Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4704,2,Mod(1,4704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4704, 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("4704.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4704.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: | \(37.5616291108\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.814115\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4704.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.04244 | 0.466195 | 0.233097 | − | 0.972453i | \(-0.425114\pi\) | ||||
0.233097 | + | 0.972453i | \(0.425114\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.93089 | −1.78823 | −0.894116 | − | 0.447836i | \(-0.852195\pi\) | ||||
−0.894116 | + | 0.447836i | \(0.852195\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.888450 | 0.246412 | 0.123206 | − | 0.992381i | \(-0.460682\pi\) | ||||
0.123206 | + | 0.992381i | \(0.460682\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.04244 | 0.269158 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.51668 | −1.09546 | −0.547728 | − | 0.836657i | \(-0.684507\pi\) | ||||
−0.547728 | + | 0.836657i | \(0.684507\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.47424 | 0.797045 | 0.398522 | − | 0.917159i | \(-0.369523\pi\) | ||||
0.398522 | + | 0.917159i | \(0.369523\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.93089 | 0.402619 | 0.201310 | − | 0.979528i | \(-0.435480\pi\) | ||||
0.201310 | + | 0.979528i | \(0.435480\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.91331 | −0.782663 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.38755 | −1.55753 | −0.778764 | − | 0.627316i | \(-0.784153\pi\) | ||||
−0.778764 | + | 0.627316i | \(0.784153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.13109 | 0.921571 | 0.460786 | − | 0.887511i | \(-0.347568\pi\) | ||||
0.460786 | + | 0.887511i | \(0.347568\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.93089 | −1.03244 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.65685 | 0.929981 | 0.464991 | − | 0.885316i | \(-0.346058\pi\) | ||||
0.464991 | + | 0.885316i | \(0.346058\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.888450 | 0.142266 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.39663 | −1.31133 | −0.655667 | − | 0.755050i | \(-0.727612\pi\) | ||||
−0.655667 | + | 0.755050i | \(0.727612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.743541 | 0.113389 | 0.0566945 | − | 0.998392i | \(-0.481944\pi\) | ||||
0.0566945 | + | 0.998392i | \(0.481944\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.04244 | 0.155398 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.21778 | −0.615226 | −0.307613 | − | 0.951512i | \(-0.599530\pi\) | ||||
−0.307613 | + | 0.951512i | \(0.599530\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.51668 | −0.632462 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.91331 | −0.949617 | −0.474808 | − | 0.880089i | \(-0.657483\pi\) | ||||
−0.474808 | + | 0.880089i | \(0.657483\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.18262 | −0.833664 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.47424 | 0.460174 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.43908 | 0.708107 | 0.354054 | − | 0.935225i | \(-0.384803\pi\) | ||||
0.354054 | + | 0.935225i | \(0.384803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.9733 | −1.40499 | −0.702496 | − | 0.711688i | \(-0.747931\pi\) | ||||
−0.702496 | + | 0.711688i | \(0.747931\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.926159 | 0.114876 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.20493 | 0.758053 | 0.379027 | − | 0.925386i | \(-0.376259\pi\) | ||||
0.379027 | + | 0.925386i | \(0.376259\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.93089 | 0.232452 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.72596 | −0.442190 | −0.221095 | − | 0.975252i | \(-0.570963\pi\) | ||||
−0.221095 | + | 0.975252i | \(0.570963\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.49910 | 0.409539 | 0.204769 | − | 0.978810i | \(-0.434356\pi\) | ||||
0.204769 | + | 0.978810i | \(0.434356\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.91331 | −0.451870 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6053 | −1.41821 | −0.709105 | − | 0.705103i | \(-0.750901\pi\) | ||||
−0.709105 | + | 0.705103i | \(0.750901\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.94847 | −0.323637 | −0.161819 | − | 0.986821i | \(-0.551736\pi\) | ||||
−0.161819 | + | 0.986821i | \(0.551736\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.70838 | −0.510696 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.38755 | −0.899240 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.00196 | 0.530207 | 0.265103 | − | 0.964220i | \(-0.414594\pi\) | ||||
0.265103 | + | 0.964220i | \(0.414594\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.13109 | 0.532069 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.62169 | 0.371578 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1578 | −1.03136 | −0.515682 | − | 0.856780i | \(-0.672461\pi\) | ||||
−0.515682 | + | 0.856780i | \(0.672461\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.93089 | −0.596077 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.78598 | −0.177712 | −0.0888560 | − | 0.996044i | \(-0.528321\pi\) | ||||
−0.0888560 | + | 0.996044i | \(0.528321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.5925 | −1.83197 | −0.915986 | − | 0.401211i | \(-0.868590\pi\) | ||||
−0.915986 | + | 0.401211i | \(0.868590\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.23888 | −0.603135 | −0.301568 | − | 0.953445i | \(-0.597510\pi\) | ||||
−0.301568 | + | 0.953445i | \(0.597510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.74354 | −0.454349 | −0.227174 | − | 0.973854i | \(-0.572949\pi\) | ||||
