.202285 | + | 0.979327i | \(0.435163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.2837 | 0.451251 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.5706 | −1.01147 | −0.505733 | − | 0.862690i | \(-0.668778\pi\) | ||||
−0.505733 | + | 0.862690i | \(0.668778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.40812 | −0.124864 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.8529 | 0.433677 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.2788 | 1.36214 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.39041 | −0.0872274 | −0.0436137 | − | 0.999048i | \(-0.513887\pi\) | ||||
−0.0436137 | + | 0.999048i | \(0.513887\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.04273 | −0.147325 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.43948 | −0.161569 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.8502 | 0.830505 | 0.415253 | − | 0.909706i | \(-0.363693\pi\) | ||||
0.415253 | + | 0.909706i | \(0.363693\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.525080 | 0.0190592 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.2537 | 1.27795 | 0.638974 | − | 0.769229i | \(-0.279359\pi\) | ||||
0.638974 | + | 0.769229i | \(0.279359\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.06532 | −0.328187 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.00372 | 0.144755 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.8535 | −0.969625 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0283 | 0.505875 | 0.252937 | − | 0.967483i | \(-0.418603\pi\) | ||||
0.252937 | + | 0.967483i | \(0.418603\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.4448 | 0.628259 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.05297 | 0.0738401 | 0.0369200 | − | 0.999318i | \(-0.488245\pi\) | ||||
0.0369200 | + | 0.999318i | \(0.488245\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.31780 | 0.226942 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.74261 | −0.134265 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.6262 | 1.13312 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.6107 | 1.38160 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −41.9563 | −1.49939 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.53710 | −0.126245 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.63128 | 0.272026 | 0.136013 | − | 0.990707i | \(-0.456571\pi\) | ||||
0.136013 | + | 0.990707i | \(0.456571\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.8589 | −0.386589 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.1800 | −0.575296 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.2786 | 0.507047 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.101317 | −0.00359333 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.8432 | 0.844570 | 0.422285 | − | 0.906463i | \(-0.361228\pi\) | ||||
0.422285 | + | 0.906463i | \(0.361228\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −71.6696 | −2.53549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.07897 | 0.144123 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.9184 | 0.738194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0991279 | 0.00349380 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.75462 | 0.343379 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.9428 | 0.701152 | 0.350576 | − | 0.936534i | \(-0.385986\pi\) | ||||
0.350576 | + | 0.936534i | \(0.385986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3626 | 0.855488 | 0.427744 | − | 0.903900i | \(-0.359308\pi\) | ||||
0.427744 | + | 0.903900i | \(0.359308\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.15639 | −0.145771 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.67272 | −0.0936212 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −63.6465 | −2.22671 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.8539 | 0.484095 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.6976 | −0.547850 | −0.273925 | − | 0.961751i | \(-0.588322\pi\) | ||||
−0.273925 | + | 0.961751i | \(0.588322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.38747 | 0.257511 | 0.128755 | − | 0.991676i | \(-0.458902\pi\) | ||||
0.128755 | + | 0.991676i | \(0.458902\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.5951 | −0.508135 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.5262 | −0.400806 | −0.200403 | − | 0.979714i | \(-0.564225\pi\) | ||||
−0.200403 | + | 0.979714i | \(0.564225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.7336 | −0.615914 | −0.307957 | − | 0.951400i | \(-0.599645\pi\) | ||||
−0.307957 | + | 0.951400i | \(0.599645\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.78169 | 0.304634 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.36516 | −0.220540 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.21107 | −0.0419109 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.07126 | 0.175288 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.6447 | 0.988924 | 0.494462 | − | 0.869199i | \(-0.335365\pi\) | ||||
0.494462 | + | 0.869199i | \(0.335365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.5332 | 2.84597 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.51332 | −0.155447 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.77138 | 0.0609374 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.6115 | −0.467695 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.40041 | −0.322621 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.371266 | 0.0127269 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.6536 | 1.42619 | 0.713097 | − | 0.701066i | \(-0.247292\pi\) | ||||
0.713097 | + | 0.701066i | \(0.247292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.15922 | 0.142242 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.05282 | −0.309238 | −0.154619 | − | 0.987974i | \(-0.549415\pi\) | ||||
−0.154619 | + | 0.987974i | \(0.549415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.47579 | −0.323310 | −0.161655 | − | 0.986847i | \(-0.551683\pi\) | ||||
−0.161655 | + | 0.986847i | \(0.551683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.59924 | −0.258981 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.6314 | 1.17887 | 0.589434 | − | 0.807817i | \(-0.299351\pi\) | ||||
0.589434 | + | 0.807817i | \(0.299351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.19633 | 0.142679 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.1939 | 0.855630 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66.5985 | 2.25920 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.4048 | −0.962461 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.27007 | −0.279899 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.53892 | −0.187250 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5441 | 0.524886 | 0.262443 | − | 0.964947i | \(-0.415472\pi\) | ||||
