Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9036,2,Mod(1,9036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9036, 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("9036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9036.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: | \(72.1528232664\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 8x^{3} - 17x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.18229\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.66714 | 0.745569 | 0.372785 | − | 0.927918i | \(-0.378403\pi\) | ||||
0.372785 | + | 0.927918i | \(0.378403\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.81734 | −0.686890 | −0.343445 | − | 0.939173i | \(-0.611594\pi\) | ||||
−0.343445 | + | 0.939173i | \(0.611594\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.97535 | 1.19861 | 0.599307 | − | 0.800519i | \(-0.295443\pi\) | ||||
0.599307 | + | 0.800519i | \(0.295443\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.88440 | −1.35469 | −0.677345 | − | 0.735666i | \(-0.736869\pi\) | ||||
−0.677345 | + | 0.735666i | \(0.736869\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.09643 | 0.750994 | 0.375497 | − | 0.926824i | \(-0.377472\pi\) | ||||
0.375497 | + | 0.926824i | \(0.377472\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.71976 | −0.853370 | −0.426685 | − | 0.904400i | \(-0.640319\pi\) | ||||
−0.426685 | + | 0.904400i | \(0.640319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.52167 | −0.525804 | −0.262902 | − | 0.964823i | \(-0.584680\pi\) | ||||
−0.262902 | + | 0.964823i | \(0.584680\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.22063 | −0.444126 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.16232 | −0.772923 | −0.386461 | − | 0.922306i | \(-0.626303\pi\) | ||||
−0.386461 | + | 0.922306i | \(0.626303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.17959 | 0.750677 | 0.375338 | − | 0.926888i | \(-0.377527\pi\) | ||||
0.375338 | + | 0.926888i | \(0.377527\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.02977 | −0.512124 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.0695 | 1.81981 | 0.909903 | − | 0.414820i | \(-0.136156\pi\) | ||||
0.909903 | + | 0.414820i | \(0.136156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0987896 | 0.0154283 | 0.00771417 | − | 0.999970i | \(-0.497544\pi\) | ||||
0.00771417 | + | 0.999970i | \(0.497544\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.04789 | −0.312301 | −0.156150 | − | 0.987733i | \(-0.549908\pi\) | ||||
−0.156150 | + | 0.987733i | \(0.549908\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.469170 | −0.0684355 | −0.0342177 | − | 0.999414i | \(-0.510894\pi\) | ||||
−0.0342177 | + | 0.999414i | \(0.510894\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.69728 | −0.528183 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.85883 | 0.530050 | 0.265025 | − | 0.964241i | \(-0.414620\pi\) | ||||
0.265025 | + | 0.964241i | \(0.414620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.62749 | 0.893650 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.09924 | −0.924242 | −0.462121 | − | 0.886817i | \(-0.652911\pi\) | ||||
−0.462121 | + | 0.886817i | \(0.652911\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.640361 | −0.0819898 | −0.0409949 | − | 0.999159i | \(-0.513053\pi\) | ||||
−0.0409949 | + | 0.999159i | \(0.513053\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.14300 | −1.01002 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.93468 | 0.236359 | 0.118180 | − | 0.992992i | \(-0.462294\pi\) | ||||
0.118180 | + | 0.992992i | \(0.462294\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.867080 | −0.102903 | −0.0514517 | − | 0.998675i | \(-0.516385\pi\) | ||||
−0.0514517 | + | 0.998675i | \(0.516385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.51437 | −0.762450 | −0.381225 | − | 0.924482i | \(-0.624498\pi\) | ||||
−0.381225 | + | 0.924482i | \(0.624498\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.22456 | −0.823315 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.82946 | −1.10590 | −0.552950 | − | 0.833214i | \(-0.686498\pi\) | ||||
−0.552950 | + | 0.833214i | \(0.686498\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.6647 | −1.39013 | −0.695064 | − | 0.718948i | \(-0.744624\pi\) | ||||
−0.695064 | + | 0.718948i | \(0.744624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.16219 | 0.559918 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.81448 | 1.04033 | 0.520166 | − | 0.854065i | \(-0.325870\pi\) | ||||
0.520166 | + | 0.854065i | \(0.325870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.87662 | 0.930522 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.20137 | −0.636247 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.98395 | −0.201439 | −0.100720 | − | 0.994915i | \(-0.532115\pi\) | ||||
−0.100720 | + | 0.994915i | \(0.532115\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.6322 | −1.15745 | −0.578724 | − | 0.815523i | \(-0.696449\pi\) | ||||
