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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} - 1655 x^{7} - 1150 x^{6} + 1279 x^{5} + 474 x^{4} - 280 x^{3} - 83 x^{2} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(1.24549\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.24549 | 0.880698 | 0.440349 | − | 0.897827i | \(-0.354855\pi\) | ||||
0.440349 | + | 0.897827i | \(0.354855\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.448744 | −0.224372 | ||||||||
\(5\) | 2.43368 | 1.08838 | 0.544188 | − | 0.838963i | \(-0.316838\pi\) | ||||
0.544188 | + | 0.838963i | \(0.316838\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.04990 | −1.07830 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.03114 | 0.958531 | ||||||||
\(11\) | 4.22568 | 1.27409 | 0.637046 | − | 0.770826i | \(-0.280156\pi\) | ||||
0.637046 | + | 0.770826i | \(0.280156\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.67912 | −1.57510 | −0.787552 | − | 0.616248i | \(-0.788652\pi\) | ||||
−0.787552 | + | 0.616248i | \(0.788652\pi\) | |||||||
\(14\) | −1.24549 | −0.332872 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.90114 | −0.725285 | ||||||||
\(17\) | 1.72874 | 0.419282 | 0.209641 | − | 0.977778i | \(-0.432771\pi\) | ||||
0.209641 | + | 0.977778i | \(0.432771\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50366 | −0.574380 | −0.287190 | − | 0.957874i | \(-0.592721\pi\) | ||||
−0.287190 | + | 0.957874i | \(0.592721\pi\) | |||||||
\(20\) | −1.09210 | −0.244201 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.26306 | 1.12209 | ||||||||
\(23\) | 3.83361 | 0.799364 | 0.399682 | − | 0.916654i | \(-0.369121\pi\) | ||||
0.399682 | + | 0.916654i | \(0.369121\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.922820 | 0.184564 | ||||||||
\(26\) | −7.07331 | −1.38719 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.448744 | 0.0848046 | ||||||||
\(29\) | −5.96884 | −1.10839 | −0.554193 | − | 0.832388i | \(-0.686973\pi\) | ||||
−0.554193 | + | 0.832388i | \(0.686973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.47757 | −0.983801 | −0.491901 | − | 0.870651i | \(-0.663698\pi\) | ||||
−0.491901 | + | 0.870651i | \(0.663698\pi\) | |||||||
\(32\) | 2.48644 | 0.439544 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.15314 | 0.369260 | ||||||||
\(35\) | −2.43368 | −0.411368 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.12052 | 1.00621 | 0.503103 | − | 0.864226i | \(-0.332191\pi\) | ||||
0.503103 | + | 0.864226i | \(0.332191\pi\) | |||||||
\(38\) | −3.11830 | −0.505855 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.42249 | −1.17360 | ||||||||
\(41\) | 4.31444 | 0.673802 | 0.336901 | − | 0.941540i | \(-0.390621\pi\) | ||||
0.336901 | + | 0.941540i | \(0.390621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.93422 | 0.752462 | 0.376231 | − | 0.926526i | \(-0.377220\pi\) | ||||
0.376231 | + | 0.926526i | \(0.377220\pi\) | |||||||
\(44\) | −1.89625 | −0.285870 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.77474 | 0.703998 | ||||||||
\(47\) | 10.9899 | 1.60304 | 0.801521 | − | 0.597966i | \(-0.204024\pi\) | ||||
0.801521 | + | 0.597966i | \(0.204024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.14937 | 0.162545 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.54847 | 0.353409 | ||||||||
\(53\) | 4.00048 | 0.549508 | 0.274754 | − | 0.961514i | \(-0.411404\pi\) | ||||
0.274754 | + | 0.961514i | \(0.411404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2840 | 1.38669 | ||||||||
\(56\) | 3.04990 | 0.407560 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.43416 | −0.976153 | ||||||||
\(59\) | 14.3016 | 1.86191 | 0.930955 | − | 0.365133i | \(-0.118977\pi\) | ||||
0.930955 | + | 0.365133i | \(0.118977\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.21888 | 0.412136 | 0.206068 | − | 0.978538i | \(-0.433933\pi\) | ||||
0.206068 | + | 0.978538i | \(0.433933\pi\) | |||||||
\(62\) | −6.82229 | −0.866431 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.89913 | 1.11239 | ||||||||
\(65\) | −13.8212 | −1.71431 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.39502 | 0.903445 | 0.451723 | − | 0.892158i | \(-0.350810\pi\) | ||||
0.451723 | + | 0.892158i | \(0.350810\pi\) | |||||||
\(68\) | −0.775763 | −0.0940750 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.03114 | −0.362291 | ||||||||
\(71\) | −7.63071 | −0.905598 | −0.452799 | − | 0.891612i | \(-0.649575\pi\) | ||||
−0.452799 | + | 0.891612i | \(0.649575\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.53588 | 0.882008 | 0.441004 | − | 0.897505i | \(-0.354622\pi\) | ||||
0.441004 | + | 0.897505i | \(0.354622\pi\) | |||||||
\(74\) | 7.62307 | 0.886164 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.12350 | 0.128875 | ||||||||
