Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.42782\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42782 | −1.71673 | −0.858363 | − | 0.513042i | \(-0.828518\pi\) | ||||
−0.858363 | + | 0.513042i | \(0.828518\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.89430 | 1.94715 | ||||||||
\(5\) | −4.13136 | −1.84760 | −0.923801 | − | 0.382873i | \(-0.874935\pi\) | ||||
−0.923801 | + | 0.382873i | \(0.874935\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −4.59902 | −1.62600 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.0302 | 3.17183 | ||||||||
\(11\) | 4.39665 | 1.32564 | 0.662820 | − | 0.748779i | \(-0.269359\pi\) | ||||
0.662820 | + | 0.748779i | \(0.269359\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.702420 | 0.194816 | 0.0974081 | − | 0.995245i | \(-0.468945\pi\) | ||||
0.0974081 | + | 0.995245i | \(0.468945\pi\) | |||||||
\(14\) | −2.42782 | −0.648862 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.37699 | 0.844246 | ||||||||
\(17\) | 0.979615 | 0.237592 | 0.118796 | − | 0.992919i | \(-0.462097\pi\) | ||||
0.118796 | + | 0.992919i | \(0.462097\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.50347 | −1.72141 | −0.860707 | − | 0.509100i | \(-0.829978\pi\) | ||||
−0.860707 | + | 0.509100i | \(0.829978\pi\) | |||||||
\(20\) | −16.0888 | −3.59756 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.6743 | −2.27576 | ||||||||
\(23\) | 4.28424 | 0.893326 | 0.446663 | − | 0.894702i | \(-0.352612\pi\) | ||||
0.446663 | + | 0.894702i | \(0.352612\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0682 | 2.41363 | ||||||||
\(26\) | −1.70535 | −0.334446 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.89430 | 0.735954 | ||||||||
\(29\) | −8.97712 | −1.66701 | −0.833505 | − | 0.552513i | \(-0.813669\pi\) | ||||
−0.833505 | + | 0.552513i | \(0.813669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.872190 | −0.156650 | −0.0783249 | − | 0.996928i | \(-0.524957\pi\) | ||||
−0.0783249 | + | 0.996928i | \(0.524957\pi\) | |||||||
\(32\) | 0.999336 | 0.176659 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.37833 | −0.407880 | ||||||||
\(35\) | −4.13136 | −0.698328 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.83153 | 1.12310 | 0.561548 | − | 0.827444i | \(-0.310206\pi\) | ||||
0.561548 | + | 0.827444i | \(0.310206\pi\) | |||||||
\(38\) | 18.2171 | 2.95520 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 19.0002 | 3.00420 | ||||||||
\(41\) | 4.36586 | 0.681833 | 0.340917 | − | 0.940094i | \(-0.389263\pi\) | ||||
0.340917 | + | 0.940094i | \(0.389263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.34656 | −0.967841 | −0.483921 | − | 0.875112i | \(-0.660788\pi\) | ||||
−0.483921 | + | 0.875112i | \(0.660788\pi\) | |||||||
\(44\) | 17.1219 | 2.58122 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.4014 | −1.53360 | ||||||||
\(47\) | −2.85801 | −0.416884 | −0.208442 | − | 0.978035i | \(-0.566839\pi\) | ||||
−0.208442 | + | 0.978035i | \(0.566839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −29.2993 | −4.14355 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.73544 | 0.379337 | ||||||||
\(53\) | 5.93310 | 0.814974 | 0.407487 | − | 0.913211i | \(-0.366405\pi\) | ||||
0.407487 | + | 0.913211i | \(0.366405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.1642 | −2.44926 | ||||||||
\(56\) | −4.59902 | −0.614570 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 21.7948 | 2.86180 | ||||||||
\(59\) | −5.83624 | −0.759814 | −0.379907 | − | 0.925025i | \(-0.624044\pi\) | ||||
−0.379907 | + | 0.925025i | \(0.624044\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.431173 | 0.0552061 | 0.0276030 | − | 0.999619i | \(-0.491213\pi\) | ||||
0.0276030 | + | 0.999619i | \(0.491213\pi\) | |||||||
\(62\) | 2.11752 | 0.268925 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.18018 | −1.14752 | ||||||||
\(65\) | −2.90195 | −0.359943 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.64991 | 0.201568 | 0.100784 | − | 0.994908i | \(-0.467865\pi\) | ||||
0.100784 | + | 0.994908i | \(0.467865\pi\) | |||||||
\(68\) | 3.81492 | 0.462627 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.0302 | 1.19884 | ||||||||
\(71\) | 15.5767 | 1.84862 | 0.924309 | − | 0.381645i | \(-0.124642\pi\) | ||||
0.924309 | + | 0.381645i | \(0.124642\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.79200 | −0.443821 | −0.221910 | − | 0.975067i | \(-0.571229\pi\) | ||||
−0.221910 | + | 0.975067i | \(0.571229\pi\) | |||||||
\(74\) | −16.5857 | −1.92805 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −29.2208 | −3.35185 | ||||||||
\(77\) | 4.39665 | 0.501045 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6779 | 1.65139 | 0.825697 | − | 0.564114i | \(-0.190782\pi\) | ||||
0.825697 | + | 0.564114i | \(0.190782\pi\) | |||||||
\(80\) | −13.9516 | −1.55983 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.5995 | −1.17052 | ||||||||
\(83\) | 5.45195 | 0.598429 | 0.299215 | − | 0.954186i | \(-0.403275\pi\) | ||||
0.299215 | + | 0.954186i | \(0.403275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.04715 | −0.438975 | ||||||||
\(86\) | 15.4083 | 1.66152 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −20.2203 | −2.15549 | ||||||||
\(89\) | 12.1433 | 1.28719 | 0.643593 | − | 0.765368i | \(-0.277443\pi\) | ||||
0.643593 | + | 0.765368i | \(0.277443\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.702420 | 0.0736336 | ||||||||
\(92\) | 16.6841 | 1.73944 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.93874 | 0.715676 | ||||||||
\(95\) | 30.9996 | 3.18049 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.29248 | 0.943509 | 0.471754 | − | 0.881730i | \(-0.343621\pi\) | ||||
0.471754 | + | 0.881730i | \(0.343621\pi\) | |||||||
\(98\) | −2.42782 | −0.245247 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 46.9971 | 4.69971 | ||||||||
\(101\) | −10.0187 | −0.996893 | −0.498447 | − | 0.866920i | \(-0.666096\pi\) | ||||
−0.498447 | + | 0.866920i | \(0.666096\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3855 | −1.02332 | −0.511659 | − | 0.859189i | \(-0.670969\pi\) | ||||
−0.511659 | + | 0.859189i | \(0.670969\pi\) | |||||||
\(104\) | −3.23045 | −0.316771 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.4045 | −1.39909 | ||||||||
\(107\) | 12.3554 | 1.19445 | 0.597223 | − | 0.802075i | \(-0.296271\pi\) | ||||
0.597223 | + | 0.802075i | \(0.296271\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.4746 | −1.19485 | −0.597423 | − | 0.801926i | \(-0.703809\pi\) | ||||
−0.597423 | + | 0.801926i | \(0.703809\pi\) | |||||||
