Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | −0.659121 | −0.380543 | −0.190272 | − | 0.981731i | \(-0.560937\pi\) | ||||
−0.190272 | + | 0.981731i | \(0.560937\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.997881 | 0.446266 | 0.223133 | − | 0.974788i | \(-0.428372\pi\) | ||||
0.223133 | + | 0.974788i | \(0.428372\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.366743 | −0.138616 | −0.0693079 | − | 0.997595i | \(-0.522079\pi\) | ||||
−0.0693079 | + | 0.997595i | \(0.522079\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.56556 | −0.855187 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.34193 | −0.706118 | −0.353059 | − | 0.935601i | \(-0.614859\pi\) | ||||
−0.353059 | + | 0.935601i | \(0.614859\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58340 | 0.439155 | 0.219578 | − | 0.975595i | \(-0.429532\pi\) | ||||
0.219578 | + | 0.975595i | \(0.429532\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.657724 | −0.169824 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.164328 | 0.0398554 | 0.0199277 | − | 0.999801i | \(-0.493656\pi\) | ||||
0.0199277 | + | 0.999801i | \(0.493656\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.94082 | 0.674671 | 0.337336 | − | 0.941384i | \(-0.390474\pi\) | ||||
0.337336 | + | 0.941384i | \(0.390474\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.241728 | 0.0527493 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.49861 | 1.35505 | 0.677527 | − | 0.735498i | \(-0.263052\pi\) | ||||
0.677527 | + | 0.735498i | \(0.263052\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00423 | −0.800847 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.66838 | 0.705979 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.89072 | −1.46527 | −0.732635 | − | 0.680622i | \(-0.761710\pi\) | ||||
−0.732635 | + | 0.680622i | \(0.761710\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.02250 | 1.26128 | 0.630640 | − | 0.776076i | \(-0.282793\pi\) | ||||
0.630640 | + | 0.776076i | \(0.282793\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.54361 | 0.268709 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.365966 | −0.0618595 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.39311 | −0.886622 | −0.443311 | − | 0.896368i | \(-0.646196\pi\) | ||||
−0.443311 | + | 0.896368i | \(0.646196\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.04365 | −0.167118 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.46312 | −0.697023 | −0.348511 | − | 0.937305i | \(-0.613313\pi\) | ||||
−0.348511 | + | 0.937305i | \(0.613313\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.37356 | −1.27696 | −0.638478 | − | 0.769640i | \(-0.720436\pi\) | ||||
−0.638478 | + | 0.769640i | \(0.720436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.56012 | −0.381641 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.8414 | 1.87311 | 0.936555 | − | 0.350520i | \(-0.113995\pi\) | ||||
0.936555 | + | 0.350520i | \(0.113995\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.86550 | −0.980786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.108312 | −0.0151667 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.7113 | 1.74603 | 0.873013 | − | 0.487697i | \(-0.162163\pi\) | ||||
0.873013 | + | 0.487697i | \(0.162163\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.33697 | −0.315116 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.93836 | −0.256742 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.64319 | −1.25544 | −0.627718 | − | 0.778440i | \(-0.716011\pi\) | ||||
−0.627718 | + | 0.778440i | \(0.716011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.98548 | 1.27851 | 0.639255 | − | 0.768995i | \(-0.279243\pi\) | ||||
0.639255 | + | 0.768995i | \(0.279243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.940901 | 0.118542 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.58004 | 0.195980 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.58675 | 0.804700 | 0.402350 | − | 0.915486i | \(-0.368193\pi\) | ||||
0.402350 | + | 0.915486i | \(0.368193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.28337 | −0.515657 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.53600 | −1.13171 | −0.565857 | − | 0.824503i | \(-0.691455\pi\) | ||||
−0.565857 | + | 0.824503i | \(0.691455\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.32994 | 0.272699 | 0.136350 | − | 0.990661i | \(-0.456463\pi\) | ||||
0.136350 | + | 0.990661i | \(0.456463\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.63927 | 0.304757 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.858886 | 0.0978791 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.51367 | −0.282810 | −0.141405 | − | 0.989952i | \(-0.545162\pi\) | ||||
−0.141405 | + | 0.989952i | \(0.545162\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.27878 | 0.586531 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.90312 | 0.318659 | 0.159330 | − | 0.987225i | \(-0.449067\pi\) | ||||
0.159330 | + | 0.987225i | \(0.449067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.163980 | 0.0177861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.20093 | 0.557599 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.3006 | −1.40986 | −0.704930 | − | 0.709276i | \(-0.749022\pi\) | ||||
−0.704930 | + | 0.709276i | \(0.749022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.580700 | −0.0608739 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.62868 | −0.479971 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.93459 | 0.301083 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.261925 | 0.0265945 | 0.0132972 | − | 0.999912i | \(-0.495767\pi\) | ||||
0.0132972 | + | 0.999912i | \(0.495767\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00836 | 0.603863 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.46200 | −0.443985 | −0.221993 | − | 0.975048i | \(-0.571256\pi\) | ||||
−0.221993 | + | 0.975048i | \(0.571256\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.734821 | 0.0724040 | 0.0362020 | − | 0.999344i | \(-0.488474\pi\) | ||||
0.0362020 | + | 0.999344i | \(0.488474\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.241216 | 0.0235402 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.54784 | 0.246309 | 0.123154 | − | 0.992388i | \(-0.460699\pi\) | ||||
0.123154 | + | 0.992388i | \(0.460699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.06803 | −0.389647 | −0.194823 | − | 0.980838i | \(-0.562413\pi\) | ||||
