Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 56 x^{10} + 26 x^{9} - 263 x^{8} + 50 x^{7} + 478 x^{6} - 174 x^{5} + \cdots - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.21702\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.21702 | −0.860567 | −0.430283 | − | 0.902694i | \(-0.641586\pi\) | ||||
−0.430283 | + | 0.902694i | \(0.641586\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.518850 | −0.259425 | ||||||||
\(5\) | 3.45145 | 1.54353 | 0.771767 | − | 0.635905i | \(-0.219373\pi\) | ||||
0.771767 | + | 0.635905i | \(0.219373\pi\) | |||||||
\(6\) | 1.21702 | 0.496848 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.06550 | 1.08382 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.20050 | −1.32831 | ||||||||
\(11\) | −4.83039 | −1.45642 | −0.728209 | − | 0.685355i | \(-0.759647\pi\) | ||||
−0.728209 | + | 0.685355i | \(0.759647\pi\) | |||||||
\(12\) | 0.518850 | 0.149779 | ||||||||
\(13\) | −4.46274 | −1.23774 | −0.618870 | − | 0.785493i | \(-0.712409\pi\) | ||||
−0.618870 | + | 0.785493i | \(0.712409\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.45145 | −0.891160 | ||||||||
\(16\) | −2.69309 | −0.673273 | ||||||||
\(17\) | 3.17502 | 0.770056 | 0.385028 | − | 0.922905i | \(-0.374192\pi\) | ||||
0.385028 | + | 0.922905i | \(0.374192\pi\) | |||||||
\(18\) | −1.21702 | −0.286856 | ||||||||
\(19\) | 1.25613 | 0.288177 | 0.144088 | − | 0.989565i | \(-0.453975\pi\) | ||||
0.144088 | + | 0.989565i | \(0.453975\pi\) | |||||||
\(20\) | −1.79078 | −0.400432 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.87871 | 1.25334 | ||||||||
\(23\) | 3.08355 | 0.642964 | 0.321482 | − | 0.946916i | \(-0.395819\pi\) | ||||
0.321482 | + | 0.946916i | \(0.395819\pi\) | |||||||
\(24\) | −3.06550 | −0.625743 | ||||||||
\(25\) | 6.91249 | 1.38250 | ||||||||
\(26\) | 5.43126 | 1.06516 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.78255 | −1.07379 | −0.536896 | − | 0.843648i | \(-0.680403\pi\) | ||||
−0.536896 | + | 0.843648i | \(0.680403\pi\) | |||||||
\(30\) | 4.20050 | 0.766902 | ||||||||
\(31\) | −8.75778 | −1.57294 | −0.786472 | − | 0.617626i | \(-0.788094\pi\) | ||||
−0.786472 | + | 0.617626i | \(0.788094\pi\) | |||||||
\(32\) | −2.85344 | −0.504423 | ||||||||
\(33\) | 4.83039 | 0.840863 | ||||||||
\(34\) | −3.86408 | −0.662685 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.518850 | −0.0864750 | ||||||||
\(37\) | −1.31531 | −0.216235 | −0.108118 | − | 0.994138i | \(-0.534482\pi\) | ||||
−0.108118 | + | 0.994138i | \(0.534482\pi\) | |||||||
\(38\) | −1.52875 | −0.247995 | ||||||||
\(39\) | 4.46274 | 0.714610 | ||||||||
\(40\) | 10.5804 | 1.67291 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.25707 | −1.10669 | −0.553346 | − | 0.832951i | \(-0.686649\pi\) | ||||
−0.553346 | + | 0.832951i | \(0.686649\pi\) | |||||||
\(44\) | 2.50625 | 0.377831 | ||||||||
\(45\) | 3.45145 | 0.514511 | ||||||||
\(46\) | −3.75275 | −0.553313 | ||||||||
\(47\) | −5.70699 | −0.832450 | −0.416225 | − | 0.909262i | \(-0.636647\pi\) | ||||
−0.416225 | + | 0.909262i | \(0.636647\pi\) | |||||||
\(48\) | 2.69309 | 0.388715 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.41267 | −1.18973 | ||||||||
\(51\) | −3.17502 | −0.444592 | ||||||||
\(52\) | 2.31549 | 0.321101 | ||||||||
\(53\) | 12.5563 | 1.72474 | 0.862370 | − | 0.506278i | \(-0.168979\pi\) | ||||
0.862370 | + | 0.506278i | \(0.168979\pi\) | |||||||
\(54\) | 1.21702 | 0.165616 | ||||||||
\(55\) | −16.6718 | −2.24803 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.25613 | −0.166379 | ||||||||
\(58\) | 7.03751 | 0.924070 | ||||||||
\(59\) | 7.77351 | 1.01202 | 0.506012 | − | 0.862526i | \(-0.331119\pi\) | ||||
0.506012 | + | 0.862526i | \(0.331119\pi\) | |||||||
\(60\) | 1.79078 | 0.231189 | ||||||||
\(61\) | 3.37698 | 0.432378 | 0.216189 | − | 0.976352i | \(-0.430637\pi\) | ||||
0.216189 | + | 0.976352i | \(0.430637\pi\) | |||||||
\(62\) | 10.6584 | 1.35362 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.85890 | 1.10736 | ||||||||
\(65\) | −15.4029 | −1.91049 | ||||||||
\(66\) | −5.87871 | −0.723619 | ||||||||
\(67\) | 8.54808 | 1.04431 | 0.522157 | − | 0.852849i | \(-0.325127\pi\) | ||||
0.522157 | + | 0.852849i | \(0.325127\pi\) | |||||||
\(68\) | −1.64736 | −0.199772 | ||||||||
\(69\) | −3.08355 | −0.371215 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.81453 | 0.927414 | 0.463707 | − | 0.885989i | \(-0.346519\pi\) | ||||
0.463707 | + | 0.885989i | \(0.346519\pi\) | |||||||
\(72\) | 3.06550 | 0.361273 | ||||||||
\(73\) | −13.4176 | −1.57041 | −0.785207 | − | 0.619234i | \(-0.787443\pi\) | ||||
−0.785207 | + | 0.619234i | \(0.787443\pi\) | |||||||
\(74\) | 1.60076 | 0.186085 | ||||||||
\(75\) | −6.91249 | −0.798186 | ||||||||
\(76\) | −0.651745 | −0.0747603 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.43126 | −0.614969 | ||||||||
\(79\) | 6.38666 | 0.718555 | 0.359277 | − | 0.933231i | \(-0.383023\pi\) | ||||
0.359277 | + | 0.933231i | \(0.383023\pi\) | |||||||
\(80\) | −9.29507 | −1.03922 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.21702 | 0.134398 | ||||||||
\(83\) | 15.6286 | 1.71546 | 0.857728 | − | 0.514103i | \(-0.171875\pi\) | ||||
0.857728 | + | 0.514103i | \(0.171875\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.9584 | 1.18861 | ||||||||
\(86\) | 8.83203 | 0.952383 | ||||||||
\(87\) | 5.78255 | 0.619954 | ||||||||
\(88\) | −14.8076 | −1.57849 | ||||||||
\(89\) | 17.4804 | 1.85292 | 0.926460 | − | 0.376393i | \(-0.122836\pi\) | ||||
0.926460 | + | 0.376393i | \(0.122836\pi\) | |||||||
\(90\) | −4.20050 | −0.442771 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.59990 | −0.166801 | ||||||||
\(93\) | 8.75778 | 0.908139 | ||||||||
\(94\) | 6.94555 | 0.716379 | ||||||||
\(95\) | 4.33548 | 0.444811 | ||||||||
\(96\) | 2.85344 | 0.291229 | ||||||||
\(97\) | −0.678629 | −0.0689044 | −0.0344522 | − | 0.999406i | \(-0.510969\pi\) | ||||
−0.0344522 | + | 0.999406i | \(0.510969\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.83039 | −0.485473 | ||||||||
\(100\) | −3.58655 | −0.358655 | ||||||||
\(101\) | −0.193417 | −0.0192457 | −0.00962284 | − | 0.999954i | \(-0.503063\pi\) | ||||
−0.00962284 | + | 0.999954i | \(0.503063\pi\) | |||||||
\(102\) | 3.86408 | 0.382601 | ||||||||
\(103\) | −4.36525 | −0.430121 | −0.215060 | − | 0.976601i | \(-0.568995\pi\) | ||||
−0.215060 | + | 0.976601i | \(0.568995\pi\) | |||||||
\(104\) | −13.6805 | −1.34149 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.2813 | −1.48425 | ||||||||
\(107\) | −5.76480 | −0.557304 | −0.278652 | − | 0.960392i | \(-0.589888\pi\) | ||||
−0.278652 | + | 0.960392i | \(0.589888\pi\) | |||||||
\(108\) | 0.518850 | 0.0499264 | ||||||||
\(109\) | −7.48956 | −0.717370 | −0.358685 | − | 0.933459i | \(-0.616775\pi\) | ||||
−0.358685 | + | 0.933459i | \(0.616775\pi\) | |||||||
\(110\) | 20.2900 | 1.93458 | ||||||||
\(111\) | 1.31531 | 0.124843 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0049 | 1.22340 | 0.611699 | − | 0.791091i | \(-0.290486\pi\) | ||||