\(110\) | 44.0993 | 4.20470 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.37699 | 0.319095 | ||||||||
\(113\) | −17.5483 | −1.65080 | −0.825400 | − | 0.564548i | \(-0.809051\pi\) | ||||
−0.825400 | + | 0.564548i | \(0.809051\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.6998 | −1.65051 | ||||||||
\(116\) | −34.9596 | −3.24592 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.1693 | 1.30439 | ||||||||
\(119\) | 0.979615 | 0.0898012 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.33054 | 0.757322 | ||||||||
\(122\) | −1.04681 | −0.0947738 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.39657 | −0.305021 | ||||||||
\(125\) | −29.2011 | −2.61183 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 20.2891 | 1.79332 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.04541 | 0.617924 | ||||||||
\(131\) | −1.03408 | −0.0903480 | −0.0451740 | − | 0.998979i | \(-0.514384\pi\) | ||||
−0.0451740 | + | 0.998979i | \(0.514384\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.50347 | −0.650633 | ||||||||
\(134\) | −4.00567 | −0.346037 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.50527 | −0.386324 | ||||||||
\(137\) | −10.4831 | −0.895629 | −0.447815 | − | 0.894126i | \(-0.647798\pi\) | ||||
−0.447815 | + | 0.894126i | \(0.647798\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.23389 | 0.783208 | 0.391604 | − | 0.920134i | \(-0.371920\pi\) | ||||
0.391604 | + | 0.920134i | \(0.371920\pi\) | |||||||
\(140\) | −16.0888 | −1.35975 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −37.8175 | −3.17357 | ||||||||
\(143\) | 3.08830 | 0.258256 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 37.0877 | 3.07997 | ||||||||
\(146\) | 9.20630 | 0.761919 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 26.6040 | 2.18684 | ||||||||
\(149\) | −11.0699 | −0.906885 | −0.453442 | − | 0.891286i | \(-0.649804\pi\) | ||||
−0.453442 | + | 0.891286i | \(0.649804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6210 | 1.02708 | 0.513540 | − | 0.858066i | \(-0.328334\pi\) | ||||
0.513540 | + | 0.858066i | \(0.328334\pi\) | |||||||
\(152\) | 34.5086 | 2.79902 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.6743 | −0.860157 | ||||||||
\(155\) | 3.60333 | 0.289427 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.436970 | −0.0348740 | −0.0174370 | − | 0.999848i | \(-0.505551\pi\) | ||||
−0.0174370 | + | 0.999848i | \(0.505551\pi\) | |||||||
\(158\) | −35.6353 | −2.83499 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.12862 | −0.326396 | ||||||||
\(161\) | 4.28424 | 0.337646 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0335 | −0.864209 | −0.432105 | − | 0.901824i | \(-0.642229\pi\) | ||||
−0.432105 | + | 0.901824i | \(0.642229\pi\) | |||||||
\(164\) | 17.0020 | 1.32763 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.2363 | −1.02734 | ||||||||
\(167\) | −22.0805 | −1.70864 | −0.854321 | − | 0.519746i | \(-0.826027\pi\) | ||||
−0.854321 | + | 0.519746i | \(0.826027\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5066 | −0.962047 | ||||||||
\(170\) | 9.82574 | 0.753600 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −24.7154 | −1.88453 | ||||||||
\(173\) | −7.62698 | −0.579868 | −0.289934 | − | 0.957047i | \(-0.593633\pi\) | ||||
−0.289934 | + | 0.957047i | \(0.593633\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.0682 | 0.912267 | ||||||||
\(176\) | 14.8474 | 1.11917 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −29.4817 | −2.20975 | ||||||||
\(179\) | 8.74055 | 0.653299 | 0.326650 | − | 0.945146i | \(-0.394080\pi\) | ||||
0.326650 | + | 0.945146i | \(0.394080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.99890 | 0.148577 | 0.0742884 | − | 0.997237i | \(-0.476331\pi\) | ||||
0.0742884 | + | 0.997237i | \(0.476331\pi\) | |||||||
\(182\) | −1.70535 | −0.126409 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.7033 | −1.45255 | ||||||||
\(185\) | −28.2235 | −2.07504 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.30703 | 0.314961 | ||||||||
\(188\) | −11.1300 | −0.811736 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −75.2613 | −5.46003 | ||||||||
\(191\) | 5.03588 | 0.364383 | 0.182192 | − | 0.983263i | \(-0.441681\pi\) | ||||
0.182192 | + | 0.983263i | \(0.441681\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.96100 | 0.357101 | 0.178550 | − | 0.983931i | \(-0.442859\pi\) | ||||
0.178550 | + | 0.983931i | \(0.442859\pi\) | |||||||
\(194\) | −22.5605 | −1.61975 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.89430 | 0.278164 | ||||||||
\(197\) | −3.19173 | −0.227401 | −0.113701 | − | 0.993515i | \(-0.536271\pi\) | ||||
−0.113701 | + | 0.993515i | \(0.536271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.96090 | −0.564333 | −0.282167 | − | 0.959365i | \(-0.591053\pi\) | ||||
−0.282167 | + | 0.959365i | \(0.591053\pi\) | |||||||
\(200\) | −55.5017 | −3.92457 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.3235 | 1.71139 | ||||||||
\(203\) | −8.97712 | −0.630070 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0370 | −1.25976 | ||||||||
\(206\) | 25.2142 | 1.75676 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.37206 | 0.164473 | ||||||||
\(209\) | −32.9901 | −2.28198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.3101 | −0.985151 | −0.492575 | − | 0.870270i | \(-0.663944\pi\) | ||||
−0.492575 | + | 0.870270i | \(0.663944\pi\) | |||||||
\(212\) | 23.1053 | 1.58688 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −29.9968 | −2.05054 | ||||||||
\(215\) | 26.2199 | 1.78819 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.872190 | −0.0592081 | ||||||||
\(218\) | 30.2860 | 2.05123 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −70.7367 | −4.76907 | ||||||||
\(221\) | 0.688101 | 0.0462867 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2261 | 0.885686 | 0.442843 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(224\) | 0.999336 | 0.0667709 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 42.6040 | 2.83397 | ||||||||
\(227\) | −29.5131 | −1.95885 | −0.979426 | − | 0.201805i | \(-0.935319\pi\) | ||||
−0.979426 | + | 0.201805i | \(0.935319\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.5215 | −1.02569 | −0.512845 | − | 0.858481i | \(-0.671409\pi\) | ||||
−0.512845 | + | 0.858481i | \(0.671409\pi\) | |||||||
\(230\) | 42.9718 | 2.83348 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 41.2860 | 2.71056 | ||||||||
\(233\) | 6.88255 | 0.450891 | 0.225445 | − | 0.974256i | \(-0.427616\pi\) | ||||
0.225445 | + | 0.974256i | \(0.427616\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.8075 | 0.770236 | ||||||||
