Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1436.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 11x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.48361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.13555 | 1.18513 | 0.592563 | − | 0.805524i | \(-0.298116\pi\) | ||||
0.592563 | + | 0.805524i | \(0.298116\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.65194 | −0.799589 | −0.399795 | − | 0.916605i | \(-0.630919\pi\) | ||||
−0.399795 | + | 0.916605i | \(0.630919\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.651938 | 0.180815 | 0.0904076 | − | 0.995905i | \(-0.471183\pi\) | ||||
0.0904076 | + | 0.995905i | \(0.471183\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.48361 | −1.08744 | −0.543718 | − | 0.839268i | \(-0.682984\pi\) | ||||
−0.543718 | + | 0.839268i | \(0.682984\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.651938 | −0.149565 | −0.0747825 | − | 0.997200i | \(-0.523826\pi\) | ||||
−0.0747825 | + | 0.997200i | \(0.523826\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.48361 | −0.461195 | −0.230598 | − | 0.973049i | \(-0.574068\pi\) | ||||
−0.230598 | + | 0.973049i | \(0.574068\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.13555 | −0.563161 | −0.281581 | − | 0.959538i | \(-0.590859\pi\) | ||||
−0.281581 | + | 0.959538i | \(0.590859\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.13555 | 0.530005 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.10277 | −1.00329 | −0.501645 | − | 0.865074i | \(-0.667272\pi\) | ||||
−0.501645 | + | 0.865074i | \(0.667272\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.820265 | −0.128104 | −0.0640519 | − | 0.997947i | \(-0.520402\pi\) | ||||
−0.0640519 | + | 0.997947i | \(0.520402\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.696123 | 0.106158 | 0.0530789 | − | 0.998590i | \(-0.483097\pi\) | ||||
0.0530789 | + | 0.998590i | \(0.483097\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.8903 | 1.73437 | 0.867186 | − | 0.497984i | \(-0.165926\pi\) | ||||
0.867186 | + | 0.497984i | \(0.165926\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.83167 | 0.404525 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.45083 | −1.29817 | −0.649086 | − | 0.760715i | \(-0.724848\pi\) | ||||
−0.649086 | + | 0.760715i | \(0.724848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.65194 | −0.357587 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.7547 | −1.66052 | −0.830261 | − | 0.557375i | \(-0.811809\pi\) | ||||
−0.830261 | + | 0.557375i | \(0.811809\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.65194 | 0.339546 | 0.169773 | − | 0.985483i | \(-0.445697\pi\) | ||||
0.169773 | + | 0.985483i | \(0.445697\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.651938 | 0.0808630 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.10277 | −0.745572 | −0.372786 | − | 0.927917i | \(-0.621598\pi\) | ||||
−0.372786 | + | 0.927917i | \(0.621598\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.48361 | −1.00682 | −0.503410 | − | 0.864048i | \(-0.667921\pi\) | ||||
−0.503410 | + | 0.864048i | \(0.667921\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.31528 | 0.739148 | 0.369574 | − | 0.929201i | \(-0.379504\pi\) | ||||
0.369574 | + | 0.929201i | \(0.379504\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.31528 | −0.947615 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.51639 | −0.605502 | −0.302751 | − | 0.953070i | \(-0.597905\pi\) | ||||
−0.302751 | + | 0.953070i | \(0.597905\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.48361 | −0.486316 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.2383 | 1.19126 | 0.595630 | − | 0.803259i | \(-0.296902\pi\) | ||||
0.595630 | + | 0.803259i | \(0.296902\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.04419 | 0.214289 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.651938 | −0.0668875 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.93445 | −0.602552 | −0.301276 | − | 0.953537i | \(-0.597413\pi\) | ||||
−0.301276 | + | 0.953537i | \(0.597413\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.75471 | −0.871126 | −0.435563 | − | 0.900158i | \(-0.643451\pi\) | ||||
−0.435563 | + | 0.900158i | \(0.643451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.66335 | −0.360960 | −0.180480 | − | 0.983579i | \(-0.557765\pi\) | ||||
−0.180480 | + | 0.983579i | \(0.557765\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.24529 | −0.313734 | −0.156867 | − | 0.987620i | \(-0.550139\pi\) | ||||
−0.156867 | + | 0.987620i | \(0.550139\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.61916 | 0.346653 | 0.173326 | − | 0.984864i | \(-0.444548\pi\) | ||||
0.173326 | + | 0.984864i | \(0.444548\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.51639 | −0.330794 | −0.165397 | − | 0.986227i | \(-0.552891\pi\) | ||||
