Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5148,2,Mod(1,5148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5148.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: | \(41.1069869606\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.815952.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 9x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.02664\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5148.1 |
$q$-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 | ||||||||
\(5\) | −0.577317 | −0.258184 | −0.129092 | − | 0.991633i | \(-0.541206\pi\) | ||||
−0.129092 | + | 0.991633i | \(0.541206\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.32465 | 0.878634 | 0.439317 | − | 0.898332i | \(-0.355221\pi\) | ||||
0.439317 | + | 0.898332i | \(0.355221\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.24402 | −1.02933 | −0.514663 | − | 0.857392i | \(-0.672083\pi\) | ||||
−0.514663 | + | 0.857392i | \(0.672083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26475 | 0.290155 | 0.145077 | − | 0.989420i | \(-0.453657\pi\) | ||||
0.145077 | + | 0.989420i | \(0.453657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.28521 | 0.685015 | 0.342507 | − | 0.939515i | \(-0.388724\pi\) | ||||
0.342507 | + | 0.939515i | \(0.388724\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.66671 | −0.933341 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.0151 | −1.85976 | −0.929882 | − | 0.367859i | \(-0.880091\pi\) | ||||
−0.929882 | + | 0.367859i | \(0.880091\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.24910 | 1.12237 | 0.561186 | − | 0.827690i | \(-0.310345\pi\) | ||||
0.561186 | + | 0.827690i | \(0.310345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.34206 | −0.226849 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.82439 | −1.61512 | −0.807560 | − | 0.589786i | \(-0.799212\pi\) | ||||
−0.807560 | + | 0.589786i | \(0.799212\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.76603 | −0.588155 | −0.294078 | − | 0.955782i | \(-0.595012\pi\) | ||||
−0.294078 | + | 0.955782i | \(0.595012\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.64801 | −0.251318 | −0.125659 | − | 0.992073i | \(-0.540105\pi\) | ||||
−0.125659 | + | 0.992073i | \(0.540105\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.17509 | −1.04660 | −0.523298 | − | 0.852150i | \(-0.675298\pi\) | ||||
−0.523298 | + | 0.852150i | \(0.675298\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.59602 | −0.228002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.94011 | −0.403855 | −0.201927 | − | 0.979400i | \(-0.564721\pi\) | ||||
−0.201927 | + | 0.979400i | \(0.564721\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.577317 | −0.0778454 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.161250 | −0.0209929 | −0.0104965 | − | 0.999945i | \(-0.503341\pi\) | ||||
−0.0104965 | + | 0.999945i | \(0.503341\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92574 | 0.630677 | 0.315339 | − | 0.948979i | \(-0.397882\pi\) | ||||
0.315339 | + | 0.948979i | \(0.397882\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.577317 | 0.0716074 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.7438 | 1.67907 | 0.839534 | − | 0.543307i | \(-0.182828\pi\) | ||||
0.839534 | + | 0.543307i | \(0.182828\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.97902 | 0.590901 | 0.295451 | − | 0.955358i | \(-0.404530\pi\) | ||||
0.295451 | + | 0.955358i | \(0.404530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.63391 | 0.776441 | 0.388221 | − | 0.921567i | \(-0.373090\pi\) | ||||
0.388221 | + | 0.921567i | \(0.373090\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.32465 | 0.264918 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.30391 | −0.596737 | −0.298368 | − | 0.954451i | \(-0.596442\pi\) | ||||
−0.298368 | + | 0.954451i | \(0.596442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.0291080 | −0.00319502 | −0.00159751 | − | 0.999999i | \(-0.500509\pi\) | ||||
−0.00159751 | + | 0.999999i | \(0.500509\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.45015 | 0.265756 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.17537 | −0.230588 | −0.115294 | − | 0.993331i | \(-0.536781\pi\) | ||||
−0.115294 | + | 0.993331i | \(0.536781\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.32465 | −0.243689 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.730164 | −0.0749133 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.70460 | −0.782284 | −0.391142 | − | 0.920330i | \(-0.627920\pi\) | ||||
−0.391142 | + | 0.920330i | \(0.627920\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.39866 | −0.537186 | −0.268593 | − | 0.963254i | \(-0.586559\pi\) | ||||
−0.268593 | + | 0.963254i | \(0.586559\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.89864 | −0.482678 | −0.241339 | − | 0.970441i | \(-0.577587\pi\) | ||||