−0.578724 | + | 0.815523i | \(0.696449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.01880 | 0.790116 | 0.395058 | − | 0.918656i | \(-0.370725\pi\) | ||||
0.395058 | + | 0.918656i | \(0.370725\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9472 | 1.34833 | 0.674165 | − | 0.738580i | \(-0.264504\pi\) | ||||
0.674165 | + | 0.738580i | \(0.264504\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.73637 | −0.741010 | −0.370505 | − | 0.928831i | \(-0.620815\pi\) | ||||
−0.370505 | + | 0.928831i | \(0.620815\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.22437 | 0.491468 | 0.245734 | − | 0.969337i | \(-0.420971\pi\) | ||||
0.245734 | + | 0.969337i | \(0.420971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.20398 | −0.392023 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.62726 | −0.515850 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.80343 | 0.436676 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0378 | −1.07670 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.3142 | −1.53639 | −0.768195 | − | 0.640215i | \(-0.778845\pi\) | ||||
−0.768195 | + | 0.640215i | \(0.778845\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.297840 | −0.0260224 | −0.0130112 | − | 0.999915i | \(-0.504142\pi\) | ||||
−0.0130112 | + | 0.999915i | \(0.504142\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.76006 | 0.586171 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.9689 | −0.937133 | −0.468567 | − | 0.883428i | \(-0.655229\pi\) | ||||
−0.468567 | + | 0.883428i | \(0.655229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.5994 | −1.91685 | −0.958427 | − | 0.285338i | \(-0.907894\pi\) | ||||
−0.958427 | + | 0.285338i | \(0.907894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.4172 | −1.62375 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.93918 | −0.576268 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.53848 | −0.699499 | −0.349750 | − | 0.936843i | \(-0.613733\pi\) | ||||
−0.349750 | + | 0.936843i | \(0.613733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5305 | −0.938341 | −0.469170 | − | 0.883108i | \(-0.655447\pi\) | ||||
−0.469170 | + | 0.883108i | \(0.655447\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.96798 | 0.559682 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.177058 | 0.0141308 | 0.00706539 | − | 0.999975i | \(-0.497751\pi\) | ||||
0.00706539 | + | 0.999975i | \(0.497751\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.58272 | 0.361169 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.7654 | −1.07819 | −0.539095 | − | 0.842245i | \(-0.681234\pi\) | ||||
−0.539095 | + | 0.842245i | \(0.681234\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.58570 | 0.741764 | 0.370882 | − | 0.928680i | \(-0.379055\pi\) | ||||
0.370882 | + | 0.928680i | \(0.379055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8574 | 0.835184 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.27316 | 0.552968 | 0.276484 | − | 0.961019i | \(-0.410831\pi\) | ||||
0.276484 | + | 0.961019i | \(0.410831\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.03564 | 0.305066 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.2832 | 1.29180 | 0.645902 | − | 0.763420i | \(-0.276481\pi\) | ||||
0.645902 | + | 0.763420i | \(0.276481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8478 | 1.47528 | 0.737639 | − | 0.675195i | \(-0.235941\pi\) | ||||
0.737639 | + | 0.675195i | \(0.235941\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.4544 | 1.35679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.3094 | 0.900152 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.3899 | 1.69244 | 0.846218 | − | 0.532837i | \(-0.178874\pi\) | ||||
0.846218 | + | 0.532837i | \(0.178874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.5992 | −0.906909 | −0.453454 | − | 0.891280i | \(-0.649808\pi\) | ||||
−0.453454 | + | 0.891280i | \(0.649808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.28151 | −0.162551 | −0.0812753 | − | 0.996692i | \(-0.525899\pi\) | ||||
−0.0812753 | + | 0.996692i | \(0.525899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.10342 | −0.149108 | −0.0745538 | − | 0.997217i | \(-0.523753\pi\) | ||||
−0.0745538 | + | 0.997217i | \(0.523753\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.56434 | 0.530913 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.164696 | 0.0115029 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.7873 | −1.02286 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.501747 | 0.0345417 | 0.0172709 | − | 0.999851i | \(-0.494502\pi\) | ||||
0.0172709 | + | 0.999851i | \(0.494502\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.41413 | −0.232842 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.59573 | −0.515632 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.1242 | −1.01736 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.964032 | 0.0645563 | 0.0322782 | − | 0.999479i | \(-0.489724\pi\) | ||||