−0.165397 | + | 0.986227i | \(0.552891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.0586 | −1.28875 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.96722 | −0.360657 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.89026 | 0.877619 | 0.438809 | − | 0.898580i | \(-0.355400\pi\) | ||||
0.438809 | + | 0.898580i | \(0.355400\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.9344 | −1.91642 | −0.958211 | − | 0.286063i | \(-0.907653\pi\) | ||||
−0.958211 | + | 0.286063i | \(0.907653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.04419 | −0.177253 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.33665 | −0.541377 | −0.270688 | − | 0.962667i | \(-0.587251\pi\) | ||||
−0.270688 | + | 0.962667i | \(0.587251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.13555 | −0.605229 | −0.302615 | − | 0.953113i | \(-0.597860\pi\) | ||||
−0.302615 | + | 0.953113i | \(0.597860\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.72890 | −0.144578 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.48361 | −0.206253 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.3153 | 1.17275 | 0.586377 | − | 0.810038i | \(-0.300554\pi\) | ||||
0.586377 | + | 0.810038i | \(0.300554\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5750 | 0.941958 | 0.470979 | − | 0.882144i | \(-0.343901\pi\) | ||||
0.470979 | + | 0.882144i | \(0.343901\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.13555 | −0.251853 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7661 | 1.09866 | 0.549328 | − | 0.835607i | \(-0.314884\pi\) | ||||
0.549328 | + | 0.835607i | \(0.314884\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.13555 | −0.247116 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.27110 | 0.491190 | 0.245595 | − | 0.969372i | \(-0.421017\pi\) | ||||
0.245595 | + | 0.969372i | \(0.421017\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.2825 | −1.02783 | −0.513916 | − | 0.857841i | \(-0.671806\pi\) | ||||
−0.513916 | + | 0.857841i | \(0.671806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5750 | −0.967306 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.27110 | 0.628840 | 0.314420 | − | 0.949284i | \(-0.398190\pi\) | ||||
0.314420 | + | 0.949284i | \(0.398190\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.13555 | 0.237025 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.64053 | −0.421593 | −0.210797 | − | 0.977530i | \(-0.567606\pi\) | ||||
−0.210797 | + | 0.977530i | \(0.567606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.359470 | 0.0267192 | 0.0133596 | − | 0.999911i | \(-0.495747\pi\) | ||||
0.0133596 | + | 0.999911i | \(0.495747\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.10277 | −0.448685 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.8903 | 0.869502 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.1286 | 1.38410 | 0.692048 | − | 0.721852i | \(-0.256709\pi\) | ||||
0.692048 | + | 0.721852i | \(0.256709\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9672 | −0.789438 | −0.394719 | − | 0.918802i | \(-0.629158\pi\) | ||||
−0.394719 | + | 0.918802i | \(0.629158\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.2383 | 0.943191 | 0.471596 | − | 0.881815i | \(-0.343678\pi\) | ||||
0.471596 | + | 0.881815i | \(0.343678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.35947 | −0.167258 | −0.0836292 | − | 0.996497i | \(-0.526651\pi\) | ||||
−0.0836292 | + | 0.996497i | \(0.526651\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.78749 | −0.546575 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.820265 | −0.0572898 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.72890 | 0.119591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1355 | 1.04197 | 0.520987 | − | 0.853565i | \(-0.325564\pi\) | ||||
0.520987 | + | 0.853565i | \(0.325564\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.696123 | 0.0474752 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.83167 | −0.667417 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.92304 | −0.196625 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6078 | −0.844278 | −0.422139 | − | 0.906531i | \(-0.638721\pi\) | ||||
−0.422139 | + | 0.906531i | \(0.638721\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.54220 | 0.301476 | 0.150738 | − | 0.988574i | \(-0.451835\pi\) | ||||
0.150738 | + | 0.988574i | \(0.451835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.57498 | 0.104077 | 0.0520387 | − | 0.998645i | \(-0.483428\pi\) | ||||
0.0520387 | + | 0.998645i | \(0.483428\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.33665 | 0.415128 | 0.207564 | − | 0.978221i | \(-0.433446\pi\) | ||||
0.207564 | + | 0.978221i | \(0.433446\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.8903 | 0.775635 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.09136 | 0.458702 | 0.229351 | − | 0.973344i | \(-0.426340\pi\) | ||||