−0.241339 | + | 0.970441i | \(0.577587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.8797 | −1.63182 | −0.815911 | − | 0.578178i | \(-0.803764\pi\) | ||||
−0.815911 | + | 0.578178i | \(0.803764\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.09117 | −0.583429 | −0.291714 | − | 0.956505i | \(-0.594226\pi\) | ||||
−0.291714 | + | 0.956505i | \(0.594226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.4691 | −1.54928 | −0.774641 | − | 0.632401i | \(-0.782070\pi\) | ||||
−0.774641 | + | 0.632401i | \(0.782070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.89661 | −0.176860 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.86585 | −0.904401 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.58075 | 0.499158 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0618 | 1.15905 | 0.579523 | − | 0.814956i | \(-0.303239\pi\) | ||||
0.579523 | + | 0.814956i | \(0.303239\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.72558 | −0.412876 | −0.206438 | − | 0.978460i | \(-0.566187\pi\) | ||||
−0.206438 | + | 0.978460i | \(0.566187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.94011 | 0.254940 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.8175 | 1.94943 | 0.974716 | − | 0.223446i | \(-0.0717305\pi\) | ||||
0.974716 | + | 0.223446i | \(0.0717305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.41912 | −0.629281 | −0.314641 | − | 0.949211i | \(-0.601884\pi\) | ||||
−0.314641 | + | 0.949211i | \(0.601884\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.78191 | 0.480161 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.17663 | −0.342163 | −0.171081 | − | 0.985257i | \(-0.554726\pi\) | ||||
−0.171081 | + | 0.985257i | \(0.554726\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.80088 | 0.227932 | 0.113966 | − | 0.993485i | \(-0.463644\pi\) | ||||
0.113966 | + | 0.993485i | \(0.463644\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.60771 | −0.289779 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.89966 | 0.550653 | 0.275326 | − | 0.961351i | \(-0.411214\pi\) | ||||
0.275326 | + | 0.961351i | \(0.411214\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.63696 | 0.601877 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.925991 | 0.0725292 | 0.0362646 | − | 0.999342i | \(-0.488454\pi\) | ||||
0.0362646 | + | 0.999342i | \(0.488454\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.9868 | −1.08233 | −0.541164 | − | 0.840917i | \(-0.682016\pi\) | ||||
−0.541164 | + | 0.840917i | \(0.682016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.86915 | 0.218137 | 0.109069 | − | 0.994034i | \(-0.465213\pi\) | ||||
0.109069 | + | 0.994034i | \(0.465213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.8484 | −0.820065 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.61294 | 0.718505 | 0.359252 | − | 0.933240i | \(-0.383032\pi\) | ||||
0.359252 | + | 0.933240i | \(0.383032\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.518713 | −0.0385557 | −0.0192778 | − | 0.999814i | \(-0.506137\pi\) | ||||
−0.0192778 | + | 0.999814i | \(0.506137\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.67179 | 0.416998 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.24402 | −0.310354 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2862 | 0.816643 | 0.408321 | − | 0.912838i | \(-0.366114\pi\) | ||||
0.408321 | + | 0.912838i | \(0.366114\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.97801 | −0.502288 | −0.251144 | − | 0.967950i | \(-0.580807\pi\) | ||||
−0.251144 | + | 0.967950i | \(0.580807\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.0338 | −1.42735 | −0.713676 | − | 0.700476i | \(-0.752971\pi\) | ||||
−0.713676 | + | 0.700476i | \(0.752971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.63035 | −0.611789 | −0.305895 | − | 0.952065i | \(-0.598956\pi\) | ||||
−0.305895 | + | 0.952065i | \(0.598956\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.2816 | −1.63405 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.17419 | 0.151852 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.26475 | 0.0874849 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.46516 | −0.376237 | −0.188119 | − | 0.982146i | \(-0.560239\pi\) | ||||
−0.188119 | + | 0.982146i | \(0.560239\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.951421 | 0.0648864 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.5270 | 0.986154 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.24402 | 0.285484 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.17740 | −0.0788445 | −0.0394222 | − | 0.999223i | \(-0.512552\pi\) | ||||
−0.0394222 | + | 0.999223i | \(0.512552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.2766 | −1.41218 | −0.706088 | − | 0.708124i | \(-0.749542\pi\) | ||||
−0.706088 | + | 0.708124i | \(0.749542\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.32973 | −0.153953 | −0.0769764 | − | 0.997033i | \(-0.524527\pi\) | ||||