−0.227174 | + | 0.973854i | \(0.572949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.65685 | 0.536925 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.3137 | −1.25245 | −0.626224 | − | 0.779643i | \(-0.715401\pi\) | ||||
−0.626224 | + | 0.779643i | \(0.715401\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.01285 | 0.187699 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.888450 | 0.0821373 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.1755 | 2.19777 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.39663 | −0.757099 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.29162 | −0.831068 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.307985 | 0.0273292 | 0.0136646 | − | 0.999907i | \(-0.495650\pi\) | ||||
0.0136646 | + | 0.999907i | \(0.495650\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.743541 | 0.0654652 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.46139 | 0.826646 | 0.413323 | − | 0.910585i | \(-0.364368\pi\) | ||||
0.413323 | + | 0.910585i | \(0.364368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.04244 | 0.0897192 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.87463 | −0.160161 | −0.0800803 | − | 0.996788i | \(-0.525518\pi\) | ||||
−0.0800803 | + | 0.996788i | \(0.525518\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.31371 | −0.620341 | −0.310170 | − | 0.950681i | \(-0.600386\pi\) | ||||
−0.310170 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.21778 | −0.355201 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.26930 | −0.440641 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.74354 | −0.726112 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.2270 | 1.82091 | 0.910454 | − | 0.413610i | \(-0.135732\pi\) | ||||
0.910454 | + | 0.413610i | \(0.135732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.4004 | 1.17189 | 0.585944 | − | 0.810352i | \(-0.300724\pi\) | ||||
0.585944 | + | 0.810352i | \(0.300724\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.51668 | −0.365152 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.34887 | 0.429632 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.9715 | −1.43428 | −0.717142 | − | 0.696927i | \(-0.754550\pi\) | ||||
−0.717142 | + | 0.696927i | \(0.754550\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.91331 | −0.548261 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.1755 | 1.81524 | 0.907622 | − | 0.419787i | \(-0.137895\pi\) | ||||
0.907622 | + | 0.419787i | \(0.137895\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.18262 | −0.481316 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.9929 | 1.00542 | 0.502710 | − | 0.864455i | \(-0.332337\pi\) | ||||
0.502710 | + | 0.864455i | \(0.332337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2107 | −0.939281 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.47424 | 0.265682 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.1846 | −1.76269 | −0.881345 | − | 0.472472i | \(-0.843362\pi\) | ||||
−0.881345 | + | 0.472472i | \(0.843362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.43908 | 0.408826 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.9366 | −1.86385 | −0.931925 | − | 0.362651i | \(-0.881872\pi\) | ||||
−0.931925 | + | 0.362651i | \(0.881872\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.3498 | −1.66125 | −0.830625 | − | 0.556832i | \(-0.812017\pi\) | ||||
−0.830625 | + | 0.556832i | \(0.812017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.9733 | −0.811172 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.89695 | 0.433552 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.7879 | 1.95893 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.03967 | −0.509373 | −0.254686 | − | 0.967024i | \(-0.581972\pi\) | ||||
−0.254686 | + | 0.967024i | \(0.581972\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.3747 | 0.890751 | 0.445375 | − | 0.895344i | \(-0.353070\pi\) | ||||
0.445375 | + | 0.895344i | \(0.353070\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.926159 | 0.0663236 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.4262 | 0.956579 | 0.478290 | − | 0.878202i | \(-0.341257\pi\) | ||||
0.478290 | + | 0.878202i | \(0.341257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.82663 | 0.696591 | 0.348296 | − | 0.937385i | \(-0.386761\pi\) | ||||
0.348296 | + | 0.937385i | \(0.386761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.20493 | 0.437662 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.75301 | −0.611337 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.93089 | 0.134206 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.6053 | −1.42530 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.1698 | 1.38854 | 0.694272 | − | 0.719713i | \(-0.255726\pi\) | ||||
0.694272 | + | 0.719713i | \(0.255726\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.72596 | −0.255299 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.775099 | 0.0528613 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.49910 | 0.236447 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.01285 | −0.269933 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.0373 | −1.81055 | −0.905275 | − | 0.424826i | \(-0.860335\pi\) | ||||
−0.905275 | + | 0.424826i | \(0.860335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.91331 | −0.260888 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.02231 | 0.532460 | 0.266230 | − | 0.963910i | \(-0.414222\pi\) | ||||
0.266230 | + | 0.963910i | \(0.414222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4920 | 0.825493 | 0.412747 | − | 0.910846i | \(-0.364570\pi\) | ||||
0.412747 | + | 0.910846i | \(0.364570\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.7013 | 1.29067 | 0.645336 | − | 0.763899i | \(-0.276717\pi\) | ||||