0.229351 | + | 0.973344i | \(0.426340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.68472 | −0.366185 | −0.183092 | − | 0.983096i | \(-0.558611\pi\) | ||||
−0.183092 | + | 0.983096i | \(0.558611\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.83167 | 0.180909 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.425024 | −0.0270436 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.9344 | −1.76321 | −0.881603 | − | 0.471991i | \(-0.843535\pi\) | ||||
−0.881603 | + | 0.471991i | \(0.843535\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.65194 | 0.166726 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.61916 | −0.475270 | −0.237635 | − | 0.971354i | \(-0.576372\pi\) | ||||
−0.237635 | + | 0.971354i | \(0.576372\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.1355 | −1.18903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.85304 | 0.360914 | 0.180457 | − | 0.983583i | \(-0.442242\pi\) | ||||
0.180457 | + | 0.983583i | \(0.442242\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.45083 | −0.580560 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.7875 | 0.962580 | 0.481290 | − | 0.876561i | \(-0.340168\pi\) | ||||
0.481290 | + | 0.876561i | \(0.340168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.56057 | 0.216289 | 0.108145 | − | 0.994135i | \(-0.465509\pi\) | ||||
0.108145 | + | 0.994135i | \(0.465509\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.65194 | −0.159918 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.8789 | −1.25449 | −0.627244 | − | 0.778823i | \(-0.715817\pi\) | ||||
−0.627244 | + | 0.778823i | \(0.715817\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.5536 | −0.689230 | −0.344615 | − | 0.938744i | \(-0.611991\pi\) | ||||
−0.344615 | + | 0.938744i | \(0.611991\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.83167 | 0.465545 | 0.232772 | − | 0.972531i | \(-0.425220\pi\) | ||||
0.232772 | + | 0.972531i | \(0.425220\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.57198 | −0.151819 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.10277 | 0.182516 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.42802 | −0.200267 | −0.100133 | − | 0.994974i | \(-0.531927\pi\) | ||||
−0.100133 | + | 0.994974i | \(0.531927\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.7547 | −0.742608 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.651938 | −0.0377026 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18273 | 0.125810 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.65194 | 0.151850 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.67475 | −0.380948 | −0.190474 | − | 0.981692i | \(-0.561003\pi\) | ||||
−0.190474 | + | 0.981692i | \(0.561003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.2055 | 0.805523 | 0.402761 | − | 0.915305i | \(-0.368050\pi\) | ||||
0.402761 | + | 0.915305i | \(0.368050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.83167 | 0.103532 | 0.0517661 | − | 0.998659i | \(-0.483515\pi\) | ||||
0.0517661 | + | 0.998659i | \(0.483515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.9230 | 0.950493 | 0.475246 | − | 0.879853i | \(-0.342359\pi\) | ||||
0.475246 | + | 0.879853i | \(0.342359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.58638 | 0.368767 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.92304 | 0.162642 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.651938 | 0.0361630 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 37.2825 | 2.05545 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.3739 | −1.00992 | −0.504960 | − | 0.863143i | \(-0.668493\pi\) | ||||
−0.504960 | + | 0.863143i | \(0.668493\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.10277 | −0.333430 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.8133 | 1.46061 | 0.730307 | − | 0.683119i | \(-0.239377\pi\) | ||||
0.730307 | + | 0.683119i | \(0.239377\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.31528 | 0.450298 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0700 | −0.705713 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.4538 | −1.52748 | −0.763741 | − | 0.645523i | \(-0.776639\pi\) | ||||
−0.763741 | + | 0.645523i | \(0.776639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.79890 | −0.256879 | −0.128440 | − | 0.991717i | \(-0.540997\pi\) | ||||
−0.128440 | + | 0.991717i | \(0.540997\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7919 | 1.10664 | 0.553321 | − | 0.832968i | \(-0.313360\pi\) | ||||
0.553321 | + | 0.832968i | \(0.313360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.48361 | −0.450263 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.04419 | −0.107888 | −0.0539440 | − | 0.998544i | \(-0.517179\pi\) | ||||