−0.0769764 | + | 0.997033i | \(0.524527\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.79489 | −0.641685 | −0.320842 | − | 0.947133i | \(-0.603966\pi\) | ||||
−0.320842 | + | 0.947133i | \(0.603966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.14230 | 0.270214 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.65808 | 0.171937 | 0.0859686 | − | 0.996298i | \(-0.472602\pi\) | ||||
0.0859686 | + | 0.996298i | \(0.472602\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.2422 | 1.17508 | 0.587542 | − | 0.809194i | \(-0.300096\pi\) | ||||
0.587542 | + | 0.809194i | \(0.300096\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.921408 | 0.0588666 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.26475 | −0.0804744 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.6677 | −1.05206 | −0.526029 | − | 0.850466i | \(-0.676320\pi\) | ||||
−0.526029 | + | 0.850466i | \(0.676320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.28521 | 0.206540 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.8608 | −1.05174 | −0.525872 | − | 0.850563i | \(-0.676261\pi\) | ||||
−0.525872 | + | 0.850563i | \(0.676261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.8382 | −1.41910 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.1127 | 1.17854 | 0.589269 | − | 0.807937i | \(-0.299416\pi\) | ||||
0.589269 | + | 0.807937i | \(0.299416\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.69737 | 0.104269 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.3876 | −0.633342 | −0.316671 | − | 0.948535i | \(-0.602565\pi\) | ||||
−0.316671 | + | 0.948535i | \(0.602565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.82592 | 0.536137 | 0.268068 | − | 0.963400i | \(-0.413615\pi\) | ||||
0.268068 | + | 0.963400i | \(0.413615\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.66671 | −0.281413 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.3810 | −1.34474 | −0.672372 | − | 0.740213i | \(-0.734724\pi\) | ||||
−0.672372 | + | 0.740213i | \(0.734724\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.44188 | 0.443945 | 0.221973 | − | 0.975053i | \(-0.428750\pi\) | ||||
0.221973 | + | 0.975053i | \(0.428750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.64342 | −0.335467 | −0.167733 | − | 0.985832i | \(-0.553645\pi\) | ||||
−0.167733 | + | 0.985832i | \(0.553645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.75469 | −0.516773 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.01172 | 0.0595131 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.64977 | −0.0963803 | −0.0481902 | − | 0.998838i | \(-0.515345\pi\) | ||||
−0.0481902 | + | 0.998838i | \(0.515345\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0930921 | 0.00542003 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.28521 | −0.189989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.83103 | −0.220817 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.84372 | −0.162831 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.4603 | 0.882368 | 0.441184 | − | 0.897417i | \(-0.354559\pi\) | ||||
0.441184 | + | 0.897417i | \(0.354559\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.8895 | −0.787603 | −0.393801 | − | 0.919196i | \(-0.628840\pi\) | ||||
−0.393801 | + | 0.919196i | \(0.628840\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.0903 | −1.75733 | −0.878664 | − | 0.477441i | \(-0.841564\pi\) | ||||
−0.878664 | + | 0.477441i | \(0.841564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.78317 | 0.212484 | 0.106242 | − | 0.994340i | \(-0.466118\pi\) | ||||
0.106242 | + | 0.994340i | \(0.466118\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0151 | −0.560740 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.36765 | −0.298664 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.66671 | 0.258862 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.6796 | −0.919574 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.3787 | 1.66976 | 0.834882 | − | 0.550429i | \(-0.185536\pi\) | ||||
0.834882 | + | 0.550429i | \(0.185536\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.93451 | −0.433508 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.95192 | 0.487642 | 0.243821 | − | 0.969820i | \(-0.421599\pi\) | ||||
0.243821 | + | 0.969820i | \(0.421599\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.24910 | 0.338408 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9827 | −1.07896 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.774206 | −0.0415616 | −0.0207808 | − | 0.999784i | \(-0.506615\pi\) | ||||
−0.0207808 | + | 0.999784i | \(0.506615\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.9289 | 1.06677 | 0.533386 | − | 0.845872i | \(-0.320919\pi\) | ||||
0.533386 | + | 0.845872i | \(0.320919\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4402 | −0.555678 | −0.277839 | − | 0.960628i | \(-0.589618\pi\) | ||||