\(236\) | −22.7281 | −1.47947 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.37833 | −0.154164 | ||||||||
\(239\) | −5.00111 | −0.323495 | −0.161747 | − | 0.986832i | \(-0.551713\pi\) | ||||
−0.161747 | + | 0.986832i | \(0.551713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.5508 | 1.00171 | 0.500856 | − | 0.865530i | \(-0.333019\pi\) | ||||
0.500856 | + | 0.865530i | \(0.333019\pi\) | |||||||
\(242\) | −20.2250 | −1.30011 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.67912 | 0.107495 | ||||||||
\(245\) | −4.13136 | −0.263943 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.27059 | −0.335360 | ||||||||
\(248\) | 4.01122 | 0.254713 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 70.8950 | 4.48380 | ||||||||
\(251\) | −24.6173 | −1.55383 | −0.776916 | − | 0.629605i | \(-0.783217\pi\) | ||||
−0.776916 | + | 0.629605i | \(0.783217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.8363 | 1.18423 | ||||||||
\(254\) | −2.42782 | −0.152335 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30.8980 | −1.93112 | ||||||||
\(257\) | −10.9511 | −0.683108 | −0.341554 | − | 0.939862i | \(-0.610953\pi\) | ||||
−0.341554 | + | 0.939862i | \(0.610953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.83153 | 0.424491 | ||||||||
\(260\) | −11.3011 | −0.700863 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.51056 | 0.155103 | ||||||||
\(263\) | 23.9422 | 1.47634 | 0.738171 | − | 0.674614i | \(-0.235690\pi\) | ||||
0.738171 | + | 0.674614i | \(0.235690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.5118 | −1.50575 | ||||||||
\(266\) | 18.2171 | 1.11696 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.42523 | 0.392484 | ||||||||
\(269\) | 17.5905 | 1.07251 | 0.536257 | − | 0.844055i | \(-0.319838\pi\) | ||||
0.536257 | + | 0.844055i | \(0.319838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.00655 | 0.425617 | 0.212809 | − | 0.977094i | \(-0.431739\pi\) | ||||
0.212809 | + | 0.977094i | \(0.431739\pi\) | |||||||
\(272\) | 3.30815 | 0.200586 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.4510 | 1.53755 | ||||||||
\(275\) | 53.0595 | 3.19961 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.00516 | 0.420899 | 0.210449 | − | 0.977605i | \(-0.432507\pi\) | ||||
0.210449 | + | 0.977605i | \(0.432507\pi\) | |||||||
\(278\) | −22.4182 | −1.34455 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.0002 | 1.13548 | ||||||||
\(281\) | 23.2539 | 1.38721 | 0.693607 | − | 0.720354i | \(-0.256021\pi\) | ||||
0.693607 | + | 0.720354i | \(0.256021\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.2416 | 1.79768 | 0.898840 | − | 0.438278i | \(-0.144411\pi\) | ||||
0.898840 | + | 0.438278i | \(0.144411\pi\) | |||||||
\(284\) | 60.6605 | 3.59954 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.49782 | −0.443355 | ||||||||
\(287\) | 4.36586 | 0.257709 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0404 | −0.943550 | ||||||||
\(290\) | −90.0423 | −5.28747 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.7672 | −0.864186 | ||||||||
\(293\) | 15.6762 | 0.915812 | 0.457906 | − | 0.889001i | \(-0.348600\pi\) | ||||
0.457906 | + | 0.889001i | \(0.348600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.1116 | 1.40383 | ||||||||
\(296\) | −31.4184 | −1.82616 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.8758 | 1.55687 | ||||||||
\(299\) | 3.00934 | 0.174034 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.34656 | −0.365810 | ||||||||
\(302\) | −30.6414 | −1.76321 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −25.3391 | −1.45330 | ||||||||
\(305\) | −1.78133 | −0.101999 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.13944 | −0.464543 | −0.232271 | − | 0.972651i | \(-0.574616\pi\) | ||||
−0.232271 | + | 0.972651i | \(0.574616\pi\) | |||||||
\(308\) | 17.1219 | 0.975610 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.74823 | −0.496866 | ||||||||
\(311\) | −10.5758 | −0.599698 | −0.299849 | − | 0.953987i | \(-0.596936\pi\) | ||||
−0.299849 | + | 0.953987i | \(0.596936\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2622 | −1.20181 | −0.600904 | − | 0.799321i | \(-0.705193\pi\) | ||||
−0.600904 | + | 0.799321i | \(0.705193\pi\) | |||||||
\(314\) | 1.06088 | 0.0598692 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 57.1602 | 3.21551 | ||||||||
\(317\) | 17.7625 | 0.997641 | 0.498820 | − | 0.866705i | \(-0.333767\pi\) | ||||
0.498820 | + | 0.866705i | \(0.333767\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.4693 | −2.20985 | ||||||||
\(320\) | 37.9266 | 2.12016 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.4014 | −0.579645 | ||||||||
\(323\) | −7.35052 | −0.408994 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.47692 | 0.470215 | ||||||||
\(326\) | 26.7873 | 1.48361 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.0787 | −1.10866 | ||||||||
\(329\) | −2.85801 | −0.157567 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.606407 | −0.0333312 | −0.0166656 | − | 0.999861i | \(-0.505305\pi\) | ||||
−0.0166656 | + | 0.999861i | \(0.505305\pi\) | |||||||
\(332\) | 21.2315 | 1.16523 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 53.6075 | 2.93327 | ||||||||
\(335\) | −6.81636 | −0.372418 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.3425 | 1.05365 | 0.526827 | − | 0.849973i | \(-0.323382\pi\) | ||||
0.526827 | + | 0.849973i | \(0.323382\pi\) | |||||||
\(338\) | 30.3638 | 1.65157 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15.7608 | −0.854750 | ||||||||
\(341\) | −3.83471 | −0.207661 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 29.1880 | 1.57371 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.5169 | 0.995475 | ||||||||
\(347\) | −17.3328 | −0.930472 | −0.465236 | − | 0.885187i | \(-0.654031\pi\) | ||||
−0.465236 | + | 0.885187i | \(0.654031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.3170 | 1.51578 | 0.757888 | − | 0.652385i | \(-0.226231\pi\) | ||||
0.757888 | + | 0.652385i | \(0.226231\pi\) | |||||||
\(350\) | −29.2993 | −1.56611 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.39373 | 0.234187 | ||||||||
\(353\) | 9.94061 | 0.529085 | 0.264543 | − | 0.964374i | \(-0.414779\pi\) | ||||
0.264543 | + | 0.964374i | \(0.414779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −64.3531 | −3.41551 | ||||||||
\(356\) | 47.2896 | 2.50635 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.2205 | −1.12154 | ||||||||
\(359\) | −12.6698 | −0.668689 | −0.334344 | − | 0.942451i | \(-0.608515\pi\) | ||||
−0.334344 | + | 0.942451i | \(0.608515\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.3021 | 1.96327 | ||||||||