0.611699 | + | 0.791091i | \(0.290486\pi\) | |||||||
\(114\) | 1.52875 | 0.143180 | ||||||||
\(115\) | 10.6427 | 0.992436 | ||||||||
\(116\) | 3.00028 | 0.278569 | ||||||||
\(117\) | −4.46274 | −0.412580 | ||||||||
\(118\) | −9.46055 | −0.870914 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.5804 | −0.965856 | ||||||||
\(121\) | 12.3327 | 1.12115 | ||||||||
\(122\) | −4.10986 | −0.372090 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 4.54398 | 0.408061 | ||||||||
\(125\) | 6.60086 | 0.590399 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.37208 | 0.121752 | 0.0608762 | − | 0.998145i | \(-0.480611\pi\) | ||||
0.0608762 | + | 0.998145i | \(0.480611\pi\) | |||||||
\(128\) | −5.07461 | −0.448537 | ||||||||
\(129\) | 7.25707 | 0.638949 | ||||||||
\(130\) | 18.7457 | 1.64411 | ||||||||
\(131\) | −1.84280 | −0.161006 | −0.0805030 | − | 0.996754i | \(-0.525653\pi\) | ||||
−0.0805030 | + | 0.996754i | \(0.525653\pi\) | |||||||
\(132\) | −2.50625 | −0.218141 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.4032 | −0.898702 | ||||||||
\(135\) | −3.45145 | −0.297053 | ||||||||
\(136\) | 9.73304 | 0.834602 | ||||||||
\(137\) | 3.30016 | 0.281951 | 0.140976 | − | 0.990013i | \(-0.454976\pi\) | ||||
0.140976 | + | 0.990013i | \(0.454976\pi\) | |||||||
\(138\) | 3.75275 | 0.319455 | ||||||||
\(139\) | 16.1445 | 1.36936 | 0.684679 | − | 0.728845i | \(-0.259943\pi\) | ||||
0.684679 | + | 0.728845i | \(0.259943\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.70699 | 0.480615 | ||||||||
\(142\) | −9.51048 | −0.798102 | ||||||||
\(143\) | 21.5568 | 1.80267 | ||||||||
\(144\) | −2.69309 | −0.224424 | ||||||||
\(145\) | −19.9582 | −1.65744 | ||||||||
\(146\) | 16.3296 | 1.35145 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.682448 | 0.0560969 | ||||||||
\(149\) | 18.5736 | 1.52161 | 0.760806 | − | 0.648979i | \(-0.224804\pi\) | ||||
0.760806 | + | 0.648979i | \(0.224804\pi\) | |||||||
\(150\) | 8.41267 | 0.686892 | ||||||||
\(151\) | 8.25131 | 0.671482 | 0.335741 | − | 0.941954i | \(-0.391013\pi\) | ||||
0.335741 | + | 0.941954i | \(0.391013\pi\) | |||||||
\(152\) | 3.85068 | 0.312332 | ||||||||
\(153\) | 3.17502 | 0.256685 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30.2270 | −2.42789 | ||||||||
\(156\) | −2.31549 | −0.185388 | ||||||||
\(157\) | 6.08420 | 0.485572 | 0.242786 | − | 0.970080i | \(-0.421939\pi\) | ||||
0.242786 | + | 0.970080i | \(0.421939\pi\) | |||||||
\(158\) | −7.77272 | −0.618364 | ||||||||
\(159\) | −12.5563 | −0.995779 | ||||||||
\(160\) | −9.84852 | −0.778594 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.21702 | −0.0956185 | ||||||||
\(163\) | −15.7777 | −1.23581 | −0.617903 | − | 0.786254i | \(-0.712018\pi\) | ||||
−0.617903 | + | 0.786254i | \(0.712018\pi\) | |||||||
\(164\) | 0.518850 | 0.0405154 | ||||||||
\(165\) | 16.6718 | 1.29790 | ||||||||
\(166\) | −19.0203 | −1.47626 | ||||||||
\(167\) | −18.3293 | −1.41836 | −0.709182 | − | 0.705026i | \(-0.750935\pi\) | ||||
−0.709182 | + | 0.705026i | \(0.750935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.91602 | 0.532002 | ||||||||
\(170\) | −13.3367 | −1.02288 | ||||||||
\(171\) | 1.25613 | 0.0960589 | ||||||||
\(172\) | 3.76533 | 0.287104 | ||||||||
\(173\) | −14.5857 | −1.10893 | −0.554466 | − | 0.832207i | \(-0.687077\pi\) | ||||
−0.554466 | + | 0.832207i | \(0.687077\pi\) | |||||||
\(174\) | −7.03751 | −0.533512 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.0087 | 0.980567 | ||||||||
\(177\) | −7.77351 | −0.584292 | ||||||||
\(178\) | −21.2741 | −1.59456 | ||||||||
\(179\) | −10.2770 | −0.768140 | −0.384070 | − | 0.923304i | \(-0.625478\pi\) | ||||
−0.384070 | + | 0.923304i | \(0.625478\pi\) | |||||||
\(180\) | −1.79078 | −0.133477 | ||||||||
\(181\) | 17.1415 | 1.27412 | 0.637061 | − | 0.770814i | \(-0.280150\pi\) | ||||
0.637061 | + | 0.770814i | \(0.280150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.37698 | −0.249633 | ||||||||
\(184\) | 9.45262 | 0.696856 | ||||||||
\(185\) | −4.53971 | −0.333766 | ||||||||
\(186\) | −10.6584 | −0.781514 | ||||||||
\(187\) | −15.3366 | −1.12152 | ||||||||
\(188\) | 2.96107 | 0.215959 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.27639 | −0.382789 | ||||||||
\(191\) | −0.203996 | −0.0147606 | −0.00738032 | − | 0.999973i | \(-0.502349\pi\) | ||||
−0.00738032 | + | 0.999973i | \(0.502349\pi\) | |||||||
\(192\) | −8.85890 | −0.639336 | ||||||||
\(193\) | 6.18102 | 0.444920 | 0.222460 | − | 0.974942i | \(-0.428591\pi\) | ||||
0.222460 | + | 0.974942i | \(0.428591\pi\) | |||||||
\(194\) | 0.825909 | 0.0592968 | ||||||||
\(195\) | 15.4029 | 1.10302 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.1141 | −0.863095 | −0.431547 | − | 0.902090i | \(-0.642032\pi\) | ||||
−0.431547 | + | 0.902090i | \(0.642032\pi\) | |||||||
\(198\) | 5.87871 | 0.417782 | ||||||||
\(199\) | 13.5038 | 0.957256 | 0.478628 | − | 0.878018i | \(-0.341134\pi\) | ||||
0.478628 | + | 0.878018i | \(0.341134\pi\) | |||||||
\(200\) | 21.1903 | 1.49838 | ||||||||
\(201\) | −8.54808 | −0.602935 | ||||||||
\(202\) | 0.235393 | 0.0165622 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.64736 | 0.115338 | ||||||||
\(205\) | −3.45145 | −0.241060 | ||||||||
\(206\) | 5.31262 | 0.370148 | ||||||||
\(207\) | 3.08355 | 0.214321 | ||||||||
\(208\) | 12.0186 | 0.833338 | ||||||||
\(209\) | −6.06762 | −0.419706 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.21679 | −0.152610 | −0.0763051 | − | 0.997085i | \(-0.524312\pi\) | ||||
−0.0763051 | + | 0.997085i | \(0.524312\pi\) | |||||||
\(212\) | −6.51484 | −0.447441 | ||||||||
\(213\) | −7.81453 | −0.535443 | ||||||||
\(214\) | 7.01591 | 0.479597 | ||||||||
\(215\) | −25.0474 | −1.70822 | ||||||||
\(216\) | −3.06550 | −0.208581 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.11498 | 0.617344 | ||||||||
\(219\) | 13.4176 | 0.906679 | ||||||||
\(220\) | 8.65019 | 0.583196 | ||||||||
\(221\) | −14.1693 | −0.953130 | ||||||||
\(222\) | −1.60076 | −0.107436 | ||||||||
\(223\) | −28.3386 | −1.89770 | −0.948848 | − | 0.315735i | \(-0.897749\pi\) | ||||
−0.948848 | + | 0.315735i | \(0.897749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.91249 | 0.460833 | ||||||||
\(226\) | −15.8273 | −1.05282 | ||||||||
\(227\) | 15.6235 | 1.03697 | 0.518485 | − | 0.855087i | \(-0.326496\pi\) | ||||
0.518485 | + | 0.855087i | \(0.326496\pi\) | |||||||
\(228\) | 0.651745 | 0.0431629 | ||||||||
\(229\) | 22.4922 | 1.48633 | 0.743163 | − | 0.669110i | \(-0.233325\pi\) | ||||
0.743163 | + | 0.669110i | \(0.233325\pi\) | |||||||
\(230\) | −12.9524 | −0.854058 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.7264 | −1.16380 | ||||||||
\(233\) | 22.1660 | 1.45215 | 0.726073 | − | 0.687618i | \(-0.241343\pi\) | ||||
0.726073 | + | 0.687618i | \(0.241343\pi\) | |||||||
\(234\) | 5.43126 | 0.355053 | ||||||||
\(235\) | −19.6974 | −1.28492 | ||||||||
\(236\) | −4.03329 | −0.262545 | ||||||||