−0.277839 | + | 0.960628i | \(0.589618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.87447 | −0.152561 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.7707 | 1.09624 | 0.548119 | − | 0.836401i | \(-0.315344\pi\) | ||||
0.548119 | + | 0.836401i | \(0.315344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4004 | −0.915810 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.82987 | −0.200465 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.0528 | 0.890147 | 0.445073 | − | 0.895494i | \(-0.353178\pi\) | ||||
0.445073 | + | 0.895494i | \(0.353178\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.83471 | −0.354841 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.25712 | −0.479316 | −0.239658 | − | 0.970857i | \(-0.577035\pi\) | ||||
−0.239658 | + | 0.970857i | \(0.577035\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.0151 | 0.515806 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.77493 | −0.0911720 | −0.0455860 | − | 0.998960i | \(-0.514516\pi\) | ||||
−0.0455860 | + | 0.998960i | \(0.514516\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.0651 | −1.58735 | −0.793677 | − | 0.608340i | \(-0.791836\pi\) | ||||
−0.793677 | + | 0.608340i | \(0.791836\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.34206 | −0.0683976 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.3228 | −0.776895 | −0.388447 | − | 0.921471i | \(-0.626988\pi\) | ||||
−0.388447 | + | 0.921471i | \(0.626988\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.9425 | −0.705104 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.06204 | 0.154068 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.6759 | −0.786750 | −0.393375 | − | 0.919378i | \(-0.628693\pi\) | ||||
−0.393375 | + | 0.919378i | \(0.628693\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.08266 | 0.253816 | 0.126908 | − | 0.991915i | \(-0.459495\pi\) | ||||
0.126908 | + | 0.991915i | \(0.459495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.24910 | −0.311290 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.82439 | −0.486977 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.5378 | −1.60889 | −0.804444 | − | 0.594028i | \(-0.797537\pi\) | ||||
−0.804444 | + | 0.594028i | \(0.797537\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.374848 | −0.0184451 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0168046 | 0.000824903 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.2864 | −1.33303 | −0.666513 | − | 0.745493i | \(-0.732214\pi\) | ||||
−0.666513 | + | 0.745493i | \(0.732214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7042 | 0.667904 | 0.333952 | − | 0.942590i | \(-0.391618\pi\) | ||||
0.333952 | + | 0.942590i | \(0.391618\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.8056 | 0.960713 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.4506 | 0.554134 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7144 | −1.33496 | −0.667478 | − | 0.744629i | \(-0.732626\pi\) | ||||
−0.667478 | + | 0.744629i | \(0.732626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3197 | 1.45707 | 0.728535 | − | 0.685009i | \(-0.240202\pi\) | ||||
0.728535 | + | 0.685009i | \(0.240202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.15499 | 0.198760 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.5272 | 1.64789 | 0.823947 | − | 0.566667i | \(-0.191767\pi\) | ||||
0.823947 | + | 0.566667i | \(0.191767\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3329 | 0.490931 | 0.245465 | − | 0.969405i | \(-0.421059\pi\) | ||||
0.245465 | + | 0.969405i | \(0.421059\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.25588 | 0.0595342 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.34288 | 0.346532 | 0.173266 | − | 0.984875i | \(-0.444568\pi\) | ||||
0.173266 | + | 0.984875i | \(0.444568\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.76603 | −0.177335 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.34206 | 0.0629167 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.7210 | −0.875730 | −0.437865 | − | 0.899041i | \(-0.644265\pi\) | ||||
−0.437865 | + | 0.899041i | \(0.644265\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.3466 | −0.668189 | −0.334094 | − | 0.942540i | \(-0.608430\pi\) | ||||
−0.334094 | + | 0.942540i | \(0.608430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.1867 | 1.35642 | 0.678210 | − | 0.734869i | \(-0.262756\pi\) | ||||
0.678210 | + | 0.734869i | \(0.262756\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.2639 | −1.53927 | −0.769634 | − | 0.638486i | \(-0.779561\pi\) | ||||
−0.769634 | + | 0.638486i | \(0.779561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.9494 | 1.47529 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.64801 | −0.0757754 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.90224 | −0.270813 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.13113 | 0.234447 | 0.117224 | − | 0.993106i | \(-0.462601\pi\) | ||||