0.0322782 | + | 0.999479i | \(0.489724\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.6598 | −1.37124 | −0.685619 | − | 0.727961i | \(-0.740468\pi\) | ||||
−0.685619 | + | 0.727961i | \(0.740468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.37963 | 0.487660 | 0.243830 | − | 0.969818i | \(-0.421596\pi\) | ||||
0.243830 | + | 0.969818i | \(0.421596\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.1272 | −1.38409 | −0.692045 | − | 0.721854i | \(-0.743290\pi\) | ||||
−0.692045 | + | 0.721854i | \(0.743290\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.782174 | −0.0510234 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.35509 | 0.0876538 | 0.0438269 | − | 0.999039i | \(-0.486045\pi\) | ||||
0.0438269 | + | 0.999039i | \(0.486045\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.2538 | 1.69115 | 0.845577 | − | 0.533854i | \(-0.179257\pi\) | ||||
0.845577 | + | 0.533854i | \(0.179257\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.16390 | −0.393797 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.1688 | 1.15605 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.0245 | −0.630236 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.74279 | −0.545360 | −0.272680 | − | 0.962105i | \(-0.587910\pi\) | ||||
−0.272680 | + | 0.962105i | \(0.587910\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.1169 | −1.25001 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.4251 | −1.19780 | −0.598901 | − | 0.800823i | \(-0.704396\pi\) | ||||
−0.598901 | + | 0.800823i | \(0.704396\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.43322 | 0.395189 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.73284 | −0.471480 | −0.235740 | − | 0.971816i | \(-0.575751\pi\) | ||||
−0.235740 | + | 0.971816i | \(0.575751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.7030 | −1.43985 | −0.719927 | − | 0.694050i | \(-0.755825\pi\) | ||||
−0.719927 | + | 0.694050i | \(0.755825\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.82779 | −0.532336 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.75856 | 0.105662 | 0.0528308 | − | 0.998603i | \(-0.483176\pi\) | ||||
0.0528308 | + | 0.998603i | \(0.483176\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0290 | −1.19483 | −0.597414 | − | 0.801933i | \(-0.703805\pi\) | ||||
−0.597414 | + | 0.801933i | \(0.703805\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.84251 | 0.347301 | 0.173651 | − | 0.984807i | \(-0.444444\pi\) | ||||
0.173651 | + | 0.984807i | \(0.444444\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.179534 | −0.0105976 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.41213 | −0.436008 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.05347 | 0.178385 | 0.0891927 | − | 0.996014i | \(-0.471571\pi\) | ||||
0.0891927 | + | 0.996014i | \(0.471571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.8354 | −0.689087 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.3168 | 0.712301 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.72172 | 0.214516 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.06757 | −0.0611291 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.0535 | −0.802073 | −0.401037 | − | 0.916062i | \(-0.631350\pi\) | ||||
−0.401037 | + | 0.916062i | \(0.631350\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.9822 | 1.35990 | 0.679952 | − | 0.733256i | \(-0.262000\pi\) | ||||
0.679952 | + | 0.733256i | \(0.262000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.3953 | 1.54847 | 0.774237 | − | 0.632896i | \(-0.218134\pi\) | ||||
0.774237 | + | 0.632896i | \(0.218134\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.5013 | 0.702143 | 0.351072 | − | 0.936349i | \(-0.385817\pi\) | ||||
0.351072 | + | 0.936349i | \(0.385817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.5467 | −0.926436 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.5180 | −0.640876 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.8465 | 0.601653 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.852641 | 0.0470076 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.6129 | 1.40782 | 0.703908 | − | 0.710292i | \(-0.251437\pi\) | ||||
0.703908 | + | 0.710292i | \(0.251437\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.22540 | 0.176222 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.84964 | −0.536544 | −0.268272 | − | 0.963343i | \(-0.586453\pi\) | ||||
−0.268272 | + | 0.963343i | \(0.586453\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.6154 | 0.899772 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4406 | 1.04969 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.11780 | 0.328421 | 0.164210 | − | 0.986425i | \(-0.447492\pi\) | ||||
0.164210 | + | 0.986425i | \(0.447492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.79907 | −0.524532 | −0.262266 | − | 0.964996i | \(-0.584470\pi\) | ||||