−0.0539440 | + | 0.998544i | \(0.517179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5750 | −0.977630 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.31528 | 0.330557 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.527797 | 0.0275508 | 0.0137754 | − | 0.999905i | \(-0.495615\pi\) | ||||
0.0137754 | + | 0.999905i | \(0.495615\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.6336 | −1.53850 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.4439 | 1.52455 | 0.762273 | − | 0.647256i | \(-0.224083\pi\) | ||||
0.762273 | + | 0.647256i | \(0.224083\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.61916 | −0.0833911 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.32669 | 0.376347 | 0.188173 | − | 0.982136i | \(-0.439743\pi\) | ||||
0.188173 | + | 0.982136i | \(0.439743\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.42802 | 0.277359 | 0.138679 | − | 0.990337i | \(-0.455714\pi\) | ||||
0.138679 | + | 0.990337i | \(0.455714\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.31528 | −0.423786 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.3883 | 1.43934 | 0.719671 | − | 0.694315i | \(-0.244292\pi\) | ||||
0.719671 | + | 0.694315i | \(0.244292\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.48361 | 0.226746 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.6078 | −0.733142 | −0.366571 | − | 0.930390i | \(-0.619468\pi\) | ||||
−0.366571 | + | 0.930390i | \(0.619468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.5750 | 0.977528 | 0.488764 | − | 0.872416i | \(-0.337448\pi\) | ||||
0.488764 | + | 0.872416i | \(0.337448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.04419 | −0.101828 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.1842 | 0.802220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5278 | −0.520566 | −0.260283 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260283 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −39.9930 | −1.96793 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.51639 | −0.270789 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.1941 | 0.546869 | 0.273435 | − | 0.961891i | \(-0.411840\pi\) | ||||
0.273435 | + | 0.961891i | \(0.411840\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.5308 | −1.14682 | −0.573410 | − | 0.819268i | \(-0.694380\pi\) | ||||
−0.573410 | + | 0.819268i | \(0.694380\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.48361 | −0.217487 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.31528 | 0.402405 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.2383 | −1.31202 | −0.656012 | − | 0.754751i | \(-0.727758\pi\) | ||||
−0.656012 | + | 0.754751i | \(0.727758\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8317 | 0.664708 | 0.332354 | − | 0.943155i | \(-0.392157\pi\) | ||||
0.332354 | + | 0.943155i | \(0.392157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.651938 | 0.0311864 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.4211 | −1.59510 | −0.797550 | − | 0.603253i | \(-0.793871\pi\) | ||||
−0.797550 | + | 0.603253i | \(0.793871\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.1286 | 1.47896 | 0.739482 | − | 0.673177i | \(-0.235071\pi\) | ||||
0.739482 | + | 0.673177i | \(0.235071\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.2383 | 0.532748 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.0030 | 1.08558 | 0.542789 | − | 0.839869i | \(-0.317368\pi\) | ||||
0.542789 | + | 0.839869i | \(0.317368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.17529 | 0.102431 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.04419 | 0.0958329 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.233880 | −0.0109405 | −0.00547023 | − | 0.999985i | \(-0.501741\pi\) | ||||
−0.00547023 | + | 0.999985i | \(0.501741\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.5094 | −0.629197 | −0.314598 | − | 0.949225i | \(-0.601870\pi\) | ||||
−0.314598 | + | 0.949225i | \(0.601870\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.3997 | −1.27337 | −0.636686 | − | 0.771123i | \(-0.719695\pi\) | ||||
−0.636686 | + | 0.771123i | \(0.719695\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.17974 | −0.424787 | −0.212394 | − | 0.977184i | \(-0.568126\pi\) | ||||
−0.212394 | + | 0.977184i | \(0.568126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.1355 | −0.883598 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.84608 | −0.0848827 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.651938 | −0.0299130 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.04419 | 0.0934012 | 0.0467006 | − | 0.998909i | \(-0.485129\pi\) | ||||
0.0467006 | + | 0.998909i | \(0.485129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.97863 | −0.181410 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.93445 | −0.269469 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.0402 | 1.31594 | 0.657969 | − | 0.753045i | \(-0.271416\pi\) | ||||