0.117224 | + | 0.993106i | \(0.462601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.82439 | 0.447954 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.44800 | 0.201973 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.97407 | −0.0894537 | −0.0447269 | − | 0.998999i | \(-0.514242\pi\) | ||||
−0.0447269 | + | 0.998999i | \(0.514242\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.20016 | −0.0992920 | −0.0496460 | − | 0.998767i | \(-0.515809\pi\) | ||||
−0.0496460 | + | 0.998767i | \(0.515809\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.5044 | 1.91430 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.5745 | 0.519186 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.3234 | −1.35746 | −0.678731 | − | 0.734387i | \(-0.737470\pi\) | ||||
−0.678731 | + | 0.734387i | \(0.737470\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.0069 | 1.15959 | 0.579795 | − | 0.814763i | \(-0.303133\pi\) | ||||
0.579795 | + | 0.814763i | \(0.303133\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.11674 | 0.138693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.82414 | 0.435447 | 0.217724 | − | 0.976010i | \(-0.430137\pi\) | ||||
0.217724 | + | 0.976010i | \(0.430137\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.4215 | 0.682207 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.82807 | 0.124620 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.17509 | −0.315560 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0343 | −0.746286 | −0.373143 | − | 0.927774i | \(-0.621720\pi\) | ||||
−0.373143 | + | 0.927774i | \(0.621720\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0598 | 0.833426 | 0.416713 | − | 0.909038i | \(-0.363182\pi\) | ||||
0.416713 | + | 0.909038i | \(0.363182\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.5213 | −1.15529 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.2074 | −0.530755 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.76603 | 0.163125 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.74494 | 0.421310 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.59602 | −0.0687453 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.0923 | −1.03581 | −0.517905 | − | 0.855438i | \(-0.673288\pi\) | ||||
−0.517905 | + | 0.855438i | \(0.673288\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.51654 | 0.150632 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.56763 | 0.0670269 | 0.0335134 | − | 0.999438i | \(-0.489330\pi\) | ||||
0.0335134 | + | 0.999438i | \(0.489330\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.6667 | −0.539619 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.3297 | −0.524313 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.65147 | 0.324203 | 0.162102 | − | 0.986774i | \(-0.448173\pi\) | ||||
0.162102 | + | 0.986774i | \(0.448173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.64801 | 0.0697032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.6704 | 0.660427 | 0.330214 | − | 0.943906i | \(-0.392879\pi\) | ||||
0.330214 | + | 0.943906i | \(0.392879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.50789 | 0.400000 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.2374 | 1.01608 | 0.508042 | − | 0.861332i | \(-0.330369\pi\) | ||||
0.508042 | + | 0.861332i | \(0.330369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.6748 | 0.907060 | 0.453530 | − | 0.891241i | \(-0.350164\pi\) | ||||
0.453530 | + | 0.891241i | \(0.350164\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.3311 | −0.639352 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3568 | 0.514422 | 0.257211 | − | 0.966355i | \(-0.417197\pi\) | ||||
0.257211 | + | 0.966355i | \(0.417197\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0676659 | −0.00280725 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.94011 | −0.121767 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.8474 | −0.819191 | −0.409595 | − | 0.912267i | \(-0.634330\pi\) | ||||
−0.409595 | + | 0.912267i | \(0.634330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.90358 | 0.325661 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.8721 | 1.47309 | 0.736545 | − | 0.676388i | \(-0.236456\pi\) | ||||
0.736545 | + | 0.676388i | \(0.236456\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.69572 | 0.233502 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.6061 | −0.515072 | −0.257536 | − | 0.966269i | \(-0.582911\pi\) | ||||
−0.257536 | + | 0.966269i | \(0.582911\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.79471 | −0.0732077 | −0.0366038 | − | 0.999330i | \(-0.511654\pi\) | ||||
−0.0366038 | + | 0.999330i | \(0.511654\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.577317 | −0.0234713 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.1856 | −0.819309 | −0.409654 | − | 0.912241i | \(-0.634351\pi\) | ||||
−0.409654 | + | 0.912241i | \(0.634351\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.17509 | 0.290273 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.6311 | −1.88341 | −0.941706 | − | 0.336438i | \(-0.890778\pi\) | ||||