\(237\) | −6.38666 | −0.414858 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.1690 | −1.43399 | −0.716997 | − | 0.697076i | \(-0.754484\pi\) | ||||
−0.716997 | + | 0.697076i | \(0.754484\pi\) | |||||||
\(240\) | 9.29507 | 0.599994 | ||||||||
\(241\) | 8.79193 | 0.566338 | 0.283169 | − | 0.959070i | \(-0.408614\pi\) | ||||
0.283169 | + | 0.959070i | \(0.408614\pi\) | |||||||
\(242\) | −15.0092 | −0.964827 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.75215 | −0.112170 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.21702 | −0.0775947 | ||||||||
\(247\) | −5.60579 | −0.356688 | ||||||||
\(248\) | −26.8470 | −1.70479 | ||||||||
\(249\) | −15.6286 | −0.990420 | ||||||||
\(250\) | −8.03341 | −0.508077 | ||||||||
\(251\) | −21.6922 | −1.36920 | −0.684599 | − | 0.728920i | \(-0.740023\pi\) | ||||
−0.684599 | + | 0.728920i | \(0.740023\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.8947 | −0.936424 | ||||||||
\(254\) | −1.66985 | −0.104776 | ||||||||
\(255\) | −10.9584 | −0.686243 | ||||||||
\(256\) | −11.5419 | −0.721367 | ||||||||
\(257\) | 27.6369 | 1.72394 | 0.861971 | − | 0.506957i | \(-0.169230\pi\) | ||||
0.861971 | + | 0.506957i | \(0.169230\pi\) | |||||||
\(258\) | −8.83203 | −0.549858 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.99180 | 0.495630 | ||||||||
\(261\) | −5.78255 | −0.357931 | ||||||||
\(262\) | 2.24273 | 0.138556 | ||||||||
\(263\) | −3.00949 | −0.185573 | −0.0927865 | − | 0.995686i | \(-0.529577\pi\) | ||||
−0.0927865 | + | 0.995686i | \(0.529577\pi\) | |||||||
\(264\) | 14.8076 | 0.911344 | ||||||||
\(265\) | 43.3374 | 2.66220 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.4804 | −1.06978 | ||||||||
\(268\) | −4.43517 | −0.270921 | ||||||||
\(269\) | 15.0373 | 0.916838 | 0.458419 | − | 0.888736i | \(-0.348416\pi\) | ||||
0.458419 | + | 0.888736i | \(0.348416\pi\) | |||||||
\(270\) | 4.20050 | 0.255634 | ||||||||
\(271\) | 7.43613 | 0.451713 | 0.225856 | − | 0.974161i | \(-0.427482\pi\) | ||||
0.225856 | + | 0.974161i | \(0.427482\pi\) | |||||||
\(272\) | −8.55063 | −0.518458 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.01637 | −0.242638 | ||||||||
\(275\) | −33.3900 | −2.01349 | ||||||||
\(276\) | 1.59990 | 0.0963026 | ||||||||
\(277\) | −3.38918 | −0.203636 | −0.101818 | − | 0.994803i | \(-0.532466\pi\) | ||||
−0.101818 | + | 0.994803i | \(0.532466\pi\) | |||||||
\(278\) | −19.6482 | −1.17842 | ||||||||
\(279\) | −8.75778 | −0.524314 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4143 | −0.979196 | −0.489598 | − | 0.871948i | \(-0.662856\pi\) | ||||
−0.489598 | + | 0.871948i | \(0.662856\pi\) | |||||||
\(282\) | −6.94555 | −0.413601 | ||||||||
\(283\) | −16.2542 | −0.966209 | −0.483105 | − | 0.875563i | \(-0.660491\pi\) | ||||
−0.483105 | + | 0.875563i | \(0.660491\pi\) | |||||||
\(284\) | −4.05457 | −0.240595 | ||||||||
\(285\) | −4.33548 | −0.256812 | ||||||||
\(286\) | −26.2351 | −1.55132 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.85344 | −0.168141 | ||||||||
\(289\) | −6.91923 | −0.407014 | ||||||||
\(290\) | 24.2896 | 1.42633 | ||||||||
\(291\) | 0.678629 | 0.0397820 | ||||||||
\(292\) | 6.96174 | 0.407405 | ||||||||
\(293\) | 13.7114 | 0.801028 | 0.400514 | − | 0.916291i | \(-0.368832\pi\) | ||||
0.400514 | + | 0.916291i | \(0.368832\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.8298 | 1.56209 | ||||||||
\(296\) | −4.03208 | −0.234360 | ||||||||
\(297\) | 4.83039 | 0.280288 | ||||||||
\(298\) | −22.6046 | −1.30945 | ||||||||
\(299\) | −13.7611 | −0.795822 | ||||||||
\(300\) | 3.58655 | 0.207069 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.0420 | −0.577855 | ||||||||
\(303\) | 0.193417 | 0.0111115 | ||||||||
\(304\) | −3.38289 | −0.194022 | ||||||||
\(305\) | 11.6555 | 0.667389 | ||||||||
\(306\) | −3.86408 | −0.220895 | ||||||||
\(307\) | 15.3651 | 0.876932 | 0.438466 | − | 0.898748i | \(-0.355522\pi\) | ||||
0.438466 | + | 0.898748i | \(0.355522\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.36525 | 0.248330 | ||||||||
\(310\) | 36.7870 | 2.08936 | ||||||||
\(311\) | 3.93179 | 0.222951 | 0.111476 | − | 0.993767i | \(-0.464442\pi\) | ||||
0.111476 | + | 0.993767i | \(0.464442\pi\) | |||||||
\(312\) | 13.6805 | 0.774508 | ||||||||
\(313\) | 21.5701 | 1.21922 | 0.609608 | − | 0.792703i | \(-0.291327\pi\) | ||||
0.609608 | + | 0.792703i | \(0.291327\pi\) | |||||||
\(314\) | −7.40462 | −0.417867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.31372 | −0.186411 | ||||||||
\(317\) | −15.7143 | −0.882603 | −0.441301 | − | 0.897359i | \(-0.645483\pi\) | ||||
−0.441301 | + | 0.897359i | \(0.645483\pi\) | |||||||
\(318\) | 15.2813 | 0.856934 | ||||||||
\(319\) | 27.9320 | 1.56389 | ||||||||
\(320\) | 30.5760 | 1.70925 | ||||||||
\(321\) | 5.76480 | 0.321760 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.98825 | 0.221912 | ||||||||
\(324\) | −0.518850 | −0.0288250 | ||||||||
\(325\) | −30.8486 | −1.71117 | ||||||||
\(326\) | 19.2019 | 1.06349 | ||||||||
\(327\) | 7.48956 | 0.414174 | ||||||||
\(328\) | −3.06550 | −0.169264 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −20.2900 | −1.11693 | ||||||||
\(331\) | 18.5423 | 1.01918 | 0.509590 | − | 0.860417i | \(-0.329797\pi\) | ||||
0.509590 | + | 0.860417i | \(0.329797\pi\) | |||||||
\(332\) | −8.10888 | −0.445033 | ||||||||
\(333\) | −1.31531 | −0.0720784 | ||||||||
\(334\) | 22.3072 | 1.22060 | ||||||||
\(335\) | 29.5033 | 1.61193 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.1548 | 0.662112 | 0.331056 | − | 0.943611i | \(-0.392595\pi\) | ||||
0.331056 | + | 0.943611i | \(0.392595\pi\) | |||||||
\(338\) | −8.41697 | −0.457823 | ||||||||
\(339\) | −13.0049 | −0.706329 | ||||||||
\(340\) | −5.68578 | −0.308355 | ||||||||
\(341\) | 42.3035 | 2.29086 | ||||||||
\(342\) | −1.52875 | −0.0826651 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −22.2466 | −1.19945 | ||||||||
\(345\) | −10.6427 | −0.572983 | ||||||||
\(346\) | 17.7512 | 0.954309 | ||||||||
\(347\) | −3.56680 | −0.191476 | −0.0957380 | − | 0.995407i | \(-0.530521\pi\) | ||||
−0.0957380 | + | 0.995407i | \(0.530521\pi\) | |||||||
\(348\) | −3.00028 | −0.160832 | ||||||||
\(349\) | 33.1135 | 1.77252 | 0.886262 | − | 0.463184i | \(-0.153293\pi\) | ||||
0.886262 | + | 0.463184i | \(0.153293\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.46274 | 0.238203 | ||||||||
\(352\) | 13.7833 | 0.734650 | ||||||||
\(353\) | 6.28782 | 0.334667 | 0.167333 | − | 0.985900i | \(-0.446484\pi\) | ||||
0.167333 | + | 0.985900i | \(0.446484\pi\) | |||||||
\(354\) | 9.46055 | 0.502823 | ||||||||
\(355\) | 26.9714 | 1.43150 | ||||||||
\(356\) | −9.06972 | −0.480694 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.5074 | 0.661036 | ||||||||
\(359\) | −19.9323 | −1.05199 | −0.525994 | − | 0.850488i | \(-0.676307\pi\) | ||||
−0.525994 | + | 0.850488i | \(0.676307\pi\) | |||||||
\(360\) | 10.5804 | 0.557637 | ||||||||
\(361\) | −17.4221 | −0.916954 | ||||||||