0.262443 | + | 0.964947i | \(0.415472\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.4156 | 0.351308 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.4905 | 1.76845 | 0.884224 | − | 0.467063i | \(-0.154688\pi\) | ||||
0.884224 | + | 0.467063i | \(0.154688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.8989 | 1.10713 | 0.553567 | − | 0.832804i | \(-0.313266\pi\) | ||||
0.553567 | + | 0.832804i | \(0.313266\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.93716 | 0.0651168 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.9458 | 1.37483 | 0.687413 | − | 0.726267i | \(-0.258746\pi\) | ||||
0.687413 | + | 0.726267i | \(0.258746\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.2145 | −1.24814 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.4261 | 0.617298 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −74.4533 | −2.49148 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.09395 | −0.170272 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.292794 | 0.00977611 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.4810 | −0.449617 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.45822 | 0.148525 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.2932 | 0.508925 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.72415 | −0.0905539 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3371 | 0.741692 | 0.370846 | − | 0.928694i | \(-0.379068\pi\) | ||||
0.370846 | + | 0.928694i | \(0.379068\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.3604 | 1.04016 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.9284 | −0.527732 | −0.263866 | − | 0.964559i | \(-0.584998\pi\) | ||||
−0.263866 | + | 0.964559i | \(0.584998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.4708 | −0.644389 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.03003 | −0.0340516 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.6741 | 0.781788 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.6296 | 1.34025 | 0.670124 | − | 0.742249i | \(-0.266241\pi\) | ||||
0.670124 | + | 0.742249i | \(0.266241\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.8632 | 0.687465 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.5300 | 0.708669 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.3197 | −0.339309 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.0748 | −0.363743 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.1089 | −1.25031 | −0.625155 | − | 0.780500i | \(-0.714964\pi\) | ||||
−0.625155 | + | 0.780500i | \(0.714964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.61238 | −0.216712 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.7527 | 0.712152 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.57689 | −0.215087 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.9882 | 0.685653 | 0.342827 | − | 0.939399i | \(-0.388616\pi\) | ||||
0.342827 | + | 0.939399i | \(0.388616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.90106 | −0.323109 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.271913 | 0.00886412 | 0.00443206 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443206 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.753843 | 0.0245485 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.21170 | −0.0719467 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.9489 | −0.615756 | −0.307878 | − | 0.951426i | \(-0.599619\pi\) | ||||
−0.307878 | + | 0.951426i | \(0.599619\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.6645 | 0.378645 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.39519 | 0.304660 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.67357 | −0.0866055 | −0.0433027 | − | 0.999062i | \(-0.513788\pi\) | ||||
−0.0433027 | + | 0.999062i | \(0.513788\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0375445 | −0.00121491 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 31.1432 | 1.00672 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.32327 | −0.171897 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3705 | −0.947437 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.2832 | 1.20143 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.72054 | 0.119769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.1196 | −0.647004 | −0.323502 | − | 0.946227i | \(-0.604860\pi\) | ||||
−0.323502 | + | 0.946227i | \(0.604860\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 38.9916 | 1.25259 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.9577 | −0.512106 | −0.256053 | − | 0.966663i | \(-0.582422\pi\) | ||||
−0.256053 | + | 0.966663i | \(0.582422\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.8998 | 0.445609 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.13848 | −0.260640 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.1759 | 1.34933 | 0.674663 | − | 0.738126i | \(-0.264289\pi\) | ||||
0.674663 | + | 0.738126i | \(0.264289\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.70051 | −0.214149 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.06639 | −0.289467 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.8772 | 1.01673 | 0.508363 | − | 0.861143i | \(-0.330251\pi\) | ||||
0.508363 | + | 0.861143i | \(0.330251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.21143 | −0.0704619 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.8899 | 0.569441 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.51708 | −0.0482404 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.4135 | −0.902584 | −0.451292 | − | 0.892376i | \(-0.649037\pi\) | ||||
−0.451292 | + | 0.892376i | \(0.649037\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.15792 | −0.195416 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.60459 | 0.0825712 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.9058 | −1.23216 | −0.616079 | − | 0.787684i | \(-0.711280\pi\) | ||||
−0.616079 | + | 0.787684i | \(0.711280\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.28355 | −0.262080 |
(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 | 9904.2.a.n.1.18 | 30 | ||
4.3 | odd | 2 | 619.2.a.b.1.8 | ✓ | 30 | ||
12.11 | even | 2 | 5571.2.a.g.1.23 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.8 | ✓ | 30 | 4.3 | odd | 2 | ||
5571.2.a.g.1.23 | 30 | 12.11 | even | 2 | |||
9904.2.a.n.1.18 | 30 | 1.1 | even | 1 | trivial |