0.657969 | + | 0.753045i | \(0.271416\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.9275 | −1.71164 | −0.855822 | − | 0.517271i | \(-0.826948\pi\) | ||||
−0.855822 | + | 0.517271i | \(0.826948\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.1355 | 0.501520 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.6008 | −1.19321 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.7761 | −0.571936 | −0.285968 | − | 0.958239i | \(-0.592315\pi\) | ||||
−0.285968 | + | 0.958239i | \(0.592315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.2641 | −1.70611 | −0.853057 | − | 0.521818i | \(-0.825254\pi\) | ||||
−0.853057 | + | 0.521818i | \(0.825254\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.75471 | −0.389580 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.0000 | 1.24108 | 0.620539 | − | 0.784176i | \(-0.286914\pi\) | ||||
0.620539 | + | 0.784176i | \(0.286914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.8019 | 0.875984 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.66335 | −0.161426 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.5322 | −1.38679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.7691 | 1.08515 | 0.542577 | − | 0.840006i | \(-0.317449\pi\) | ||||
0.542577 | + | 0.840006i | \(0.317449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.271100 | −0.0118544 | −0.00592718 | − | 0.999982i | \(-0.501887\pi\) | ||||
−0.00592718 | + | 0.999982i | \(0.501887\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.0586 | 0.612402 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.534762 | −0.0231631 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.24529 | −0.140306 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.50942 | −0.323454 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.1400 | −1.72575 | −0.862877 | − | 0.505415i | \(-0.831340\pi\) | ||||
−0.862877 | + | 0.505415i | \(0.831340\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.61916 | 0.155028 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.67331 | −0.199816 | −0.0999081 | − | 0.994997i | \(-0.531855\pi\) | ||||
−0.0999081 | + | 0.994997i | \(0.531855\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.61916 | 0.0689786 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.0844 | −1.06670 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.5680 | 0.913866 | 0.456933 | − | 0.889501i | \(-0.348948\pi\) | ||||
0.456933 | + | 0.889501i | \(0.348948\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.453830 | 0.0191949 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.9047 | −1.34462 | −0.672311 | − | 0.740269i | \(-0.734698\pi\) | ||||
−0.672311 | + | 0.740269i | \(0.734698\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.51639 | −0.147936 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.4439 | −0.647441 | −0.323720 | − | 0.946153i | \(-0.604934\pi\) | ||||
−0.323720 | + | 0.946153i | \(0.604934\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.6380 | −1.19846 | −0.599232 | − | 0.800576i | \(-0.704527\pi\) | ||||
−0.599232 | + | 0.800576i | \(0.704527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.12115 | −0.0466740 | −0.0233370 | − | 0.999728i | \(-0.507429\pi\) | ||||
−0.0233370 | + | 0.999728i | \(0.507429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.2969 | −0.717597 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.0630 | 1.03800 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.2055 | −1.16417 | −0.582084 | − | 0.813129i | \(-0.697762\pi\) | ||||
−0.582084 | + | 0.813129i | \(0.697762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.04419 | 0.0842292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.5308 | −0.802033 | −0.401017 | − | 0.916071i | \(-0.631343\pi\) | ||||
−0.401017 | + | 0.916071i | \(0.631343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.0586 | −0.576346 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.9017 | 1.34433 | 0.672163 | − | 0.740403i | \(-0.265365\pi\) | ||||
0.672163 | + | 0.740403i | \(0.265365\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2011 | −0.783229 | −0.391615 | − | 0.920129i | \(-0.628083\pi\) | ||||
−0.391615 | + | 0.920129i | \(0.628083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.96722 | −0.161291 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.2825 | −0.945008 | −0.472504 | − | 0.881329i | \(-0.656650\pi\) | ||||
−0.472504 | + | 0.881329i | \(0.656650\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.75172 | 0.313601 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.86889 | −0.237042 | −0.118521 | − | 0.992952i | \(-0.537815\pi\) | ||||
−0.118521 | + | 0.992952i | \(0.537815\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.2314 | −1.33784 | −0.668922 | − | 0.743333i | \(-0.733244\pi\) | ||||