\(362\) | −20.8617 | −1.09647 | ||||||||
\(363\) | −12.3327 | −0.647298 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −46.3102 | −2.42399 | ||||||||
\(366\) | 4.10986 | 0.214826 | ||||||||
\(367\) | −1.14472 | −0.0597542 | −0.0298771 | − | 0.999554i | \(-0.509512\pi\) | ||||
−0.0298771 | + | 0.999554i | \(0.509512\pi\) | |||||||
\(368\) | −8.30428 | −0.432890 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 5.52495 | 0.287228 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.54398 | −0.235594 | ||||||||
\(373\) | 20.3354 | 1.05293 | 0.526464 | − | 0.850197i | \(-0.323517\pi\) | ||||
0.526464 | + | 0.850197i | \(0.323517\pi\) | |||||||
\(374\) | 18.6650 | 0.965146 | ||||||||
\(375\) | −6.60086 | −0.340867 | ||||||||
\(376\) | −17.4948 | −0.902225 | ||||||||
\(377\) | 25.8060 | 1.32908 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5603 | −1.10748 | −0.553740 | − | 0.832689i | \(-0.686800\pi\) | ||||
−0.553740 | + | 0.832689i | \(0.686800\pi\) | |||||||
\(380\) | −2.24946 | −0.115395 | ||||||||
\(381\) | −1.37208 | −0.0702937 | ||||||||
\(382\) | 0.248268 | 0.0127025 | ||||||||
\(383\) | 24.1750 | 1.23528 | 0.617642 | − | 0.786459i | \(-0.288088\pi\) | ||||
0.617642 | + | 0.786459i | \(0.288088\pi\) | |||||||
\(384\) | 5.07461 | 0.258963 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.52246 | −0.382883 | ||||||||
\(387\) | −7.25707 | −0.368898 | ||||||||
\(388\) | 0.352107 | 0.0178755 | ||||||||
\(389\) | 12.6428 | 0.641013 | 0.320507 | − | 0.947246i | \(-0.396147\pi\) | ||||
0.320507 | + | 0.947246i | \(0.396147\pi\) | |||||||
\(390\) | −18.7457 | −0.949226 | ||||||||
\(391\) | 9.79033 | 0.495118 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.84280 | 0.0929569 | ||||||||
\(394\) | 14.7432 | 0.742750 | ||||||||
\(395\) | 22.0432 | 1.10911 | ||||||||
\(396\) | 2.50625 | 0.125944 | ||||||||
\(397\) | 19.1228 | 0.959745 | 0.479873 | − | 0.877338i | \(-0.340683\pi\) | ||||
0.479873 | + | 0.877338i | \(0.340683\pi\) | |||||||
\(398\) | −16.4344 | −0.823783 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.6160 | −0.930799 | ||||||||
\(401\) | 10.6363 | 0.531151 | 0.265576 | − | 0.964090i | \(-0.414438\pi\) | ||||
0.265576 | + | 0.964090i | \(0.414438\pi\) | |||||||
\(402\) | 10.4032 | 0.518866 | ||||||||
\(403\) | 39.0837 | 1.94690 | ||||||||
\(404\) | 0.100354 | 0.00499281 | ||||||||
\(405\) | 3.45145 | 0.171504 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.35345 | 0.314929 | ||||||||
\(408\) | −9.73304 | −0.481857 | ||||||||
\(409\) | −2.06871 | −0.102291 | −0.0511457 | − | 0.998691i | \(-0.516287\pi\) | ||||
−0.0511457 | + | 0.998691i | \(0.516287\pi\) | |||||||
\(410\) | 4.20050 | 0.207448 | ||||||||
\(411\) | −3.30016 | −0.162785 | ||||||||
\(412\) | 2.26491 | 0.111584 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.75275 | −0.184438 | ||||||||
\(415\) | 53.9411 | 2.64787 | ||||||||
\(416\) | 12.7342 | 0.624344 | ||||||||
\(417\) | −16.1445 | −0.790599 | ||||||||
\(418\) | 7.38444 | 0.361185 | ||||||||
\(419\) | 23.0843 | 1.12774 | 0.563871 | − | 0.825863i | \(-0.309312\pi\) | ||||
0.563871 | + | 0.825863i | \(0.309312\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0077 | 0.731432 | 0.365716 | − | 0.930727i | \(-0.380824\pi\) | ||||
0.365716 | + | 0.930727i | \(0.380824\pi\) | |||||||
\(422\) | 2.69789 | 0.131331 | ||||||||
\(423\) | −5.70699 | −0.277483 | ||||||||
\(424\) | 38.4914 | 1.86931 | ||||||||
\(425\) | 21.9473 | 1.06460 | ||||||||
\(426\) | 9.51048 | 0.460784 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.99107 | 0.144579 | ||||||||
\(429\) | −21.5568 | −1.04077 | ||||||||
\(430\) | 30.4833 | 1.47004 | ||||||||
\(431\) | −22.6029 | −1.08874 | −0.544372 | − | 0.838844i | \(-0.683232\pi\) | ||||
−0.544372 | + | 0.838844i | \(0.683232\pi\) | |||||||
\(432\) | 2.69309 | 0.129572 | ||||||||
\(433\) | 33.1526 | 1.59321 | 0.796606 | − | 0.604499i | \(-0.206627\pi\) | ||||
0.796606 | + | 0.604499i | \(0.206627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.9582 | 0.956921 | ||||||||
\(436\) | 3.88596 | 0.186104 | ||||||||
\(437\) | 3.87335 | 0.185287 | ||||||||
\(438\) | −16.3296 | −0.780257 | ||||||||
\(439\) | −15.8397 | −0.755990 | −0.377995 | − | 0.925808i | \(-0.623386\pi\) | ||||
−0.377995 | + | 0.925808i | \(0.623386\pi\) | |||||||
\(440\) | −51.1076 | −2.43646 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.2444 | 0.820232 | ||||||||
\(443\) | 15.4030 | 0.731819 | 0.365909 | − | 0.930651i | \(-0.380758\pi\) | ||||
0.365909 | + | 0.930651i | \(0.380758\pi\) | |||||||
\(444\) | −0.682448 | −0.0323875 | ||||||||
\(445\) | 60.3327 | 2.86005 | ||||||||
\(446\) | 34.4888 | 1.63309 | ||||||||
\(447\) | −18.5736 | −0.878503 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −41.9052 | −1.97763 | −0.988813 | − | 0.149159i | \(-0.952343\pi\) | ||||
−0.988813 | + | 0.149159i | \(0.952343\pi\) | |||||||
\(450\) | −8.41267 | −0.396577 | ||||||||
\(451\) | 4.83039 | 0.227454 | ||||||||
\(452\) | −6.74760 | −0.317380 | ||||||||
\(453\) | −8.25131 | −0.387680 | ||||||||
\(454\) | −19.0142 | −0.892382 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.85068 | −0.180325 | ||||||||
\(457\) | 3.86106 | 0.180613 | 0.0903064 | − | 0.995914i | \(-0.471215\pi\) | ||||
0.0903064 | + | 0.995914i | \(0.471215\pi\) | |||||||
\(458\) | −27.3736 | −1.27908 | ||||||||
\(459\) | −3.17502 | −0.148197 | ||||||||
\(460\) | −5.52197 | −0.257463 | ||||||||
\(461\) | −18.4765 | −0.860537 | −0.430268 | − | 0.902701i | \(-0.641581\pi\) | ||||
−0.430268 | + | 0.902701i | \(0.641581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.4051 | 1.59894 | 0.799470 | − | 0.600706i | \(-0.205114\pi\) | ||||
0.799470 | + | 0.600706i | \(0.205114\pi\) | |||||||
\(464\) | 15.5730 | 0.722956 | ||||||||
\(465\) | 30.2270 | 1.40174 | ||||||||
\(466\) | −26.9766 | −1.24967 | ||||||||
\(467\) | 3.76316 | 0.174138 | 0.0870690 | − | 0.996202i | \(-0.472250\pi\) | ||||
0.0870690 | + | 0.996202i | \(0.472250\pi\) | |||||||
\(468\) | 2.31549 | 0.107034 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 23.9722 | 1.10576 | ||||||||
\(471\) | −6.08420 | −0.280345 | ||||||||
\(472\) | 23.8297 | 1.09685 | ||||||||
\(473\) | 35.0545 | 1.61181 | ||||||||
\(474\) | 7.77272 | 0.357013 | ||||||||
\(475\) | 8.68301 | 0.398404 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.5563 | 0.574914 | ||||||||
\(478\) | 26.9803 | 1.23405 | ||||||||
\(479\) | 39.8663 | 1.82154 | 0.910769 | − | 0.412917i | \(-0.135490\pi\) | ||||
0.910769 | + | 0.412917i | \(0.135490\pi\) | |||||||
\(480\) | 9.84852 | 0.449521 | ||||||||
\(481\) | 5.86987 | 0.267643 | ||||||||
\(482\) | −10.7000 | −0.487371 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.39882 | −0.290855 | ||||||||
\(485\) | −2.34225 | −0.106356 | ||||||||
\(486\) | 1.21702 | 0.0552054 | ||||||||
\(487\) | 22.6171 | 1.02488 | 0.512440 | − | 0.858723i | \(-0.328742\pi\) | ||||
0.512440 | + | 0.858723i | \(0.328742\pi\) | |||||||