−0.194823 | + | 0.980838i | \(0.562413\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.55471 | 0.337398 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.4829 | 1.36243 | 0.681216 | − | 0.732082i | \(-0.261451\pi\) | ||||
0.681216 | + | 0.732082i | \(0.261451\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.48484 | 0.604714 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.06230 | −0.375560 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0602661 | −0.00552458 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.51537 | −0.501397 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.94174 | 0.265248 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.98515 | −0.803656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.68557 | 0.238306 | 0.119153 | − | 0.992876i | \(-0.461982\pi\) | ||||
0.119153 | + | 0.992876i | \(0.461982\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.51918 | 0.485937 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.68434 | −0.846125 | −0.423062 | − | 0.906101i | \(-0.639045\pi\) | ||||
−0.423062 | + | 0.906101i | \(0.639045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.07853 | −0.0935201 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.66060 | 0.315054 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.8157 | −1.60753 | −0.803766 | − | 0.594945i | \(-0.797174\pi\) | ||||
−0.803766 | + | 0.594945i | \(0.797174\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5214 | −1.40132 | −0.700662 | − | 0.713493i | \(-0.747112\pi\) | ||||
−0.700662 | + | 0.713493i | \(0.747112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.46403 | −0.712800 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.70820 | −0.310096 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.87399 | −0.653899 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.52519 | 0.373232 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.9148 | −0.894173 | −0.447086 | − | 0.894491i | \(-0.647538\pi\) | ||||
−0.447086 | + | 0.894491i | \(0.647538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.258942 | 0.0210724 | 0.0105362 | − | 0.999944i | \(-0.496646\pi\) | ||||
0.0105362 | + | 0.999944i | \(0.496646\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.421593 | −0.0340838 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.00762 | 0.562866 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.76206 | 0.300245 | 0.150123 | − | 0.988667i | \(-0.452033\pi\) | ||||
0.150123 | + | 0.988667i | \(0.452033\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.37826 | −0.664439 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.38332 | −0.187832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.1296 | 1.18504 | 0.592520 | − | 0.805556i | \(-0.298133\pi\) | ||||
0.592520 | + | 0.805556i | \(0.298133\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.54034 | 0.119915 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.73732 | 0.443967 | 0.221983 | − | 0.975050i | \(-0.428747\pi\) | ||||
0.221983 | + | 0.975050i | \(0.428747\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4929 | −0.807143 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.54486 | −0.576970 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.95955 | 0.377068 | 0.188534 | − | 0.982067i | \(-0.439626\pi\) | ||||
0.188534 | + | 0.982067i | \(0.439626\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.46852 | 0.111010 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.35603 | 0.477748 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.47906 | 0.559011 | 0.279506 | − | 0.960144i | \(-0.409829\pi\) | ||||
0.279506 | + | 0.960144i | \(0.409829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.26533 | −0.614357 | −0.307179 | − | 0.951652i | \(-0.599385\pi\) | ||||
−0.307179 | + | 0.951652i | \(0.599385\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.58164 | −0.486528 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.38168 | −0.395669 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.384844 | −0.0281426 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.34535 | −0.0978599 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.25713 | 0.163320 | 0.0816601 | − | 0.996660i | \(-0.473978\pi\) | ||||
0.0816601 | + | 0.996660i | \(0.473978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.4007 | −1.32451 | −0.662257 | − | 0.749277i | \(-0.730401\pi\) | ||||
−0.662257 | + | 0.749277i | \(0.730401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.04144 | −0.0745789 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.6058 | −0.826877 | −0.413438 | − | 0.910532i | \(-0.635672\pi\) | ||||
−0.413438 | + | 0.910532i | \(0.635672\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8781 | −1.19646 | −0.598228 | − | 0.801326i | \(-0.704128\pi\) | ||||
−0.598228 | + | 0.801326i | \(0.704128\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.34147 | −0.306223 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.89386 | 0.203109 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.45367 | −0.311057 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.6726 | −1.15882 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.88720 | −0.476397 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.12192 | −0.559136 | −0.279568 | − | 0.960126i | \(-0.590191\pi\) | ||||
−0.279568 | + | 0.960126i | \(0.590191\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.28537 | 0.430667 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.35581 | −0.569862 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.57545 | −0.174833 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.53571 | −0.103774 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.260196 | 0.0175027 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.67745 | −0.380190 | −0.190095 | − | 0.981766i | \(-0.560880\pi\) | ||||
−0.190095 | + | 0.981766i | \(0.560880\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.2731 | 0.684874 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.0486 | −0.866063 | −0.433032 | − | 0.901379i | \(-0.642556\pi\) | ||||
−0.433032 | + | 0.901379i | \(0.642556\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.823786 | 0.0544373 | 0.0272187 | − | 0.999630i | \(-0.491335\pi\) | ||||
0.0272187 | + | 0.999630i | \(0.491335\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.566109 | −0.0372473 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.0371 | 0.723065 | 0.361532 | − | 0.932360i | \(-0.382254\pi\) | ||||