−0.262266 | + | 0.964996i | \(0.584470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.86642 | 0.365463 | 0.182731 | − | 0.983163i | \(-0.441506\pi\) | ||||
0.182731 | + | 0.983163i | \(0.441506\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.44555 | −0.0767216 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.4483 | −1.81811 | −0.909055 | − | 0.416676i | \(-0.863195\pi\) | ||||
−0.909055 | + | 0.416676i | \(0.863195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.16342 | −0.271759 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.8604 | −0.568459 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.8538 | −1.76716 | −0.883578 | − | 0.468285i | \(-0.844872\pi\) | ||||
−0.883578 | + | 0.468285i | \(0.844872\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.01279 | −0.364086 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.7580 | −1.90325 | −0.951627 | − | 0.307254i | \(-0.900590\pi\) | ||||
−0.951627 | + | 0.307254i | \(0.900590\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.3304 | 1.04707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6407 | −1.11161 | −0.555803 | − | 0.831314i | \(-0.687589\pi\) | ||||
−0.555803 | + | 0.831314i | \(0.687589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.3327 | −1.24334 | −0.621671 | − | 0.783279i | \(-0.713546\pi\) | ||||
−0.621671 | + | 0.783279i | \(0.713546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0444 | −0.613839 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.6714 | −1.30159 | −0.650797 | − | 0.759252i | \(-0.725565\pi\) | ||||
−0.650797 | + | 0.759252i | \(0.725565\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.80816 | −0.394876 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.3871 | −0.824526 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.8682 | 0.946970 | 0.473485 | − | 0.880802i | \(-0.342996\pi\) | ||||
0.473485 | + | 0.880802i | \(0.342996\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.851616 | 0.0425277 | 0.0212638 | − | 0.999774i | \(-0.493231\pi\) | ||||
0.0212638 | + | 0.999774i | \(0.493231\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.4148 | −1.01693 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.0050 | 2.18125 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.86899 | 0.240756 | 0.120378 | − | 0.992728i | \(-0.461589\pi\) | ||||
0.120378 | + | 0.992728i | \(0.461589\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.9017 | 0.634852 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.1138 | −1.03644 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.3339 | −0.504843 | −0.252422 | − | 0.967617i | \(-0.581227\pi\) | ||||
−0.252422 | + | 0.967617i | \(0.581227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.5337 | 1.19570 | 0.597849 | − | 0.801608i | \(-0.296022\pi\) | ||||
0.597849 | + | 0.801608i | \(0.296022\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.87602 | −0.333536 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.16375 | 0.0563179 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.65100 | −0.0795257 | −0.0397628 | − | 0.999209i | \(-0.512660\pi\) | ||||
−0.0397628 | + | 0.999209i | \(0.512660\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.0172 | 0.913907 | 0.456953 | − | 0.889491i | \(-0.348941\pi\) | ||||
0.456953 | + | 0.889491i | \(0.348941\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.37998 | 0.448705 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.7908 | −1.51729 | −0.758645 | − | 0.651504i | \(-0.774138\pi\) | ||||
−0.758645 | + | 0.651504i | \(0.774138\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.00408 | −0.332774 | −0.166387 | − | 0.986061i | \(-0.553210\pi\) | ||||
−0.166387 | + | 0.986061i | \(0.553210\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.3621 | 0.775640 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.4671 | 1.86257 | 0.931283 | − | 0.364295i | \(-0.118690\pi\) | ||||
0.931283 | + | 0.364295i | \(0.118690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.392723 | 0.0184926 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.7986 | 0.693769 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.8500 | −0.694654 | −0.347327 | − | 0.937744i | \(-0.612911\pi\) | ||||
−0.347327 | + | 0.937744i | \(0.612911\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.5063 | 1.09480 | 0.547399 | − | 0.836872i | \(-0.315618\pi\) | ||||
0.547399 | + | 0.836872i | \(0.315618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.59484 | −0.352962 | −0.176481 | − | 0.984304i | \(-0.556471\pi\) | ||||
−0.176481 | + | 0.984304i | \(0.556471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.26788 | −0.0586707 | −0.0293354 | − | 0.999570i | \(-0.509339\pi\) | ||||
−0.0293354 | + | 0.999570i | \(0.509339\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.51597 | −0.162353 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.14110 | −0.374328 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.26020 | 0.379004 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.4831 | 0.524674 | 0.262337 | − | 0.964976i | \(-0.415507\pi\) | ||||
