Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.35771\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35771 | −0.960049 | −0.480024 | − | 0.877255i | \(-0.659372\pi\) | ||||
−0.480024 | + | 0.877255i | \(0.659372\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.156613 | −0.0783063 | ||||||||
\(5\) | −4.06757 | −1.81907 | −0.909536 | − | 0.415625i | \(-0.863563\pi\) | ||||
−0.909536 | + | 0.415625i | \(0.863563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.92806 | 1.03523 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.52260 | 1.74640 | ||||||||
\(11\) | −4.14107 | −1.24858 | −0.624290 | − | 0.781193i | \(-0.714612\pi\) | ||||
−0.624290 | + | 0.781193i | \(0.714612\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.33246 | 0.924258 | 0.462129 | − | 0.886813i | \(-0.347086\pi\) | ||||
0.462129 | + | 0.886813i | \(0.347086\pi\) | |||||||
\(14\) | −1.35771 | −0.362864 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.66225 | −0.915562 | ||||||||
\(17\) | 1.50369 | 0.364698 | 0.182349 | − | 0.983234i | \(-0.441630\pi\) | ||||
0.182349 | + | 0.983234i | \(0.441630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.47517 | 1.25609 | 0.628045 | − | 0.778177i | \(-0.283855\pi\) | ||||
0.628045 | + | 0.778177i | \(0.283855\pi\) | |||||||
\(20\) | 0.637032 | 0.142445 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.62239 | 1.19870 | ||||||||
\(23\) | 6.86481 | 1.43141 | 0.715706 | − | 0.698401i | \(-0.246105\pi\) | ||||
0.715706 | + | 0.698401i | \(0.246105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.5451 | 2.30902 | ||||||||
\(26\) | −4.52453 | −0.887333 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.156613 | −0.0295970 | ||||||||
\(29\) | 9.24608 | 1.71695 | 0.858477 | − | 0.512852i | \(-0.171411\pi\) | ||||
0.858477 | + | 0.512852i | \(0.171411\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.77701 | −1.39679 | −0.698396 | − | 0.715711i | \(-0.746103\pi\) | ||||
−0.698396 | + | 0.715711i | \(0.746103\pi\) | |||||||
\(32\) | −0.883841 | −0.156243 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.04158 | −0.350128 | ||||||||
\(35\) | −4.06757 | −0.687545 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24505 | 1.35548 | 0.677739 | − | 0.735303i | \(-0.262960\pi\) | ||||
0.677739 | + | 0.735303i | \(0.262960\pi\) | |||||||
\(38\) | −7.43372 | −1.20591 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.9101 | −1.88315 | ||||||||
\(41\) | 4.27213 | 0.667194 | 0.333597 | − | 0.942716i | \(-0.391737\pi\) | ||||
0.333597 | + | 0.942716i | \(0.391737\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.47938 | −0.683099 | −0.341550 | − | 0.939864i | \(-0.610952\pi\) | ||||
−0.341550 | + | 0.939864i | \(0.610952\pi\) | |||||||
\(44\) | 0.648543 | 0.0977716 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.32046 | −1.37423 | ||||||||
\(47\) | 8.84174 | 1.28970 | 0.644850 | − | 0.764309i | \(-0.276920\pi\) | ||||
0.644850 | + | 0.764309i | \(0.276920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −15.6750 | −2.21677 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.521905 | −0.0723752 | ||||||||
\(53\) | −4.29491 | −0.589952 | −0.294976 | − | 0.955505i | \(-0.595312\pi\) | ||||
−0.294976 | + | 0.955505i | \(0.595312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.8441 | 2.27126 | ||||||||
\(56\) | 2.92806 | 0.391279 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.5535 | −1.64836 | ||||||||
\(59\) | −3.63171 | −0.472808 | −0.236404 | − | 0.971655i | \(-0.575969\pi\) | ||||
−0.236404 | + | 0.971655i | \(0.575969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.59520 | −0.460318 | −0.230159 | − | 0.973153i | \(-0.573925\pi\) | ||||
−0.230159 | + | 0.973153i | \(0.573925\pi\) | |||||||
\(62\) | 10.5590 | 1.34099 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.52450 | 1.06556 | ||||||||
\(65\) | −13.5550 | −1.68129 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.939878 | −0.114824 | −0.0574122 | − | 0.998351i | \(-0.518285\pi\) | ||||
−0.0574122 | + | 0.998351i | \(0.518285\pi\) | |||||||
\(68\) | −0.235496 | −0.0285581 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.52260 | 0.660076 | ||||||||
\(71\) | −4.09929 | −0.486496 | −0.243248 | − | 0.969964i | \(-0.578213\pi\) | ||||
−0.243248 | + | 0.969964i | \(0.578213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.53569 | 0.764945 | 0.382472 | − | 0.923967i | \(-0.375073\pi\) | ||||
0.382472 | + | 0.923967i | \(0.375073\pi\) | |||||||
\(74\) | −11.1944 | −1.30132 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.857480 | −0.0983597 | ||||||||
\(77\) | −4.14107 | −0.471919 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.66941 | −0.862876 | −0.431438 | − | 0.902143i | \(-0.641994\pi\) | ||||
−0.431438 | + | 0.902143i | \(0.641994\pi\) | |||||||
\(80\) | 14.8964 | 1.66547 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.80033 | −0.640539 | ||||||||
\(83\) | 0.904225 | 0.0992515 | 0.0496258 | − | 0.998768i | \(-0.484197\pi\) | ||||
0.0496258 | + | 0.998768i | \(0.484197\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.11635 | −0.663412 | ||||||||
\(86\) | 6.08172 | 0.655808 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.1253 | −1.29256 | ||||||||
\(89\) | 0.889515 | 0.0942884 | 0.0471442 | − | 0.998888i | \(-0.484988\pi\) | ||||
0.0471442 | + | 0.998888i | \(0.484988\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.33246 | 0.349337 | ||||||||
\(92\) | −1.07512 | −0.112089 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.0046 | −1.23818 | ||||||||
\(95\) | −22.2706 | −2.28492 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8632 | −1.10299 | −0.551497 | − | 0.834177i | \(-0.685943\pi\) | ||||
−0.551497 | + | 0.834177i | \(0.685943\pi\) | |||||||
\(98\) | −1.35771 | −0.137150 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.80811 | −0.180811 | ||||||||
\(101\) | −7.33839 | −0.730197 | −0.365098 | − | 0.930969i | \(-0.618965\pi\) | ||||
−0.365098 | + | 0.930969i | \(0.618965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.53321 | 0.446670 | 0.223335 | − | 0.974742i | \(-0.428306\pi\) | ||||
0.223335 | + | 0.974742i | \(0.428306\pi\) | |||||||
\(104\) | 9.75766 | 0.956817 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.83126 | 0.566382 | ||||||||
\(107\) | 3.67395 | 0.355175 | 0.177587 | − | 0.984105i | \(-0.443171\pi\) | ||||
0.177587 | + | 0.984105i | \(0.443171\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0170 | 1.34259 | 0.671293 | − | 0.741192i | \(-0.265739\pi\) | ||||
0.671293 | + | 0.741192i | \(0.265739\pi\) | |||||||