0.361532 | + | 0.932360i | \(0.382254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8142 | 0.835905 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.65681 | 0.107621 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.2559 | −1.56898 | −0.784491 | − | 0.620140i | \(-0.787076\pi\) | ||||
−0.784491 | + | 0.620140i | \(0.787076\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3061 | −0.857121 | −0.428560 | − | 0.903513i | \(-0.640979\pi\) | ||||
−0.428560 | + | 0.903513i | \(0.640979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.4845 | −0.929180 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.85095 | −0.437691 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.65649 | 0.296285 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.91351 | −0.121264 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.73438 | −0.425071 | −0.212535 | − | 0.977153i | \(-0.568172\pi\) | ||||
−0.212535 | + | 0.977153i | \(0.568172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.2193 | −0.956828 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.108082 | −0.00676838 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.0972 | −1.69028 | −0.845138 | − | 0.534549i | \(-0.820482\pi\) | ||||
−0.845138 | + | 0.534549i | \(0.820482\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.97789 | 0.122900 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.2441 | 1.25308 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.5250 | 1.26562 | 0.632811 | − | 0.774306i | \(-0.281901\pi\) | ||||
0.632811 | + | 0.774306i | \(0.281901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.6843 | 0.779192 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.76670 | 0.536513 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.6469 | 1.38081 | 0.690404 | − | 0.723424i | \(-0.257433\pi\) | ||||
0.690404 | + | 0.723424i | \(0.257433\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.87654 | 0.539211 | 0.269606 | − | 0.962971i | \(-0.413107\pi\) | ||||
0.269606 | + | 0.962971i | \(0.413107\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.382751 | 0.0231652 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.37763 | 0.565492 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.6591 | 1.18120 | 0.590602 | − | 0.806963i | \(-0.298890\pi\) | ||||
0.590602 | + | 0.806963i | \(0.298890\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.0167 | −1.07863 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.2756 | 0.911265 | 0.455632 | − | 0.890168i | \(-0.349413\pi\) | ||||
0.455632 | + | 0.890168i | \(0.349413\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.6629 | −1.28773 | −0.643864 | − | 0.765140i | \(-0.722670\pi\) | ||||
−0.643864 | + | 0.765140i | \(0.722670\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.93425 | −0.114575 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.63682 | 0.0966184 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9730 | −0.998412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.172640 | −0.0101204 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.59095 | 0.560310 | 0.280155 | − | 0.959955i | \(-0.409614\pi\) | ||||
0.280155 | + | 0.959955i | \(0.409614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.62276 | −0.560259 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.59107 | −0.498505 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2899 | 0.595079 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.07094 | 0.177006 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.94099 | 0.168956 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.96432 | 0.570555 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.78430 | 0.444273 | 0.222137 | − | 0.975016i | \(-0.428697\pi\) | ||||
0.222137 | + | 0.975016i | \(0.428697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.484335 | −0.0275529 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.5497 | 1.90243 | 0.951216 | − | 0.308527i | \(-0.0998360\pi\) | ||||
0.951216 | + | 0.308527i | \(0.0998360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.19902 | −0.350390 | −0.175195 | − | 0.984534i | \(-0.556056\pi\) | ||||
−0.175195 | + | 0.984534i | \(0.556056\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.938907 | 0.0529014 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.4833 | −0.644968 | −0.322484 | − | 0.946575i | \(-0.604518\pi\) | ||||
−0.322484 | + | 0.946575i | \(0.604518\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.4795 | 1.03465 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.67933 | −0.0937313 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.483259 | 0.0268893 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.34029 | −0.351696 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.68132 | 0.148278 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.70949 | −0.259643 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.29804 | 0.181277 | 0.0906383 | − | 0.995884i | \(-0.471109\pi\) | ||||
0.0906383 | + | 0.995884i | \(0.471109\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.8363 | 0.758227 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.57280 | 0.359110 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.62848 | 0.415550 | 0.207775 | − | 0.978177i | \(-0.433378\pi\) | ||||
0.207775 | + | 0.978177i | \(0.433378\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.54595 | −0.518465 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.4462 | −0.890612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.08508 | 0.274568 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.27429 | −0.230120 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.6857 | −1.64730 | −0.823648 | − | 0.567102i | \(-0.808065\pi\) | ||||
−0.823648 | + | 0.567102i | \(0.808065\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.46969 | −0.506901 | −0.253450 | − | 0.967348i | \(-0.581565\pi\) | ||||
−0.253450 | + | 0.967348i | \(0.581565\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.80850 | 0.310035 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.2010 | −0.915516 | −0.457758 | − | 0.889077i | \(-0.651347\pi\) | ||||
−0.457758 | + | 0.889077i | \(0.651347\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.51579 | −0.505046 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0397226 | 0.00210234 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.41231 | 0.391207 | 0.195603 | − | 0.980683i | \(-0.437333\pi\) | ||||
