Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, 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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | −3.25521 | −1.87940 | −0.939699 | − | 0.342002i | \(-0.888895\pi\) | ||||
−0.939699 | + | 0.342002i | \(0.888895\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.40628 | −1.07612 | −0.538059 | − | 0.842907i | \(-0.680842\pi\) | ||||
−0.538059 | + | 0.842907i | \(0.680842\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.10646 | −1.55209 | −0.776047 | − | 0.630675i | \(-0.782778\pi\) | ||||
−0.776047 | + | 0.630675i | \(0.782778\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.59642 | 2.53214 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.28963 | 1.59488 | 0.797442 | − | 0.603395i | \(-0.206186\pi\) | ||||
0.797442 | + | 0.603395i | \(0.206186\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.26582 | −0.351075 | −0.175537 | − | 0.984473i | \(-0.556166\pi\) | ||||
−0.175537 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.83294 | 2.02246 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.46967 | −0.598982 | −0.299491 | − | 0.954099i | \(-0.596817\pi\) | ||||
−0.299491 | + | 0.954099i | \(0.596817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.09764 | −0.940063 | −0.470031 | − | 0.882650i | \(-0.655757\pi\) | ||||
−0.470031 | + | 0.882650i | \(0.655757\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.3674 | 2.91700 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.252316 | −0.0526116 | −0.0263058 | − | 0.999654i | \(-0.508374\pi\) | ||||
−0.0263058 | + | 0.999654i | \(0.508374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.790160 | 0.158032 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.9623 | −2.87950 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.53768 | −0.471235 | −0.235617 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235617 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.649483 | 0.116651 | 0.0583253 | − | 0.998298i | \(-0.481424\pi\) | ||||
0.0583253 | + | 0.998298i | \(0.481424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.2189 | −2.99742 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.88126 | 1.67024 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.06797 | 0.997568 | 0.498784 | − | 0.866726i | \(-0.333780\pi\) | ||||
0.498784 | + | 0.866726i | \(0.333780\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.12051 | 0.659809 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.02841 | −1.41000 | −0.705000 | − | 0.709207i | \(-0.749053\pi\) | ||||
−0.705000 | + | 0.709207i | \(0.749053\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.38864 | −1.27926 | −0.639628 | − | 0.768685i | \(-0.720911\pi\) | ||||
−0.639628 | + | 0.768685i | \(0.720911\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −18.2791 | −2.72488 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.6116 | −1.54787 | −0.773933 | − | 0.633267i | \(-0.781713\pi\) | ||||
−0.773933 | + | 0.633267i | \(0.781713\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.86298 | 1.40900 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.03929 | 1.12573 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.73201 | 0.787352 | 0.393676 | − | 0.919249i | \(-0.371203\pi\) | ||||
0.393676 | + | 0.919249i | \(0.371203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.7283 | −1.71629 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.3387 | 1.76675 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.3778 | −1.48126 | −0.740632 | − | 0.671911i | \(-0.765474\pi\) | ||||
−0.740632 | + | 0.671911i | \(0.765474\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7202 | 1.50062 | 0.750312 | − | 0.661084i | \(-0.229903\pi\) | ||||
0.750312 | + | 0.661084i | \(0.229903\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −31.1944 | −3.93012 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.04590 | 0.377798 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.70586 | −1.18576 | −0.592880 | − | 0.805291i | \(-0.702009\pi\) | ||||
−0.592880 | + | 0.805291i | \(0.702009\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.821344 | 0.0988782 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4974 | −1.24582 | −0.622908 | − | 0.782295i | \(-0.714049\pi\) | ||||
−0.622908 | + | 0.782295i | \(0.714049\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.98428 | −0.934489 | −0.467244 | − | 0.884128i | \(-0.654753\pi\) | ||||
−0.467244 | + | 0.884128i | \(0.654753\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.57214 | −0.297005 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.7217 | −2.47541 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.1209 | −1.58873 | −0.794364 | − | 0.607442i | \(-0.792196\pi\) | ||||
−0.794364 | + | 0.607442i | \(0.792196\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 25.9163 | 2.87959 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.38495 | 0.261782 | 0.130891 | − | 0.991397i | \(-0.458216\pi\) | ||||
0.130891 | + | 0.991397i | \(0.458216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.94269 | 0.644576 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.26068 | 0.885638 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.16486 | −0.229474 | −0.114737 | − | 0.993396i | \(-0.536603\pi\) | ||||
−0.114737 | + | 0.993396i | \(0.536603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.19802 | 0.544901 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.11421 | −0.219233 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.86004 | 1.01162 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.81629 | 0.895158 | 0.447579 | − | 0.894244i | \(-0.352286\pi\) | ||||
0.447579 | + | 0.894244i | \(0.352286\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 40.1823 | 4.03847 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.63682 | 0.162870 | 0.0814348 | − | 0.996679i | \(-0.474050\pi\) | ||||
0.0814348 | + | 0.996679i | \(0.474050\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.44485 | −0.832096 | −0.416048 | − | 0.909343i | \(-0.636585\pi\) | ||||
−0.416048 | + | 0.909343i | \(0.636585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −32.1656 | −3.13904 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.2332 | −1.37598 | −0.687989 | − | 0.725721i | \(-0.741506\pi\) | ||||