\(362\) | −4.85296 | −0.255066 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.73544 | 0.143376 | ||||||||
\(365\) | 15.6661 | 0.820004 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.6547 | 0.712772 | 0.356386 | − | 0.934339i | \(-0.384009\pi\) | ||||
0.356386 | + | 0.934339i | \(0.384009\pi\) | |||||||
\(368\) | 14.4678 | 0.754187 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 68.5216 | 3.56227 | ||||||||
\(371\) | 5.93310 | 0.308031 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.79015 | −0.506915 | −0.253457 | − | 0.967347i | \(-0.581568\pi\) | ||||
−0.253457 | + | 0.967347i | \(0.581568\pi\) | |||||||
\(374\) | −10.4567 | −0.540702 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.1441 | 0.677853 | ||||||||
\(377\) | −6.30571 | −0.324761 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.07864 | −0.106772 | −0.0533862 | − | 0.998574i | \(-0.517001\pi\) | ||||
−0.0533862 | + | 0.998574i | \(0.517001\pi\) | |||||||
\(380\) | 120.722 | 6.19289 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.2262 | −0.625546 | ||||||||
\(383\) | 6.32519 | 0.323202 | 0.161601 | − | 0.986856i | \(-0.448334\pi\) | ||||
0.161601 | + | 0.986856i | \(0.448334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.1642 | −0.925731 | ||||||||
\(386\) | −12.0444 | −0.613044 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 36.1877 | 1.83715 | ||||||||
\(389\) | 10.0363 | 0.508859 | 0.254429 | − | 0.967091i | \(-0.418112\pi\) | ||||
0.254429 | + | 0.967091i | \(0.418112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.19691 | 0.212247 | ||||||||
\(392\) | −4.59902 | −0.232286 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.74895 | 0.390386 | ||||||||
\(395\) | −60.6398 | −3.05112 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.9023 | −1.75170 | −0.875848 | − | 0.482588i | \(-0.839697\pi\) | ||||
−0.875848 | + | 0.482588i | \(0.839697\pi\) | |||||||
\(398\) | 19.3276 | 0.968806 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 40.7540 | 2.03770 | ||||||||
\(401\) | 22.2029 | 1.10876 | 0.554380 | − | 0.832264i | \(-0.312955\pi\) | ||||
0.554380 | + | 0.832264i | \(0.312955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.612643 | −0.0305179 | ||||||||
\(404\) | −39.0157 | −1.94110 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.7948 | 1.08166 | ||||||||
\(407\) | 30.0359 | 1.48882 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.9983 | 1.53277 | 0.766384 | − | 0.642383i | \(-0.222054\pi\) | ||||
0.766384 | + | 0.642383i | \(0.222054\pi\) | |||||||
\(410\) | 43.7905 | 2.16266 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −40.4444 | −1.99255 | ||||||||
\(413\) | −5.83624 | −0.287183 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.5240 | −1.10566 | ||||||||
\(416\) | 0.701953 | 0.0344161 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 80.0941 | 3.91753 | ||||||||
\(419\) | −21.8162 | −1.06579 | −0.532894 | − | 0.846182i | \(-0.678896\pi\) | ||||
−0.532894 | + | 0.846182i | \(0.678896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.803041 | 0.0391378 | 0.0195689 | − | 0.999809i | \(-0.493771\pi\) | ||||
0.0195689 | + | 0.999809i | \(0.493771\pi\) | |||||||
\(422\) | 34.7424 | 1.69123 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −27.2865 | −1.32515 | ||||||||
\(425\) | 11.8222 | 0.573459 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.431173 | 0.0208659 | ||||||||
\(428\) | 48.1158 | 2.32577 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −63.6573 | −3.06983 | ||||||||
\(431\) | 26.8778 | 1.29466 | 0.647328 | − | 0.762211i | \(-0.275886\pi\) | ||||
0.647328 | + | 0.762211i | \(0.275886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.181842 | −0.00873876 | −0.00436938 | − | 0.999990i | \(-0.501391\pi\) | ||||
−0.00436938 | + | 0.999990i | \(0.501391\pi\) | |||||||
\(434\) | 2.11752 | 0.101644 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −48.5797 | −2.32655 | ||||||||
\(437\) | −32.1467 | −1.53778 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.9576 | 1.95480 | 0.977401 | − | 0.211395i | \(-0.0678008\pi\) | ||||
0.977401 | + | 0.211395i | \(0.0678008\pi\) | |||||||
\(440\) | 83.5374 | 3.98249 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.67059 | −0.0794616 | ||||||||
\(443\) | −2.65537 | −0.126161 | −0.0630803 | − | 0.998008i | \(-0.520092\pi\) | ||||
−0.0630803 | + | 0.998008i | \(0.520092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −50.1683 | −2.37821 | ||||||||
\(446\) | −32.1106 | −1.52048 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.18018 | −0.433723 | ||||||||
\(449\) | −41.8175 | −1.97349 | −0.986744 | − | 0.162285i | \(-0.948114\pi\) | ||||
−0.986744 | + | 0.162285i | \(0.948114\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1952 | 0.903865 | ||||||||
\(452\) | −68.3382 | −3.21436 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 71.6524 | 3.36281 | ||||||||
\(455\) | −2.90195 | −0.136046 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.99792 | −0.420905 | −0.210452 | − | 0.977604i | \(-0.567494\pi\) | ||||
−0.210452 | + | 0.977604i | \(0.567494\pi\) | |||||||
\(458\) | 37.6834 | 1.76083 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −68.9282 | −3.21379 | ||||||||
\(461\) | 8.15332 | 0.379738 | 0.189869 | − | 0.981809i | \(-0.439194\pi\) | ||||
0.189869 | + | 0.981809i | \(0.439194\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.5221 | −0.907270 | −0.453635 | − | 0.891188i | \(-0.649873\pi\) | ||||
−0.453635 | + | 0.891188i | \(0.649873\pi\) | |||||||
\(464\) | −30.3156 | −1.40737 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.7096 | −0.774057 | ||||||||
\(467\) | −18.3081 | −0.847197 | −0.423598 | − | 0.905850i | \(-0.639233\pi\) | ||||
−0.423598 | + | 0.905850i | \(0.639233\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.64991 | 0.0761856 | ||||||||
\(470\) | −28.6664 | −1.32228 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 26.8410 | 1.23546 | ||||||||
\(473\) | −27.9036 | −1.28301 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −90.5531 | −4.15486 | ||||||||
\(476\) | 3.81492 | 0.174856 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.1418 | 0.555352 | ||||||||
\(479\) | −20.4221 | −0.933111 | −0.466555 | − | 0.884492i | \(-0.654505\pi\) | ||||
−0.466555 | + | 0.884492i | \(0.654505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.79860 | 0.218798 | ||||||||
\(482\) | −37.7544 | −1.71967 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 32.4416 | 1.47462 | ||||||||
\(485\) | −38.3906 | −1.74323 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.4355 | −1.24322 | −0.621610 | − | 0.783327i | \(-0.713521\pi\) | ||||