−0.668922 | + | 0.743333i | \(0.733244\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.3267 | −0.776805 | −0.388403 | − | 0.921490i | \(-0.626973\pi\) | ||||
−0.388403 | + | 0.921490i | \(0.626973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.2383 | 1.41179 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.3625 | 1.09101 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.39968 | 0.374196 | 0.187098 | − | 0.982341i | \(-0.440092\pi\) | ||||
0.187098 | + | 0.982341i | \(0.440092\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.89026 | 0.392483 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.84608 | 0.0731442 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.0303 | 1.66010 | 0.830048 | − | 0.557693i | \(-0.188313\pi\) | ||||
0.830048 | + | 0.557693i | \(0.188313\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.9488 | −1.25994 | −0.629970 | − | 0.776620i | \(-0.716933\pi\) | ||||
−0.629970 | + | 0.776620i | \(0.716933\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7691 | −0.816518 | −0.408259 | − | 0.912866i | \(-0.633864\pi\) | ||||
−0.408259 | + | 0.912866i | \(0.633864\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.8247 | 1.32774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.3481 | −0.522350 | −0.261175 | − | 0.965291i | \(-0.584110\pi\) | ||||
−0.261175 | + | 0.965291i | \(0.584110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.9344 | −0.857050 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.5636 | 0.723134 | 0.361567 | − | 0.932346i | \(-0.382242\pi\) | ||||
0.361567 | + | 0.932346i | \(0.382242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.1728 | 0.901316 | 0.450658 | − | 0.892697i | \(-0.351189\pi\) | ||||
0.450658 | + | 0.892697i | \(0.351189\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.04419 | −0.0792701 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.48361 | 0.0961658 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.03278 | −0.271497 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 51.0630 | 1.96834 | 0.984168 | − | 0.177240i | \(-0.0567170\pi\) | ||||
0.984168 | + | 0.177240i | \(0.0567170\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.87586 | −0.225828 | −0.112914 | − | 0.993605i | \(-0.536018\pi\) | ||||
−0.112914 | + | 0.993605i | \(0.536018\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.6078 | −0.714100 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.2597 | −0.736952 | −0.368476 | − | 0.929637i | \(-0.620120\pi\) | ||||
−0.368476 | + | 0.929637i | \(0.620120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.33665 | −0.242111 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.16136 | −0.234729 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.11718 | 0.308792 | 0.154396 | − | 0.988009i | \(-0.450657\pi\) | ||||
0.154396 | + | 0.988009i | \(0.450657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.13555 | −0.270667 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.67775 | 0.139305 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.9459 | 0.715575 | 0.357788 | − | 0.933803i | \(-0.383531\pi\) | ||||
0.357788 | + | 0.933803i | \(0.383531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.97863 | 0.150057 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.4508 | −1.03239 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.06700 | −0.227851 | −0.113926 | − | 0.993489i | \(-0.536343\pi\) | ||||
−0.113926 | + | 0.993489i | \(0.536343\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.13555 | 0.117427 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.72890 | −0.0646572 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.4737 | 0.726245 | 0.363122 | − | 0.931741i | \(-0.381711\pi\) | ||||
0.363122 | + | 0.931741i | \(0.381711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.4866 | −0.427784 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.48361 | −0.0922390 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.5238 | −1.54003 | −0.770017 | − | 0.638024i | \(-0.779752\pi\) | ||||
−0.770017 | + | 0.638024i | \(0.779752\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.12115 | −0.115440 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.8833 | −0.512791 | −0.256396 | − | 0.966572i | \(-0.582535\pi\) | ||||
−0.256396 | + | 0.966572i | \(0.582535\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.1842 | 0.596152 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.7661 | −0.874251 | −0.437125 | − | 0.899401i | \(-0.644003\pi\) | ||||
−0.437125 | + | 0.899401i | \(0.644003\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.9344 | 1.53843 | 0.769213 | − | 0.638993i | \(-0.220649\pi\) | ||||
0.769213 | + | 0.638993i | \(0.220649\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.3153 | 0.524471 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1758 | −0.371814 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.89026 | 0.287920 | 0.143960 | − | 0.989584i | \(-0.454016\pi\) | ||||