0.262337 | + | 0.964976i | \(0.415507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −54.0677 | −2.46527 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.30752 | −0.150187 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5144 | −0.838968 | −0.419484 | − | 0.907763i | \(-0.637789\pi\) | ||||
−0.419484 | + | 0.907763i | \(0.637789\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.3486 | −0.512155 | −0.256077 | − | 0.966656i | \(-0.582430\pi\) | ||||
−0.256077 | + | 0.966656i | \(0.582430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.8883 | −0.580461 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.57578 | 0.0706833 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.8934 | −0.532423 | −0.266212 | − | 0.963915i | \(-0.585772\pi\) | ||||
−0.266212 | + | 0.963915i | \(0.585772\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.9893 | 1.20339 | 0.601697 | − | 0.798725i | \(-0.294492\pi\) | ||||
0.601697 | + | 0.798725i | \(0.294492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.3926 | −0.862958 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.334531 | −0.0148278 | −0.00741391 | − | 0.999973i | \(-0.502360\pi\) | ||||
−0.00741391 | + | 0.999973i | \(0.502360\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.8388 | 0.523719 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.3685 | 0.589086 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.86512 | −0.0820277 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.3238 | −0.978023 | −0.489012 | − | 0.872277i | \(-0.662642\pi\) | ||||
−0.489012 | + | 0.872277i | \(0.662642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.1603 | −0.619188 | −0.309594 | − | 0.950869i | \(-0.600193\pi\) | ||||
−0.309594 | + | 0.950869i | \(0.600193\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.9418 | 0.563754 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6412 | −0.723530 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.482528 | −0.0209006 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.2521 | 1.00527 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.6980 | −0.633087 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.9931 | 0.816577 | 0.408289 | − | 0.912853i | \(-0.366126\pi\) | ||||
0.408289 | + | 0.912853i | \(0.366126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.8976 | −0.552474 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.9596 | −1.28098 | −0.640490 | − | 0.767967i | \(-0.721269\pi\) | ||||
−0.640490 | + | 0.767967i | \(0.721269\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.4828 | 0.659589 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.8635 | 0.759632 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.9749 | 1.65142 | 0.825709 | − | 0.564096i | \(-0.190775\pi\) | ||||
0.825709 | + | 0.564096i | \(0.190775\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0027 | 0.423071 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.0149 | −0.422080 | −0.211040 | − | 0.977477i | \(-0.567685\pi\) | ||||
−0.211040 | + | 0.977477i | \(0.567685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.70978 | 0.366423 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.81832 | −0.243917 | −0.121958 | − | 0.992535i | \(-0.538917\pi\) | ||||
−0.121958 | + | 0.992535i | \(0.538917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0941 | −0.673516 | −0.336758 | − | 0.941591i | \(-0.609330\pi\) | ||||
−0.336758 | + | 0.941591i | \(0.609330\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.59969 | 0.233523 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.178763 | 0.00744199 | 0.00372100 | − | 0.999993i | \(-0.498816\pi\) | ||||
0.00372100 | + | 0.999993i | \(0.498816\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.0160 | 0.954864 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.3402 | 0.635326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.2001 | −1.04012 | −0.520060 | − | 0.854130i | \(-0.674090\pi\) | ||||
−0.520060 | + | 0.854130i | \(0.674090\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.5471 | −0.640605 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.9359 | 0.777605 | 0.388802 | − | 0.921321i | \(-0.372889\pi\) | ||||
0.388802 | + | 0.921321i | \(0.372889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.38145 | −0.384602 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.8791 | 0.853097 | 0.426549 | − | 0.904465i | \(-0.359729\pi\) | ||||
0.426549 | + | 0.904465i | \(0.359729\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7344 | −0.764193 | −0.382097 | − | 0.924122i | \(-0.624798\pi\) | ||||
−0.382097 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.00801 | 0.325572 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1694 | 0.493943 | 0.246971 | − | 0.969023i | \(-0.420565\pi\) | ||||