−0.621610 | + | 0.783327i | \(0.713521\pi\) | |||||||
\(488\) | −1.98298 | −0.0897651 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.0302 | 0.453118 | ||||||||
\(491\) | −18.0466 | −0.814431 | −0.407215 | − | 0.913332i | \(-0.633500\pi\) | ||||
−0.407215 | + | 0.913332i | \(0.633500\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.79412 | −0.396067 | ||||||||
\(494\) | 12.7960 | 0.575721 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.94537 | −0.132251 | ||||||||
\(497\) | 15.5767 | 0.698712 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.6544 | 1.10368 | 0.551842 | − | 0.833949i | \(-0.313925\pi\) | ||||
0.551842 | + | 0.833949i | \(0.313925\pi\) | |||||||
\(500\) | −113.718 | −5.08563 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 59.7664 | 2.66750 | ||||||||
\(503\) | 13.5368 | 0.603577 | 0.301789 | − | 0.953375i | \(-0.402416\pi\) | ||||
0.301789 | + | 0.953375i | \(0.402416\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.3907 | 1.84186 | ||||||||
\(506\) | −45.7312 | −2.03300 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.89430 | 0.172782 | ||||||||
\(509\) | 44.1678 | 1.95770 | 0.978851 | − | 0.204576i | \(-0.0655815\pi\) | ||||
0.978851 | + | 0.204576i | \(0.0655815\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.79200 | −0.167748 | ||||||||
\(512\) | 34.4364 | 1.52189 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.5872 | 1.17271 | ||||||||
\(515\) | 42.9064 | 1.89068 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.5657 | −0.552638 | ||||||||
\(518\) | −16.5857 | −0.728735 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13.3461 | 0.585267 | ||||||||
\(521\) | 44.2787 | 1.93989 | 0.969943 | − | 0.243331i | \(-0.0782400\pi\) | ||||
0.969943 | + | 0.243331i | \(0.0782400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.707142 | 0.0309212 | 0.0154606 | − | 0.999880i | \(-0.495079\pi\) | ||||
0.0154606 | + | 0.999880i | \(0.495079\pi\) | |||||||
\(524\) | −4.02702 | −0.175921 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −58.1274 | −2.53448 | ||||||||
\(527\) | −0.854410 | −0.0372187 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.64527 | −0.201968 | ||||||||
\(530\) | 59.5102 | 2.58496 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −29.2208 | −1.26688 | ||||||||
\(533\) | 3.06667 | 0.132832 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −51.0448 | −2.20686 | ||||||||
\(536\) | −7.58796 | −0.327750 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −42.7066 | −1.84121 | ||||||||
\(539\) | 4.39665 | 0.189377 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.3076 | 1.26003 | 0.630015 | − | 0.776583i | \(-0.283049\pi\) | ||||
0.630015 | + | 0.776583i | \(0.283049\pi\) | |||||||
\(542\) | −17.0106 | −0.730669 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.978964 | 0.0419728 | ||||||||
\(545\) | 51.5370 | 2.20760 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.9550 | 1.49457 | 0.747285 | − | 0.664504i | \(-0.231357\pi\) | ||||
0.747285 | + | 0.664504i | \(0.231357\pi\) | |||||||
\(548\) | −40.8242 | −1.74393 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −128.819 | −5.49285 | ||||||||
\(551\) | 67.3595 | 2.86961 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.6779 | 0.624168 | ||||||||
\(554\) | −17.0072 | −0.722569 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 35.9596 | 1.52502 | ||||||||
\(557\) | 0.580975 | 0.0246167 | 0.0123083 | − | 0.999924i | \(-0.496082\pi\) | ||||
0.0123083 | + | 0.999924i | \(0.496082\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.45795 | −0.188551 | ||||||||
\(560\) | −13.9516 | −0.589561 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −56.4563 | −2.38147 | ||||||||
\(563\) | 17.2618 | 0.727497 | 0.363748 | − | 0.931497i | \(-0.381497\pi\) | ||||
0.363748 | + | 0.931497i | \(0.381497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 72.4982 | 3.05002 | ||||||||
\(566\) | −73.4212 | −3.08612 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −71.6377 | −3.00585 | ||||||||
\(569\) | −13.6965 | −0.574188 | −0.287094 | − | 0.957902i | \(-0.592689\pi\) | ||||
−0.287094 | + | 0.957902i | \(0.592689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.5296 | −1.69611 | −0.848055 | − | 0.529909i | \(-0.822226\pi\) | ||||
−0.848055 | + | 0.529909i | \(0.822226\pi\) | |||||||
\(572\) | 12.0268 | 0.502864 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.5995 | −0.442415 | ||||||||
\(575\) | 51.7029 | 2.15616 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.5066 | −0.812069 | −0.406035 | − | 0.913858i | \(-0.633089\pi\) | ||||
−0.406035 | + | 0.913858i | \(0.633089\pi\) | |||||||
\(578\) | 38.9431 | 1.61982 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 144.431 | 5.99716 | ||||||||
\(581\) | 5.45195 | 0.226185 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.0858 | 1.08036 | ||||||||
\(584\) | 17.4395 | 0.721652 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.0589 | −1.57220 | ||||||||
\(587\) | −20.5249 | −0.847155 | −0.423578 | − | 0.905860i | \(-0.639226\pi\) | ||||
−0.423578 | + | 0.905860i | \(0.639226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.54445 | 0.269659 | ||||||||
\(590\) | −58.5387 | −2.41000 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.0700 | 0.948170 | ||||||||
\(593\) | 24.3206 | 0.998726 | 0.499363 | − | 0.866393i | \(-0.333567\pi\) | ||||
0.499363 | + | 0.866393i | \(0.333567\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.04715 | −0.165917 | ||||||||
\(596\) | −43.1097 | −1.76584 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.30612 | −0.298770 | ||||||||
\(599\) | 38.6834 | 1.58056 | 0.790280 | − | 0.612746i | \(-0.209935\pi\) | ||||
0.790280 | + | 0.612746i | \(0.209935\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.4855 | 0.794831 | 0.397416 | − | 0.917639i | \(-0.369907\pi\) | ||||
0.397416 | + | 0.917639i | \(0.369907\pi\) | |||||||
\(602\) | 15.4083 | 0.627995 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 49.1498 | 1.99988 | ||||||||
\(605\) | −34.4165 | −1.39923 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.3703 | −1.15152 | −0.575758 | − | 0.817620i | \(-0.695293\pi\) | ||||
−0.575758 | + | 0.817620i | \(0.695293\pi\) | |||||||
\(608\) | −7.49849 | −0.304104 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.32475 | 0.175104 | ||||||||
\(611\) | −2.00753 | −0.0812158 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.5222 | 1.19239 | 0.596196 | − | 0.802839i | \(-0.296678\pi\) | ||||
0.596196 | + | 0.802839i | \(0.296678\pi\) | |||||||