−0.687989 | + | 0.725721i | \(0.741506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.69013 | −0.545016 | −0.272508 | − | 0.962154i | \(-0.587853\pi\) | ||||
−0.272508 | + | 0.962154i | \(0.587853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.7525 | −1.87483 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.3843 | −1.44724 | −0.723618 | − | 0.690200i | \(-0.757522\pi\) | ||||
−0.723618 | + | 0.690200i | \(0.757522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.607143 | 0.0566163 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.61568 | −0.888970 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.1416 | 0.929676 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.9802 | 1.54366 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 29.3894 | 2.64995 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.1300 | 0.906058 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.18636 | 0.637687 | 0.318843 | − | 0.947807i | \(-0.396706\pi\) | ||||
0.318843 | + | 0.947807i | \(0.396706\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 27.3068 | 2.40423 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6507 | 1.54215 | 0.771075 | − | 0.636744i | \(-0.219719\pi\) | ||||
0.771075 | + | 0.636744i | \(0.219719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.8268 | 1.45907 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 36.0035 | 3.09869 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.77593 | −0.151728 | −0.0758640 | − | 0.997118i | \(-0.524171\pi\) | ||||
−0.0758640 | + | 0.997118i | \(0.524171\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.95724 | −0.505287 | −0.252643 | − | 0.967559i | \(-0.581300\pi\) | ||||
−0.252643 | + | 0.967559i | \(0.581300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 34.5432 | 2.90906 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.69571 | −0.559924 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.10635 | 0.507105 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −32.1061 | −2.64807 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.90990 | 0.238388 | 0.119194 | − | 0.992871i | \(-0.461969\pi\) | ||||
0.119194 | + | 0.992871i | \(0.461969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.3331 | 1.57331 | 0.786653 | − | 0.617395i | \(-0.211812\pi\) | ||||
0.786653 | + | 0.617395i | \(0.211812\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.7606 | −1.51671 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.56284 | −0.125530 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.6310 | 1.32730 | 0.663649 | − | 0.748044i | \(-0.269007\pi\) | ||||
0.663649 | + | 0.748044i | \(0.269007\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.6589 | −1.47975 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.03613 | 0.0816582 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.87957 | 0.773828 | 0.386914 | − | 0.922116i | \(-0.373541\pi\) | ||||
0.386914 | + | 0.922116i | \(0.373541\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 41.4334 | 3.22559 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.3025 | 1.02938 | 0.514688 | − | 0.857377i | \(-0.327908\pi\) | ||||
0.514688 | + | 0.857377i | \(0.327908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3977 | −0.876747 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −31.1274 | −2.38037 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.428435 | 0.0325733 | 0.0162867 | − | 0.999867i | \(-0.494816\pi\) | ||||
0.0162867 | + | 0.999867i | \(0.494816\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.24476 | −0.245281 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 37.0372 | 2.78389 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.266575 | −0.0199248 | −0.00996238 | − | 0.999950i | \(-0.503171\pi\) | ||||
−0.00996238 | + | 0.999950i | \(0.503171\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.6324 | −1.23628 | −0.618138 | − | 0.786069i | \(-0.712113\pi\) | ||||
−0.618138 | + | 0.786069i | \(0.712113\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −38.1519 | −2.82027 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.6012 | −1.07350 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.0636 | −0.955307 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 61.4421 | 4.46926 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.36977 | −0.243828 | −0.121914 | − | 0.992541i | \(-0.538903\pi\) | ||||
−0.121914 | + | 0.992541i | \(0.538903\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.3264 | −1.67907 | −0.839534 | − | 0.543307i | \(-0.817172\pi\) | ||||
−0.839534 | + | 0.543307i | \(0.817172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.91507 | −0.710033 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.9865 | 1.13899 | 0.569496 | − | 0.821994i | \(-0.307138\pi\) | ||||
0.569496 | + | 0.821994i | \(0.307138\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.39616 | 0.453412 | 0.226706 | − | 0.973963i | \(-0.427204\pi\) | ||||
0.226706 | + | 0.973963i | \(0.427204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.5947 | 2.22852 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.4209 | 0.731401 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.7248 | 1.51733 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.91670 | −0.133220 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.6750 | −1.49929 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.5924 | 1.14227 | 0.571135 | − | 0.820856i | \(-0.306503\pi\) | ||||
0.571135 | + | 0.820856i | \(0.306503\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.1714 | 2.34138 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.1854 | 1.37663 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.66707 | −0.181053 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 25.9905 | 1.75628 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.12615 | 0.210287 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.77535 | −0.587641 | −0.293821 | − | 0.955861i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955861i | \(0.594927\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.00238 | 0.400159 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.4584 | −1.75610 | −0.878052 | − | 0.478566i | \(-0.841157\pi\) | ||||
−0.878052 | + | 0.478566i | \(0.841157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.4646 | 0.955847 | 0.477924 | − | 0.878401i | \(-0.341390\pi\) | ||||