\(488\) | 10.3521 | 0.468619 | ||||||||
\(489\) | 15.7777 | 0.713493 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.9802 | 0.991952 | 0.495976 | − | 0.868336i | \(-0.334810\pi\) | ||||
0.495976 | + | 0.868336i | \(0.334810\pi\) | |||||||
\(492\) | −0.518850 | −0.0233916 | ||||||||
\(493\) | −18.3597 | −0.826881 | ||||||||
\(494\) | 6.82239 | 0.306954 | ||||||||
\(495\) | −16.6718 | −0.749344 | ||||||||
\(496\) | 23.5855 | 1.05902 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 19.0203 | 0.852322 | ||||||||
\(499\) | −27.7097 | −1.24045 | −0.620227 | − | 0.784422i | \(-0.712960\pi\) | ||||
−0.620227 | + | 0.784422i | \(0.712960\pi\) | |||||||
\(500\) | −3.42486 | −0.153164 | ||||||||
\(501\) | 18.3293 | 0.818893 | ||||||||
\(502\) | 26.3999 | 1.17829 | ||||||||
\(503\) | −6.49879 | −0.289767 | −0.144883 | − | 0.989449i | \(-0.546281\pi\) | ||||
−0.144883 | + | 0.989449i | \(0.546281\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.667568 | −0.0297064 | ||||||||
\(506\) | 18.1273 | 0.805855 | ||||||||
\(507\) | −6.91602 | −0.307151 | ||||||||
\(508\) | −0.711904 | −0.0315856 | ||||||||
\(509\) | 22.6588 | 1.00433 | 0.502167 | − | 0.864771i | \(-0.332536\pi\) | ||||
0.502167 | + | 0.864771i | \(0.332536\pi\) | |||||||
\(510\) | 13.3367 | 0.590558 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.1960 | 1.06932 | ||||||||
\(513\) | −1.25613 | −0.0554597 | ||||||||
\(514\) | −33.6348 | −1.48357 | ||||||||
\(515\) | −15.0664 | −0.663906 | ||||||||
\(516\) | −3.76533 | −0.165760 | ||||||||
\(517\) | 27.5670 | 1.21240 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.5857 | 0.640242 | ||||||||
\(520\) | −47.2177 | −2.07063 | ||||||||
\(521\) | 13.4737 | 0.590293 | 0.295147 | − | 0.955452i | \(-0.404631\pi\) | ||||
0.295147 | + | 0.955452i | \(0.404631\pi\) | |||||||
\(522\) | 7.03751 | 0.308023 | ||||||||
\(523\) | 26.6708 | 1.16623 | 0.583116 | − | 0.812389i | \(-0.301833\pi\) | ||||
0.583116 | + | 0.812389i | \(0.301833\pi\) | |||||||
\(524\) | 0.956136 | 0.0417690 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.66262 | 0.159698 | ||||||||
\(527\) | −27.8061 | −1.21125 | ||||||||
\(528\) | −13.0087 | −0.566131 | ||||||||
\(529\) | −13.4917 | −0.586598 | ||||||||
\(530\) | −52.7427 | −2.29100 | ||||||||
\(531\) | 7.77351 | 0.337341 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.46274 | 0.193303 | ||||||||
\(534\) | 21.2741 | 0.920620 | ||||||||
\(535\) | −19.8969 | −0.860218 | ||||||||
\(536\) | 26.2042 | 1.13185 | ||||||||
\(537\) | 10.2770 | 0.443486 | ||||||||
\(538\) | −18.3007 | −0.789000 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.79078 | 0.0770631 | ||||||||
\(541\) | 26.9550 | 1.15889 | 0.579443 | − | 0.815013i | \(-0.303270\pi\) | ||||
0.579443 | + | 0.815013i | \(0.303270\pi\) | |||||||
\(542\) | −9.04996 | −0.388729 | ||||||||
\(543\) | −17.1415 | −0.735614 | ||||||||
\(544\) | −9.05975 | −0.388434 | ||||||||
\(545\) | −25.8498 | −1.10728 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.3424 | 0.827021 | 0.413510 | − | 0.910499i | \(-0.364303\pi\) | ||||
0.413510 | + | 0.910499i | \(0.364303\pi\) | |||||||
\(548\) | −1.71229 | −0.0731453 | ||||||||
\(549\) | 3.37698 | 0.144126 | ||||||||
\(550\) | 40.6365 | 1.73275 | ||||||||
\(551\) | −7.26366 | −0.309442 | ||||||||
\(552\) | −9.45262 | −0.402330 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.12471 | 0.175242 | ||||||||
\(555\) | 4.53971 | 0.192700 | ||||||||
\(556\) | −8.37657 | −0.355246 | ||||||||
\(557\) | −6.78595 | −0.287530 | −0.143765 | − | 0.989612i | \(-0.545921\pi\) | ||||
−0.143765 | + | 0.989612i | \(0.545921\pi\) | |||||||
\(558\) | 10.6584 | 0.451207 | ||||||||
\(559\) | 32.3864 | 1.36980 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.3366 | 0.647512 | ||||||||
\(562\) | 19.9766 | 0.842663 | ||||||||
\(563\) | −14.2309 | −0.599761 | −0.299880 | − | 0.953977i | \(-0.596947\pi\) | ||||
−0.299880 | + | 0.953977i | \(0.596947\pi\) | |||||||
\(564\) | −2.96107 | −0.124684 | ||||||||
\(565\) | 44.8857 | 1.88836 | ||||||||
\(566\) | 19.7817 | 0.831487 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.9555 | 1.00515 | ||||||||
\(569\) | 16.8913 | 0.708119 | 0.354059 | − | 0.935223i | \(-0.384801\pi\) | ||||
0.354059 | + | 0.935223i | \(0.384801\pi\) | |||||||
\(570\) | 5.27639 | 0.221004 | ||||||||
\(571\) | −32.8000 | −1.37264 | −0.686318 | − | 0.727302i | \(-0.740774\pi\) | ||||
−0.686318 | + | 0.727302i | \(0.740774\pi\) | |||||||
\(572\) | −11.1847 | −0.467657 | ||||||||
\(573\) | 0.203996 | 0.00852206 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.3150 | 0.888896 | ||||||||
\(576\) | 8.85890 | 0.369121 | ||||||||
\(577\) | −36.2224 | −1.50796 | −0.753979 | − | 0.656898i | \(-0.771868\pi\) | ||||
−0.753979 | + | 0.656898i | \(0.771868\pi\) | |||||||
\(578\) | 8.42088 | 0.350262 | ||||||||
\(579\) | −6.18102 | −0.256874 | ||||||||
\(580\) | 10.3553 | 0.429980 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.825909 | −0.0342350 | ||||||||
\(583\) | −60.6518 | −2.51194 | ||||||||
\(584\) | −41.1318 | −1.70204 | ||||||||
\(585\) | −15.4029 | −0.636832 | ||||||||
\(586\) | −16.6871 | −0.689338 | ||||||||
\(587\) | −18.3704 | −0.758227 | −0.379114 | − | 0.925350i | \(-0.623771\pi\) | ||||
−0.379114 | + | 0.925350i | \(0.623771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.0009 | −0.453286 | ||||||||
\(590\) | −32.6526 | −1.34429 | ||||||||
\(591\) | 12.1141 | 0.498308 | ||||||||
\(592\) | 3.54225 | 0.145585 | ||||||||
\(593\) | −37.8015 | −1.55232 | −0.776161 | − | 0.630535i | \(-0.782836\pi\) | ||||
−0.776161 | + | 0.630535i | \(0.782836\pi\) | |||||||
\(594\) | −5.87871 | −0.241206 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.63694 | −0.394744 | ||||||||
\(597\) | −13.5038 | −0.552672 | ||||||||
\(598\) | 16.7475 | 0.684858 | ||||||||
\(599\) | −28.6011 | −1.16861 | −0.584306 | − | 0.811534i | \(-0.698633\pi\) | ||||
−0.584306 | + | 0.811534i | \(0.698633\pi\) | |||||||
\(600\) | −21.1903 | −0.865089 | ||||||||
\(601\) | −35.6300 | −1.45338 | −0.726690 | − | 0.686966i | \(-0.758942\pi\) | ||||
−0.726690 | + | 0.686966i | \(0.758942\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.54808 | 0.348105 | ||||||||
\(604\) | −4.28119 | −0.174199 | ||||||||
\(605\) | 42.5656 | 1.73054 | ||||||||
\(606\) | −0.235393 | −0.00956218 | ||||||||
\(607\) | −10.5051 | −0.426387 | −0.213193 | − | 0.977010i | \(-0.568386\pi\) | ||||
−0.213193 | + | 0.977010i | \(0.568386\pi\) | |||||||
\(608\) | −3.58431 | −0.145363 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.1850 | −0.574333 | ||||||||
\(611\) | 25.4688 | 1.03036 | ||||||||
\(612\) | −1.64736 | −0.0665906 | ||||||||
\(613\) | −12.6573 | −0.511223 | −0.255611 | − | 0.966780i | \(-0.582277\pi\) | ||||
−0.255611 | + | 0.966780i | \(0.582277\pi\) | |||||||
\(614\) | −18.6997 | −0.754658 | ||||||||
\(615\) | 3.45145 | 0.139176 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.2258 | 1.09607 | 0.548034 | − | 0.836456i | \(-0.315376\pi\) | ||||