\(614\) | 19.7611 | 0.797493 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −20.2203 | −0.814699 | ||||||||
\(617\) | 31.1688 | 1.25481 | 0.627405 | − | 0.778693i | \(-0.284117\pi\) | ||||
0.627405 | + | 0.778693i | \(0.284117\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1738 | 0.449113 | 0.224556 | − | 0.974461i | \(-0.427907\pi\) | ||||
0.224556 | + | 0.974461i | \(0.427907\pi\) | |||||||
\(620\) | 14.0325 | 0.563557 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.6761 | 1.02952 | ||||||||
\(623\) | 12.1433 | 0.486511 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 60.2997 | 2.41199 | ||||||||
\(626\) | 51.6207 | 2.06318 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.70169 | −0.0679050 | ||||||||
\(629\) | 6.69227 | 0.266838 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.63983 | 0.304137 | 0.152068 | − | 0.988370i | \(-0.451407\pi\) | ||||
0.152068 | + | 0.988370i | \(0.451407\pi\) | |||||||
\(632\) | −67.5040 | −2.68517 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −43.1241 | −1.71268 | ||||||||
\(635\) | −4.13136 | −0.163948 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.702420 | 0.0278309 | ||||||||
\(638\) | 95.8242 | 3.79372 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −83.8218 | −3.31335 | ||||||||
\(641\) | −11.2917 | −0.445994 | −0.222997 | − | 0.974819i | \(-0.571584\pi\) | ||||
−0.222997 | + | 0.974819i | \(0.571584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.4181 | −0.805212 | −0.402606 | − | 0.915373i | \(-0.631896\pi\) | ||||
−0.402606 | + | 0.915373i | \(0.631896\pi\) | |||||||
\(644\) | 16.6841 | 0.657447 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.8457 | 0.702130 | ||||||||
\(647\) | 25.7217 | 1.01122 | 0.505612 | − | 0.862761i | \(-0.331267\pi\) | ||||
0.505612 | + | 0.862761i | \(0.331267\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.6599 | −1.00724 | ||||||||
\(650\) | −20.5804 | −0.807230 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −42.9677 | −1.68275 | ||||||||
\(653\) | 23.4539 | 0.917821 | 0.458910 | − | 0.888483i | \(-0.348240\pi\) | ||||
0.458910 | + | 0.888483i | \(0.348240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.27216 | 0.166927 | ||||||||
\(656\) | 14.7435 | 0.575635 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.93874 | 0.270500 | ||||||||
\(659\) | 5.91947 | 0.230590 | 0.115295 | − | 0.993331i | \(-0.463219\pi\) | ||||
0.115295 | + | 0.993331i | \(0.463219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.2744 | 1.44981 | 0.724903 | − | 0.688851i | \(-0.241885\pi\) | ||||
0.724903 | + | 0.688851i | \(0.241885\pi\) | |||||||
\(662\) | 1.47225 | 0.0572205 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −25.0736 | −0.973046 | ||||||||
\(665\) | 30.9996 | 1.20211 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.4601 | −1.48918 | ||||||||
\(668\) | −85.9882 | −3.32698 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.5489 | 0.639339 | ||||||||
\(671\) | 1.89572 | 0.0731834 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.6036 | −0.755662 | −0.377831 | − | 0.925875i | \(-0.623330\pi\) | ||||
−0.377831 | + | 0.925875i | \(0.623330\pi\) | |||||||
\(674\) | −46.9601 | −1.80884 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −48.7045 | −1.87325 | ||||||||
\(677\) | 17.6369 | 0.677839 | 0.338920 | − | 0.940815i | \(-0.389939\pi\) | ||||
0.338920 | + | 0.940815i | \(0.389939\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.29248 | 0.356613 | ||||||||
\(680\) | 18.6129 | 0.713773 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.30999 | 0.356498 | ||||||||
\(683\) | −23.3875 | −0.894896 | −0.447448 | − | 0.894310i | \(-0.647667\pi\) | ||||
−0.447448 | + | 0.894310i | \(0.647667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.3094 | 1.65477 | ||||||||
\(686\) | −2.42782 | −0.0926945 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −21.4322 | −0.817097 | ||||||||
\(689\) | 4.16753 | 0.158770 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.8622 | 1.82077 | 0.910383 | − | 0.413767i | \(-0.135787\pi\) | ||||
0.910383 | + | 0.413767i | \(0.135787\pi\) | |||||||
\(692\) | −29.7018 | −1.12909 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 42.0808 | 1.59737 | ||||||||
\(695\) | −38.1485 | −1.44706 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.27687 | 0.161998 | ||||||||
\(698\) | −68.7486 | −2.60217 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 46.9971 | 1.77632 | ||||||||
\(701\) | 18.8401 | 0.711580 | 0.355790 | − | 0.934566i | \(-0.384212\pi\) | ||||
0.355790 | + | 0.934566i | \(0.384212\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −51.2602 | −1.93331 | ||||||||
\(704\) | −40.3620 | −1.52120 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.1340 | −0.908295 | ||||||||
\(707\) | −10.0187 | −0.376790 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.4274 | −0.654499 | −0.327250 | − | 0.944938i | \(-0.606122\pi\) | ||||
−0.327250 | + | 0.944938i | \(0.606122\pi\) | |||||||
\(710\) | 156.238 | 5.86350 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −55.8473 | −2.09296 | ||||||||
\(713\) | −3.73667 | −0.139939 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.7589 | −0.477155 | ||||||||
\(716\) | 34.0383 | 1.27207 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 30.7601 | 1.14796 | ||||||||
\(719\) | −28.3723 | −1.05811 | −0.529055 | − | 0.848588i | \(-0.677453\pi\) | ||||
−0.529055 | + | 0.848588i | \(0.677453\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.3855 | −0.386778 | ||||||||
\(722\) | −90.5627 | −3.37039 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.78431 | 0.289302 | ||||||||
\(725\) | −108.337 | −4.02355 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.0293 | −1.44752 | −0.723758 | − | 0.690054i | \(-0.757587\pi\) | ||||
−0.723758 | + | 0.690054i | \(0.757587\pi\) | |||||||
\(728\) | −3.23045 | −0.119728 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −38.0346 | −1.40772 | ||||||||
\(731\) | −6.21719 | −0.229951 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.4181 | −1.45594 | −0.727970 | − | 0.685609i | \(-0.759536\pi\) | ||||
−0.727970 | + | 0.685609i | \(0.759536\pi\) | |||||||
\(734\) | −33.1512 | −1.22363 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.28140 | 0.157814 | ||||||||
\(737\) | 7.25406 | 0.267207 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.0447 | 1.43628 | 0.718141 | − | 0.695897i | \(-0.244993\pi\) | ||||
0.718141 | + | 0.695897i | \(0.244993\pi\) | |||||||
\(740\) | −109.911 | −4.04041 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.4045 | −0.528806 | ||||||||