0.195603 | + | 0.980683i | \(0.437333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3516 | −0.544819 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.63530 | 0.190804 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.32500 | 0.121696 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.7723 | −1.13651 | −0.568253 | − | 0.822854i | \(-0.692381\pi\) | ||||
−0.568253 | + | 0.822854i | \(0.692381\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.4504 | 0.596085 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.66177 | −0.242027 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.7062 | −1.17568 | −0.587841 | − | 0.808977i | \(-0.700022\pi\) | ||||
−0.587841 | + | 0.808977i | \(0.700022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.92230 | 0.305826 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.4941 | −0.643481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5815 | −1.15994 | −0.579968 | − | 0.814639i | \(-0.696935\pi\) | ||||
−0.579968 | + | 0.814639i | \(0.696935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.77011 | −0.0906857 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.5809 | 1.51151 | 0.755756 | − | 0.654854i | \(-0.227270\pi\) | ||||
0.755756 | + | 0.654854i | \(0.227270\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.857066 | 0.0436801 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.4829 | 1.09204 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.11718 | 0.208749 | 0.104375 | − | 0.994538i | \(-0.466716\pi\) | ||||
0.104375 | + | 0.994538i | \(0.466716\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.06790 | 0.0540061 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.38315 | 0.321987 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.50834 | −0.126208 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.4331 | −0.975319 | −0.487660 | − | 0.873034i | \(-0.662149\pi\) | ||||
−0.487660 | + | 0.873034i | \(0.662149\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.710879 | 0.0355885 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.1714 | 0.757621 | 0.378811 | − | 0.925474i | \(-0.376333\pi\) | ||||
0.378811 | + | 0.925474i | \(0.376333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.1194 | 0.553898 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.26759 | 0.261749 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.6303 | 0.626059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.6254 | 1.61322 | 0.806610 | − | 0.591083i | \(-0.201300\pi\) | ||||
0.806610 | + | 0.591083i | \(0.201300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.4018 | 0.611736 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.53657 | 0.174023 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.89697 | 0.142207 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.8896 | 0.533265 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.1541 | −1.47312 | −0.736562 | − | 0.676370i | \(-0.763552\pi\) | ||||
−0.736562 | + | 0.676370i | \(0.763552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0071 | −0.780140 | −0.390070 | − | 0.920785i | \(-0.627549\pi\) | ||||
−0.390070 | + | 0.920785i | \(0.627549\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −32.9454 | −1.60186 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.658007 | −0.0319180 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.66211 | −0.177222 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.44415 | 0.118005 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3797 | 0.885321 | 0.442661 | − | 0.896689i | \(-0.354035\pi\) | ||||
0.442661 | + | 0.896689i | \(0.354035\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.9237 | −0.957471 | −0.478735 | − | 0.877959i | \(-0.658905\pi\) | ||||
−0.478735 | + | 0.877959i | \(0.658905\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.18991 | 0.248837 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.1113 | 0.914215 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.5087 | −1.21747 | −0.608733 | − | 0.793375i | \(-0.708322\pi\) | ||||
−0.608733 | + | 0.793375i | \(0.708322\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.6139 | 0.838755 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.79329 | −0.180225 | −0.0901124 | − | 0.995932i | \(-0.528723\pi\) | ||||
−0.0901124 | + | 0.995932i | \(0.528723\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.2724 | −0.629173 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.19415 | 0.340272 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.08159 | 0.0982363 | 0.0491182 | − | 0.998793i | \(-0.484359\pi\) | ||||
0.0491182 | + | 0.998793i | \(0.484359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.4523 | 0.492180 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.170674 | −0.00801895 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.579469 | −0.0271659 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.4508 | 1.61154 | 0.805771 | − | 0.592227i | \(-0.201751\pi\) | ||||
0.805771 | + | 0.592227i | \(0.201751\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.602816 | 0.0281370 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.3819 | −1.18215 | −0.591076 | − | 0.806616i | \(-0.701297\pi\) | ||||
−0.591076 | + | 0.806616i | \(0.701297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.2540 | −0.708912 | −0.354456 | − | 0.935073i | \(-0.615334\pi\) | ||||
−0.354456 | + | 0.935073i | \(0.615334\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.61887 | −0.214195 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.38856 | −0.295627 | −0.147814 | − | 0.989015i | \(-0.547224\pi\) | ||||
−0.147814 | + | 0.989015i | \(0.547224\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.41565 | −0.111544 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.47965 | −0.114256 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.6103 | 0.901681 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.7757 | −0.540308 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.6115 | −1.49318 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.5331 | 1.71493 | 0.857464 | − | 0.514543i | \(-0.172038\pi\) | ||||