0.143960 | + | 0.989584i | \(0.454016\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.5750 | 0.421257 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.5566 | −0.965216 | −0.482608 | − | 0.875836i | \(-0.660310\pi\) | ||||
−0.482608 | + | 0.875836i | \(0.660310\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.1241 | 0.657000 | 0.328500 | − | 0.944504i | \(-0.393457\pi\) | ||||
0.328500 | + | 0.944504i | \(0.393457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.3481 | 0.410827 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.31528 | −0.300248 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.86744 | 0.283707 | 0.141854 | − | 0.989888i | \(-0.454694\pi\) | ||||
0.141854 | + | 0.989888i | \(0.454694\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.17277 | 0.257987 | 0.128993 | − | 0.991645i | \(-0.458825\pi\) | ||||
0.128993 | + | 0.991645i | \(0.458825\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.13555 | −0.112632 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.534762 | 0.0191598 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.4980 | 0.805042 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7661 | 0.491334 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.01440 | −0.214390 | −0.107195 | − | 0.994238i | \(-0.534187\pi\) | ||||
−0.107195 | + | 0.994238i | \(0.534187\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0258 | −0.392033 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.72890 | 0.0613950 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.45083 | 0.0513912 | 0.0256956 | − | 0.999670i | \(-0.491820\pi\) | ||||
0.0256956 | + | 0.999670i | \(0.491820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −53.3113 | −1.88602 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.7477 | −0.591015 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.13555 | −0.110514 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.11418 | −0.320438 | −0.160219 | − | 0.987082i | \(-0.551220\pi\) | ||||
−0.160219 | + | 0.987082i | \(0.551220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0044 | 0.667336 | 0.333668 | − | 0.942691i | \(-0.391714\pi\) | ||||
0.333668 | + | 0.942691i | \(0.391714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.27110 | 0.219667 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.453830 | −0.0158775 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 55.5610 | 1.93909 | 0.969547 | − | 0.244906i | \(-0.0787570\pi\) | ||||
0.969547 | + | 0.244906i | \(0.0787570\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.66335 | 0.197412 | 0.0987059 | − | 0.995117i | \(-0.468530\pi\) | ||||
0.0987059 | + | 0.995117i | \(0.468530\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.0586 | −1.60161 | −0.800807 | − | 0.598922i | \(-0.795596\pi\) | ||||
−0.800807 | + | 0.598922i | \(0.795596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.710526 | −0.0246776 | −0.0123388 | − | 0.999924i | \(-0.503928\pi\) | ||||
−0.0123388 | + | 0.999924i | \(0.503928\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.6961 | −0.439895 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.2825 | −0.459660 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.9444 | 0.377843 | 0.188921 | − | 0.981992i | \(-0.439501\pi\) | ||||
0.188921 | + | 0.981992i | \(0.439501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8317 | −0.787299 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.5750 | −0.432592 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.4394 | −0.427424 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.10277 | 0.209200 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.81727 | −0.0622222 | −0.0311111 | − | 0.999516i | \(-0.509905\pi\) | ||||
−0.0311111 | + | 0.999516i | \(0.509905\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.8033 | 0.949744 | 0.474872 | − | 0.880055i | \(-0.342494\pi\) | ||||
0.474872 | + | 0.880055i | \(0.342494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.4066 | −0.730385 | −0.365193 | − | 0.930932i | \(-0.618997\pi\) | ||||
−0.365193 | + | 0.930932i | \(0.618997\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.2284 | 0.620501 | 0.310250 | − | 0.950655i | \(-0.399587\pi\) | ||||
0.310250 | + | 0.950655i | \(0.399587\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.27110 | 0.281226 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.2155 | 0.719687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.97863 | −0.134811 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.13555 | 0.106001 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.2671 | −1.59610 | −0.798049 | − | 0.602593i | \(-0.794134\pi\) | ||||