0.246971 | + | 0.969023i | \(0.420565\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.29162 | 0.0927089 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.7814 | 1.76832 | 0.884158 | − | 0.467188i | \(-0.154733\pi\) | ||||
0.884158 | + | 0.467188i | \(0.154733\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.6870 | 1.91980 | 0.959902 | − | 0.280335i | \(-0.0904454\pi\) | ||||
0.959902 | + | 0.280335i | \(0.0904454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.3980 | −1.02083 | −0.510416 | − | 0.859927i | \(-0.670509\pi\) | ||||
−0.510416 | + | 0.859927i | \(0.670509\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.8362 | −0.714593 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.96565 | −0.358626 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.2758 | 1.36666 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.7365 | 0.467221 | 0.233611 | − | 0.972330i | \(-0.424946\pi\) | ||||
0.233611 | + | 0.972330i | \(0.424946\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.8653 | −1.14549 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0590 | 0.715524 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.1285 | −1.30850 | −0.654250 | − | 0.756279i | \(-0.727015\pi\) | ||||
−0.654250 | + | 0.756279i | \(0.727015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.01084 | 0.158172 | 0.0790861 | − | 0.996868i | \(-0.474800\pi\) | ||||
0.0790861 | + | 0.996868i | \(0.474800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.5470 | −0.571903 | −0.285952 | − | 0.958244i | \(-0.592310\pi\) | ||||
−0.285952 | + | 0.958244i | \(0.592310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.2220 | −1.10781 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.2618 | −0.910306 | −0.455153 | − | 0.890413i | \(-0.650415\pi\) | ||||
−0.455153 | + | 0.890413i | \(0.650415\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.496542 | −0.0194015 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.0497 | −0.936843 | −0.468422 | − | 0.883505i | \(-0.655177\pi\) | ||||
−0.468422 | + | 0.883505i | \(0.655177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.5895 | 0.917526 | 0.458763 | − | 0.888559i | \(-0.348293\pi\) | ||||
0.458763 | + | 0.888559i | \(0.348293\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.2700 | 0.437031 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.4960 | 0.406406 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.54566 | −0.0982741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.6895 | 1.76120 | 0.880600 | − | 0.473861i | \(-0.157140\pi\) | ||||
0.880600 | + | 0.473861i | \(0.157140\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.6141 | −1.17660 | −0.588298 | − | 0.808644i | \(-0.700202\pi\) | ||||
−0.588298 | + | 0.808644i | \(0.700202\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.60550 | 0.138367 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.23237 | −0.200211 | −0.100106 | − | 0.994977i | \(-0.531918\pi\) | ||||
−0.100106 | + | 0.994977i | \(0.531918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.2867 | −0.698698 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.8481 | −0.718054 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1535 | −0.956884 | −0.478442 | − | 0.878119i | \(-0.658798\pi\) | ||||
−0.478442 | + | 0.878119i | \(0.658798\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −37.6764 | −1.42915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.305895 | 0.0115866 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.9520 | 1.24458 | 0.622291 | − | 0.782786i | \(-0.286202\pi\) | ||||
0.622291 | + | 0.782786i | \(0.286202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.1757 | −1.55297 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.1397 | 0.795039 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.6164 | 1.48782 | 0.743912 | − | 0.668278i | \(-0.232968\pi\) | ||||
0.743912 | + | 0.668278i | \(0.232968\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.5395 | −0.394709 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32.3713 | −1.21062 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.58402 | −0.320130 | −0.160065 | − | 0.987106i | \(-0.551170\pi\) | ||||
−0.160065 | + | 0.987106i | \(0.551170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.5729 | −0.542722 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.24297 | 0.343275 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.3751 | 0.458968 | 0.229484 | − | 0.973312i | \(-0.426296\pi\) | ||||
0.229484 | + | 0.973312i | \(0.426296\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.34116 | −0.234536 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.5222 | 1.01656 | 0.508278 | − | 0.861193i | \(-0.330282\pi\) | ||||
0.508278 | + | 0.861193i | \(0.330282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.69105 | 0.283303 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.1948 | −1.25788 | −0.628938 | − | 0.777455i | \(-0.716510\pi\) | ||||