0.645336 | + | 0.763899i | \(0.276717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.39679 | −0.286815 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.6053 | −0.818804 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.93089 | 0.124899 | 0.0624496 | − | 0.998048i | \(-0.480109\pi\) | ||||
0.0624496 | + | 0.998048i | \(0.480109\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.1026 | 0.972846 | 0.486423 | − | 0.873724i | \(-0.338301\pi\) | ||||
0.486423 | + | 0.873724i | \(0.338301\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.08669 | 0.196401 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.94847 | −0.186852 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.5982 | 1.86822 | 0.934111 | − | 0.356982i | \(-0.116194\pi\) | ||||
0.934111 | + | 0.356982i | \(0.116194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.4519 | −0.719976 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.70838 | −0.294850 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.8580 | −0.864440 | −0.432220 | − | 0.901768i | \(-0.642270\pi\) | ||||
−0.432220 | + | 0.901768i | \(0.642270\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.38755 | −0.519176 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.78696 | −0.171851 | −0.0859255 | − | 0.996302i | \(-0.527385\pi\) | ||||
−0.0859255 | + | 0.996302i | \(0.527385\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.20673 | −0.442706 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.00196 | 0.306115 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.44104 | 0.392717 | 0.196358 | − | 0.980532i | \(-0.437088\pi\) | ||||
0.196358 | + | 0.980532i | \(0.437088\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8547 | 1.26683 | 0.633415 | − | 0.773812i | \(-0.281652\pi\) | ||||
0.633415 | + | 0.773812i | \(0.281652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.2094 | 1.39958 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.0724 | −1.62663 | −0.813313 | − | 0.581827i | \(-0.802338\pi\) | ||||
−0.813313 | + | 0.581827i | \(0.802338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.13109 | 0.307190 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.28450 | 0.374902 | 0.187451 | − | 0.982274i | \(-0.439977\pi\) | ||||
0.187451 | + | 0.982274i | \(0.439977\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.57729 | 0.331535 | 0.165768 | − | 0.986165i | \(-0.446990\pi\) | ||||
0.165768 | + | 0.986165i | \(0.446990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.62169 | 0.214531 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.40040 | 0.200023 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.1578 | −0.595458 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6460 | 0.738785 | 0.369393 | − | 0.929273i | \(-0.379566\pi\) | ||||
0.369393 | + | 0.929273i | \(0.379566\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.66993 | 0.330116 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.93089 | −0.344145 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.71550 | 0.0992101 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.78598 | −0.102602 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.4391 | −0.655000 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.2750 | −0.928865 | −0.464432 | − | 0.885609i | \(-0.653742\pi\) | ||||
−0.464432 | + | 0.885609i | \(0.653742\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.5925 | −1.05769 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.9929 | −1.64404 | −0.822018 | − | 0.569462i | \(-0.807152\pi\) | ||||
−0.822018 | + | 0.569462i | \(0.807152\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.5840 | −0.767812 | −0.383906 | − | 0.923372i | \(-0.625421\pi\) | ||||
−0.383906 | + | 0.923372i | \(0.625421\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.1240 | 1.35494 | 0.677469 | − | 0.735552i | \(-0.263077\pi\) | ||||
0.677469 | + | 0.735552i | \(0.263077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 49.7457 | 2.78522 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.23888 | −0.348220 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.6920 | −0.873127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.47678 | −0.192857 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.74354 | −0.262318 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.72357 | −0.424526 | −0.212263 | − | 0.977213i | \(-0.568083\pi\) | ||||
−0.212263 | + | 0.977213i | \(0.568083\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.65685 | 0.309994 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.46829 | 0.353400 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.05153 | 0.0572803 | 0.0286401 | − | 0.999590i | \(-0.490882\pi\) | ||||
0.0286401 | + | 0.999590i | \(0.490882\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.3137 | −0.723101 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.4320 | −1.64798 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.01285 | 0.108368 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.52103 | −0.0816531 | −0.0408265 | − | 0.999166i | \(-0.512999\pi\) | ||||
−0.0408265 | + | 0.999166i | \(0.512999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.1670 | −0.972457 | −0.486229 | − | 0.873832i | \(-0.661628\pi\) | ||||
−0.486229 | + | 0.873832i | \(0.661628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.888450 | 0.0474220 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.2069 | −0.596483 | −0.298241 | − | 0.954490i | \(-0.596400\pi\) | ||||
−0.298241 | + | 0.954490i | \(0.596400\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.88410 | −0.206147 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.44381 | −0.445647 | −0.222824 | − | 0.974859i | \(-0.571527\pi\) | ||||