0.548034 | + | 0.836456i | \(0.315376\pi\) | |||||||
\(618\) | −5.31262 | −0.213705 | ||||||||
\(619\) | −5.26084 | −0.211451 | −0.105726 | − | 0.994395i | \(-0.533717\pi\) | ||||
−0.105726 | + | 0.994395i | \(0.533717\pi\) | |||||||
\(620\) | 15.6833 | 0.629856 | ||||||||
\(621\) | −3.08355 | −0.123738 | ||||||||
\(622\) | −4.78508 | −0.191864 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12.0186 | −0.481128 | ||||||||
\(625\) | −11.7799 | −0.471197 | ||||||||
\(626\) | −26.2514 | −1.04922 | ||||||||
\(627\) | 6.06762 | 0.242317 | ||||||||
\(628\) | −3.15679 | −0.125970 | ||||||||
\(629\) | −4.17613 | −0.166513 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3193 | 0.570043 | 0.285022 | − | 0.958521i | \(-0.407999\pi\) | ||||
0.285022 | + | 0.958521i | \(0.407999\pi\) | |||||||
\(632\) | 19.5783 | 0.778784 | ||||||||
\(633\) | 2.21679 | 0.0881095 | ||||||||
\(634\) | 19.1247 | 0.759539 | ||||||||
\(635\) | 4.73566 | 0.187929 | ||||||||
\(636\) | 6.51484 | 0.258330 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −33.9939 | −1.34583 | ||||||||
\(639\) | 7.81453 | 0.309138 | ||||||||
\(640\) | −17.5148 | −0.692332 | ||||||||
\(641\) | −45.5986 | −1.80104 | −0.900518 | − | 0.434819i | \(-0.856812\pi\) | ||||
−0.900518 | + | 0.434819i | \(0.856812\pi\) | |||||||
\(642\) | −7.01591 | −0.276896 | ||||||||
\(643\) | 32.7732 | 1.29245 | 0.646224 | − | 0.763148i | \(-0.276347\pi\) | ||||
0.646224 | + | 0.763148i | \(0.276347\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.0474 | 0.986240 | ||||||||
\(646\) | −4.85380 | −0.190970 | ||||||||
\(647\) | 7.14896 | 0.281055 | 0.140527 | − | 0.990077i | \(-0.455120\pi\) | ||||
0.140527 | + | 0.990077i | \(0.455120\pi\) | |||||||
\(648\) | 3.06550 | 0.120424 | ||||||||
\(649\) | −37.5491 | −1.47393 | ||||||||
\(650\) | 37.5435 | 1.47258 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.18627 | 0.320599 | ||||||||
\(653\) | 37.0774 | 1.45095 | 0.725475 | − | 0.688248i | \(-0.241620\pi\) | ||||
0.725475 | + | 0.688248i | \(0.241620\pi\) | |||||||
\(654\) | −9.11498 | −0.356424 | ||||||||
\(655\) | −6.36032 | −0.248518 | ||||||||
\(656\) | 2.69309 | 0.105148 | ||||||||
\(657\) | −13.4176 | −0.523471 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.3010 | −1.68677 | −0.843384 | − | 0.537311i | \(-0.819440\pi\) | ||||
−0.843384 | + | 0.537311i | \(0.819440\pi\) | |||||||
\(660\) | −8.65019 | −0.336708 | ||||||||
\(661\) | 39.0356 | 1.51831 | 0.759154 | − | 0.650910i | \(-0.225613\pi\) | ||||
0.759154 | + | 0.650910i | \(0.225613\pi\) | |||||||
\(662\) | −22.5665 | −0.877072 | ||||||||
\(663\) | 14.1693 | 0.550290 | ||||||||
\(664\) | 47.9094 | 1.85925 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.60076 | 0.0620283 | ||||||||
\(667\) | −17.8308 | −0.690410 | ||||||||
\(668\) | 9.51016 | 0.367959 | ||||||||
\(669\) | 28.3386 | 1.09563 | ||||||||
\(670\) | −35.9062 | −1.38718 | ||||||||
\(671\) | −16.3121 | −0.629722 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0321 | 0.386708 | 0.193354 | − | 0.981129i | \(-0.438063\pi\) | ||||
0.193354 | + | 0.981129i | \(0.438063\pi\) | |||||||
\(674\) | −14.7926 | −0.569792 | ||||||||
\(675\) | −6.91249 | −0.266062 | ||||||||
\(676\) | −3.58838 | −0.138015 | ||||||||
\(677\) | −9.61097 | −0.369380 | −0.184690 | − | 0.982797i | \(-0.559128\pi\) | ||||
−0.184690 | + | 0.982797i | \(0.559128\pi\) | |||||||
\(678\) | 15.8273 | 0.607843 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 33.5931 | 1.28824 | ||||||||
\(681\) | −15.6235 | −0.598695 | ||||||||
\(682\) | −51.4844 | −1.97144 | ||||||||
\(683\) | 12.6126 | 0.482606 | 0.241303 | − | 0.970450i | \(-0.422425\pi\) | ||||
0.241303 | + | 0.970450i | \(0.422425\pi\) | |||||||
\(684\) | −0.651745 | −0.0249201 | ||||||||
\(685\) | 11.3903 | 0.435202 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.4922 | −0.858131 | ||||||||
\(688\) | 19.5440 | 0.745107 | ||||||||
\(689\) | −56.0355 | −2.13478 | ||||||||
\(690\) | 12.9524 | 0.493090 | ||||||||
\(691\) | 8.45068 | 0.321479 | 0.160740 | − | 0.986997i | \(-0.448612\pi\) | ||||
0.160740 | + | 0.986997i | \(0.448612\pi\) | |||||||
\(692\) | 7.56780 | 0.287685 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.34089 | 0.164778 | ||||||||
\(695\) | 55.7218 | 2.11365 | ||||||||
\(696\) | 17.7264 | 0.671919 | ||||||||
\(697\) | −3.17502 | −0.120263 | ||||||||
\(698\) | −40.2999 | −1.52538 | ||||||||
\(699\) | −22.1660 | −0.838397 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.7541 | 1.57703 | 0.788515 | − | 0.615015i | \(-0.210850\pi\) | ||||
0.788515 | + | 0.615015i | \(0.210850\pi\) | |||||||
\(702\) | −5.43126 | −0.204990 | ||||||||
\(703\) | −1.65220 | −0.0623140 | ||||||||
\(704\) | −42.7920 | −1.61278 | ||||||||
\(705\) | 19.6974 | 0.741846 | ||||||||
\(706\) | −7.65243 | −0.288003 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.03329 | 0.151580 | ||||||||
\(709\) | 25.5670 | 0.960189 | 0.480094 | − | 0.877217i | \(-0.340602\pi\) | ||||
0.480094 | + | 0.877217i | \(0.340602\pi\) | |||||||
\(710\) | −32.8249 | −1.23190 | ||||||||
\(711\) | 6.38666 | 0.239518 | ||||||||
\(712\) | 53.5863 | 2.00823 | ||||||||
\(713\) | −27.0050 | −1.01135 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 74.4020 | 2.78248 | ||||||||
\(716\) | 5.33223 | 0.199275 | ||||||||
\(717\) | 22.1690 | 0.827917 | ||||||||
\(718\) | 24.2581 | 0.905305 | ||||||||
\(719\) | 46.9973 | 1.75270 | 0.876351 | − | 0.481672i | \(-0.159970\pi\) | ||||
0.876351 | + | 0.481672i | \(0.159970\pi\) | |||||||
\(720\) | −9.29507 | −0.346407 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 21.2032 | 0.789100 | ||||||||
\(723\) | −8.79193 | −0.326975 | ||||||||
\(724\) | −8.89390 | −0.330539 | ||||||||
\(725\) | −39.9718 | −1.48452 | ||||||||
\(726\) | 15.0092 | 0.557043 | ||||||||
\(727\) | 21.2532 | 0.788239 | 0.394119 | − | 0.919059i | \(-0.371050\pi\) | ||||
0.394119 | + | 0.919059i | \(0.371050\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 56.3607 | 2.08600 | ||||||||
\(731\) | −23.0414 | −0.852215 | ||||||||
\(732\) | 1.75215 | 0.0647611 | ||||||||
\(733\) | 0.210397 | 0.00777120 | 0.00388560 | − | 0.999992i | \(-0.498763\pi\) | ||||
0.00388560 | + | 0.999992i | \(0.498763\pi\) | |||||||
\(734\) | 1.39316 | 0.0514224 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.79873 | −0.324325 | ||||||||
\(737\) | −41.2906 | −1.52096 | ||||||||
\(738\) | 1.21702 | 0.0447993 | ||||||||
\(739\) | 1.91323 | 0.0703794 | 0.0351897 | − | 0.999381i | \(-0.488796\pi\) | ||||
0.0351897 | + | 0.999381i | \(0.488796\pi\) | |||||||
\(740\) | 2.35543 | 0.0865874 | ||||||||
\(741\) | 5.60579 | 0.205934 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.3853 | −0.564430 | −0.282215 | − | 0.959351i | \(-0.591069\pi\) | ||||
−0.282215 | + | 0.959351i | \(0.591069\pi\) | |||||||
\(744\) | 26.8470 | 0.984259 | ||||||||
\(745\) | 64.1060 | 2.34866 | ||||||||