−0.628938 | + | 0.777455i | \(0.716510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.7219 | 1.75075 | 0.875373 | − | 0.483448i | \(-0.160616\pi\) | ||||
0.875373 | + | 0.483448i | \(0.160616\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.2349 | −0.521525 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.3469 | −0.926154 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.0917 | −0.842627 | −0.421313 | − | 0.906915i | \(-0.638431\pi\) | ||||
−0.421313 | + | 0.906915i | \(0.638431\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.2230 | −0.699598 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.4049 | −1.46854 | −0.734271 | − | 0.678856i | \(-0.762476\pi\) | ||||
−0.734271 | + | 0.678856i | \(0.762476\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.33788 | 0.229748 | 0.114874 | − | 0.993380i | \(-0.463354\pi\) | ||||
0.114874 | + | 0.993380i | \(0.463354\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0596 | 0.508992 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.6755 | 1.25206 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.8100 | −0.858612 | −0.429306 | − | 0.903159i | \(-0.641242\pi\) | ||||
−0.429306 | + | 0.903159i | \(0.641242\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.96887 | −0.106783 | −0.0533914 | − | 0.998574i | \(-0.517003\pi\) | ||||
−0.0533914 | + | 0.998574i | \(0.517003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.28133 | −0.333395 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.367473 | −0.0131661 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.44695 | −0.123341 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.295182 | 0.0105355 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7084 | 0.453004 | 0.226502 | − | 0.974011i | \(-0.427271\pi\) | ||||
0.226502 | + | 0.974011i | \(0.427271\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.49446 | −0.337584 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.12778 | 0.111071 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.5534 | 1.40105 | 0.700526 | − | 0.713627i | \(-0.252949\pi\) | ||||
0.700526 | + | 0.713627i | \(0.252949\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45275 | −0.0513947 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.8969 | −0.913883 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.64006 | 0.269277 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.6668 | −1.11335 | −0.556673 | − | 0.830732i | \(-0.687922\pi\) | ||||
−0.556673 | + | 0.830732i | \(0.687922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.5085 | 1.07130 | 0.535650 | − | 0.844440i | \(-0.320067\pi\) | ||||
0.535650 | + | 0.844440i | \(0.320067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.9489 | −0.803865 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.61766 | 0.266508 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.76561 | 0.0616202 | 0.0308101 | − | 0.999525i | \(-0.490191\pi\) | ||||
0.0308101 | + | 0.999525i | \(0.490191\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.9524 | −0.730356 | −0.365178 | − | 0.930938i | \(-0.618992\pi\) | ||||
−0.365178 | + | 0.930938i | \(0.618992\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.7468 | 0.686663 | 0.343331 | − | 0.939214i | \(-0.388445\pi\) | ||||
0.343331 | + | 0.939214i | \(0.388445\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.1170 | −0.351379 | −0.175689 | − | 0.984446i | \(-0.556215\pi\) | ||||
−0.175689 | + | 0.984446i | \(0.556215\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.4484 | −0.396662 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.9807 | 0.553036 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.51976 | 0.225087 | 0.112544 | − | 0.993647i | \(-0.464100\pi\) | ||||
0.112544 | + | 0.993647i | \(0.464100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.6751 | −0.402590 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.1008 | 0.622688 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.72946 | −0.299948 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.9135 | −0.956861 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2508 | 0.693375 | 0.346688 | − | 0.937981i | \(-0.387306\pi\) | ||||
0.346688 | + | 0.937981i | \(0.387306\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.2976 | −0.385919 | −0.192960 | − | 0.981207i | \(-0.561809\pi\) | ||||
−0.192960 | + | 0.981207i | \(0.561809\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.6057 | −0.498341 | −0.249171 | − | 0.968460i | \(-0.580158\pi\) | ||||
−0.249171 | + | 0.968460i | \(0.580158\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.5862 | −1.24541 | −0.622704 | − | 0.782457i | \(-0.713966\pi\) | ||||
−0.622704 | + | 0.782457i | \(0.713966\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.1254 | 0.412276 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.0756 | −1.32555 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.44977 | −0.320193 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.8768 | 0.739571 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.6561 | −0.427366 | −0.213683 | − | 0.976903i | \(-0.568546\pi\) | ||||