−0.941706 | + | 0.336438i | \(0.890778\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.5397 | 1.22948 | 0.614740 | − | 0.788730i | \(-0.289261\pi\) | ||||
0.614740 | + | 0.788730i | \(0.289261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.372313 | −0.0149645 | −0.00748226 | − | 0.999972i | \(-0.502382\pi\) | ||||
−0.00748226 | + | 0.999972i | \(0.502382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.05696 | −0.202603 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.1117 | 0.804466 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 41.6949 | 1.66249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.9298 | −1.47015 | −0.735076 | − | 0.677985i | \(-0.762854\pi\) | ||||
−0.735076 | + | 0.677985i | \(0.762854\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.54080 | −0.299247 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.59602 | 0.0632365 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.3642 | 1.55479 | 0.777396 | − | 0.629012i | \(-0.216540\pi\) | ||||
0.777396 | + | 0.629012i | \(0.216540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.22345 | −0.166556 | −0.0832782 | − | 0.996526i | \(-0.526539\pi\) | ||||
−0.0832782 | + | 0.996526i | \(0.526539\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.51054 | 0.373898 | 0.186949 | − | 0.982370i | \(-0.440140\pi\) | ||||
0.186949 | + | 0.982370i | \(0.440140\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.161250 | −0.00632960 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.2209 | 1.65223 | 0.826115 | − | 0.563502i | \(-0.190546\pi\) | ||||
0.826115 | + | 0.563502i | \(0.190546\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.72816 | 0.106598 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.7083 | 1.66368 | 0.831840 | − | 0.555016i | \(-0.187288\pi\) | ||||
0.831840 | + | 0.555016i | \(0.187288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.89699 | 0.112680 | 0.0563400 | − | 0.998412i | \(-0.482057\pi\) | ||||
0.0563400 | + | 0.998412i | \(0.482057\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.69737 | −0.0658213 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.9019 | −1.27397 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.92574 | 0.190156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.71339 | −0.297329 | −0.148665 | − | 0.988888i | \(-0.547497\pi\) | ||||
−0.148665 | + | 0.988888i | \(0.547497\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.15703 | −0.351933 | −0.175967 | − | 0.984396i | \(-0.556305\pi\) | ||||
−0.175967 | + | 0.984396i | \(0.556305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.9105 | −0.687341 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.8023 | 1.17862 | 0.589308 | − | 0.807908i | \(-0.299400\pi\) | ||||
0.589308 | + | 0.807908i | \(0.299400\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.1729 | −0.503312 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.94011 | 0.112009 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.0928 | −0.574159 | −0.287079 | − | 0.957907i | \(-0.592684\pi\) | ||||
−0.287079 | + | 0.957907i | \(0.592684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.28318 | 0.162470 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.9831 | 0.605404 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.62906 | 0.363685 | 0.181842 | − | 0.983328i | \(-0.441794\pi\) | ||||
0.181842 | + | 0.983328i | \(0.441794\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.4254 | −0.468634 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.5500 | −0.471990 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.58482 | −0.0595191 | −0.0297596 | − | 0.999557i | \(-0.509474\pi\) | ||||
−0.0297596 | + | 0.999557i | \(0.509474\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.5296 | 0.768841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.577317 | 0.0215904 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.7830 | −1.55824 | −0.779122 | − | 0.626873i | \(-0.784335\pi\) | ||||
−0.779122 | + | 0.626873i | \(0.784335\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.3876 | −0.424097 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 46.7377 | 1.73579 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.0272 | −0.520240 | −0.260120 | − | 0.965576i | \(-0.583762\pi\) | ||||
−0.260120 | + | 0.965576i | \(0.583762\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.99417 | 0.258689 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.14183 | −0.0421745 | −0.0210873 | − | 0.999778i | \(-0.506713\pi\) | ||||
−0.0210873 | + | 0.999778i | \(0.506713\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.7438 | 0.506258 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.2412 | 0.781370 | 0.390685 | − | 0.920524i | \(-0.372238\pi\) | ||||