\(77\) | −4.22568 | −0.481561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4421 | −1.73737 | −0.868685 | − | 0.495365i | \(-0.835034\pi\) | ||||
−0.868685 | + | 0.495365i | \(0.835034\pi\) | |||||||
\(80\) | −7.06046 | −0.789384 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.37361 | 0.593416 | ||||||||
\(83\) | 12.7925 | 1.40415 | 0.702077 | − | 0.712101i | \(-0.252256\pi\) | ||||
0.702077 | + | 0.712101i | \(0.252256\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.20722 | 0.456337 | ||||||||
\(86\) | 6.14555 | 0.662691 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.8879 | −1.37385 | ||||||||
\(89\) | −3.88584 | −0.411898 | −0.205949 | − | 0.978563i | \(-0.566028\pi\) | ||||
−0.205949 | + | 0.978563i | \(0.566028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.67912 | 0.595333 | ||||||||
\(92\) | −1.72031 | −0.179355 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.6879 | 1.41180 | ||||||||
\(95\) | −6.09313 | −0.625142 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.24345 | 0.430857 | 0.215429 | − | 0.976520i | \(-0.430885\pi\) | ||||
0.215429 | + | 0.976520i | \(0.430885\pi\) | |||||||
\(98\) | 1.24549 | 0.125814 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.414110 | −0.0414110 | ||||||||
\(101\) | 17.4200 | 1.73335 | 0.866677 | − | 0.498870i | \(-0.166251\pi\) | ||||
0.866677 | + | 0.498870i | \(0.166251\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.42750 | −0.436254 | −0.218127 | − | 0.975920i | \(-0.569995\pi\) | ||||
−0.218127 | + | 0.975920i | \(0.569995\pi\) | |||||||
\(104\) | 17.3207 | 1.69844 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.98258 | 0.483951 | ||||||||
\(107\) | 5.71893 | 0.552869 | 0.276435 | − | 0.961033i | \(-0.410847\pi\) | ||||
0.276435 | + | 0.961033i | \(0.410847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.5703 | 1.39558 | 0.697790 | − | 0.716302i | \(-0.254167\pi\) | ||||
0.697790 | + | 0.716302i | \(0.254167\pi\) | |||||||
\(110\) | 12.8086 | 1.22126 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.90114 | 0.274132 | ||||||||
\(113\) | −5.91261 | −0.556212 | −0.278106 | − | 0.960550i | \(-0.589707\pi\) | ||||
−0.278106 | + | 0.960550i | \(0.589707\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.32981 | 0.870009 | ||||||||
\(116\) | 2.67848 | 0.248691 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.8126 | 1.63978 | ||||||||
\(119\) | −1.72874 | −0.158474 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.85640 | 0.623309 | ||||||||
\(122\) | 4.00910 | 0.362967 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.45803 | 0.220737 | ||||||||
\(125\) | −9.92257 | −0.887502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 6.11094 | 0.540136 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −17.2142 | −1.50979 | ||||||||
\(131\) | −19.7982 | −1.72978 | −0.864890 | − | 0.501962i | \(-0.832612\pi\) | ||||
−0.864890 | + | 0.501962i | \(0.832612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.50366 | 0.217095 | ||||||||
\(134\) | 9.21045 | 0.795662 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.27249 | −0.452112 | ||||||||
\(137\) | −8.97609 | −0.766879 | −0.383439 | − | 0.923566i | \(-0.625261\pi\) | ||||
−0.383439 | + | 0.923566i | \(0.625261\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.86647 | 0.497587 | 0.248794 | − | 0.968557i | \(-0.419966\pi\) | ||||
0.248794 | + | 0.968557i | \(0.419966\pi\) | |||||||
\(140\) | 1.09210 | 0.0922993 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.50400 | −0.797558 | ||||||||
\(143\) | −23.9982 | −2.00683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.5263 | −1.20634 | ||||||||
\(146\) | 9.38590 | 0.776782 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.74654 | −0.225764 | ||||||||
\(149\) | 21.5978 | 1.76936 | 0.884679 | − | 0.466201i | \(-0.154378\pi\) | ||||
0.884679 | + | 0.466201i | \(0.154378\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.8490 | −0.882877 | −0.441439 | − | 0.897291i | \(-0.645532\pi\) | ||||
−0.441439 | + | 0.897291i | \(0.645532\pi\) | |||||||
\(152\) | 7.63591 | 0.619354 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.26306 | −0.424110 | ||||||||
\(155\) | −13.3307 | −1.07075 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.59825 | −0.287171 | −0.143586 | − | 0.989638i | \(-0.545863\pi\) | ||||
−0.143586 | + | 0.989638i | \(0.545863\pi\) | |||||||
\(158\) | −19.2330 | −1.53010 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.05120 | 0.478390 | ||||||||
\(161\) | −3.83361 | −0.302131 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.95370 | −0.466330 | −0.233165 | − | 0.972437i | \(-0.574908\pi\) | ||||
−0.233165 | + | 0.972437i | \(0.574908\pi\) | |||||||