0.477924 | + | 0.878401i | \(0.341390\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 70.7086 | 4.65229 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.4922 | 0.818394 | 0.409197 | − | 0.912446i | \(-0.365809\pi\) | ||||
0.409197 | + | 0.912446i | \(0.365809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.5345 | 1.66569 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 45.9666 | 2.98585 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6048 | 0.815339 | 0.407669 | − | 0.913130i | \(-0.366342\pi\) | ||||
0.407669 | + | 0.913130i | \(0.366342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.80699 | −0.245230 | −0.122615 | − | 0.992454i | \(-0.539128\pi\) | ||||
−0.122615 | + | 0.992454i | \(0.539128\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −39.4762 | −2.53240 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −23.7330 | −1.51625 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.18686 | 0.330032 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.76353 | −0.491994 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.38969 | 0.340194 | 0.170097 | − | 0.985427i | \(-0.445592\pi\) | ||||
0.170097 | + | 0.985427i | \(0.445592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.33466 | −0.0839095 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.3447 | −1.21141 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.0557 | −1.37580 | −0.687898 | − | 0.725807i | \(-0.741467\pi\) | ||||
−0.687898 | + | 0.725807i | \(0.741467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.9179 | −1.54832 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.2773 | −1.19323 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.8780 | 1.84236 | 0.921179 | − | 0.389140i | \(-0.127228\pi\) | ||||
0.921179 | + | 0.389140i | \(0.127228\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.7928 | −0.847284 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.04707 | 0.431274 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.08688 | 0.432095 | 0.216047 | − | 0.976383i | \(-0.430683\pi\) | ||||
0.216047 | + | 0.976383i | \(0.430683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.1505 | −0.859580 | −0.429790 | − | 0.902929i | \(-0.641412\pi\) | ||||
−0.429790 | + | 0.902929i | \(0.641412\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.9207 | −1.02409 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.17966 | 0.252043 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4681 | −0.628965 | −0.314483 | − | 0.949263i | \(-0.601831\pi\) | ||||
−0.314483 | + | 0.949263i | \(0.601831\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.93375 | 0.295376 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.74438 | −0.163716 | −0.0818581 | − | 0.996644i | \(-0.526085\pi\) | ||||
−0.0818581 | + | 0.996644i | \(0.526085\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.9530 | 1.42386 | 0.711928 | − | 0.702253i | \(-0.247822\pi\) | ||||
0.711928 | + | 0.702253i | \(0.247822\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −32.0966 | −1.90124 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 37.0748 | 2.18845 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.9008 | −0.641221 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.6989 | −1.68236 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.7289 | −1.79520 | −0.897600 | − | 0.440810i | \(-0.854691\pi\) | ||||
−0.897600 | + | 0.440810i | \(0.854691\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.3781 | 1.59402 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −79.1453 | −4.59247 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.319386 | 0.0184706 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.4476 | 1.98552 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.32820 | −0.306097 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −28.2021 | −1.61485 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4645 | 1.22504 | 0.612522 | − | 0.790454i | \(-0.290155\pi\) | ||||
0.612522 | + | 0.790454i | \(0.290155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.4898 | 1.56384 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.1022 | −0.913072 | −0.456536 | − | 0.889705i | \(-0.650910\pi\) | ||||
−0.456536 | + | 0.889705i | \(0.650910\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0064 | 0.848213 | 0.424107 | − | 0.905612i | \(-0.360588\pi\) | ||||
0.424107 | + | 0.905612i | \(0.360588\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 75.0622 | 4.22928 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.7864 | 1.22364 | 0.611822 | − | 0.790996i | \(-0.290437\pi\) | ||||
0.611822 | + | 0.790996i | \(0.290437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.4234 | −0.751565 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 46.3322 | 2.58601 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.1198 | 0.563080 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00020 | −0.0554810 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.5226 | 1.02430 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 43.5762 | 2.40244 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.6668 | −1.74056 | −0.870282 | − | 0.492554i | \(-0.836064\pi\) | ||||
−0.870282 | + | 0.492554i | \(0.836064\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 46.0949 | 2.52598 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.3550 | 1.27602 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.1984 | −1.10028 | −0.550139 | − | 0.835073i | \(-0.685425\pi\) | ||||
−0.550139 | + | 0.835073i | \(0.685425\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 50.0793 | 2.71994 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.43553 | 0.186044 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.7567 | −0.634802 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.97638 | −0.106405 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.7591 | −0.845993 | −0.422997 | − | 0.906131i | \(-0.639022\pi\) | ||||
−0.422997 | + | 0.906131i | \(0.639022\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.2997 | −1.56838 | −0.784189 | − | 0.620523i | \(-0.786921\pi\) | ||||
−0.784189 | + | 0.620523i | \(0.786921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9396 | 1.01092 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.9507 | −1.22154 | −0.610772 | − | 0.791806i | \(-0.709141\pi\) | ||||