\(110\) | −22.8695 | −2.18052 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.66225 | −0.346050 | ||||||||
\(113\) | −10.5328 | −0.990845 | −0.495423 | − | 0.868652i | \(-0.664987\pi\) | ||||
−0.495423 | + | 0.868652i | \(0.664987\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.9231 | −2.60384 | ||||||||
\(116\) | −1.44805 | −0.134448 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.93082 | 0.453919 | ||||||||
\(119\) | 1.50369 | 0.137843 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.14846 | 0.558951 | ||||||||
\(122\) | 4.88126 | 0.441928 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.21798 | 0.109378 | ||||||||
\(125\) | −26.6227 | −2.38121 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −9.80615 | −0.866749 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 18.4038 | 1.61412 | ||||||||
\(131\) | 13.5622 | 1.18493 | 0.592466 | − | 0.805595i | \(-0.298154\pi\) | ||||
0.592466 | + | 0.805595i | \(0.298154\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.47517 | 0.474758 | ||||||||
\(134\) | 1.27609 | 0.110237 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.40289 | 0.377545 | ||||||||
\(137\) | 21.5286 | 1.83931 | 0.919656 | − | 0.392724i | \(-0.128467\pi\) | ||||
0.919656 | + | 0.392724i | \(0.128467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.20276 | 0.526111 | 0.263056 | − | 0.964781i | \(-0.415270\pi\) | ||||
0.263056 | + | 0.964781i | \(0.415270\pi\) | |||||||
\(140\) | 0.637032 | 0.0538390 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.56566 | 0.467060 | ||||||||
\(143\) | −13.8000 | −1.15401 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −37.6091 | −3.12326 | ||||||||
\(146\) | −8.87360 | −0.734384 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.29128 | −0.106142 | ||||||||
\(149\) | −20.7051 | −1.69622 | −0.848112 | − | 0.529817i | \(-0.822261\pi\) | ||||
−0.848112 | + | 0.529817i | \(0.822261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.24264 | 0.345261 | 0.172631 | − | 0.984987i | \(-0.444773\pi\) | ||||
0.172631 | + | 0.984987i | \(0.444773\pi\) | |||||||
\(152\) | 16.0316 | 1.30034 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.62239 | 0.453065 | ||||||||
\(155\) | 31.6335 | 2.54087 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.13470 | −0.569411 | −0.284705 | − | 0.958615i | \(-0.591896\pi\) | ||||
−0.284705 | + | 0.958615i | \(0.591896\pi\) | |||||||
\(158\) | 10.4129 | 0.828403 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.59509 | 0.284216 | ||||||||
\(161\) | 6.86481 | 0.541023 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.3942 | 1.91070 | 0.955349 | − | 0.295479i | \(-0.0954793\pi\) | ||||
0.955349 | + | 0.295479i | \(0.0954793\pi\) | |||||||
\(164\) | −0.669069 | −0.0522455 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.22768 | −0.0952863 | ||||||||
\(167\) | 15.1000 | 1.16847 | 0.584237 | − | 0.811583i | \(-0.301394\pi\) | ||||
0.584237 | + | 0.811583i | \(0.301394\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.89470 | −0.145746 | ||||||||
\(170\) | 8.30426 | 0.636908 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.701527 | 0.0534909 | ||||||||
\(173\) | 3.35769 | 0.255281 | 0.127640 | − | 0.991821i | \(-0.459260\pi\) | ||||
0.127640 | + | 0.991821i | \(0.459260\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.5451 | 0.872729 | ||||||||
\(176\) | 15.1656 | 1.14315 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.20771 | −0.0905215 | ||||||||
\(179\) | 2.72845 | 0.203934 | 0.101967 | − | 0.994788i | \(-0.467486\pi\) | ||||
0.101967 | + | 0.994788i | \(0.467486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.5927 | −1.15899 | −0.579497 | − | 0.814974i | \(-0.696751\pi\) | ||||
−0.579497 | + | 0.814974i | \(0.696751\pi\) | |||||||
\(182\) | −4.52453 | −0.335380 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 20.1006 | 1.48184 | ||||||||
\(185\) | −33.5373 | −2.46571 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.22688 | −0.455354 | ||||||||
\(188\) | −1.38473 | −0.100992 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 30.2372 | 2.19363 | ||||||||
\(191\) | 6.09888 | 0.441299 | 0.220650 | − | 0.975353i | \(-0.429182\pi\) | ||||
0.220650 | + | 0.975353i | \(0.429182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7723 | −0.847390 | −0.423695 | − | 0.905805i | \(-0.639267\pi\) | ||||
−0.423695 | + | 0.905805i | \(0.639267\pi\) | |||||||
\(194\) | 14.7492 | 1.05893 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.156613 | −0.0111866 | ||||||||
\(197\) | −9.06253 | −0.645679 | −0.322839 | − | 0.946454i | \(-0.604637\pi\) | ||||
−0.322839 | + | 0.946454i | \(0.604637\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7682 | −1.04689 | −0.523446 | − | 0.852059i | \(-0.675354\pi\) | ||||
−0.523446 | + | 0.852059i | \(0.675354\pi\) | |||||||
\(200\) | 33.8048 | 2.39036 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.96343 | 0.701024 | ||||||||
\(203\) | 9.24608 | 0.648948 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.3772 | −1.21367 | ||||||||
\(206\) | −6.15480 | −0.428825 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.2043 | −0.846216 | ||||||||
\(209\) | −22.6731 | −1.56833 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.40152 | −0.578385 | −0.289192 | − | 0.957271i | \(-0.593387\pi\) | ||||
−0.289192 | + | 0.957271i | \(0.593387\pi\) | |||||||
\(212\) | 0.672637 | 0.0461969 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.98818 | −0.340985 | ||||||||
\(215\) | 18.2202 | 1.24261 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.77701 | −0.527938 | ||||||||
\(218\) | −19.0311 | −1.28895 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.63799 | −0.177854 | ||||||||
\(221\) | 5.01098 | 0.337075 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.1977 | 1.35254 | 0.676268 | − | 0.736656i | \(-0.263596\pi\) | ||||
0.676268 | + | 0.736656i | \(0.263596\pi\) | |||||||
\(224\) | −0.883841 | −0.0590541 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.3006 | 0.951260 | ||||||||
\(227\) | 6.19838 | 0.411401 | 0.205700 | − | 0.978615i | \(-0.434053\pi\) | ||||
0.205700 | + | 0.978615i | \(0.434053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.1653 | −1.26648 | −0.633240 | − | 0.773955i | \(-0.718275\pi\) | ||||
−0.633240 | + | 0.773955i | \(0.718275\pi\) | |||||||
\(230\) | 37.9116 | 2.49982 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 27.0731 | 1.77744 | ||||||||
\(233\) | 28.1199 | 1.84220 | 0.921098 | − | 0.389331i | \(-0.127294\pi\) | ||||
0.921098 | + | 0.389331i | \(0.127294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.9644 | −2.34606 | ||||||||