\(746\) | −24.7487 | −0.906115 | ||||||||
\(747\) | 15.6286 | 0.571819 | ||||||||
\(748\) | 7.95740 | 0.290951 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.03341 | 0.293339 | ||||||||
\(751\) | 52.1464 | 1.90285 | 0.951425 | − | 0.307882i | \(-0.0996202\pi\) | ||||
0.951425 | + | 0.307882i | \(0.0996202\pi\) | |||||||
\(752\) | 15.3695 | 0.560467 | ||||||||
\(753\) | 21.6922 | 0.790507 | ||||||||
\(754\) | −31.4065 | −1.14376 | ||||||||
\(755\) | 28.4790 | 1.03646 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.60797 | −0.312862 | −0.156431 | − | 0.987689i | \(-0.549999\pi\) | ||||
−0.156431 | + | 0.987689i | \(0.549999\pi\) | |||||||
\(758\) | 26.2395 | 0.953061 | ||||||||
\(759\) | 14.8947 | 0.540644 | ||||||||
\(760\) | 13.2904 | 0.482095 | ||||||||
\(761\) | 20.6394 | 0.748176 | 0.374088 | − | 0.927393i | \(-0.377956\pi\) | ||||
0.374088 | + | 0.927393i | \(0.377956\pi\) | |||||||
\(762\) | 1.66985 | 0.0604924 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.105843 | 0.00382928 | ||||||||
\(765\) | 10.9584 | 0.396203 | ||||||||
\(766\) | −29.4216 | −1.06304 | ||||||||
\(767\) | −34.6911 | −1.25262 | ||||||||
\(768\) | 11.5419 | 0.416481 | ||||||||
\(769\) | 6.64543 | 0.239640 | 0.119820 | − | 0.992796i | \(-0.461768\pi\) | ||||
0.119820 | + | 0.992796i | \(0.461768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.6369 | −0.995319 | ||||||||
\(772\) | −3.20702 | −0.115423 | ||||||||
\(773\) | 27.6536 | 0.994632 | 0.497316 | − | 0.867570i | \(-0.334319\pi\) | ||||
0.497316 | + | 0.867570i | \(0.334319\pi\) | |||||||
\(774\) | 8.83203 | 0.317461 | ||||||||
\(775\) | −60.5380 | −2.17459 | ||||||||
\(776\) | −2.08034 | −0.0746799 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.3866 | −0.551635 | ||||||||
\(779\) | −1.25613 | −0.0450057 | ||||||||
\(780\) | −7.99180 | −0.286152 | ||||||||
\(781\) | −37.7472 | −1.35070 | ||||||||
\(782\) | −11.9151 | −0.426082 | ||||||||
\(783\) | 5.78255 | 0.206651 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.9993 | 0.749497 | ||||||||
\(786\) | −2.24273 | −0.0799956 | ||||||||
\(787\) | −8.07633 | −0.287890 | −0.143945 | − | 0.989586i | \(-0.545979\pi\) | ||||
−0.143945 | + | 0.989586i | \(0.545979\pi\) | |||||||
\(788\) | 6.28541 | 0.223908 | ||||||||
\(789\) | 3.00949 | 0.107141 | ||||||||
\(790\) | −26.8271 | −0.954467 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.8076 | −0.526165 | ||||||||
\(793\) | −15.0706 | −0.535171 | ||||||||
\(794\) | −23.2729 | −0.825925 | ||||||||
\(795\) | −43.3374 | −1.53702 | ||||||||
\(796\) | −7.00643 | −0.248336 | ||||||||
\(797\) | −15.8738 | −0.562278 | −0.281139 | − | 0.959667i | \(-0.590712\pi\) | ||||
−0.281139 | + | 0.959667i | \(0.590712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.1198 | −0.641033 | ||||||||
\(800\) | −19.7244 | −0.697363 | ||||||||
\(801\) | 17.4804 | 0.617640 | ||||||||
\(802\) | −12.9446 | −0.457091 | ||||||||
\(803\) | 64.8124 | 2.28718 | ||||||||
\(804\) | 4.43517 | 0.156417 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −47.5658 | −1.67543 | ||||||||
\(807\) | −15.0373 | −0.529337 | ||||||||
\(808\) | −0.592920 | −0.0208588 | ||||||||
\(809\) | −28.2948 | −0.994793 | −0.497396 | − | 0.867523i | \(-0.665710\pi\) | ||||
−0.497396 | + | 0.867523i | \(0.665710\pi\) | |||||||
\(810\) | −4.20050 | −0.147590 | ||||||||
\(811\) | 43.6617 | 1.53317 | 0.766584 | − | 0.642144i | \(-0.221955\pi\) | ||||
0.766584 | + | 0.642144i | \(0.221955\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.43613 | −0.260797 | ||||||||
\(814\) | −7.73231 | −0.271017 | ||||||||
\(815\) | −54.4560 | −1.90751 | ||||||||
\(816\) | 8.55063 | 0.299332 | ||||||||
\(817\) | −9.11585 | −0.318923 | ||||||||
\(818\) | 2.51768 | 0.0880285 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.79078 | 0.0625369 | ||||||||
\(821\) | −39.3347 | −1.37279 | −0.686395 | − | 0.727229i | \(-0.740808\pi\) | ||||
−0.686395 | + | 0.727229i | \(0.740808\pi\) | |||||||
\(822\) | 4.01637 | 0.140087 | ||||||||
\(823\) | 6.95585 | 0.242466 | 0.121233 | − | 0.992624i | \(-0.461315\pi\) | ||||
0.121233 | + | 0.992624i | \(0.461315\pi\) | |||||||
\(824\) | −13.3817 | −0.466173 | ||||||||
\(825\) | 33.3900 | 1.16249 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.5819 | 1.13298 | 0.566491 | − | 0.824068i | \(-0.308301\pi\) | ||||
0.566491 | + | 0.824068i | \(0.308301\pi\) | |||||||
\(828\) | −1.59990 | −0.0556003 | ||||||||
\(829\) | 30.6404 | 1.06419 | 0.532093 | − | 0.846686i | \(-0.321406\pi\) | ||||
0.532093 | + | 0.846686i | \(0.321406\pi\) | |||||||
\(830\) | −65.6477 | −2.27867 | ||||||||
\(831\) | 3.38918 | 0.117569 | ||||||||
\(832\) | −39.5349 | −1.37063 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.6482 | 0.680363 | ||||||||
\(835\) | −63.2626 | −2.18929 | ||||||||
\(836\) | 3.14819 | 0.108882 | ||||||||
\(837\) | 8.75778 | 0.302713 | ||||||||
\(838\) | −28.0942 | −0.970497 | ||||||||
\(839\) | 44.2762 | 1.52859 | 0.764293 | − | 0.644870i | \(-0.223088\pi\) | ||||
0.764293 | + | 0.644870i | \(0.223088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.43789 | 0.153031 | ||||||||
\(842\) | −18.2648 | −0.629446 | ||||||||
\(843\) | 16.4143 | 0.565339 | ||||||||
\(844\) | 1.15018 | 0.0395909 | ||||||||
\(845\) | 23.8703 | 0.821163 | ||||||||
\(846\) | 6.94555 | 0.238793 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −33.8153 | −1.16122 | ||||||||
\(849\) | 16.2542 | 0.557841 | ||||||||
\(850\) | −26.7104 | −0.916160 | ||||||||
\(851\) | −4.05581 | −0.139031 | ||||||||
\(852\) | 4.05457 | 0.138907 | ||||||||
\(853\) | −37.5296 | −1.28499 | −0.642495 | − | 0.766290i | \(-0.722101\pi\) | ||||
−0.642495 | + | 0.766290i | \(0.722101\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.33548 | 0.148270 | ||||||||
\(856\) | −17.6720 | −0.604017 | ||||||||
\(857\) | −15.6067 | −0.533116 | −0.266558 | − | 0.963819i | \(-0.585886\pi\) | ||||
−0.266558 | + | 0.963819i | \(0.585886\pi\) | |||||||
\(858\) | 26.2351 | 0.895652 | ||||||||
\(859\) | −30.4859 | −1.04016 | −0.520082 | − | 0.854116i | \(-0.674099\pi\) | ||||
−0.520082 | + | 0.854116i | \(0.674099\pi\) | |||||||
\(860\) | 12.9958 | 0.443155 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.5083 | 0.936937 | ||||||||
\(863\) | 20.2797 | 0.690328 | 0.345164 | − | 0.938542i | \(-0.387823\pi\) | ||||
0.345164 | + | 0.938542i | \(0.387823\pi\) | |||||||
\(864\) | 2.85344 | 0.0970762 | ||||||||
\(865\) | −50.3418 | −1.71167 | ||||||||
\(866\) | −40.3475 | −1.37107 | ||||||||
\(867\) | 6.91923 | 0.234989 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.8501 | −1.04652 | ||||||||
\(870\) | −24.2896 | −0.823494 | ||||||||
\(871\) | −38.1478 | −1.29259 | ||||||||
\(872\) | −22.9593 | −0.777499 | ||||||||
\(873\) | −0.678629 | −0.0229681 | ||||||||
\(874\) | −4.71396 | −0.159452 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.96174 | −0.235215 | ||||||||
\(877\) | 3.03871 | 0.102610 | 0.0513049 | − | 0.998683i | \(-0.483662\pi\) | ||||