−0.610772 | + | 0.791806i | \(0.709141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.2597 | 1.34065 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33.0130 | −1.74723 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.4211 | 0.761118 | 0.380559 | − | 0.924757i | \(-0.375732\pi\) | ||||
0.380559 | + | 0.924757i | \(0.375732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.20936 | −0.116282 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −55.2743 | −2.90115 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.2124 | 1.00562 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.5746 | −1.64818 | −0.824090 | − | 0.566459i | \(-0.808313\pi\) | ||||
−0.824090 | + | 0.566459i | \(0.808313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −68.5836 | −3.57032 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.5382 | −1.22204 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.37124 | 0.226334 | 0.113167 | − | 0.993576i | \(-0.463900\pi\) | ||||
0.113167 | + | 0.993576i | \(0.463900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −32.9754 | −1.70284 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.21224 | 0.165439 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2334 | 1.14205 | 0.571026 | − | 0.820932i | \(-0.306546\pi\) | ||||
0.571026 | + | 0.820932i | \(0.306546\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.3931 | −1.19847 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.11809 | 0.159327 | 0.0796634 | − | 0.996822i | \(-0.474615\pi\) | ||||
0.0796634 | + | 0.996822i | \(0.474615\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 52.2683 | 2.66384 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −63.7236 | −3.23925 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.36393 | 0.170558 | 0.0852789 | − | 0.996357i | \(-0.472822\pi\) | ||||
0.0852789 | + | 0.996357i | \(0.472822\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.623137 | 0.0315134 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −57.4569 | −2.89832 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.9788 | 1.70966 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.52178 | −0.277130 | −0.138565 | − | 0.990353i | \(-0.544249\pi\) | ||||
−0.138565 | + | 0.990353i | \(0.544249\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −54.7747 | −2.74217 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.7239 | −0.735278 | −0.367639 | − | 0.929969i | \(-0.619834\pi\) | ||||
−0.367639 | + | 0.929969i | \(0.619834\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.822127 | −0.0409531 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −62.3618 | −3.09878 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.0974 | 1.59101 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.49688 | 0.0740162 | 0.0370081 | − | 0.999315i | \(-0.488217\pi\) | ||||
0.0370081 | + | 0.999315i | \(0.488217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.78104 | 0.285158 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 46.7225 | 2.29906 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.73885 | −0.281709 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.3921 | 0.949636 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8227 | 0.821842 | 0.410921 | − | 0.911671i | \(-0.365207\pi\) | ||||
0.410921 | + | 0.911671i | \(0.365207\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.6728 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −80.6105 | −3.91941 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.95143 | −0.0946583 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.1287 | −2.32911 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.7960 | 1.05232 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.38342 | 0.162974 | 0.0814868 | − | 0.996674i | \(-0.474033\pi\) | ||||
0.0814868 | + | 0.996674i | \(0.474033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.1465 | −1.54486 | −0.772432 | − | 0.635098i | \(-0.780960\pi\) | ||||
−0.772432 | + | 0.635098i | \(0.780960\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.8775 | −0.953052 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.03390 | 0.0494582 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.94804 | −0.331612 | −0.165806 | − | 0.986158i | \(-0.553023\pi\) | ||||
−0.165806 | + | 0.986158i | \(0.553023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 74.9233 | 3.56778 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0116 | −0.855759 | −0.427879 | − | 0.903836i | \(-0.640739\pi\) | ||||
−0.427879 | + | 0.903836i | \(0.640739\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.20924 | 0.246942 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.47235 | −0.448027 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.4214 | 1.48287 | 0.741435 | − | 0.671025i | \(-0.234146\pi\) | ||||
0.741435 | + | 0.671025i | \(0.234146\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −47.7570 | −2.24879 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −62.9334 | −2.95687 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.5079 | −0.586378 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.4785 | 1.19184 | 0.595918 | − | 0.803046i | \(-0.296789\pi\) | ||||
0.595918 | + | 0.803046i | \(0.296789\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 36.9519 | 1.72477 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.35058 | 0.388925 | 0.194463 | − | 0.980910i | \(-0.437704\pi\) | ||||
0.194463 | + | 0.980910i | \(0.437704\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.11130 | 0.0981204 | 0.0490602 | − | 0.998796i | \(-0.484377\pi\) | ||||
0.0490602 | + | 0.998796i | \(0.484377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.08736 | 0.235921 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.56158 | −0.164810 | −0.0824052 | − | 0.996599i | \(-0.526260\pi\) | ||||
−0.0824052 | + | 0.996599i | \(0.526260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.8567 | 1.84041 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −54.1375 | −2.49452 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44.3728 | −2.04026 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.23779 | −0.148560 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 43.5427 | 1.99368 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.0318 | 1.78341 | 0.891704 | − | 0.452620i | \(-0.149510\pi\) | ||||