\(236\) | 0.568771 | 0.0370238 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.04158 | −0.132336 | ||||||||
\(239\) | 1.16086 | 0.0750897 | 0.0375448 | − | 0.999295i | \(-0.488046\pi\) | ||||
0.0375448 | + | 0.999295i | \(0.488046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.36538 | −0.216783 | −0.108391 | − | 0.994108i | \(-0.534570\pi\) | ||||
−0.108391 | + | 0.994108i | \(0.534570\pi\) | |||||||
\(242\) | −8.34785 | −0.536620 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.563054 | 0.0360458 | ||||||||
\(245\) | −4.06757 | −0.259867 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.2458 | 1.16095 | ||||||||
\(248\) | −22.7716 | −1.44600 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 36.1460 | 2.28607 | ||||||||
\(251\) | −27.6043 | −1.74237 | −0.871185 | − | 0.490955i | \(-0.836648\pi\) | ||||
−0.871185 | + | 0.490955i | \(0.836648\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.4277 | −1.78723 | ||||||||
\(254\) | −1.35771 | −0.0851906 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.73505 | −0.233441 | ||||||||
\(257\) | 26.7692 | 1.66981 | 0.834907 | − | 0.550391i | \(-0.185521\pi\) | ||||
0.834907 | + | 0.550391i | \(0.185521\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.24505 | 0.512322 | ||||||||
\(260\) | 2.12288 | 0.131656 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.4136 | −1.13759 | ||||||||
\(263\) | −8.17676 | −0.504201 | −0.252100 | − | 0.967701i | \(-0.581121\pi\) | ||||
−0.252100 | + | 0.967701i | \(0.581121\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.4698 | 1.07316 | ||||||||
\(266\) | −7.43372 | −0.455790 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.147197 | 0.00899147 | ||||||||
\(269\) | −10.2343 | −0.623994 | −0.311997 | − | 0.950083i | \(-0.600998\pi\) | ||||
−0.311997 | + | 0.950083i | \(0.600998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6853 | 0.952814 | 0.476407 | − | 0.879225i | \(-0.341939\pi\) | ||||
0.476407 | + | 0.879225i | \(0.341939\pi\) | |||||||
\(272\) | −5.50688 | −0.333904 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −29.2297 | −1.76583 | ||||||||
\(275\) | −47.8091 | −2.88300 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1536 | 0.910489 | 0.455244 | − | 0.890366i | \(-0.349552\pi\) | ||||
0.455244 | + | 0.890366i | \(0.349552\pi\) | |||||||
\(278\) | −8.42157 | −0.505092 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.9101 | −0.711764 | ||||||||
\(281\) | −19.6547 | −1.17250 | −0.586250 | − | 0.810130i | \(-0.699396\pi\) | ||||
−0.586250 | + | 0.810130i | \(0.699396\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.3642 | −1.74552 | −0.872761 | − | 0.488148i | \(-0.837672\pi\) | ||||
−0.872761 | + | 0.488148i | \(0.837672\pi\) | |||||||
\(284\) | 0.642000 | 0.0380957 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.7364 | 1.10791 | ||||||||
\(287\) | 4.27213 | 0.252176 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7389 | −0.866995 | ||||||||
\(290\) | 51.0624 | 2.99849 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.02357 | −0.0599000 | ||||||||
\(293\) | −4.40237 | −0.257189 | −0.128594 | − | 0.991697i | \(-0.541047\pi\) | ||||
−0.128594 | + | 0.991697i | \(0.541047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.7722 | 0.860072 | ||||||||
\(296\) | 24.1420 | 1.40323 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 28.1115 | 1.62846 | ||||||||
\(299\) | 22.8767 | 1.32300 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.47938 | −0.258187 | ||||||||
\(302\) | −5.76030 | −0.331468 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.0514 | −1.15003 | ||||||||
\(305\) | 14.6237 | 0.837352 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.2964 | 1.90032 | 0.950162 | − | 0.311756i | \(-0.100917\pi\) | ||||
0.950162 | + | 0.311756i | \(0.100917\pi\) | |||||||
\(308\) | 0.648543 | 0.0369542 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −42.9493 | −2.43936 | ||||||||
\(311\) | −30.8539 | −1.74956 | −0.874782 | − | 0.484517i | \(-0.838995\pi\) | ||||
−0.874782 | + | 0.484517i | \(0.838995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.70430 | −0.548519 | −0.274260 | − | 0.961656i | \(-0.588433\pi\) | ||||
−0.274260 | + | 0.961656i | \(0.588433\pi\) | |||||||
\(314\) | 9.68688 | 0.546662 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.20113 | 0.0675686 | ||||||||
\(317\) | 12.8962 | 0.724322 | 0.362161 | − | 0.932116i | \(-0.382039\pi\) | ||||
0.362161 | + | 0.932116i | \(0.382039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −38.2887 | −2.14375 | ||||||||
\(320\) | −34.6740 | −1.93833 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.32046 | −0.519409 | ||||||||
\(323\) | 8.23295 | 0.458094 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.4736 | 2.13413 | ||||||||
\(326\) | −33.1203 | −1.83436 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.5091 | 0.690697 | ||||||||
\(329\) | 8.84174 | 0.487461 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.3548 | −1.83335 | −0.916674 | − | 0.399636i | \(-0.869137\pi\) | ||||
−0.916674 | + | 0.399636i | \(0.869137\pi\) | |||||||
\(332\) | −0.141613 | −0.00777202 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.5015 | −1.12179 | ||||||||
\(335\) | 3.82302 | 0.208874 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.6811 | 1.72578 | 0.862891 | − | 0.505390i | \(-0.168651\pi\) | ||||
0.862891 | + | 0.505390i | \(0.168651\pi\) | |||||||
\(338\) | 2.57246 | 0.139924 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.957898 | 0.0519493 | ||||||||
\(341\) | 32.2052 | 1.74401 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −13.1159 | −0.707162 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.55879 | −0.245082 | ||||||||
\(347\) | 32.2561 | 1.73160 | 0.865800 | − | 0.500390i | \(-0.166810\pi\) | ||||
0.865800 | + | 0.500390i | \(0.166810\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.2214 | 1.13596 | 0.567978 | − | 0.823044i | \(-0.307726\pi\) | ||||
0.567978 | + | 0.823044i | \(0.307726\pi\) | |||||||
\(350\) | −15.6750 | −0.837862 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.66005 | 0.195081 | ||||||||
\(353\) | −21.6154 | −1.15047 | −0.575235 | − | 0.817988i | \(-0.695089\pi\) | ||||
−0.575235 | + | 0.817988i | \(0.695089\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6741 | 0.884971 | ||||||||
\(356\) | −0.139309 | −0.00738337 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.70445 | −0.195786 | ||||||||
\(359\) | 9.14005 | 0.482393 | 0.241197 | − | 0.970476i | \(-0.422460\pi\) | ||||
0.241197 | + | 0.970476i | \(0.422460\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.9775 | 0.577763 | ||||||||