−0.798049 | + | 0.602593i | \(0.794134\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.71749 | 0.0915546 | 0.0457773 | − | 0.998952i | \(-0.485424\pi\) | ||||
0.0457773 | + | 0.998952i | \(0.485424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.6380 | 0.694524 | 0.347262 | − | 0.937768i | \(-0.387111\pi\) | ||||
0.347262 | + | 0.937768i | \(0.387111\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.1172 | 1.61562 | 0.807808 | − | 0.589445i | \(-0.200654\pi\) | ||||
0.807808 | + | 0.589445i | \(0.200654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.0114 | 1.04009 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.75172 | −0.259401 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.64053 | −0.188542 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.78749 | 0.259727 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.3739 | 1.41168 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.359470 | 0.0119492 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.30832 | 0.0766465 | 0.0383232 | − | 0.999265i | \(-0.487798\pi\) | ||||
0.0383232 | + | 0.999265i | \(0.487798\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.4766 | −1.67237 | −0.836183 | − | 0.548451i | \(-0.815218\pi\) | ||||
−0.836183 | + | 0.548451i | \(0.815218\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6291 | 0.484153 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −68.7766 | −2.27120 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.0000 | −1.05558 | −0.527791 | − | 0.849374i | \(-0.676980\pi\) | ||||
−0.527791 | + | 0.849374i | \(0.676980\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.53079 | −0.182048 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.10277 | −0.200658 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.6336 | 1.30034 | 0.650168 | − | 0.759791i | \(-0.274699\pi\) | ||||
0.650168 | + | 0.759791i | \(0.274699\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.84608 | −0.0605027 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.8903 | 0.388853 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.4766 | −1.38765 | −0.693826 | − | 0.720143i | \(-0.744076\pi\) | ||||
−0.693826 | + | 0.720143i | \(0.744076\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.2497 | −0.399330 | −0.199665 | − | 0.979864i | \(-0.563985\pi\) | ||||
−0.199665 | + | 0.979864i | \(0.563985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.820265 | 0.0267115 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.3039 | −0.952248 | −0.476124 | − | 0.879378i | \(-0.657959\pi\) | ||||
−0.476124 | + | 0.879378i | \(0.657959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.11718 | 0.133649 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.32669 | 0.172549 | 0.0862743 | − | 0.996271i | \(-0.472504\pi\) | ||||
0.0862743 | + | 0.996271i | \(0.472504\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.1286 | 0.618986 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.8689 | −0.641600 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.1683 | −0.682849 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.9672 | −0.353047 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.1097 | −0.325107 | −0.162554 | − | 0.986700i | \(-0.551973\pi\) | ||||
−0.162554 | + | 0.986700i | \(0.551973\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.7249 | 0.665095 | 0.332547 | − | 0.943087i | \(-0.392092\pi\) | ||||
0.332547 | + | 0.943087i | \(0.392092\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.3739 | −0.717273 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.37242 | 0.203872 | 0.101936 | − | 0.994791i | \(-0.467496\pi\) | ||||
0.101936 | + | 0.994791i | \(0.467496\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.8033 | −0.952519 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.6008 | −0.848433 | −0.424217 | − | 0.905561i | \(-0.639451\pi\) | ||||
−0.424217 | + | 0.905561i | \(0.639451\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.2383 | 0.421808 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.696123 | −0.0221354 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.0332 | −1.62112 | −0.810562 | − | 0.585652i | \(-0.800838\pi\) | ||||
−0.810562 | + | 0.585652i | \(0.800838\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.35947 | −0.0748002 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0883702 | 0.00279871 | 0.00139936 | − | 0.999999i | \(-0.499555\pi\) | ||||
0.00139936 | + | 0.999999i | \(0.499555\pi\) | |||||||
\(998\) | 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 | 8280.2.a.bn.1.3 | 3 | ||
3.2 | odd | 2 | 2760.2.a.s.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 5520.2.a.bw.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.s.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
5520.2.a.bw.1.1 | 3 | 12.11 | even | 2 | |||
8280.2.a.bn.1.3 | 3 | 1.1 | even | 1 | trivial |