0.891704 | + | 0.452620i | \(0.149510\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.68094 | −0.350221 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.37281 | −0.153468 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.2144 | −0.963297 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0484 | 0.953795 | 0.476898 | − | 0.878959i | \(-0.341761\pi\) | ||||
0.476898 | + | 0.878959i | \(0.341761\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.1601 | −1.45433 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.2629 | −0.959580 | −0.479790 | − | 0.877383i | \(-0.659287\pi\) | ||||
−0.479790 | + | 0.877383i | \(0.659287\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.26721 | 0.282261 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −96.6896 | −4.34588 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 43.1072 | 1.93362 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.9707 | −0.938776 | −0.469388 | − | 0.882992i | \(-0.655525\pi\) | ||||
−0.469388 | + | 0.882992i | \(0.655525\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −43.3024 | −1.93461 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.93864 | −0.175267 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.1020 | 1.64776 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.29606 | −0.101771 | −0.0508855 | − | 0.998704i | \(-0.516204\pi\) | ||||
−0.0508855 | + | 0.998704i | \(0.516204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.7871 | 1.45042 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 61.3102 | 2.70691 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.3206 | 0.895434 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −56.1317 | −2.46867 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.39465 | −0.0612182 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.1927 | 1.10371 | 0.551856 | − | 0.833939i | \(-0.313920\pi\) | ||||
0.551856 | + | 0.833939i | \(0.313920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.6038 | −1.07585 | −0.537924 | − | 0.842993i | \(-0.680791\pi\) | ||||
−0.537924 | + | 0.842993i | \(0.680791\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.5624 | 0.460980 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.60401 | −0.0698716 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9363 | −0.997232 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −86.4306 | −3.75077 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.4283 | 0.495015 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.2491 | 1.48072 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.867759 | 0.0374466 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 52.1716 | 2.24719 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.79885 | 0.292305 | 0.146153 | − | 0.989262i | \(-0.453311\pi\) | ||||
0.146153 | + | 0.989262i | \(0.453311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 54.1420 | 2.32346 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.6920 | 0.586502 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.4669 | 0.490288 | 0.245144 | − | 0.969487i | \(-0.421165\pi\) | ||||
0.245144 | + | 0.969487i | \(0.421165\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 89.0319 | 3.79979 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.3985 | 0.442990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 57.9870 | 2.46586 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 47.5301 | 2.01754 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.2963 | 0.521010 | 0.260505 | − | 0.965473i | \(-0.416111\pi\) | ||||
0.260505 | + | 0.965473i | \(0.416111\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6185 | 0.449114 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 42.5249 | 1.79540 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.0148 | 1.09639 | 0.548197 | − | 0.836349i | \(-0.315314\pi\) | ||||
0.548197 | + | 0.836349i | \(0.315314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.0190 | 1.55740 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −106.424 | −4.46940 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.80442 | −0.0756452 | −0.0378226 | − | 0.999284i | \(-0.512042\pi\) | ||||
−0.0378226 | + | 0.999284i | \(0.512042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.1365 | 1.09378 | 0.546889 | − | 0.837205i | \(-0.315812\pi\) | ||||
0.546889 | + | 0.837205i | \(0.315812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.9693 | 0.458251 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.199370 | −0.00831431 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.24477 | 0.0934509 | 0.0467255 | − | 0.998908i | \(-0.485121\pi\) | ||||
0.0467255 | + | 0.998908i | \(0.485121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 75.9323 | 3.15564 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.79370 | −0.406311 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.3202 | 1.25574 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.1380 | 0.956637 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.2957 | 1.04406 | 0.522032 | − | 0.852926i | \(-0.325174\pi\) | ||||
0.522032 | + | 0.852926i | \(0.325174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.66135 | −0.109659 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −52.0395 | −2.14062 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.9152 | 1.22847 | 0.614236 | − | 0.789122i | \(-0.289464\pi\) | ||||
0.614236 | + | 0.789122i | \(0.289464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.4034 | −1.00044 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.8209 | −0.852142 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.7572 | −0.439528 | −0.219764 | − | 0.975553i | \(-0.570529\pi\) | ||||
−0.219764 | + | 0.975553i | \(0.570529\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.266854 | −0.0108852 | −0.00544260 | − | 0.999985i | \(-0.501732\pi\) | ||||
−0.00544260 | + | 0.999985i | \(0.501732\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −73.7298 | −3.00251 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40.8591 | −1.66116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.9146 | −1.29537 | −0.647687 | − | 0.761906i | \(-0.724264\pi\) | ||||
−0.647687 | + | 0.761906i | \(0.724264\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33.9221 | −1.37459 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.4324 | 0.543417 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.4937 | −1.11046 | −0.555231 | − | 0.831696i | \(-0.687370\pi\) | ||||