0.857464 | + | 0.514543i | \(0.172038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.53943 | −0.389365 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.57089 | 0.0714782 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.261370 | 0.0118682 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.33788 | 0.196568 | 0.0982840 | − | 0.995158i | \(-0.468665\pi\) | ||||
0.0982840 | + | 0.995158i | \(0.468665\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.97221 | −0.450959 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.0024 | −1.44425 | −0.722124 | − | 0.691764i | \(-0.756834\pi\) | ||||
−0.722124 | + | 0.691764i | \(0.756834\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.29666 | −0.0583988 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.99562 | 0.269483 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.49726 | 0.156874 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.66389 | −0.164018 | −0.0820091 | − | 0.996632i | \(-0.526134\pi\) | ||||
−0.0820091 | + | 0.996632i | \(0.526134\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.78158 | −0.168949 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.45254 | −0.198135 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.91606 | 0.307153 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.8313 | −1.54387 | −0.771936 | − | 0.635700i | \(-0.780711\pi\) | ||||
−0.771936 | + | 0.635700i | \(0.780711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.854490 | −0.0378004 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.7880 | 0.476304 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.733263 | 0.0323114 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.0736 | −1.32264 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.26894 | −0.143491 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0129 | −1.05202 | −0.526012 | − | 0.850477i | \(-0.676313\pi\) | ||||
−0.526012 | + | 0.850477i | \(0.676313\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.8701 | −1.30613 | −0.653064 | − | 0.757303i | \(-0.726517\pi\) | ||||
−0.653064 | + | 0.757303i | \(0.726517\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.967935 | −0.0422441 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.15399 | 0.0502687 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.2319 | 0.836170 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.7402 | 1.07363 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.06690 | −0.306101 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.54244 | 0.109919 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.92960 | −0.212728 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.0785 | 0.692550 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.2005 | 0.481547 | 0.240774 | − | 0.970581i | \(-0.422599\pi\) | ||||
0.240774 | + | 0.970581i | \(0.422599\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.44785 | 0.233790 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.05941 | −0.173886 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.3236 | 1.04000 | 0.520001 | − | 0.854166i | \(-0.325932\pi\) | ||||
0.520001 | + | 0.854166i | \(0.325932\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.6183 | −1.09336 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.2052 | −0.988575 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.921870 | 0.0392019 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.54718 | 0.150569 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.5932 | −0.660705 | −0.330353 | − | 0.943858i | \(-0.607168\pi\) | ||||
−0.330353 | + | 0.943858i | \(0.607168\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.2587 | −0.560782 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.253659 | 0.0107095 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.04046 | 0.0859952 | 0.0429976 | − | 0.999075i | \(-0.486309\pi\) | ||||
0.0429976 | + | 0.999075i | \(0.486309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.4522 | 0.608007 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.93596 | −0.0813025 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.7908 | 1.24890 | 0.624448 | − | 0.781067i | \(-0.285324\pi\) | ||||
0.624448 | + | 0.781067i | \(0.285324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.67514 | 0.0701025 | 0.0350513 | − | 0.999386i | \(-0.488841\pi\) | ||||
0.0350513 | + | 0.999386i | \(0.488841\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.48772 | −0.0621504 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.0220 | −1.08519 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.76042 | 0.156548 | 0.0782742 | − | 0.996932i | \(-0.475059\pi\) | ||||
0.0782742 | + | 0.996932i | \(0.475059\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.1283 | 0.504035 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.06470 | −0.0441712 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.7689 | −1.23290 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.05369 | −0.167600 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.9499 | 1.07107 | 0.535533 | − | 0.844514i | \(-0.320111\pi\) | ||||
0.535533 | + | 0.844514i | \(0.320111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.6519 | 0.850949 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.64960 | 0.314663 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.45049 | 0.388085 | 0.194043 | − | 0.980993i | \(-0.437840\pi\) | ||||
0.194043 | + | 0.980993i | \(0.437840\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0601384 | −0.00246543 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.1247 | 0.455304 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.7653 | −1.25703 | −0.628517 | − | 0.777796i | \(-0.716338\pi\) | ||||
−0.628517 | + | 0.777796i | \(0.716338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.70280 | 0.395785 | 0.197893 | − | 0.980224i | \(-0.436590\pi\) | ||||
0.197893 | + | 0.980224i | \(0.436590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.8987 | −0.688169 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.50368 | −0.223757 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.66881 | 0.148912 | 0.0744562 | − | 0.997224i | \(-0.476278\pi\) | ||||
0.0744562 | + | 0.997224i | \(0.476278\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.90741 | −0.0772920 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.3330 | 0.822587 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.3930 | 1.79302 | 0.896509 | − | 0.443025i | \(-0.146095\pi\) | ||||