0.0513049 | + | 0.998683i | \(0.483662\pi\) | |||||||
\(878\) | 19.2774 | 0.650580 | ||||||||
\(879\) | −13.7114 | −0.462474 | ||||||||
\(880\) | 44.8988 | 1.51354 | ||||||||
\(881\) | 0.553699 | 0.0186546 | 0.00932729 | − | 0.999956i | \(-0.497031\pi\) | ||||
0.00932729 | + | 0.999956i | \(0.497031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.12193 | −0.273325 | −0.136662 | − | 0.990618i | \(-0.543638\pi\) | ||||
−0.136662 | + | 0.990618i | \(0.543638\pi\) | |||||||
\(884\) | 7.35174 | 0.247266 | ||||||||
\(885\) | −26.8298 | −0.901875 | ||||||||
\(886\) | −18.7458 | −0.629779 | ||||||||
\(887\) | 2.48356 | 0.0833899 | 0.0416950 | − | 0.999130i | \(-0.486724\pi\) | ||||
0.0416950 | + | 0.999130i | \(0.486724\pi\) | |||||||
\(888\) | 4.03208 | 0.135308 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −73.4264 | −2.46126 | ||||||||
\(891\) | −4.83039 | −0.161824 | ||||||||
\(892\) | 14.7035 | 0.492310 | ||||||||
\(893\) | −7.16874 | −0.239893 | ||||||||
\(894\) | 22.6046 | 0.756011 | ||||||||
\(895\) | −35.4706 | −1.18565 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.7611 | 0.459468 | ||||||||
\(898\) | 50.9996 | 1.70188 | ||||||||
\(899\) | 50.6423 | 1.68901 | ||||||||
\(900\) | −3.58655 | −0.119552 | ||||||||
\(901\) | 39.8665 | 1.32815 | ||||||||
\(902\) | −5.87871 | −0.195740 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39.8666 | 1.32594 | ||||||||
\(905\) | 59.1632 | 1.96665 | ||||||||
\(906\) | 10.0420 | 0.333625 | ||||||||
\(907\) | −26.5825 | −0.882657 | −0.441328 | − | 0.897346i | \(-0.645493\pi\) | ||||
−0.441328 | + | 0.897346i | \(0.645493\pi\) | |||||||
\(908\) | −8.10627 | −0.269016 | ||||||||
\(909\) | −0.193417 | −0.00641523 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.9262 | −1.68726 | −0.843631 | − | 0.536924i | \(-0.819586\pi\) | ||||
−0.843631 | + | 0.536924i | \(0.819586\pi\) | |||||||
\(912\) | 3.38289 | 0.112019 | ||||||||
\(913\) | −75.4920 | −2.49842 | ||||||||
\(914\) | −4.69901 | −0.155429 | ||||||||
\(915\) | −11.6555 | −0.385317 | ||||||||
\(916\) | −11.6701 | −0.385590 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.86408 | 0.127534 | ||||||||
\(919\) | 44.8158 | 1.47834 | 0.739169 | − | 0.673520i | \(-0.235219\pi\) | ||||
0.739169 | + | 0.673520i | \(0.235219\pi\) | |||||||
\(920\) | 32.6252 | 1.07562 | ||||||||
\(921\) | −15.3651 | −0.506297 | ||||||||
\(922\) | 22.4864 | 0.740549 | ||||||||
\(923\) | −34.8742 | −1.14790 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.09205 | −0.298945 | ||||||||
\(926\) | −41.8719 | −1.37599 | ||||||||
\(927\) | −4.36525 | −0.143374 | ||||||||
\(928\) | 16.5002 | 0.541645 | ||||||||
\(929\) | 13.5038 | 0.443046 | 0.221523 | − | 0.975155i | \(-0.428897\pi\) | ||||
0.221523 | + | 0.975155i | \(0.428897\pi\) | |||||||
\(930\) | −36.7870 | −1.20629 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.5009 | −0.376723 | ||||||||
\(933\) | −3.93179 | −0.128721 | ||||||||
\(934\) | −4.57985 | −0.149857 | ||||||||
\(935\) | −52.9335 | −1.73111 | ||||||||
\(936\) | −13.6805 | −0.447162 | ||||||||
\(937\) | 31.8314 | 1.03989 | 0.519944 | − | 0.854200i | \(-0.325953\pi\) | ||||
0.519944 | + | 0.854200i | \(0.325953\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.5701 | −0.703914 | ||||||||
\(940\) | 10.2200 | 0.333339 | ||||||||
\(941\) | 20.3471 | 0.663298 | 0.331649 | − | 0.943403i | \(-0.392395\pi\) | ||||
0.331649 | + | 0.943403i | \(0.392395\pi\) | |||||||
\(942\) | 7.40462 | 0.241256 | ||||||||
\(943\) | −3.08355 | −0.100414 | ||||||||
\(944\) | −20.9348 | −0.681369 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.6622 | −1.38707 | ||||||||
\(947\) | 11.4063 | 0.370656 | 0.185328 | − | 0.982677i | \(-0.440665\pi\) | ||||
0.185328 | + | 0.982677i | \(0.440665\pi\) | |||||||
\(948\) | 3.31372 | 0.107625 | ||||||||
\(949\) | 59.8793 | 1.94376 | ||||||||
\(950\) | −10.5674 | −0.342853 | ||||||||
\(951\) | 15.7143 | 0.509571 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.1678 | 0.329369 | 0.164684 | − | 0.986346i | \(-0.447339\pi\) | ||||
0.164684 | + | 0.986346i | \(0.447339\pi\) | |||||||
\(954\) | −15.2813 | −0.494751 | ||||||||
\(955\) | −0.704082 | −0.0227836 | ||||||||
\(956\) | 11.5024 | 0.372014 | ||||||||
\(957\) | −27.9320 | −0.902913 | ||||||||
\(958\) | −48.5183 | −1.56755 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −30.5760 | −0.986837 | ||||||||
\(961\) | 45.6987 | 1.47415 | ||||||||
\(962\) | −7.14378 | −0.230325 | ||||||||
\(963\) | −5.76480 | −0.185768 | ||||||||
\(964\) | −4.56169 | −0.146922 | ||||||||
\(965\) | 21.3335 | 0.686749 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.46761 | −0.175826 | −0.0879132 | − | 0.996128i | \(-0.528020\pi\) | ||||
−0.0879132 | + | 0.996128i | \(0.528020\pi\) | |||||||
\(968\) | 37.8059 | 1.21513 | ||||||||
\(969\) | −3.98825 | −0.128121 | ||||||||
\(970\) | 2.85058 | 0.0915267 | ||||||||
\(971\) | −47.3251 | −1.51873 | −0.759367 | − | 0.650663i | \(-0.774491\pi\) | ||||
−0.759367 | + | 0.650663i | \(0.774491\pi\) | |||||||
\(972\) | 0.518850 | 0.0166421 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −27.5256 | −0.881977 | ||||||||
\(975\) | 30.8486 | 0.987947 | ||||||||
\(976\) | −9.09451 | −0.291108 | ||||||||
\(977\) | 11.4544 | 0.366459 | 0.183230 | − | 0.983070i | \(-0.441345\pi\) | ||||
0.183230 | + | 0.983070i | \(0.441345\pi\) | |||||||
\(978\) | −19.2019 | −0.614008 | ||||||||
\(979\) | −84.4373 | −2.69863 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.48956 | −0.239123 | ||||||||
\(982\) | −26.7504 | −0.853640 | ||||||||
\(983\) | −29.3612 | −0.936478 | −0.468239 | − | 0.883602i | \(-0.655111\pi\) | ||||
−0.468239 | + | 0.883602i | \(0.655111\pi\) | |||||||
\(984\) | 3.06550 | 0.0977247 | ||||||||
\(985\) | −41.8112 | −1.33222 | ||||||||
\(986\) | 22.3442 | 0.711586 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.90857 | 0.0925339 | ||||||||
\(989\) | −22.3775 | −0.711563 | ||||||||
\(990\) | 20.2900 | 0.644860 | ||||||||
\(991\) | −45.9550 | −1.45981 | −0.729904 | − | 0.683550i | \(-0.760435\pi\) | ||||
−0.729904 | + | 0.683550i | \(0.760435\pi\) | |||||||
\(992\) | 24.9898 | 0.793428 | ||||||||
\(993\) | −18.5423 | −0.588424 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.6075 | 1.47756 | ||||||||
\(996\) | 8.10888 | 0.256940 | ||||||||
\(997\) | 23.3905 | 0.740783 | 0.370392 | − | 0.928876i | \(-0.379223\pi\) | ||||
0.370392 | + | 0.928876i | \(0.379223\pi\) | |||||||
\(998\) | 33.7234 | 1.06749 | ||||||||
\(999\) | 1.31531 | 0.0416145 |
(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 | 6027.2.a.bh.1.5 | 13 | ||
7.3 | odd | 6 | 861.2.i.f.247.9 | ✓ | 26 | ||
7.5 | odd | 6 | 861.2.i.f.739.9 | yes | 26 | ||
7.6 | odd | 2 | 6027.2.a.bi.1.5 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.f.247.9 | ✓ | 26 | 7.3 | odd | 6 | ||
861.2.i.f.739.9 | yes | 26 | 7.5 | odd | 6 | ||
6027.2.a.bh.1.5 | 13 | 1.1 | even | 1 | trivial | ||
6027.2.a.bi.1.5 | 13 | 7.6 | odd | 2 |