−0.555231 | + | 0.831696i | \(0.687370\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −70.7190 | −2.85166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.9882 | 1.40857 | 0.704285 | − | 0.709917i | \(-0.251268\pi\) | ||||
0.704285 | + | 0.709917i | \(0.251268\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.3070 | 1.01717 | 0.508587 | − | 0.861011i | \(-0.330168\pi\) | ||||
0.508587 | + | 0.861011i | \(0.330168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.77524 | 0.151495 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.88989 | 0.356166 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.3264 | −1.13306 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 70.5568 | 2.81777 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.9859 | −0.597525 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.6669 | 1.30045 | 0.650225 | − | 0.759742i | \(-0.274675\pi\) | ||||
0.650225 | + | 0.759742i | \(0.274675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −54.0119 | −2.14678 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.2924 | −0.686227 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.4847 | −0.494663 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −79.7429 | −3.15458 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.6682 | 1.13233 | 0.566163 | − | 0.824294i | \(-0.308427\pi\) | ||||
0.566163 | + | 0.824294i | \(0.308427\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.4939 | 1.79410 | 0.897052 | − | 0.441924i | \(-0.145704\pi\) | ||||
0.897052 | + | 0.441924i | \(0.145704\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −65.7077 | −2.58724 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.9384 | −0.823172 | −0.411586 | − | 0.911371i | \(-0.635025\pi\) | ||||
−0.411586 | + | 0.911371i | \(0.635025\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −60.1844 | −2.36245 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.68190 | 0.340270 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.8939 | 1.40464 | 0.702319 | − | 0.711862i | \(-0.252148\pi\) | ||||
0.702319 | + | 0.711862i | \(0.252148\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −42.4725 | −1.65954 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −60.6519 | −2.36626 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.77565 | −0.186033 | −0.0930165 | − | 0.995665i | \(-0.529651\pi\) | ||||
−0.0930165 | + | 0.995665i | \(0.529651\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.8545 | 1.78353 | 0.891766 | − | 0.452496i | \(-0.149466\pi\) | ||||
0.891766 | + | 0.452496i | \(0.149466\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.1763 | −0.395214 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −40.4898 | −1.57013 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.640298 | 0.0247924 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.5657 | 1.10441 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 61.9958 | 2.39332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.53461 | 0.290438 | 0.145219 | − | 0.989400i | \(-0.453611\pi\) | ||||
0.145219 | + | 0.989400i | \(0.453611\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.8226 | −0.455053 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.974883 | −0.0374678 | −0.0187339 | − | 0.999825i | \(-0.505964\pi\) | ||||
−0.0187339 | + | 0.999825i | \(0.505964\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.2037 | −1.38937 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 86.1276 | 3.30042 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.2762 | 0.814111 | 0.407056 | − | 0.913403i | \(-0.366555\pi\) | ||||
0.407056 | + | 0.913403i | \(0.366555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.27338 | 0.163277 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −47.0854 | −1.79642 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.25567 | −0.276419 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.1922 | 1.41486 | 0.707429 | − | 0.706784i | \(-0.249855\pi\) | ||||
0.707429 | + | 0.706784i | \(0.249855\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −165.007 | −6.26809 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.3348 | 0.543749 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.2971 | 0.844565 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −40.6649 | −1.53809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.74162 | 0.216858 | 0.108429 | − | 0.994104i | \(-0.465418\pi\) | ||||
0.108429 | + | 0.994104i | \(0.465418\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.8643 | −0.937777 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −83.1203 | −3.13049 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.72153 | −0.252789 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.7887 | −0.818293 | −0.409147 | − | 0.912469i | \(-0.634174\pi\) | ||||
−0.409147 | + | 0.912469i | \(0.634174\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −107.268 | −4.02288 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.163875 | −0.00613718 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.1117 | 0.602544 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −41.0314 | −1.53235 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.81695 | 0.291523 | 0.145761 | − | 0.989320i | \(-0.453437\pi\) | ||||
0.145761 | + | 0.989320i | \(0.453437\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.6784 | 1.29149 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.3926 | 0.460884 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00517 | −0.0744702 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.5520 | −0.539703 | −0.269852 | − | 0.962902i | \(-0.586975\pi\) | ||||
−0.269852 | + | 0.962902i | \(0.586975\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 50.7545 | 1.87980 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.7171 | 0.766251 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.2639 | −0.896209 | −0.448105 | − | 0.893981i | \(-0.647901\pi\) | ||||
−0.448105 | + | 0.893981i | \(0.647901\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 77.2561 | 2.84964 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −51.3405 | −1.89115 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.3852 | −1.19131 | −0.595654 | − | 0.803241i | \(-0.703107\pi\) | ||||
−0.595654 | + | 0.803241i | \(0.703107\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.8843 | −0.620262 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.2046 | 1.14479 | 0.572394 | − | 0.819979i | \(-0.306015\pi\) | ||||