0.390685 | + | 0.920524i | \(0.372238\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.10797 | −0.224080 | −0.112040 | − | 0.993704i | \(-0.535738\pi\) | ||||
−0.112040 | + | 0.993704i | \(0.535738\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.41124 | 0.0883409 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −39.2393 | −1.43377 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.5690 | −1.37091 | −0.685457 | − | 0.728113i | \(-0.740397\pi\) | ||||
−0.685457 | + | 0.728113i | \(0.740397\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.61700 | −0.0588485 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.2962 | 0.774022 | 0.387011 | − | 0.922075i | \(-0.373508\pi\) | ||||
0.387011 | + | 0.922075i | \(0.373508\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.6289 | 1.32780 | 0.663899 | − | 0.747823i | \(-0.268901\pi\) | ||||
0.663899 | + | 0.747823i | \(0.268901\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.1598 | −0.512620 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.161250 | 0.00582238 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.2465 | −0.477680 | −0.238840 | − | 0.971059i | \(-0.576767\pi\) | ||||
−0.238840 | + | 0.971059i | \(0.576767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.8912 | −0.895276 | −0.447638 | − | 0.894215i | \(-0.647735\pi\) | ||||
−0.447638 | + | 0.894215i | \(0.647735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.1627 | −1.04756 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.76310 | −0.170656 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.97902 | 0.178163 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.98329 | −0.142170 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.6156 | 1.23391 | 0.616956 | − | 0.786998i | \(-0.288366\pi\) | ||||
0.616956 | + | 0.786998i | \(0.288366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38.2848 | −1.36125 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.92574 | −0.174918 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.4262 | 1.67992 | 0.839961 | − | 0.542647i | \(-0.182578\pi\) | ||||
0.839961 | + | 0.542647i | \(0.182578\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.4513 | 1.07729 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.63391 | 0.234106 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.40895 | −0.155395 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.5375 | −1.60101 | −0.800507 | − | 0.599324i | \(-0.795436\pi\) | ||||
−0.800507 | + | 0.599324i | \(0.795436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.6530 | 1.67332 | 0.836662 | − | 0.547720i | \(-0.184504\pi\) | ||||
0.836662 | + | 0.547720i | \(0.184504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.534590 | −0.0187259 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.08432 | −0.0729212 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.4373 | −0.713267 | −0.356633 | − | 0.934244i | \(-0.616075\pi\) | ||||
−0.356633 | + | 0.934244i | \(0.616075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.7858 | 0.585117 | 0.292559 | − | 0.956248i | \(-0.405493\pi\) | ||||
0.292559 | + | 0.956248i | \(0.405493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.2453 | −1.39947 | −0.699733 | − | 0.714405i | \(-0.746698\pi\) | ||||
−0.699733 | + | 0.714405i | \(0.746698\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.5946 | −0.680549 | −0.340275 | − | 0.940326i | \(-0.610520\pi\) | ||||
−0.340275 | + | 0.940326i | \(0.610520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.77353 | 0.234689 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.07480 | 0.279440 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.2515 | 1.52773 | 0.763866 | − | 0.645375i | \(-0.223299\pi\) | ||||
0.763866 | + | 0.645375i | \(0.223299\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 71.3029 | 2.45872 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.577317 | −0.0198603 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.32465 | 0.0798758 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.2752 | −1.10638 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.94453 | 0.0665794 | 0.0332897 | − | 0.999446i | \(-0.489402\pi\) | ||||
0.0332897 | + | 0.999446i | \(0.489402\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.2112 | 0.690402 | 0.345201 | − | 0.938529i | \(-0.387811\pi\) | ||||
0.345201 | + | 0.938529i | \(0.387811\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.9473 | 1.36299 | 0.681493 | − | 0.731825i | \(-0.261331\pi\) | ||||
0.681493 | + | 0.731825i | \(0.261331\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.0748 | 1.29608 | 0.648040 | − | 0.761606i | \(-0.275589\pi\) | ||||
0.648040 | + | 0.761606i | \(0.275589\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.65641 | −0.0563195 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.30391 | −0.179923 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.7438 | −0.465690 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.9733 | 0.438577 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.9780 | −0.809679 | −0.404840 | − | 0.914388i | \(-0.632673\pi\) | ||||