\(743\) | −49.4864 | −1.81548 | −0.907741 | − | 0.419532i | \(-0.862194\pi\) | ||||
−0.907741 | + | 0.419532i | \(0.862194\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.7339 | 1.67556 | ||||||||
\(746\) | 23.7687 | 0.870234 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.7729 | 0.613277 | ||||||||
\(749\) | 12.3554 | 0.451458 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.6553 | 0.717231 | 0.358616 | − | 0.933485i | \(-0.383249\pi\) | ||||
0.358616 | + | 0.933485i | \(0.383249\pi\) | |||||||
\(752\) | −9.65147 | −0.351953 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.3091 | 0.557525 | ||||||||
\(755\) | −52.1418 | −1.89763 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.7636 | −1.15447 | −0.577234 | − | 0.816579i | \(-0.695868\pi\) | ||||
−0.577234 | + | 0.816579i | \(0.695868\pi\) | |||||||
\(758\) | 5.04655 | 0.183299 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −142.568 | −5.17147 | ||||||||
\(761\) | 17.6652 | 0.640365 | 0.320182 | − | 0.947356i | \(-0.396256\pi\) | ||||
0.320182 | + | 0.947356i | \(0.396256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.4746 | −0.451610 | ||||||||
\(764\) | 19.6112 | 0.709509 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.3564 | −0.554850 | ||||||||
\(767\) | −4.09949 | −0.148024 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.2679 | 1.63240 | 0.816201 | − | 0.577769i | \(-0.196076\pi\) | ||||
0.816201 | + | 0.577769i | \(0.196076\pi\) | |||||||
\(770\) | 44.0993 | 1.58923 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.3196 | 0.695329 | ||||||||
\(773\) | 12.0686 | 0.434079 | 0.217039 | − | 0.976163i | \(-0.430360\pi\) | ||||
0.217039 | + | 0.976163i | \(0.430360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.5257 | −0.378095 | ||||||||
\(776\) | −42.7363 | −1.53415 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.3662 | −0.873572 | ||||||||
\(779\) | −32.7591 | −1.17372 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 68.4855 | 2.45060 | ||||||||
\(782\) | −10.1893 | −0.364370 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.37699 | 0.120607 | ||||||||
\(785\) | 1.80528 | 0.0644333 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.7311 | 0.881569 | 0.440785 | − | 0.897613i | \(-0.354700\pi\) | ||||
0.440785 | + | 0.897613i | \(0.354700\pi\) | |||||||
\(788\) | −12.4296 | −0.442785 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 147.222 | 5.23793 | ||||||||
\(791\) | −17.5483 | −0.623944 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.302865 | 0.0107550 | ||||||||
\(794\) | 84.7364 | 3.00718 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.0022 | −1.09884 | ||||||||
\(797\) | 16.3346 | 0.578603 | 0.289301 | − | 0.957238i | \(-0.406577\pi\) | ||||
0.289301 | + | 0.957238i | \(0.406577\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.79975 | −0.0990482 | ||||||||
\(800\) | 12.0601 | 0.426390 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −53.9046 | −1.90344 | ||||||||
\(803\) | −16.6721 | −0.588346 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.6998 | −0.623834 | ||||||||
\(806\) | 1.48739 | 0.0523910 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 46.0760 | 1.62095 | ||||||||
\(809\) | 48.7035 | 1.71232 | 0.856162 | − | 0.516707i | \(-0.172843\pi\) | ||||
0.856162 | + | 0.516707i | \(0.172843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.69549 | 0.199996 | 0.0999978 | − | 0.994988i | \(-0.468116\pi\) | ||||
0.0999978 | + | 0.994988i | \(0.468116\pi\) | |||||||
\(812\) | −34.9596 | −1.22684 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −72.9216 | −2.55590 | ||||||||
\(815\) | 45.5833 | 1.59671 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.6212 | 1.66606 | ||||||||
\(818\) | −75.2582 | −2.63134 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −70.2414 | −2.45294 | ||||||||
\(821\) | 30.3036 | 1.05760 | 0.528802 | − | 0.848745i | \(-0.322641\pi\) | ||||
0.528802 | + | 0.848745i | \(0.322641\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.13612 | −0.0396027 | −0.0198014 | − | 0.999804i | \(-0.506303\pi\) | ||||
−0.0198014 | + | 0.999804i | \(0.506303\pi\) | |||||||
\(824\) | 47.7633 | 1.66391 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.1693 | 0.493014 | ||||||||
\(827\) | 34.1644 | 1.18801 | 0.594006 | − | 0.804460i | \(-0.297545\pi\) | ||||
0.594006 | + | 0.804460i | \(0.297545\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.2966 | −0.566004 | −0.283002 | − | 0.959119i | \(-0.591330\pi\) | ||||
−0.283002 | + | 0.959119i | \(0.591330\pi\) | |||||||
\(830\) | 54.6842 | 1.89811 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.44834 | −0.223556 | ||||||||
\(833\) | 0.979615 | 0.0339417 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 91.2227 | 3.15689 | ||||||||
\(836\) | −128.474 | −4.44335 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 52.9657 | 1.82967 | ||||||||
\(839\) | −26.2732 | −0.907053 | −0.453526 | − | 0.891243i | \(-0.649834\pi\) | ||||
−0.453526 | + | 0.891243i | \(0.649834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.5887 | 1.77892 | ||||||||
\(842\) | −1.94964 | −0.0671890 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −55.7280 | −1.91824 | ||||||||
\(845\) | 51.6693 | 1.77748 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.33054 | 0.286241 | ||||||||
\(848\) | 20.0360 | 0.688039 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −28.7020 | −0.984472 | ||||||||
\(851\) | 29.2679 | 1.00329 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.7979 | 1.70505 | 0.852524 | − | 0.522689i | \(-0.175071\pi\) | ||||
0.852524 | + | 0.522689i | \(0.175071\pi\) | |||||||
\(854\) | −1.04681 | −0.0358211 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −56.8230 | −1.94217 | ||||||||
\(857\) | −31.7264 | −1.08375 | −0.541877 | − | 0.840458i | \(-0.682286\pi\) | ||||
−0.541877 | + | 0.840458i | \(0.682286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.93883 | 0.100272 | 0.0501359 | − | 0.998742i | \(-0.484035\pi\) | ||||
0.0501359 | + | 0.998742i | \(0.484035\pi\) | |||||||
\(860\) | 102.108 | 3.48187 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −65.2543 | −2.22257 | ||||||||
\(863\) | −48.0520 | −1.63571 | −0.817854 | − | 0.575425i | \(-0.804837\pi\) | ||||
−0.817854 | + | 0.575425i | \(0.804837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.5098 | 1.07137 | ||||||||
\(866\) | 0.441479 | 0.0150021 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.39657 | −0.115287 | ||||||||
\(869\) | 64.5336 | 2.18915 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.15893 | 0.0392688 | ||||||||