−0.222824 | + | 0.974859i | \(0.571527\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.92968 | −0.364720 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.1755 | 1.26888 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.64761 | 0.190925 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.2880 | −1.21562 | −0.607812 | − | 0.794081i | \(-0.707953\pi\) | ||||
−0.607812 | + | 0.794081i | \(0.707953\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.39663 | −0.437111 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.5502 | 1.84072 | 0.920360 | − | 0.391073i | \(-0.127896\pi\) | ||||
0.920360 | + | 0.391073i | \(0.127896\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.29162 | −0.479817 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.45192 | −0.383794 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.4168 | 0.689173 | 0.344586 | − | 0.938755i | \(-0.388019\pi\) | ||||
0.344586 | + | 0.938755i | \(0.388019\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.307985 | 0.0157785 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.6533 | −1.82180 | −0.910898 | − | 0.412632i | \(-0.864610\pi\) | ||||
−0.910898 | + | 0.412632i | \(0.864610\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.743541 | 0.0377963 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.3360 | 1.18318 | 0.591592 | − | 0.806238i | \(-0.298500\pi\) | ||||
0.591592 | + | 0.806238i | \(0.298500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.72123 | −0.441051 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.46139 | 0.477264 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.1403 | −0.661162 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.63199 | 0.483416 | 0.241708 | − | 0.970349i | \(-0.422292\pi\) | ||||
0.241708 | + | 0.970349i | \(0.422292\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.61245 | −0.380148 | −0.190074 | − | 0.981770i | \(-0.560873\pi\) | ||||
−0.190074 | + | 0.981770i | \(0.560873\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.55872 | 0.227086 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.04244 | 0.0517994 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.5502 | −1.66302 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.6564 | −1.71365 | −0.856825 | − | 0.515607i | \(-0.827566\pi\) | ||||
−0.856825 | + | 0.515607i | \(0.827566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.87463 | −0.0924688 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.07362 | −0.150878 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.31371 | −0.358154 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.53523 | −0.319267 | −0.159633 | − | 0.987176i | \(-0.551031\pi\) | ||||
−0.159633 | + | 0.987176i | \(0.551031\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4778 | −0.510655 | −0.255327 | − | 0.966855i | \(-0.582183\pi\) | ||||
−0.255327 | + | 0.966855i | \(0.582183\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.21778 | −0.205075 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.6752 | 0.857372 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.26930 | −0.254404 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.9682 | 1.39535 | 0.697674 | − | 0.716415i | \(-0.254218\pi\) | ||||
0.697674 | + | 0.716415i | \(0.254218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.31116 | 0.351352 | 0.175676 | − | 0.984448i | \(-0.443789\pi\) | ||||
0.175676 | + | 0.984448i | \(0.443789\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.74354 | −0.419221 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.70838 | 0.320905 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.6863 | −0.605484 | −0.302742 | − | 0.953073i | \(-0.597902\pi\) | ||||
−0.302742 | + | 0.953073i | \(0.597902\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.6136 | 0.789335 | 0.394668 | − | 0.918824i | \(-0.370860\pi\) | ||||
0.394668 | + | 0.918824i | \(0.370860\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.21426 | 0.247180 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.2270 | 1.05130 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 49.7995 | 2.34497 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.4004 | 0.676590 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.72357 | −0.454850 | −0.227425 | − | 0.973796i | \(-0.573031\pi\) | ||||
−0.227425 | + | 0.973796i | \(0.573031\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.51668 | −0.210821 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.9451 | 0.835787 | 0.417894 | − | 0.908496i | \(-0.362768\pi\) | ||||
0.417894 | + | 0.908496i | \(0.362768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.37470 | −0.110362 | −0.0551809 | − | 0.998476i | \(-0.517574\pi\) | ||||
−0.0551809 | + | 0.998476i | \(0.517574\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.34887 | 0.248048 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.3617 | 0.710855 | 0.355428 | − | 0.934704i | \(-0.384335\pi\) | ||||
0.355428 | + | 0.934704i | \(0.384335\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.9715 | −0.828085 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.40986 | −0.202766 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.5958 | −0.623817 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.91331 | −0.316539 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.0444 | −0.641705 | −0.320853 | − | 0.947129i | \(-0.603969\pi\) | ||||
−0.320853 | + | 0.947129i | \(0.603969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.02583 | 0.229158 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.5889 | −0.480816 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.4004 | 1.37757 | 0.688787 | − | 0.724964i | \(-0.258144\pi\) | ||||
0.688787 | + | 0.724964i | \(0.258144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.1755 | 1.04803 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.5526 | 1.15317 | 0.576586 | − | 0.817036i | \(-0.304385\pi\) | ||||