\(362\) | 21.1704 | 1.11269 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.521905 | −0.0273553 | ||||||||
\(365\) | −26.5844 | −1.39149 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4322 | 0.909954 | 0.454977 | − | 0.890503i | \(-0.349647\pi\) | ||||
0.454977 | + | 0.890503i | \(0.349647\pi\) | |||||||
\(368\) | −25.1406 | −1.31055 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 45.5341 | 2.36720 | ||||||||
\(371\) | −4.29491 | −0.222981 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.2475 | 1.20371 | 0.601855 | − | 0.798606i | \(-0.294429\pi\) | ||||
0.601855 | + | 0.798606i | \(0.294429\pi\) | |||||||
\(374\) | 8.45432 | 0.437162 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 25.8892 | 1.33513 | ||||||||
\(377\) | 30.8122 | 1.58691 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.8749 | −1.02090 | −0.510452 | − | 0.859906i | \(-0.670522\pi\) | ||||
−0.510452 | + | 0.859906i | \(0.670522\pi\) | |||||||
\(380\) | 3.48786 | 0.178923 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.28053 | −0.423669 | ||||||||
\(383\) | −29.4149 | −1.50303 | −0.751514 | − | 0.659717i | \(-0.770676\pi\) | ||||
−0.751514 | + | 0.659717i | \(0.770676\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.8441 | 0.858454 | ||||||||
\(386\) | 15.9834 | 0.813536 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.70132 | 0.0863713 | ||||||||
\(389\) | 7.56699 | 0.383662 | 0.191831 | − | 0.981428i | \(-0.438557\pi\) | ||||
0.191831 | + | 0.981428i | \(0.438557\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3225 | 0.522033 | ||||||||
\(392\) | 2.92806 | 0.147890 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.3043 | 0.619883 | ||||||||
\(395\) | 31.1958 | 1.56963 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.8178 | 0.643305 | 0.321653 | − | 0.946858i | \(-0.395762\pi\) | ||||
0.321653 | + | 0.946858i | \(0.395762\pi\) | |||||||
\(398\) | 20.0510 | 1.00507 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −42.2811 | −2.11405 | ||||||||
\(401\) | −33.4344 | −1.66963 | −0.834816 | − | 0.550528i | \(-0.814426\pi\) | ||||
−0.834816 | + | 0.550528i | \(0.814426\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.9166 | −1.29100 | ||||||||
\(404\) | 1.14928 | 0.0571790 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.5535 | −0.623021 | ||||||||
\(407\) | −34.1433 | −1.69242 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.1785 | −0.849422 | −0.424711 | − | 0.905329i | \(-0.639624\pi\) | ||||
−0.424711 | + | 0.905329i | \(0.639624\pi\) | |||||||
\(410\) | 23.5932 | 1.16519 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.709957 | −0.0349771 | ||||||||
\(413\) | −3.63171 | −0.178705 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.67800 | −0.180546 | ||||||||
\(416\) | −2.94537 | −0.144408 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30.7835 | 1.50567 | ||||||||
\(419\) | 29.5133 | 1.44182 | 0.720910 | − | 0.693029i | \(-0.243724\pi\) | ||||
0.720910 | + | 0.693029i | \(0.243724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.9064 | −1.01892 | −0.509458 | − | 0.860495i | \(-0.670154\pi\) | ||||
−0.509458 | + | 0.860495i | \(0.670154\pi\) | |||||||
\(422\) | 11.4069 | 0.555278 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.5758 | −0.610734 | ||||||||
\(425\) | 17.3603 | 0.842096 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.59520 | −0.173984 | ||||||||
\(428\) | −0.575387 | −0.0278124 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.7378 | −1.19296 | ||||||||
\(431\) | 21.1316 | 1.01787 | 0.508937 | − | 0.860804i | \(-0.330039\pi\) | ||||
0.508937 | + | 0.860804i | \(0.330039\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.15711 | 0.199778 | 0.0998890 | − | 0.994999i | \(-0.468151\pi\) | ||||
0.0998890 | + | 0.994999i | \(0.468151\pi\) | |||||||
\(434\) | 10.5590 | 0.506846 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.19524 | −0.105133 | ||||||||
\(437\) | 37.5860 | 1.79798 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.72225 | −0.320835 | −0.160418 | − | 0.987049i | \(-0.551284\pi\) | ||||
−0.160418 | + | 0.987049i | \(0.551284\pi\) | |||||||
\(440\) | 49.3205 | 2.35126 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.80348 | −0.323609 | ||||||||
\(443\) | 22.5903 | 1.07330 | 0.536649 | − | 0.843805i | \(-0.319690\pi\) | ||||
0.536649 | + | 0.843805i | \(0.319690\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.61816 | −0.171517 | ||||||||
\(446\) | −27.4227 | −1.29850 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.52450 | 0.402745 | ||||||||
\(449\) | 40.0006 | 1.88775 | 0.943873 | − | 0.330308i | \(-0.107153\pi\) | ||||
0.943873 | + | 0.330308i | \(0.107153\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.6912 | −0.833045 | ||||||||
\(452\) | 1.64957 | 0.0775894 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.41563 | −0.394965 | ||||||||
\(455\) | −13.5550 | −0.635469 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.14695 | 0.240764 | 0.120382 | − | 0.992728i | \(-0.461588\pi\) | ||||
0.120382 | + | 0.992728i | \(0.461588\pi\) | |||||||
\(458\) | 26.0210 | 1.21588 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.37311 | 0.203897 | ||||||||
\(461\) | 1.65601 | 0.0771279 | 0.0385639 | − | 0.999256i | \(-0.487722\pi\) | ||||
0.0385639 | + | 0.999256i | \(0.487722\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.8032 | 1.38507 | 0.692537 | − | 0.721383i | \(-0.256493\pi\) | ||||
0.692537 | + | 0.721383i | \(0.256493\pi\) | |||||||
\(464\) | −33.8614 | −1.57198 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −38.1788 | −1.76860 | ||||||||
\(467\) | 12.4102 | 0.574277 | 0.287139 | − | 0.957889i | \(-0.407296\pi\) | ||||
0.287139 | + | 0.957889i | \(0.407296\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.939878 | −0.0433995 | ||||||||
\(470\) | 48.8294 | 2.25233 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.6339 | −0.489464 | ||||||||
\(473\) | 18.5494 | 0.852904 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 63.2115 | 2.90034 | ||||||||
\(476\) | −0.235496 | −0.0107940 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.57611 | −0.0720898 | ||||||||
\(479\) | 23.2909 | 1.06419 | 0.532095 | − | 0.846685i | \(-0.321405\pi\) | ||||
0.532095 | + | 0.846685i | \(0.321405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.4763 | 1.25281 | ||||||||
\(482\) | 4.56922 | 0.208122 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.962926 | −0.0437694 | ||||||||
\(485\) | 44.1869 | 2.00642 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8607 | −0.537460 | −0.268730 | − | 0.963216i | \(-0.586604\pi\) | ||||