0.896509 | + | 0.443025i | \(0.146095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.93550 | 0.118371 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.0543 | 1.57227 | 0.786134 | − | 0.618057i | \(-0.212080\pi\) | ||||
0.786134 | + | 0.618057i | \(0.212080\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.2073 | −0.972973 | −0.486487 | − | 0.873688i | \(-0.661722\pi\) | ||||
−0.486487 | + | 0.873688i | \(0.661722\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.8393 | 0.956640 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.87790 | 0.195429 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0551 | 0.442202 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.53949 | 0.181290 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.886238 | −0.0353366 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.3183 | −0.490385 | −0.245193 | − | 0.969474i | \(-0.578851\pi\) | ||||
−0.245193 | + | 0.969474i | \(0.578851\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.35332 | 0.212775 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.67988 | 0.106348 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.8708 | −0.430717 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.4652 | 0.967828 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.9113 | −0.667956 | −0.333978 | − | 0.942581i | \(-0.608391\pi\) | ||||
−0.333978 | + | 0.942581i | \(0.608391\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.1189 | −1.03003 | −0.515015 | − | 0.857181i | \(-0.672213\pi\) | ||||
−0.515015 | + | 0.857181i | \(0.672213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.50749 | 0.216857 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.24455 | −0.324127 | −0.162063 | − | 0.986780i | \(-0.551815\pi\) | ||||
−0.162063 | + | 0.986780i | \(0.551815\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.5837 | 0.886486 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.69754 | 0.0665317 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.8697 | −1.56022 | −0.780110 | − | 0.625642i | \(-0.784837\pi\) | ||||
−0.780110 | + | 0.625642i | \(0.784837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.66382 | −0.377597 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.97761 | −0.233209 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.2594 | −1.68515 | −0.842573 | − | 0.538582i | \(-0.818960\pi\) | ||||
−0.842573 | + | 0.538582i | \(0.818960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.2663 | −1.41059 | −0.705297 | − | 0.708912i | \(-0.749187\pi\) | ||||
−0.705297 | + | 0.708912i | \(0.749187\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.171501 | −0.00666054 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.07624 | −0.0417348 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −51.2787 | −1.98552 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.74212 | 0.144679 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.3853 | −0.902779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.83729 | 0.263558 | 0.131779 | − | 0.991279i | \(-0.457931\pi\) | ||||
0.131779 | + | 0.991279i | \(0.457931\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.6890 | −0.565381 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.3308 | −1.08884 | −0.544420 | − | 0.838812i | \(-0.683250\pi\) | ||||
−0.544420 | + | 0.838812i | \(0.683250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0960593 | −0.00368642 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.60057 | 0.329575 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.3969 | 0.856995 | 0.428497 | − | 0.903543i | \(-0.359043\pi\) | ||||
0.428497 | + | 0.903543i | \(0.359043\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.7758 | −0.717387 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.542975 | −0.0207158 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.1270 | 0.766777 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.86769 | −0.337343 | −0.168671 | − | 0.985672i | \(-0.553948\pi\) | ||||
−0.168671 | + | 0.985672i | \(0.553948\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.20352 | −0.0837049 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.4864 | −0.625363 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.733416 | −0.0277801 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.27478 | −0.275158 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.7295 | −1.08510 | −0.542550 | − | 0.840024i | \(-0.682541\pi\) | ||||
−0.542550 | + | 0.840024i | \(0.682541\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.8602 | −0.598178 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.44609 | −0.318098 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.63641 | 0.0615434 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.2925 | −0.611878 | −0.305939 | − | 0.952051i | \(-0.598970\pi\) | ||||
−0.305939 | + | 0.952051i | \(0.598970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.44896 | 0.241855 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.6365 | 1.70910 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.70034 | −0.138385 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.9876 | 0.597066 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.67655 | −0.323581 | −0.161790 | − | 0.986825i | \(-0.551727\pi\) | ||||
−0.161790 | + | 0.986825i | \(0.551727\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.269490 | −0.0100363 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.77032 | 0.326172 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31.5963 | 1.17346 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.9559 | 1.44479 | 0.722396 | − | 0.691479i | \(-0.243041\pi\) | ||||
0.722396 | + | 0.691479i | \(0.243041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.28932 | −0.232938 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.37601 | −0.0508935 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.822898 | −0.0303944 | −0.0151972 | − | 0.999885i | \(-0.504838\pi\) | ||||
−0.0151972 | + | 0.999885i | \(0.504838\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.51560 | 0.166560 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.4257 | −0.568213 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.6813 | 1.38613 | 0.693065 | − | 0.720875i | \(-0.256260\pi\) | ||||
0.693065 | + | 0.720875i | \(0.256260\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.06919 | −0.112749 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.6314 | −1.30719 | −0.653594 | − | 0.756845i | \(-0.726740\pi\) | ||||