0.576586 | + | 0.817036i | \(0.304385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.8839 | 1.70620 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.18262 | −0.277888 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.2270 | 0.726421 | 0.363211 | − | 0.931707i | \(-0.381681\pi\) | ||||
0.363211 | + | 0.931707i | \(0.381681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.9929 | 0.580479 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.2880 | −1.75177 | −0.875883 | − | 0.482523i | \(-0.839720\pi\) | ||||
−0.875883 | + | 0.482523i | \(0.839720\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.86179 | −0.0828484 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.2107 | −0.542294 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.93187 | 0.129953 | 0.0649763 | − | 0.997887i | \(-0.479303\pi\) | ||||
0.0649763 | + | 0.997887i | \(0.479303\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.47424 | 0.153391 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.3816 | −0.854055 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.0152 | 1.10017 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.1846 | −1.01769 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.3508 | −1.15445 | −0.577225 | − | 0.816585i | \(-0.695865\pi\) | ||||
−0.577225 | + | 0.816585i | \(0.695865\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.7048 | 1.77990 | 0.889948 | − | 0.456062i | \(-0.150741\pi\) | ||||
0.889948 | + | 0.456062i | \(0.150741\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.1755 | −1.00954 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2717 | −0.837898 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.43908 | 0.236036 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.45999 | −0.323128 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.50367 | −0.281178 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.9366 | −1.07609 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.3489 | −0.659899 | −0.329950 | − | 0.943999i | \(-0.607032\pi\) | ||||
−0.329950 | + | 0.943999i | \(0.607032\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.3498 | −0.959123 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.94487 | −0.211815 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.2258 | 1.46339 | 0.731696 | − | 0.681631i | \(-0.238729\pi\) | ||||
0.731696 | + | 0.681631i | \(0.238729\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.9733 | −0.468331 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.1403 | −1.24142 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.89695 | 0.250311 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.6369 | −0.789670 | −0.394835 | − | 0.918752i | \(-0.629198\pi\) | ||||
−0.394835 | + | 0.918752i | \(0.629198\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.660600 | 0.0279404 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.7879 | 1.13099 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.90047 | −0.122240 | −0.0611201 | − | 0.998130i | \(-0.519467\pi\) | ||||
−0.0611201 | + | 0.998130i | \(0.519467\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.8788 | −0.583885 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.0853 | −1.13547 | −0.567737 | − | 0.823210i | \(-0.692181\pi\) | ||||
−0.567737 | + | 0.823210i | \(0.692181\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.39467 | 0.142063 | 0.0710313 | − | 0.997474i | \(-0.477371\pi\) | ||||
0.0710313 | + | 0.997474i | \(0.477371\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.03967 | −0.294086 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.55619 | −0.315115 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5545 | 0.938958 | 0.469479 | − | 0.882944i | \(-0.344442\pi\) | ||||
0.469479 | + | 0.882944i | \(0.344442\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.3747 | 0.514275 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.0021 | 1.69813 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.926159 | 0.0382920 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.4391 | 1.21508 | 0.607540 | − | 0.794289i | \(-0.292156\pi\) | ||||
0.607540 | + | 0.794289i | \(0.292156\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8266 | 0.734533 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.4262 | 0.552281 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.9153 | 1.39273 | 0.696367 | − | 0.717686i | \(-0.254799\pi\) | ||||
0.696367 | + | 0.717686i | \(0.254799\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.82663 | 0.402177 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.0655 | −1.14673 | −0.573363 | − | 0.819302i | \(-0.694361\pi\) | ||||
−0.573363 | + | 0.819302i | \(0.694361\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0434 | 0.695216 | 0.347608 | − | 0.937640i | \(-0.386994\pi\) | ||||
0.347608 | + | 0.937640i | \(0.386994\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.20493 | 0.252684 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.2016 | 1.02459 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.8639 | 1.49626 | 0.748130 | − | 0.663552i | \(-0.230952\pi\) | ||||
0.748130 | + | 0.663552i | \(0.230952\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.74729 | −0.151599 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.4483 | 1.02785 | 0.513924 | − | 0.857836i | \(-0.328191\pi\) | ||||
0.513924 | + | 0.857836i | \(0.328191\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.75301 | −0.352955 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.3103 | −1.42154 | −0.710770 | − | 0.703424i | \(-0.751653\pi\) | ||||
−0.710770 | + | 0.703424i | \(0.751653\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.9599 | 1.64632 | 0.823159 | − | 0.567811i | \(-0.192209\pi\) | ||||