0.572394 | + | 0.819979i | \(0.306015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.00202 | −0.256534 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.1171 | 0.662870 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 58.4481 | 2.13565 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.88757 | 0.214841 | 0.107420 | − | 0.994214i | \(-0.465741\pi\) | ||||
0.107420 | + | 0.994214i | \(0.465741\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.5446 | −0.639361 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46.5208 | −1.69306 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.3540 | −1.57573 | −0.787863 | − | 0.615850i | \(-0.788813\pi\) | ||||
−0.787863 | + | 0.615850i | \(0.788813\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.34461 | 0.157699 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.2883 | −0.989199 | −0.494599 | − | 0.869121i | \(-0.664685\pi\) | ||||
−0.494599 | + | 0.869121i | \(0.664685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.3663 | 0.845916 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 45.1432 | 1.63216 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.4022 | 0.520034 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.4898 | −1.20767 | −0.603837 | − | 0.797108i | \(-0.706362\pi\) | ||||
−0.603837 | + | 0.797108i | \(0.706362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 71.7960 | 2.58567 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.4526 | −0.915468 | −0.457734 | − | 0.889089i | \(-0.651339\pi\) | ||||
−0.457734 | + | 0.889089i | \(0.651339\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.513195 | 0.0184345 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 81.1130 | 2.90991 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.9951 | 1.32549 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.5276 | −1.98693 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37.9696 | 1.35692 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.0188 | −1.42833 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.1253 | −1.57290 | −0.786448 | − | 0.617656i | \(-0.788082\pi\) | ||||
−0.786448 | + | 0.617656i | \(0.788082\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −97.2593 | −3.46252 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.1751 | 2.24625 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.8357 | −0.526831 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 44.8985 | 1.59238 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.71322 | −0.0961071 | −0.0480535 | − | 0.998845i | \(-0.515302\pi\) | ||||
−0.0480535 | + | 0.998845i | \(0.515302\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.2072 | 0.927144 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.4452 | −0.581061 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −42.2339 | −1.49040 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.49320 | −0.0878739 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.0693 | −0.812078 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.0664 | −0.670339 | −0.335170 | − | 0.942158i | \(-0.608794\pi\) | ||||
−0.335170 | + | 0.942158i | \(0.608794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.04639 | −0.106973 | −0.0534865 | − | 0.998569i | \(-0.517033\pi\) | ||||
−0.0534865 | + | 0.998569i | \(0.517033\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 46.0628 | 1.61549 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.7730 | −0.832730 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.3736 | 1.20258 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 39.4864 | 1.37977 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.5826 | 0.823040 | 0.411520 | − | 0.911401i | \(-0.364998\pi\) | ||||
0.411520 | + | 0.911401i | \(0.364998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.0761 | −1.74554 | −0.872772 | − | 0.488128i | \(-0.837680\pi\) | ||||
−0.872772 | + | 0.488128i | \(0.837680\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.6057 | −0.473689 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.20587 | 0.215799 | 0.107900 | − | 0.994162i | \(-0.465587\pi\) | ||||
0.107900 | + | 0.994162i | \(0.465587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.3173 | 0.914039 | 0.457019 | − | 0.889457i | \(-0.348917\pi\) | ||||
0.457019 | + | 0.889457i | \(0.348917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34.0758 | 1.18208 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.3583 | −0.843964 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.0094 | −1.10773 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.71778 | −0.335896 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.8788 | 0.927960 | 0.463980 | − | 0.885846i | \(-0.346421\pi\) | ||||
0.463980 | + | 0.885846i | \(0.346421\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.5602 | −0.777938 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.93356 | 0.307688 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.4260 | 0.943484 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −69.7286 | −2.39590 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −77.9720 | −2.67599 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.53105 | −0.0524837 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.6574 | 0.604576 | 0.302288 | − | 0.953217i | \(-0.402250\pi\) | ||||
0.302288 | + | 0.953217i | \(0.402250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 74.9010 | 2.56156 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.3209 | −0.420875 | −0.210437 | − | 0.977607i | \(-0.567489\pi\) | ||||
−0.210437 | + | 0.977607i | \(0.567489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.9895 | −0.954990 | −0.477495 | − | 0.878635i | \(-0.658455\pi\) | ||||
−0.477495 | + | 0.878635i | \(0.658455\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −120.686 | −4.11298 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.7895 | 1.42253 | 0.711265 | − | 0.702924i | \(-0.248123\pi\) | ||||
0.711265 | + | 0.702924i | \(0.248123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.03093 | −0.0350528 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.4843 | 1.20511 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −74.6946 | −2.53384 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.2859 | 0.416290 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 66.9722 | 2.26667 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.5985 | −1.40629 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.7739 | 0.363809 | 0.181905 | − | 0.983316i | \(-0.441774\pi\) | ||||