−0.653594 | + | 0.756845i | \(0.726740\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.8916 | −0.399039 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.44814 | −0.272513 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.934403 | −0.0341423 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.1886 | −0.590731 | −0.295366 | − | 0.955384i | \(-0.595441\pi\) | ||||
−0.295366 | + | 0.955384i | \(0.595441\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.43877 | 0.161758 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.258393 | 0.00940388 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.2456 | 1.20833 | 0.604165 | − | 0.796859i | \(-0.293507\pi\) | ||||
0.604165 | + | 0.796859i | \(0.293507\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.0313 | 0.364114 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −54.0682 | −1.95997 | −0.979985 | − | 0.199074i | \(-0.936207\pi\) | ||||
−0.979985 | + | 0.199074i | \(0.936207\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.49192 | 0.0540112 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.420699 | −0.0152104 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.2690 | −0.551332 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.35847 | 0.157171 | 0.0785853 | − | 0.996907i | \(-0.474960\pi\) | ||||
0.0785853 | + | 0.996907i | \(0.474960\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.8603 | 0.643223 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.6469 | −1.56987 | −0.784936 | − | 0.619577i | \(-0.787304\pi\) | ||||
−0.784936 | + | 0.619577i | \(0.787304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.1198 | −1.01009 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.30366 | −0.0467687 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.1253 | −0.470261 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.3326 | 0.799124 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.9461 | −1.03445 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.75409 | 0.133989 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.1261 | −1.39469 | −0.697347 | − | 0.716734i | \(-0.745636\pi\) | ||||
−0.697347 | + | 0.716734i | \(0.745636\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.5284 | −0.481624 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.31149 | −0.188855 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.8110 | 0.561464 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.36050 | −0.296516 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.4918 | 0.513326 | 0.256663 | − | 0.966501i | \(-0.417377\pi\) | ||||
0.256663 | + | 0.966501i | \(0.417377\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.11020 | 0.0746535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.1235 | 1.20569 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.45656 | −0.192558 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.37827 | −0.0838230 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.9271 | −0.525458 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.26269 | 0.220184 | 0.110092 | − | 0.993921i | \(-0.464885\pi\) | ||||
0.110092 | + | 0.993921i | \(0.464885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8822 | 0.417240 | 0.208620 | − | 0.977997i | \(-0.433103\pi\) | ||||
0.208620 | + | 0.977997i | \(0.433103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.85071 | −0.205193 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.0975 | 0.528843 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.6252 | −0.861525 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.48982 | 0.0520585 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.4622 | −0.504735 | −0.252367 | − | 0.967631i | \(-0.581209\pi\) | ||||
−0.252367 | + | 0.967631i | \(0.581209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.0941 | −0.630719 | −0.315360 | − | 0.948972i | \(-0.602125\pi\) | ||||
−0.315360 | + | 0.948972i | \(0.602125\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.18099 | −0.215194 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.61196 | 0.229920 | 0.114960 | − | 0.993370i | \(-0.463326\pi\) | ||||
0.114960 | + | 0.993370i | \(0.463326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.1172 | −0.872356 | −0.436178 | − | 0.899860i | \(-0.643668\pi\) | ||||
−0.436178 | + | 0.899860i | \(0.643668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.9577 | −0.449499 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.12819 | −0.0390896 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.72516 | 0.198127 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.7612 | 0.890437 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.13587 | 0.246358 | 0.123179 | − | 0.992384i | \(-0.460691\pi\) | ||||
0.123179 | + | 0.992384i | \(0.460691\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.2634 | 1.14701 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.0684 | −0.346776 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.4706 | −0.360200 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.02272 | 0.0695016 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.2785 | 0.490036 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.0477 | −1.20142 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.1428 | −0.347281 | −0.173641 | − | 0.984809i | \(-0.555553\pi\) | ||||
−0.173641 | + | 0.984809i | \(0.555553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.52887 | −0.257482 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.1710 | 1.13310 | 0.566550 | − | 0.824027i | \(-0.308278\pi\) | ||||
0.566550 | + | 0.824027i | \(0.308278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.8176 | 0.539691 | 0.269845 | − | 0.962904i | \(-0.413027\pi\) | ||||
0.269845 | + | 0.962904i | \(0.413027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.07886 | −0.0367675 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.9450 | −0.610856 | −0.305428 | − | 0.952215i | \(-0.598800\pi\) | ||||
−0.305428 | + | 0.952215i | \(0.598800\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.94904 | 0.168272 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.1873 | 0.379939 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.88683 | 0.199697 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.4294 | 0.353388 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.671985 | −0.0227432 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.29524 | 0.111400 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.5719 | 0.694664 | 0.347332 | − | 0.937742i | \(-0.387088\pi\) | ||||