0.823159 | + | 0.567811i | \(0.192209\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.93089 | 0.0774841 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.88058 | 0.395223 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.6053 | −0.822898 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.5502 | −1.01875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9648 | 0.874406 | 0.437203 | − | 0.899363i | \(-0.355969\pi\) | ||||
0.437203 | + | 0.899363i | \(0.355969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.1698 | 0.801676 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.321057 | 0.0127407 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.72596 | −0.147397 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.9520 | −1.26203 | −0.631014 | − | 0.775772i | \(-0.717361\pi\) | ||||
−0.631014 | + | 0.775772i | \(0.717361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.0501 | −1.61886 | −0.809430 | − | 0.587217i | \(-0.800223\pi\) | ||||
−0.809430 | + | 0.587217i | \(0.800223\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.775099 | 0.0305195 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.67917 | 0.380527 | 0.190264 | − | 0.981733i | \(-0.439066\pi\) | ||||
0.190264 | + | 0.981733i | \(0.439066\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.2586 | −1.26626 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.5982 | −0.688671 | −0.344336 | − | 0.938847i | \(-0.611896\pi\) | ||||
−0.344336 | + | 0.938847i | \(0.611896\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.86296 | 0.385378 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.49910 | 0.136513 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.10427 | −0.159880 | −0.0799398 | − | 0.996800i | \(-0.525473\pi\) | ||||
−0.0799398 | + | 0.996800i | \(0.525473\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −47.0124 | −1.82857 | −0.914286 | − | 0.405070i | \(-0.867247\pi\) | ||||
−0.914286 | + | 0.405070i | \(0.867247\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.01285 | −0.155846 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.1955 | −0.627091 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.0373 | −1.04532 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 65.0817 | 2.51245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.7587 | 0.838738 | 0.419369 | − | 0.907816i | \(-0.362251\pi\) | ||||
0.419369 | + | 0.907816i | \(0.362251\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.91331 | −0.150623 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.6829 | 0.910209 | 0.455105 | − | 0.890438i | \(-0.349602\pi\) | ||||
0.455105 | + | 0.890438i | \(0.349602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.02231 | 0.307416 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.0655 | −1.22695 | −0.613476 | − | 0.789713i | \(-0.710229\pi\) | ||||
−0.613476 | + | 0.789713i | \(0.710229\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.95420 | −0.0746660 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.4920 | 0.476599 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.14214 | −0.233997 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.8782 | −0.565992 | −0.282996 | − | 0.959121i | \(-0.591328\pi\) | ||||
−0.282996 | + | 0.959121i | \(0.591328\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.62412 | −0.289199 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.9249 | 1.43651 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.7013 | 0.745170 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.0150 | 1.17142 | 0.585710 | − | 0.810521i | \(-0.300816\pi\) | ||||
0.585710 | + | 0.810521i | \(0.300816\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.6533 | 0.741236 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.39679 | −0.165593 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −51.7105 | −1.94203 | −0.971014 | − | 0.239021i | \(-0.923173\pi\) | ||||
−0.971014 | + | 0.239021i | \(0.923173\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.6053 | −0.472737 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.90759 | 0.371042 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.49295 | −0.205425 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.93089 | 0.0721105 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.7493 | 0.736523 | 0.368262 | − | 0.929722i | \(-0.379953\pi\) | ||||
0.368262 | + | 0.929722i | \(0.379953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.1026 | 0.561673 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.8231 | 1.21902 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.3230 | −1.90346 | −0.951731 | − | 0.306932i | \(-0.900698\pi\) | ||||
−0.951731 | + | 0.306932i | \(0.900698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.35834 | −0.124213 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.1230 | 1.07568 | 0.537841 | − | 0.843046i | \(-0.319240\pi\) | ||||
0.537841 | + | 0.843046i | \(0.319240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.8008 | −1.35557 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.27855 | −0.341317 | −0.170658 | − | 0.985330i | \(-0.554589\pi\) | ||||
−0.170658 | + | 0.985330i | \(0.554589\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.08669 | 0.113392 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.5935 | −0.975620 | −0.487810 | − | 0.872950i | \(-0.662204\pi\) | ||||
−0.487810 | + | 0.872950i | \(0.662204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.1704 | 0.848898 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.94847 | −0.107879 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.2843 | −1.03211 | −0.516054 | − | 0.856556i | \(-0.672600\pi\) | ||||