0.181905 | + | 0.983316i | \(0.441774\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 100.029 | 3.37390 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6210 | 0.458904 | 0.229452 | − | 0.973320i | \(-0.426307\pi\) | ||||
0.229452 | + | 0.973320i | \(0.426307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.70995 | −0.0911969 | −0.0455985 | − | 0.998960i | \(-0.514519\pi\) | ||||
−0.0455985 | + | 0.998960i | \(0.514519\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −89.1217 | −2.99579 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.4039 | 0.483636 | 0.241818 | − | 0.970322i | \(-0.422256\pi\) | ||||
0.241818 | + | 0.970322i | \(0.422256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.5105 | −0.989750 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 137.088 | 4.59262 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43.4827 | 1.45509 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.641453 | 0.0214414 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.03967 | −0.0347136 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.64818 | −0.0549698 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.1561 | −0.471609 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −112.134 | −3.73159 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 40.0221 | 1.33038 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6036 | 0.717335 | 0.358667 | − | 0.933465i | \(-0.383231\pi\) | ||||
0.358667 | + | 0.933465i | \(0.383231\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.4340 | 0.412409 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.7033 | −1.61361 | −0.806806 | − | 0.590816i | \(-0.798806\pi\) | ||||
−0.806806 | + | 0.590816i | \(0.798806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.6155 | 0.417513 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 91.8040 | 3.03495 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −72.4819 | −2.39356 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.9195 | −1.74565 | −0.872826 | − | 0.488031i | \(-0.837715\pi\) | ||||
−0.872826 | + | 0.488031i | \(0.837715\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −69.8715 | −2.30234 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.2878 | 0.437374 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.79467 | 0.157648 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −64.1506 | −2.10698 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.6654 | 0.940482 | 0.470241 | − | 0.882538i | \(-0.344167\pi\) | ||||
0.470241 | + | 0.882538i | \(0.344167\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.4149 | −1.32455 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 52.4161 | 1.71603 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.4347 | 1.02802 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.3214 | 1.61126 | 0.805630 | − | 0.592419i | \(-0.201827\pi\) | ||||
0.805630 | + | 0.592419i | \(0.201827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.8491 | −1.59413 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.8399 | −0.711961 | −0.355981 | − | 0.934493i | \(-0.615853\pi\) | ||||
−0.355981 | + | 0.934493i | \(0.615853\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.27801 | 0.0741824 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −147.847 | −4.80945 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.2937 | −1.73181 | −0.865906 | − | 0.500208i | \(-0.833257\pi\) | ||||
−0.865906 | + | 0.500208i | \(0.833257\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.1066 | 0.328075 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −70.9192 | −2.29971 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.36995 | 0.271129 | 0.135565 | − | 0.990769i | \(-0.456715\pi\) | ||||
0.135565 | + | 0.990769i | \(0.456715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.10860 | 0.262388 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 43.6960 | 1.41249 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.29278 | 0.235496 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5782 | −0.986393 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −108.122 | −3.48417 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 56.1296 | 1.80688 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.0798 | 0.870827 | 0.435414 | − | 0.900230i | \(-0.356602\pi\) | ||||
0.435414 | + | 0.900230i | \(0.356602\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.9421 | −1.05825 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.6669 | 1.33715 | 0.668577 | − | 0.743643i | \(-0.266904\pi\) | ||||
0.668577 | + | 0.743643i | \(0.266904\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.4632 | 0.784253 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.25586 | 0.104271 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.48703 | −0.303517 | −0.151758 | − | 0.988418i | \(-0.548494\pi\) | ||||
−0.151758 | + | 0.988418i | \(0.548494\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.4513 | −0.365985 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43.2246 | −1.38006 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.8921 | 1.08099 | 0.540495 | − | 0.841347i | \(-0.318237\pi\) | ||||
0.540495 | + | 0.841347i | \(0.318237\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.4680 | −1.22569 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −141.850 | −4.51513 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.11659 | 0.0673037 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.6630 | −0.497553 | −0.248776 | − | 0.968561i | \(-0.580028\pi\) | ||||
−0.248776 | + | 0.968561i | \(0.580028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 103.082 | 3.27121 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.3909 | −0.487925 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.9055 | 1.45384 | 0.726920 | − | 0.686722i | \(-0.240951\pi\) | ||||
0.726920 | + | 0.686722i | \(0.240951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −90.7910 | −2.87250 |
(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 | 4024.2.a.f.1.1 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.y.1.33 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.f.1.1 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.y.1.33 | 33 | 4.3 | odd | 2 |