−0.213683 | + | 0.976903i | \(0.568546\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.7832 | 1.67724 | 0.838619 | − | 0.544719i | \(-0.183364\pi\) | ||||
0.838619 | + | 0.544719i | \(0.183364\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.1957 | −1.58826 | −0.794132 | − | 0.607746i | \(-0.792074\pi\) | ||||
−0.794132 | + | 0.607746i | \(0.792074\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.6299 | 0.424070 | 0.212035 | − | 0.977262i | \(-0.431991\pi\) | ||||
0.212035 | + | 0.977262i | \(0.431991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.4659 | 1.05533 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.74520 | 0.0584008 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.8135 | 0.963130 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.3968 | −0.580215 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.9486 | 0.398065 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.0892 | 1.09992 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.5677 | 0.450510 | 0.225255 | − | 0.974300i | \(-0.427679\pi\) | ||||
0.225255 | + | 0.974300i | \(0.427679\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.1151 | 1.42847 | 0.714233 | − | 0.699908i | \(-0.246776\pi\) | ||||
0.714233 | + | 0.699908i | \(0.246776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.3465 | −1.66623 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.541276 | 0.0178745 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.3464 | 1.56181 | 0.780906 | − | 0.624649i | \(-0.214758\pi\) | ||||
0.780906 | + | 0.624649i | \(0.214758\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.23517 | 0.139402 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.5812 | −0.808224 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.3288 | −0.470111 | −0.235056 | − | 0.971982i | \(-0.575527\pi\) | ||||
−0.235056 | + | 0.971982i | \(0.575527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.7530 | 0.450736 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.5215 | 0.671126 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.34255 | −0.141865 | −0.0709324 | − | 0.997481i | \(-0.522597\pi\) | ||||
−0.0709324 | + | 0.997481i | \(0.522597\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.8718 | −0.810798 | −0.405399 | − | 0.914140i | \(-0.632867\pi\) | ||||
−0.405399 | + | 0.914140i | \(0.632867\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.249114 | −0.00811228 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.0827 | −0.620105 | −0.310053 | − | 0.950719i | \(-0.600347\pi\) | ||||
−0.310053 | + | 0.950719i | \(0.600347\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.8188 | 1.03288 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.9942 | 1.97580 | 0.987899 | − | 0.155102i | \(-0.0495705\pi\) | ||||
0.987899 | + | 0.155102i | \(0.0495705\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.9944 | 1.26183 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.9341 | 0.643707 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5310 | −0.436484 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.0046 | −0.676163 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.1329 | 0.840377 | 0.420188 | − | 0.907437i | \(-0.361964\pi\) | ||||
0.420188 | + | 0.907437i | \(0.361964\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.1801 | −0.936435 | −0.468217 | − | 0.883613i | \(-0.655104\pi\) | ||||
−0.468217 | + | 0.883613i | \(0.655104\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.0707 | 1.31667 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.9495 | −1.56603 | −0.783017 | − | 0.622000i | \(-0.786320\pi\) | ||||
−0.783017 | + | 0.622000i | \(0.786320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 39.0160 | 1.24696 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.2456 | −1.79396 | −0.896979 | − | 0.442074i | \(-0.854243\pi\) | ||||
−0.896979 | + | 0.442074i | \(0.854243\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.80360 | −0.121193 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.16411 | 0.164209 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.10217 | −0.289140 | −0.144570 | − | 0.989495i | \(-0.546180\pi\) | ||||
−0.144570 | + | 0.989495i | \(0.546180\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.50671 | −0.111170 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.1557 | 1.24007 | 0.620037 | − | 0.784573i | \(-0.287118\pi\) | ||||
0.620037 | + | 0.784573i | \(0.287118\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 9036.2.a.i.1.5 | 7 | ||
3.2 | odd | 2 | 1004.2.a.a.1.7 | ✓ | 7 | ||
12.11 | even | 2 | 4016.2.a.g.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.a.1.7 | ✓ | 7 | 3.2 | odd | 2 | ||
4016.2.a.g.1.1 | 7 | 12.11 | even | 2 | |||
9036.2.a.i.1.5 | 7 | 1.1 | even | 1 | trivial |