−0.268730 | + | 0.963216i | \(0.586604\pi\) | |||||||
\(488\) | −10.5270 | −0.476534 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.52260 | 0.249485 | ||||||||
\(491\) | 34.9281 | 1.57628 | 0.788142 | − | 0.615493i | \(-0.211043\pi\) | ||||
0.788142 | + | 0.615493i | \(0.211043\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.9032 | 0.626170 | ||||||||
\(494\) | −24.7726 | −1.11457 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.4813 | 1.27885 | ||||||||
\(497\) | −4.09929 | −0.183878 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.9524 | 0.624597 | 0.312299 | − | 0.949984i | \(-0.398901\pi\) | ||||
0.312299 | + | 0.949984i | \(0.398901\pi\) | |||||||
\(500\) | 4.16945 | 0.186463 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 37.4788 | 1.67276 | ||||||||
\(503\) | 33.5301 | 1.49504 | 0.747518 | − | 0.664242i | \(-0.231246\pi\) | ||||
0.747518 | + | 0.664242i | \(0.231246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.8494 | 1.32828 | ||||||||
\(506\) | 38.5967 | 1.71583 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.156613 | −0.00694856 | ||||||||
\(509\) | −8.96936 | −0.397560 | −0.198780 | − | 0.980044i | \(-0.563698\pi\) | ||||
−0.198780 | + | 0.980044i | \(0.563698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.53569 | 0.289122 | ||||||||
\(512\) | 24.6834 | 1.09086 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −36.3449 | −1.60310 | ||||||||
\(515\) | −18.4391 | −0.812525 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.6143 | −1.61029 | ||||||||
\(518\) | −11.1944 | −0.491855 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −39.6899 | −1.74052 | ||||||||
\(521\) | −3.45790 | −0.151493 | −0.0757467 | − | 0.997127i | \(-0.524134\pi\) | ||||
−0.0757467 | + | 0.997127i | \(0.524134\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.35603 | 0.321657 | 0.160828 | − | 0.986982i | \(-0.448583\pi\) | ||||
0.160828 | + | 0.986982i | \(0.448583\pi\) | |||||||
\(524\) | −2.12401 | −0.0927877 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.1017 | 0.484057 | ||||||||
\(527\) | −11.6942 | −0.509407 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.1257 | 1.04894 | ||||||||
\(530\) | −23.7191 | −1.03029 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.857480 | −0.0371765 | ||||||||
\(533\) | 14.2367 | 0.616660 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.9441 | −0.646088 | ||||||||
\(536\) | −2.75202 | −0.118869 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.8952 | 0.599065 | ||||||||
\(539\) | −4.14107 | −0.178369 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1595 | 0.565769 | 0.282884 | − | 0.959154i | \(-0.408709\pi\) | ||||
0.282884 | + | 0.959154i | \(0.408709\pi\) | |||||||
\(542\) | −21.2961 | −0.914748 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.32902 | −0.0569813 | ||||||||
\(545\) | −57.0151 | −2.44226 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.0280 | −1.75423 | −0.877116 | − | 0.480279i | \(-0.840535\pi\) | ||||
−0.877116 | + | 0.480279i | \(0.840535\pi\) | |||||||
\(548\) | −3.37165 | −0.144030 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 64.9111 | 2.76782 | ||||||||
\(551\) | 50.6239 | 2.15665 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.66941 | −0.326136 | ||||||||
\(554\) | −20.5742 | −0.874114 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.971430 | −0.0411978 | ||||||||
\(557\) | −22.0235 | −0.933165 | −0.466582 | − | 0.884478i | \(-0.654515\pi\) | ||||
−0.466582 | + | 0.884478i | \(0.654515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.9274 | −0.631360 | ||||||||
\(560\) | 14.8964 | 0.629490 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.6854 | 1.12566 | ||||||||
\(563\) | −25.8895 | −1.09111 | −0.545556 | − | 0.838074i | \(-0.683682\pi\) | ||||
−0.545556 | + | 0.838074i | \(0.683682\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 42.8430 | 1.80242 | ||||||||
\(566\) | 39.8682 | 1.67579 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0030 | −0.503634 | ||||||||
\(569\) | −16.3568 | −0.685713 | −0.342856 | − | 0.939388i | \(-0.611394\pi\) | ||||
−0.342856 | + | 0.939388i | \(0.611394\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.7952 | −1.83277 | −0.916385 | − | 0.400298i | \(-0.868907\pi\) | ||||
−0.916385 | + | 0.400298i | \(0.868907\pi\) | |||||||
\(572\) | 2.16125 | 0.0903662 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.80033 | −0.242101 | ||||||||
\(575\) | 79.2551 | 3.30516 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.4323 | 0.684087 | 0.342043 | − | 0.939684i | \(-0.388881\pi\) | ||||
0.342043 | + | 0.939684i | \(0.388881\pi\) | |||||||
\(578\) | 20.0112 | 0.832358 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.89005 | 0.244571 | ||||||||
\(581\) | 0.904225 | 0.0375136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.7855 | 0.736601 | ||||||||
\(584\) | 19.1369 | 0.791891 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.97715 | 0.246914 | ||||||||
\(587\) | 18.2183 | 0.751951 | 0.375976 | − | 0.926630i | \(-0.377308\pi\) | ||||
0.375976 | + | 0.926630i | \(0.377308\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.5805 | −1.75450 | ||||||||
\(590\) | −20.0565 | −0.825711 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.1954 | −1.24102 | ||||||||
\(593\) | −0.539852 | −0.0221691 | −0.0110845 | − | 0.999939i | \(-0.503528\pi\) | ||||
−0.0110845 | + | 0.999939i | \(0.503528\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.11635 | −0.250746 | ||||||||
\(596\) | 3.24267 | 0.132825 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −31.0601 | −1.27014 | ||||||||
\(599\) | 28.9266 | 1.18191 | 0.590954 | − | 0.806705i | \(-0.298752\pi\) | ||||
0.590954 | + | 0.806705i | \(0.298752\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.27630 | 0.256016 | 0.128008 | − | 0.991773i | \(-0.459142\pi\) | ||||
0.128008 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(602\) | 6.08172 | 0.247872 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.664451 | −0.0270361 | ||||||||
\(605\) | −25.0093 | −1.01677 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.9901 | −0.486664 | −0.243332 | − | 0.969943i | \(-0.578240\pi\) | ||||
−0.243332 | + | 0.969943i | \(0.578240\pi\) | |||||||
\(608\) | −4.83918 | −0.196255 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.8548 | −0.803899 | ||||||||
\(611\) | 29.4648 | 1.19202 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.0885 | −0.730588 | −0.365294 | − | 0.930892i | \(-0.619031\pi\) | ||||
−0.365294 | + | 0.930892i | \(0.619031\pi\) | |||||||
\(614\) | −45.2069 | −1.82440 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.1253 | −0.488543 | ||||||||