−0.516054 | + | 0.856556i | \(0.672600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.5982 | 1.07862 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.0116 | 0.546328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.8839 | 0.650001 | 0.325000 | − | 0.945714i | \(-0.394636\pi\) | ||||
0.325000 | + | 0.945714i | \(0.394636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.4519 | −0.415678 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.5263 | 1.79533 | 0.897664 | − | 0.440681i | \(-0.145263\pi\) | ||||
0.897664 | + | 0.440681i | \(0.145263\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.70838 | −0.170232 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.83235 | 0.174486 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.0675 | 1.62517 | 0.812587 | − | 0.582840i | \(-0.198058\pi\) | ||||
0.812587 | + | 0.582840i | \(0.198058\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.8580 | −0.499085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.45051 | −0.160074 | −0.0800368 | − | 0.996792i | \(-0.525504\pi\) | ||||
−0.0800368 | + | 0.996792i | \(0.525504\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.0796 | −0.721279 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.1719 | −1.04519 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.0983 | 0.790739 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.38755 | −0.299747 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.7343 | −0.668656 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.1919 | 0.648470 | 0.324235 | − | 0.945977i | \(-0.394893\pi\) | ||||
0.324235 | + | 0.945977i | \(0.394893\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.78696 | −0.0992183 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.74926 | −0.346207 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.20673 | −0.255597 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.8005 | 0.843059 | 0.421529 | − | 0.906815i | \(-0.361493\pi\) | ||||
0.421529 | + | 0.906815i | \(0.361493\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.0504 | 0.673953 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.00196 | 0.176736 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.7528 | −0.732350 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.44104 | 0.226735 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 51.8897 | 1.82435 | 0.912173 | − | 0.409805i | \(-0.134403\pi\) | ||||
0.912173 | + | 0.409805i | \(0.134403\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6462 | −0.479183 | −0.239592 | − | 0.970874i | \(-0.577014\pi\) | ||||
−0.239592 | + | 0.970874i | \(0.577014\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.8547 | 0.731405 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.1591 | 0.846257 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.58324 | 0.0903761 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.69576 | 0.163883 | 0.0819416 | − | 0.996637i | \(-0.473888\pi\) | ||||
0.0819416 | + | 0.996637i | \(0.473888\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.8045 | 0.550912 | 0.275456 | − | 0.961314i | \(-0.411171\pi\) | ||||
0.275456 | + | 0.961314i | \(0.411171\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.2094 | 0.808049 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.8221 | −1.14134 | −0.570668 | − | 0.821181i | \(-0.693316\pi\) | ||||
−0.570668 | + | 0.821181i | \(0.693316\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.71688 | −0.129092 | −0.0645462 | − | 0.997915i | \(-0.520560\pi\) | ||||
−0.0645462 | + | 0.997915i | \(0.520560\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.0724 | −0.939133 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.5443 | 0.468721 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.13109 | 0.177356 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.16625 | 0.109311 | 0.0546556 | − | 0.998505i | \(-0.482594\pi\) | ||||
0.0546556 | + | 0.998505i | \(0.482594\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.3510 | 1.42590 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.28450 | 0.216450 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7289 | −0.437888 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.57729 | 0.191412 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9228 | 0.374428 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.30404 | −0.284325 | −0.142162 | − | 0.989843i | \(-0.545406\pi\) | ||||
−0.142162 | + | 0.989843i | \(0.545406\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.62169 | 0.123859 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.3117 | −0.488880 | −0.244440 | − | 0.969664i | \(-0.578604\pi\) | ||||
−0.244440 | + | 0.969664i | \(0.578604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.1463 | 1.16506 | 0.582528 | − | 0.812811i | \(-0.302064\pi\) | ||||
0.582528 | + | 0.812811i | \(0.302064\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.0397 | −1.32893 | −0.664463 | − | 0.747321i | \(-0.731340\pi\) | ||||
−0.664463 | + | 0.747321i | \(0.731340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.1686 | −0.821757 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.40040 | 0.115483 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 74.7609 | 2.53609 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.51277 | 0.186793 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.1578 | −0.343788 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.4225 | −0.419478 | −0.209739 | − | 0.977757i | \(-0.567261\pi\) | ||||
−0.209739 | + | 0.977757i | \(0.567261\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.6460 | 0.426538 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.4282 | 1.09253 | 0.546267 | − | 0.837611i | \(-0.316048\pi\) | ||||
0.546267 | + | 0.837611i | \(0.316048\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.8475 | −0.735228 | −0.367614 | − | 0.929978i | \(-0.619825\pi\) | ||||