−0.404840 | + | 0.914388i | \(0.632673\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.70216 | 0.326874 | 0.163437 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163437 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.1937 | −0.847835 | −0.423917 | − | 0.905701i | \(-0.639345\pi\) | ||||
−0.423917 | + | 0.905701i | \(0.639345\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.3766 | 1.42287 | 0.711434 | − | 0.702753i | \(-0.248046\pi\) | ||||
0.711434 | + | 0.702753i | \(0.248046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.3641 | 1.01838 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.07473 | −0.303674 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.54971 | −0.185506 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −62.5856 | −2.08735 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.4779 | 0.415699 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.299462 | 0.00995445 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.41088 | −0.279279 | −0.139639 | − | 0.990202i | \(-0.544594\pi\) | ||||
−0.139639 | + | 0.990202i | \(0.544594\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.389007 | −0.0128884 | −0.00644419 | − | 0.999979i | \(-0.502051\pi\) | ||||
−0.00644419 | + | 0.999979i | \(0.502051\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0291080 | −0.000963335 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.9853 | −0.362767 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.6999 | 1.21062 | 0.605309 | − | 0.795990i | \(-0.293049\pi\) | ||||
0.605309 | + | 0.795990i | \(0.293049\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.97902 | −0.163886 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.8475 | 1.50746 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.3490 | 1.58628 | 0.793140 | − | 0.609039i | \(-0.208445\pi\) | ||||
0.793140 | + | 0.609039i | \(0.208445\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.01857 | −0.0661559 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.45015 | 0.0801283 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.0605 | −1.21071 | −0.605357 | − | 0.795954i | \(-0.706970\pi\) | ||||
−0.605357 | + | 0.795954i | \(0.706970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.9386 | −0.421788 | −0.210894 | − | 0.977509i | \(-0.567637\pi\) | ||||
−0.210894 | + | 0.977509i | \(0.567637\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.3722 | −0.402895 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.23237 | −0.170029 | −0.0850145 | − | 0.996380i | \(-0.527094\pi\) | ||||
−0.0850145 | + | 0.996380i | \(0.527094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.63391 | −0.215346 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.9464 | 1.03485 | 0.517423 | − | 0.855730i | \(-0.326891\pi\) | ||||
0.517423 | + | 0.855730i | \(0.326891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.51573 | −0.210844 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.0427 | 1.71284 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.05129 | 0.259719 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.02852 | 0.129683 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.4290 | −0.431849 | −0.215924 | − | 0.976410i | \(-0.569276\pi\) | ||||
−0.215924 | + | 0.976410i | \(0.569276\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.7906 | 1.05230 | 0.526150 | − | 0.850392i | \(-0.323635\pi\) | ||||
0.526150 | + | 0.850392i | \(0.323635\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.2468 | −0.552908 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.5258 | 0.752657 | 0.376329 | − | 0.926486i | \(-0.377186\pi\) | ||||
0.376329 | + | 0.926486i | \(0.377186\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.17537 | −0.0695250 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.6643 | 1.55215 | 0.776075 | − | 0.630641i | \(-0.217208\pi\) | ||||
0.776075 | + | 0.630641i | \(0.217208\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5659 | 0.368519 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.41405 | −0.172157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.8776 | 0.377306 | 0.188653 | − | 0.982044i | \(-0.439588\pi\) | ||||
0.188653 | + | 0.982044i | \(0.439588\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.98245 | 0.157954 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.6861 | −0.401774 | −0.200887 | − | 0.979614i | \(-0.564382\pi\) | ||||
−0.200887 | + | 0.979614i | \(0.564382\pi\) | |||||||
\(998\) | 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 | 5148.2.a.s.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 5148.2.a.t.1.3 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5148.2.a.s.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
5148.2.a.t.1.3 | yes | 5 | 3.2 | odd | 2 |