\(617\) | 33.8316 | 1.36201 | 0.681004 | − | 0.732280i | \(-0.261544\pi\) | ||||
0.681004 | + | 0.732280i | \(0.261544\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.0117 | 0.683759 | 0.341879 | − | 0.939744i | \(-0.388937\pi\) | ||||
0.341879 | + | 0.939744i | \(0.388937\pi\) | |||||||
\(620\) | −4.95421 | −0.198966 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 41.8908 | 1.67967 | ||||||||
\(623\) | 0.889515 | 0.0356377 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 50.5641 | 2.02256 | ||||||||
\(626\) | 13.1757 | 0.526605 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.11738 | 0.0445884 | ||||||||
\(629\) | 12.3980 | 0.494340 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.9850 | 1.63159 | 0.815794 | − | 0.578342i | \(-0.196300\pi\) | ||||
0.815794 | + | 0.578342i | \(0.196300\pi\) | |||||||
\(632\) | −22.4565 | −0.893272 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.5093 | −0.695384 | ||||||||
\(635\) | −4.06757 | −0.161417 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.33246 | 0.132037 | ||||||||
\(638\) | 51.9851 | 2.05811 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 39.8872 | 1.57668 | ||||||||
\(641\) | −18.3751 | −0.725773 | −0.362887 | − | 0.931833i | \(-0.618209\pi\) | ||||
−0.362887 | + | 0.931833i | \(0.618209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.6254 | −1.60211 | −0.801054 | − | 0.598592i | \(-0.795727\pi\) | ||||
−0.801054 | + | 0.598592i | \(0.795727\pi\) | |||||||
\(644\) | −1.07512 | −0.0423655 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.1780 | −0.439792 | ||||||||
\(647\) | 17.3245 | 0.681095 | 0.340548 | − | 0.940227i | \(-0.389388\pi\) | ||||
0.340548 | + | 0.940227i | \(0.389388\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.0392 | 0.590339 | ||||||||
\(650\) | −52.2362 | −2.04887 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.82043 | −0.149620 | ||||||||
\(653\) | −3.87508 | −0.151644 | −0.0758219 | − | 0.997121i | \(-0.524158\pi\) | ||||
−0.0758219 | + | 0.997121i | \(0.524158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −55.1651 | −2.15548 | ||||||||
\(656\) | −15.6456 | −0.610858 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0046 | −0.467986 | ||||||||
\(659\) | −23.7917 | −0.926795 | −0.463397 | − | 0.886151i | \(-0.653370\pi\) | ||||
−0.463397 | + | 0.886151i | \(0.653370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.3539 | 1.06394 | 0.531972 | − | 0.846762i | \(-0.321451\pi\) | ||||
0.531972 | + | 0.846762i | \(0.321451\pi\) | |||||||
\(662\) | 45.2863 | 1.76010 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.64763 | 0.102748 | ||||||||
\(665\) | −22.2706 | −0.863618 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 63.4726 | 2.45767 | ||||||||
\(668\) | −2.36485 | −0.0914988 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.19057 | −0.200529 | ||||||||
\(671\) | 14.8880 | 0.574744 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.3576 | 1.01601 | 0.508006 | − | 0.861354i | \(-0.330383\pi\) | ||||
0.508006 | + | 0.861354i | \(0.330383\pi\) | |||||||
\(674\) | −43.0139 | −1.65684 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.296734 | 0.0114128 | ||||||||
\(677\) | −39.4511 | −1.51623 | −0.758115 | − | 0.652121i | \(-0.773879\pi\) | ||||
−0.758115 | + | 0.652121i | \(0.773879\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.8632 | −0.416892 | ||||||||
\(680\) | −17.9091 | −0.686782 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −43.7254 | −1.67433 | ||||||||
\(683\) | 8.64860 | 0.330930 | 0.165465 | − | 0.986216i | \(-0.447088\pi\) | ||||
0.165465 | + | 0.986216i | \(0.447088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −87.5691 | −3.34584 | ||||||||
\(686\) | −1.35771 | −0.0518378 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.4046 | 0.625419 | ||||||||
\(689\) | −14.3126 | −0.545268 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.10919 | −0.346530 | −0.173265 | − | 0.984875i | \(-0.555432\pi\) | ||||
−0.173265 | + | 0.984875i | \(0.555432\pi\) | |||||||
\(692\) | −0.525857 | −0.0199901 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −43.7946 | −1.66242 | ||||||||
\(695\) | −25.2301 | −0.957034 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.42395 | 0.243324 | ||||||||
\(698\) | −28.8126 | −1.09057 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.80811 | −0.0683401 | ||||||||
\(701\) | −9.44526 | −0.356743 | −0.178371 | − | 0.983963i | \(-0.557083\pi\) | ||||
−0.178371 | + | 0.983963i | \(0.557083\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45.1431 | 1.70260 | ||||||||
\(704\) | −35.3005 | −1.33044 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.3475 | 1.10451 | ||||||||
\(707\) | −7.33839 | −0.275988 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.58727 | −0.172279 | −0.0861393 | − | 0.996283i | \(-0.527453\pi\) | ||||
−0.0861393 | + | 0.996283i | \(0.527453\pi\) | |||||||
\(710\) | −22.6387 | −0.849616 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.60456 | 0.0976099 | ||||||||
\(713\) | −53.3878 | −1.99939 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 56.1323 | 2.09923 | ||||||||
\(716\) | −0.427309 | −0.0159693 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.4096 | −0.463121 | ||||||||
\(719\) | 2.72744 | 0.101716 | 0.0508581 | − | 0.998706i | \(-0.483804\pi\) | ||||
0.0508581 | + | 0.998706i | \(0.483804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.53321 | 0.168825 | ||||||||
\(722\) | −14.9043 | −0.554681 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.44201 | 0.0907565 | ||||||||
\(725\) | 106.747 | 3.96449 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.5557 | 0.688194 | 0.344097 | − | 0.938934i | \(-0.388185\pi\) | ||||
0.344097 | + | 0.938934i | \(0.388185\pi\) | |||||||
\(728\) | 9.75766 | 0.361643 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 36.0940 | 1.33590 | ||||||||
\(731\) | −6.73559 | −0.249125 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.8879 | 1.06700 | 0.533499 | − | 0.845801i | \(-0.320877\pi\) | ||||
0.533499 | + | 0.845801i | \(0.320877\pi\) | |||||||
\(734\) | −23.6680 | −0.873600 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.06741 | −0.223648 | ||||||||
\(737\) | 3.89210 | 0.143367 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.6965 | 1.34990 | 0.674951 | − | 0.737863i | \(-0.264165\pi\) | ||||
0.674951 | + | 0.737863i | \(0.264165\pi\) | |||||||
\(740\) | 5.25236 | 0.193081 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.83126 | 0.214072 | ||||||||