0.347332 | + | 0.937742i | \(0.387088\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.32160 | −0.213222 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.5457 | −0.658510 | −0.329255 | − | 0.944241i | \(-0.606798\pi\) | ||||
−0.329255 | + | 0.944241i | \(0.606798\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5650 | 0.725719 | 0.362859 | − | 0.931844i | \(-0.381800\pi\) | ||||
0.362859 | + | 0.931844i | \(0.381800\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.34256 | 0.213203 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50.5182 | 1.69624 | 0.848118 | − | 0.529808i | \(-0.177736\pi\) | ||||
0.848118 | + | 0.529808i | \(0.177736\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.984914 | −0.0330329 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.3625 | −0.414160 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.7643 | 1.26373 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.46321 | 0.249468 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.78227 | −0.226453 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −55.4126 | −1.84811 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.08881 | 0.0695885 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.02412 | −0.0673586 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.24781 | −0.274167 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.9017 | 0.627622 | 0.313811 | − | 0.949486i | \(-0.398394\pi\) | ||||
0.313811 | + | 0.949486i | \(0.398394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.4475 | 0.379690 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.1637 | 1.72826 | 0.864130 | − | 0.503268i | \(-0.167869\pi\) | ||||
0.864130 | + | 0.503268i | \(0.167869\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.79891 | −0.225011 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.56769 | −0.217121 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.55166 | 0.117286 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.7580 | 0.882665 | 0.441332 | − | 0.897344i | \(-0.354506\pi\) | ||||
0.441332 | + | 0.897344i | \(0.354506\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.13079 | −0.169065 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.0993 | −0.496999 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.5953 | 0.710048 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.88523 | −0.0619190 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.6778 | 1.03931 | 0.519657 | − | 0.854375i | \(-0.326060\pi\) | ||||
0.519657 | + | 0.854375i | \(0.326060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.1902 | −0.661708 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.1133 | −0.723958 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.384028 | −0.0125591 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.1014 | −1.14671 | −0.573356 | − | 0.819307i | \(-0.694359\pi\) | ||||
−0.573356 | + | 0.819307i | \(0.694359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.08590 | 0.133338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.2279 | 0.887604 | 0.443802 | − | 0.896125i | \(-0.353629\pi\) | ||||
0.443802 | + | 0.896125i | \(0.353629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.0041 | −0.944503 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.34250 | −0.0436715 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.6119 | 0.799779 | 0.399890 | − | 0.916563i | \(-0.369048\pi\) | ||||
0.399890 | + | 0.916563i | \(0.369048\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.68922 | 0.119757 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.56890 | 0.245438 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.01549 | 0.0976813 | 0.0488407 | − | 0.998807i | \(-0.484447\pi\) | ||||
0.0488407 | + | 0.998807i | \(0.484447\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.25235 | 0.0728842 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.1802 | −0.393730 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.90052 | 0.222829 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.3156 | 0.590825 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.53664 | −0.210640 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.3617 | −0.591085 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.03746 | −0.194152 | −0.0970758 | − | 0.995277i | \(-0.530949\pi\) | ||||
−0.0970758 | + | 0.995277i | \(0.530949\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.318526 | −0.0102325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.23721 | 0.264345 | 0.132172 | − | 0.991227i | \(-0.457805\pi\) | ||||
0.132172 | + | 0.991227i | \(0.457805\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.05910 | 0.194246 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.17902 | 0.133836 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.4331 | −1.16560 | −0.582799 | − | 0.812617i | \(-0.698042\pi\) | ||||
−0.582799 | + | 0.812617i | \(0.698042\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.1491 | 0.995528 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4368 | 0.333221 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.4411 | −0.524391 | −0.262195 | − | 0.965015i | \(-0.584447\pi\) | ||||
−0.262195 | + | 0.965015i | \(0.584447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.5812 | −0.369007 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.10412 | 0.0988054 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −54.4165 | −1.73034 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0291 | −0.382118 | −0.191059 | − | 0.981579i | \(-0.561192\pi\) | ||||
−0.191059 | + | 0.981579i | \(0.561192\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.17381 | −0.0689837 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.8423 | −0.533937 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.9894 | 0.348037 | 0.174019 | − | 0.984742i | \(-0.444325\pi\) | ||||
0.174019 | + | 0.984742i | \(0.444325\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.7839 | −0.625936 |
(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 | 8048.2.a.v.1.14 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.15 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.15 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.14 | 28 | 1.1 | even | 1 | trivial |