−0.367614 | + | 0.929978i | \(0.619825\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.66993 | 0.190592 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.2035 | −1.81998 | −0.909988 | − | 0.414634i | \(-0.863910\pi\) | ||||
−0.909988 | + | 0.414634i | \(0.863910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.93089 | −0.198692 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.6536 | −0.490363 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.9950 | −0.868917 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.71550 | 0.0572790 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −43.0373 | −1.43537 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.2252 | 1.04026 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.2984 | −0.774466 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.8172 | 0.658018 | 0.329009 | − | 0.944327i | \(-0.393285\pi\) | ||||
0.329009 | + | 0.944327i | \(0.393285\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.78598 | −0.0592374 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.5583 | 1.07870 | 0.539352 | − | 0.842080i | \(-0.318669\pi\) | ||||
0.539352 | + | 0.842080i | \(0.318669\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.4871 | 0.578738 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.4391 | −0.378164 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.95420 | 0.0644630 | 0.0322315 | − | 0.999480i | \(-0.489739\pi\) | ||||
0.0322315 | + | 0.999480i | \(0.489739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.2750 | −0.536280 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.31033 | −0.108961 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.1370 | −0.727861 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.5925 | −0.610657 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.2641 | 0.763272 | 0.381636 | − | 0.924313i | \(-0.375361\pi\) | ||||
0.381636 | + | 0.924313i | \(0.375361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.9929 | −0.949184 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.9249 | 0.913242 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.1244 | 0.820778 | 0.410389 | − | 0.911911i | \(-0.365393\pi\) | ||||
0.410389 | + | 0.911911i | \(0.365393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.5840 | −0.443297 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.67721 | −0.152473 | −0.0762363 | − | 0.997090i | \(-0.524290\pi\) | ||||
−0.0762363 | + | 0.997090i | \(0.524290\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.2130 | −0.527968 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.24460 | 0.0404441 | 0.0202221 | − | 0.999796i | \(-0.493563\pi\) | ||||
0.0202221 | + | 0.999796i | \(0.493563\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.10878 | 0.100915 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.1240 | 0.782273 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.0373 | −1.07018 | −0.535091 | − | 0.844794i | \(-0.679723\pi\) | ||||
−0.535091 | + | 0.844794i | \(0.679723\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.33845 | −0.237467 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 49.7457 | 1.60805 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.67190 | −0.150707 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.23888 | −0.201045 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.8999 | 0.415263 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.9799 | −0.449563 | −0.224781 | − | 0.974409i | \(-0.572167\pi\) | ||||
−0.224781 | + | 0.974409i | \(0.572167\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.6920 | −0.504100 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.48708 | 0.176089 | 0.0880444 | − | 0.996117i | \(-0.471938\pi\) | ||||
0.0880444 | + | 0.996117i | \(0.471938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.47678 | −0.111346 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.324434 | −0.0103796 | −0.00518978 | − | 0.999987i | \(-0.501652\pi\) | ||||
−0.00518978 | + | 0.999987i | \(0.501652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.6661 | −0.948133 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.74354 | −0.151450 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.5129 | −0.718051 | −0.359025 | − | 0.933328i | \(-0.616891\pi\) | ||||
−0.359025 | + | 0.933328i | \(0.616891\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.9961 | 0.445952 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.43570 | 0.0456526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.1649 | 1.37118 | 0.685588 | − | 0.727989i | \(-0.259545\pi\) | ||||
0.685588 | + | 0.727989i | \(0.259545\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.72357 | −0.245100 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.2437 | 0.324747 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.7743 | 0.784609 | 0.392305 | − | 0.919835i | \(-0.371678\pi\) | ||||
0.392305 | + | 0.919835i | \(0.371678\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.65685 | 0.178975 |
(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 | 4704.2.a.by.1.3 | yes | 4 | |
4.3 | odd | 2 | 4704.2.a.bw.1.3 | ✓ | 4 | ||
7.6 | odd | 2 | 4704.2.a.bx.1.2 | yes | 4 | ||
8.3 | odd | 2 | 9408.2.a.en.1.2 | 4 | |||
8.5 | even | 2 | 9408.2.a.el.1.2 | 4 | |||
28.27 | even | 2 | 4704.2.a.bz.1.2 | yes | 4 | ||
56.13 | odd | 2 | 9408.2.a.em.1.3 | 4 | |||
56.27 | even | 2 | 9408.2.a.ek.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4704.2.a.bw.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
4704.2.a.bx.1.2 | yes | 4 | 7.6 | odd | 2 | ||
4704.2.a.by.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
4704.2.a.bz.1.2 | yes | 4 | 28.27 | even | 2 | ||
9408.2.a.ek.1.3 | 4 | 56.27 | even | 2 | |||
9408.2.a.el.1.2 | 4 | 8.5 | even | 2 | |||
9408.2.a.em.1.3 | 4 | 56.13 | odd | 2 | |||
9408.2.a.en.1.2 | 4 | 8.3 | odd | 2 |