\(743\) | −23.9221 | −0.877618 | −0.438809 | − | 0.898580i | \(-0.644600\pi\) | ||||
−0.438809 | + | 0.898580i | \(0.644600\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 84.2192 | 3.08555 | ||||||||
\(746\) | −31.5634 | −1.15562 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.975207 | 0.0356571 | ||||||||
\(749\) | 3.67395 | 0.134243 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.6390 | −1.30049 | −0.650243 | − | 0.759727i | \(-0.725333\pi\) | ||||
−0.650243 | + | 0.759727i | \(0.725333\pi\) | |||||||
\(752\) | −32.3806 | −1.18080 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −41.8342 | −1.52351 | ||||||||
\(755\) | −17.2572 | −0.628055 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.0965 | −1.02118 | −0.510592 | − | 0.859823i | \(-0.670574\pi\) | ||||
−0.510592 | + | 0.859823i | \(0.670574\pi\) | |||||||
\(758\) | 26.9844 | 0.980118 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −65.2098 | −2.36541 | ||||||||
\(761\) | −22.6232 | −0.820091 | −0.410045 | − | 0.912065i | \(-0.634487\pi\) | ||||
−0.410045 | + | 0.912065i | \(0.634487\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0170 | 0.507450 | ||||||||
\(764\) | −0.955161 | −0.0345565 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 39.9370 | 1.44298 | ||||||||
\(767\) | −12.1025 | −0.436997 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.2047 | 0.548295 | 0.274148 | − | 0.961688i | \(-0.411604\pi\) | ||||
0.274148 | + | 0.961688i | \(0.411604\pi\) | |||||||
\(770\) | −22.8695 | −0.824158 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.84369 | 0.0663559 | ||||||||
\(773\) | −7.25076 | −0.260792 | −0.130396 | − | 0.991462i | \(-0.541625\pi\) | ||||
−0.130396 | + | 0.991462i | \(0.541625\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −89.7865 | −3.22523 | ||||||||
\(776\) | −31.8082 | −1.14185 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.2738 | −0.368334 | ||||||||
\(779\) | 23.3906 | 0.838056 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9754 | 0.607429 | ||||||||
\(782\) | −14.0151 | −0.501177 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.66225 | −0.130795 | ||||||||
\(785\) | 29.0209 | 1.03580 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.1413 | −0.504083 | −0.252041 | − | 0.967716i | \(-0.581102\pi\) | ||||
−0.252041 | + | 0.967716i | \(0.581102\pi\) | |||||||
\(788\) | 1.41931 | 0.0505607 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −42.3550 | −1.50692 | ||||||||
\(791\) | −10.5328 | −0.374504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.9809 | −0.425453 | ||||||||
\(794\) | −17.4029 | −0.617604 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.31289 | 0.0819782 | ||||||||
\(797\) | −46.8079 | −1.65802 | −0.829010 | − | 0.559234i | \(-0.811095\pi\) | ||||
−0.829010 | + | 0.559234i | \(0.811095\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2952 | 0.470351 | ||||||||
\(800\) | −10.2040 | −0.360768 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 45.3943 | 1.60293 | ||||||||
\(803\) | −27.0648 | −0.955094 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.9231 | −0.984160 | ||||||||
\(806\) | 35.1873 | 1.23942 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.4873 | −0.755919 | ||||||||
\(809\) | −23.7428 | −0.834753 | −0.417377 | − | 0.908734i | \(-0.637050\pi\) | ||||
−0.417377 | + | 0.908734i | \(0.637050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.4329 | 0.612150 | 0.306075 | − | 0.952007i | \(-0.400984\pi\) | ||||
0.306075 | + | 0.952007i | \(0.400984\pi\) | |||||||
\(812\) | −1.44805 | −0.0508167 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 46.3569 | 1.62481 | ||||||||
\(815\) | −99.2249 | −3.47570 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.5254 | −0.858034 | ||||||||
\(818\) | 23.3235 | 0.815486 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.72148 | 0.0950383 | ||||||||
\(821\) | 0.499582 | 0.0174355 | 0.00871777 | − | 0.999962i | \(-0.497225\pi\) | ||||
0.00871777 | + | 0.999962i | \(0.497225\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.5433 | 1.76183 | 0.880915 | − | 0.473274i | \(-0.156928\pi\) | ||||
0.880915 | + | 0.473274i | \(0.156928\pi\) | |||||||
\(824\) | 13.2735 | 0.462405 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.93082 | 0.171565 | ||||||||
\(827\) | 5.11034 | 0.177704 | 0.0888520 | − | 0.996045i | \(-0.471680\pi\) | ||||
0.0888520 | + | 0.996045i | \(0.471680\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.7911 | −1.76405 | −0.882025 | − | 0.471203i | \(-0.843820\pi\) | ||||
−0.882025 | + | 0.471203i | \(0.843820\pi\) | |||||||
\(830\) | 4.99367 | 0.173333 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.4076 | 0.984855 | ||||||||
\(833\) | 1.50369 | 0.0520997 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −61.4203 | −2.12554 | ||||||||
\(836\) | 3.55089 | 0.122810 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −40.0706 | −1.38422 | ||||||||
\(839\) | 12.1037 | 0.417865 | 0.208932 | − | 0.977930i | \(-0.433001\pi\) | ||||
0.208932 | + | 0.977930i | \(0.433001\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56.4900 | 1.94793 | ||||||||
\(842\) | 28.3849 | 0.978210 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.31578 | 0.0452911 | ||||||||
\(845\) | 7.70683 | 0.265123 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.14846 | 0.211264 | ||||||||
\(848\) | 15.7290 | 0.540137 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −23.5703 | −0.808453 | ||||||||
\(851\) | 56.6007 | 1.94025 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.5795 | 1.08126 | 0.540631 | − | 0.841260i | \(-0.318185\pi\) | ||||
0.540631 | + | 0.841260i | \(0.318185\pi\) | |||||||
\(854\) | 4.88126 | 0.167033 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.7576 | 0.367686 | ||||||||
\(857\) | 36.7530 | 1.25546 | 0.627729 | − | 0.778432i | \(-0.283985\pi\) | ||||
0.627729 | + | 0.778432i | \(0.283985\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.9999 | 0.921225 | 0.460613 | − | 0.887601i | \(-0.347630\pi\) | ||||
0.460613 | + | 0.887601i | \(0.347630\pi\) | |||||||
\(860\) | −2.85351 | −0.0973038 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.6907 | −0.977209 | ||||||||
\(863\) | −10.8508 | −0.369365 | −0.184682 | − | 0.982798i | \(-0.559126\pi\) | ||||
−0.184682 | + | 0.982798i | \(0.559126\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.6576 | −0.464374 | ||||||||
\(866\) | −5.64417 | −0.191797 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.21798 | 0.0413408 | ||||||||
\(869\) | 31.7596 | 1.07737 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.13211 | −0.106127 | ||||||||