\(872\) | 57.3708 | 1.94282 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 78.0463 | 2.63996 | ||||||||
\(875\) | −29.2011 | −0.987178 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.45427 | 0.0491073 | 0.0245537 | − | 0.999699i | \(-0.492184\pi\) | ||||
0.0245537 | + | 0.999699i | \(0.492184\pi\) | |||||||
\(878\) | −99.4377 | −3.35586 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −61.3401 | −2.06777 | ||||||||
\(881\) | −54.9217 | −1.85036 | −0.925179 | − | 0.379530i | \(-0.876086\pi\) | ||||
−0.925179 | + | 0.379530i | \(0.876086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.7578 | 1.60718 | 0.803590 | − | 0.595184i | \(-0.202921\pi\) | ||||
0.803590 | + | 0.595184i | \(0.202921\pi\) | |||||||
\(884\) | 2.67968 | 0.0901272 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.44676 | 0.216583 | ||||||||
\(887\) | 13.5209 | 0.453987 | 0.226994 | − | 0.973896i | \(-0.427110\pi\) | ||||
0.226994 | + | 0.973896i | \(0.427110\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 121.800 | 4.08273 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 51.5065 | 1.72456 | ||||||||
\(893\) | 21.4450 | 0.717630 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.1104 | −1.20704 | ||||||||
\(896\) | 20.2891 | 0.677812 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 101.525 | 3.38794 | ||||||||
\(899\) | 7.82975 | 0.261137 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.81216 | 0.193631 | ||||||||
\(902\) | −46.6024 | −1.55169 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 80.7048 | 2.68420 | ||||||||
\(905\) | −8.25817 | −0.274511 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.1164 | −1.69729 | −0.848646 | − | 0.528962i | \(-0.822581\pi\) | ||||
−0.848646 | + | 0.528962i | \(0.822581\pi\) | |||||||
\(908\) | −114.933 | −3.81418 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.04541 | 0.233553 | ||||||||
\(911\) | 33.9841 | 1.12594 | 0.562972 | − | 0.826476i | \(-0.309658\pi\) | ||||
0.562972 | + | 0.826476i | \(0.309658\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.9703 | 0.793302 | ||||||||
\(914\) | 21.8453 | 0.722579 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −60.4455 | −1.99717 | ||||||||
\(917\) | −1.03408 | −0.0341483 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.3987 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(920\) | 81.4016 | 2.68373 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.7948 | −0.651907 | ||||||||
\(923\) | 10.9414 | 0.360141 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 82.4440 | 2.71074 | ||||||||
\(926\) | 47.3962 | 1.55754 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.97115 | −0.294493 | ||||||||
\(929\) | 24.3384 | 0.798518 | 0.399259 | − | 0.916838i | \(-0.369267\pi\) | ||||
0.399259 | + | 0.916838i | \(0.369267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.50347 | −0.245916 | ||||||||
\(932\) | 26.8027 | 0.877953 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 44.4487 | 1.45441 | ||||||||
\(935\) | −17.7939 | −0.581922 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.36212 | 0.207841 | 0.103921 | − | 0.994586i | \(-0.466861\pi\) | ||||
0.103921 | + | 0.994586i | \(0.466861\pi\) | |||||||
\(938\) | −4.00567 | −0.130790 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 45.9819 | 1.49977 | ||||||||
\(941\) | 21.9441 | 0.715358 | 0.357679 | − | 0.933845i | \(-0.383568\pi\) | ||||
0.357679 | + | 0.933845i | \(0.383568\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.7044 | 0.609099 | ||||||||
\(944\) | −19.7089 | −0.641470 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 67.7449 | 2.20258 | ||||||||
\(947\) | 25.7408 | 0.836463 | 0.418232 | − | 0.908340i | \(-0.362650\pi\) | ||||
0.418232 | + | 0.908340i | \(0.362650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.66358 | −0.0864635 | ||||||||
\(950\) | 219.846 | 7.13276 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.50527 | −0.146017 | ||||||||
\(953\) | −9.17939 | −0.297350 | −0.148675 | − | 0.988886i | \(-0.547501\pi\) | ||||
−0.148675 | + | 0.988886i | \(0.547501\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.8050 | −0.673235 | ||||||||
\(956\) | −19.4758 | −0.629893 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 49.5812 | 1.60190 | ||||||||
\(959\) | −10.4831 | −0.338516 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2393 | −0.975461 | ||||||||
\(962\) | −11.6501 | −0.375616 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 60.5594 | 1.95049 | ||||||||
\(965\) | −20.4957 | −0.659780 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.5730 | 1.85142 | 0.925711 | − | 0.378231i | \(-0.123467\pi\) | ||||
0.925711 | + | 0.378231i | \(0.123467\pi\) | |||||||
\(968\) | −38.3123 | −1.23141 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 93.2055 | 2.99265 | ||||||||
\(971\) | 9.99471 | 0.320745 | 0.160373 | − | 0.987057i | \(-0.448730\pi\) | ||||
0.160373 | + | 0.987057i | \(0.448730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.23389 | 0.296025 | ||||||||
\(974\) | 66.6084 | 2.13427 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.45607 | 0.0466075 | ||||||||
\(977\) | −21.4270 | −0.685510 | −0.342755 | − | 0.939425i | \(-0.611360\pi\) | ||||
−0.342755 | + | 0.939425i | \(0.611360\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53.3898 | 1.70635 | ||||||||
\(980\) | −16.0888 | −0.513937 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 43.8138 | 1.39816 | ||||||||
\(983\) | 5.16510 | 0.164741 | 0.0823705 | − | 0.996602i | \(-0.473751\pi\) | ||||
0.0823705 | + | 0.996602i | \(0.473751\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1862 | 0.420147 | ||||||||
\(986\) | 21.3505 | 0.679940 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.5253 | −0.652996 | ||||||||
\(989\) | −27.1902 | −0.864598 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.8521 | 1.52007 | 0.760036 | − | 0.649881i | \(-0.225181\pi\) | ||||
0.760036 | + | 0.649881i | \(0.225181\pi\) | |||||||
\(992\) | −0.871610 | −0.0276736 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −37.8175 | −1.19950 | ||||||||
\(995\) | 32.8894 | 1.04266 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.8952 | 0.693429 | 0.346714 | − | 0.937971i | \(-0.387297\pi\) | ||||
0.346714 | + | 0.937971i | \(0.387297\pi\) | |||||||
\(998\) | −59.8564 | −1.89472 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.v.1.3 | 19 | ||
3.2 | odd | 2 | 2667.2.a.q.1.17 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.q.1.17 | ✓ | 19 | 3.2 | odd | 2 | ||
8001.2.a.v.1.3 | 19 | 1.1 | even | 1 | trivial |