\(872\) | 41.0427 | 1.38988 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −51.0311 | −1.72615 | ||||||||
\(875\) | −26.6227 | −0.900011 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.3835 | −0.418162 | −0.209081 | − | 0.977898i | \(-0.567047\pi\) | ||||
−0.209081 | + | 0.977898i | \(0.567047\pi\) | |||||||
\(878\) | 9.12689 | 0.308018 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −61.6872 | −2.07948 | ||||||||
\(881\) | −32.1116 | −1.08187 | −0.540933 | − | 0.841066i | \(-0.681929\pi\) | ||||
−0.540933 | + | 0.841066i | \(0.681929\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.1303 | 0.441870 | 0.220935 | − | 0.975289i | \(-0.429089\pi\) | ||||
0.220935 | + | 0.975289i | \(0.429089\pi\) | |||||||
\(884\) | −0.784783 | −0.0263951 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.6712 | −1.03042 | ||||||||
\(887\) | −16.1209 | −0.541289 | −0.270644 | − | 0.962679i | \(-0.587237\pi\) | ||||
−0.270644 | + | 0.962679i | \(0.587237\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 4.91243 | 0.164665 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.16321 | −0.105912 | ||||||||
\(893\) | 48.4101 | 1.61998 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.0982 | −0.370970 | ||||||||
\(896\) | −9.80615 | −0.327600 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −54.3094 | −1.81233 | ||||||||
\(899\) | −71.9069 | −2.39823 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.45821 | −0.215154 | ||||||||
\(902\) | 24.0196 | 0.799764 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.8408 | −1.02575 | ||||||||
\(905\) | 63.4242 | 2.10829 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.43444 | −0.246857 | −0.123428 | − | 0.992353i | \(-0.539389\pi\) | ||||
−0.123428 | + | 0.992353i | \(0.539389\pi\) | |||||||
\(908\) | −0.970744 | −0.0322153 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18.4038 | 0.610081 | ||||||||
\(911\) | 18.7356 | 0.620740 | 0.310370 | − | 0.950616i | \(-0.399547\pi\) | ||||
0.310370 | + | 0.950616i | \(0.399547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.74446 | −0.123923 | ||||||||
\(914\) | −6.98809 | −0.231145 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.00153 | 0.0991733 | ||||||||
\(917\) | 13.5622 | 0.447863 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.5412 | 1.96408 | 0.982041 | − | 0.188666i | \(-0.0604165\pi\) | ||||
0.982041 | + | 0.188666i | \(0.0604165\pi\) | |||||||
\(920\) | −81.7606 | −2.69557 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.24838 | −0.0740465 | ||||||||
\(923\) | −13.6607 | −0.449648 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 95.1900 | 3.12983 | ||||||||
\(926\) | −40.4643 | −1.32974 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.17207 | −0.268261 | ||||||||
\(929\) | −8.96931 | −0.294274 | −0.147137 | − | 0.989116i | \(-0.547006\pi\) | ||||
−0.147137 | + | 0.989116i | \(0.547006\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.47517 | 0.179441 | ||||||||
\(932\) | −4.40393 | −0.144255 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.8496 | −0.551334 | ||||||||
\(935\) | 25.3283 | 0.828322 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.6061 | 0.640503 | 0.320252 | − | 0.947333i | \(-0.396233\pi\) | ||||
0.320252 | + | 0.947333i | \(0.396233\pi\) | |||||||
\(938\) | 1.27609 | 0.0416657 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.63247 | 0.183711 | ||||||||
\(941\) | −31.9202 | −1.04057 | −0.520285 | − | 0.853993i | \(-0.674174\pi\) | ||||
−0.520285 | + | 0.853993i | \(0.674174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.3274 | 0.955030 | ||||||||
\(944\) | 13.3002 | 0.432885 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.1848 | −0.818829 | ||||||||
\(947\) | 1.95493 | 0.0635265 | 0.0317633 | − | 0.999495i | \(-0.489888\pi\) | ||||
0.0317633 | + | 0.999495i | \(0.489888\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.7799 | 0.707007 | ||||||||
\(950\) | −85.8231 | −2.78447 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.40289 | 0.142699 | ||||||||
\(953\) | 3.28363 | 0.106367 | 0.0531836 | − | 0.998585i | \(-0.483063\pi\) | ||||
0.0531836 | + | 0.998585i | \(0.483063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.8076 | −0.802755 | ||||||||
\(956\) | −0.181805 | −0.00587999 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.6224 | −1.02167 | ||||||||
\(959\) | 21.5286 | 0.695195 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.4819 | 0.951030 | ||||||||
\(962\) | −37.3050 | −1.20276 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.527060 | 0.0169755 | ||||||||
\(965\) | 47.8847 | 1.54146 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −58.3821 | −1.87744 | −0.938720 | − | 0.344680i | \(-0.887987\pi\) | ||||
−0.938720 | + | 0.344680i | \(0.887987\pi\) | |||||||
\(968\) | 18.0031 | 0.578641 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −59.9932 | −1.92627 | ||||||||
\(971\) | 31.4550 | 1.00944 | 0.504719 | − | 0.863284i | \(-0.331596\pi\) | ||||
0.504719 | + | 0.863284i | \(0.331596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.20276 | 0.198851 | ||||||||
\(974\) | 16.1034 | 0.515988 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.1665 | 0.421450 | ||||||||
\(977\) | 13.3824 | 0.428141 | 0.214070 | − | 0.976818i | \(-0.431328\pi\) | ||||
0.214070 | + | 0.976818i | \(0.431328\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.68354 | −0.117727 | ||||||||
\(980\) | 0.637032 | 0.0203492 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −47.4224 | −1.51331 | ||||||||
\(983\) | 59.8159 | 1.90783 | 0.953915 | − | 0.300077i | \(-0.0970124\pi\) | ||||
0.953915 | + | 0.300077i | \(0.0970124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.8625 | 1.17454 | ||||||||
\(986\) | −18.8766 | −0.601153 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.85752 | −0.0909098 | ||||||||
\(989\) | −30.7501 | −0.977797 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.0477 | 0.732134 | 0.366067 | − | 0.930588i | \(-0.380704\pi\) | ||||
0.366067 | + | 0.930588i | \(0.380704\pi\) | |||||||
\(992\) | 6.87365 | 0.218238 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.56566 | 0.176532 | ||||||||
\(995\) | 60.0708 | 1.90437 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0638 | −0.350395 | −0.175197 | − | 0.984533i | \(-0.556056\pi\) | ||||
−0.175197 | + | 0.984533i | \(0.556056\pi\) | |||||||
\(998\) | −18.9434 | −0.599644 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.v.1.7 | 19 | ||
3.2 | odd | 2 | 2667.2.a.q.1.13 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.q.1.13 | ✓ | 19 | 3.2 | odd | 2 | ||
8001.2.a.v.1.7 | 19 | 1.1 | even | 1 | trivial |