\(164\) | −1.93608 | −0.151182 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.9329 | 1.23663 | ||||||||
\(167\) | −15.7608 | −1.21961 | −0.609805 | − | 0.792552i | \(-0.708752\pi\) | ||||
−0.609805 | + | 0.792552i | \(0.708752\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.2524 | 1.48095 | ||||||||
\(170\) | 5.24006 | 0.401895 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.21420 | −0.168831 | ||||||||
\(173\) | 17.0465 | 1.29602 | 0.648010 | − | 0.761632i | \(-0.275602\pi\) | ||||
0.648010 | + | 0.761632i | \(0.275602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.922820 | −0.0697587 | ||||||||
\(176\) | −12.2593 | −0.924080 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.83979 | −0.362758 | ||||||||
\(179\) | −6.68379 | −0.499570 | −0.249785 | − | 0.968301i | \(-0.580360\pi\) | ||||
−0.249785 | + | 0.968301i | \(0.580360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1820 | 0.979813 | 0.489906 | − | 0.871775i | \(-0.337031\pi\) | ||||
0.489906 | + | 0.871775i | \(0.337031\pi\) | |||||||
\(182\) | 7.07331 | 0.524309 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.6921 | −0.861955 | ||||||||
\(185\) | 14.8954 | 1.09513 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.30512 | 0.534203 | ||||||||
\(188\) | −4.93165 | −0.359678 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.58896 | −0.550561 | ||||||||
\(191\) | −17.4273 | −1.26100 | −0.630498 | − | 0.776191i | \(-0.717149\pi\) | ||||
−0.630498 | + | 0.776191i | \(0.717149\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.81879 | 0.634790 | 0.317395 | − | 0.948293i | \(-0.397192\pi\) | ||||
0.317395 | + | 0.948293i | \(0.397192\pi\) | |||||||
\(194\) | 5.28520 | 0.379455 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.448744 | −0.0320531 | ||||||||
\(197\) | 22.4395 | 1.59874 | 0.799372 | − | 0.600836i | \(-0.205166\pi\) | ||||
0.799372 | + | 0.600836i | \(0.205166\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.40127 | 0.453774 | 0.226887 | − | 0.973921i | \(-0.427145\pi\) | ||||
0.226887 | + | 0.973921i | \(0.427145\pi\) | |||||||
\(200\) | −2.81451 | −0.199016 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 21.6965 | 1.52656 | ||||||||
\(203\) | 5.96884 | 0.418931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.5000 | 0.733351 | ||||||||
\(206\) | −5.51443 | −0.384208 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.4759 | 1.14240 | ||||||||
\(209\) | −10.5797 | −0.731812 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0999 | 1.17721 | 0.588604 | − | 0.808422i | \(-0.299678\pi\) | ||||
0.588604 | + | 0.808422i | \(0.299678\pi\) | |||||||
\(212\) | −1.79519 | −0.123294 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.12289 | 0.486911 | ||||||||
\(215\) | 12.0083 | 0.818962 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.47757 | 0.371842 | ||||||||
\(218\) | 18.1472 | 1.22908 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.61487 | −0.311135 | ||||||||
\(221\) | −9.81774 | −0.660413 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.55249 | −0.237892 | −0.118946 | − | 0.992901i | \(-0.537952\pi\) | ||||
−0.118946 | + | 0.992901i | \(0.537952\pi\) | |||||||
\(224\) | −2.48644 | −0.166132 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.36413 | −0.489854 | ||||||||
\(227\) | 0.461961 | 0.0306614 | 0.0153307 | − | 0.999882i | \(-0.495120\pi\) | ||||
0.0153307 | + | 0.999882i | \(0.495120\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.8631 | 1.51084 | 0.755418 | − | 0.655244i | \(-0.227434\pi\) | ||||
0.755418 | + | 0.655244i | \(0.227434\pi\) | |||||||
\(230\) | 11.6202 | 0.766215 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.2044 | 1.19517 | ||||||||
\(233\) | −2.25856 | −0.147963 | −0.0739816 | − | 0.997260i | \(-0.523571\pi\) | ||||
−0.0739816 | + | 0.997260i | \(0.523571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.7460 | 1.74471 | ||||||||
\(236\) | −6.41776 | −0.417760 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.15314 | −0.139567 | ||||||||
\(239\) | 28.5593 | 1.84735 | 0.923673 | − | 0.383182i | \(-0.125172\pi\) | ||||
0.923673 | + | 0.383182i | \(0.125172\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6906 | −0.881888 | −0.440944 | − | 0.897535i | \(-0.645356\pi\) | ||||
−0.440944 | + | 0.897535i | \(0.645356\pi\) | |||||||
\(242\) | 8.53960 | 0.548947 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.44445 | −0.0924717 | ||||||||
\(245\) | 2.43368 | 0.155482 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2186 | 0.904708 | ||||||||
\(248\) | 16.7060 | 1.06083 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.3585 | −0.781620 | ||||||||
\(251\) | −7.41487 | −0.468022 | −0.234011 | − | 0.972234i | \(-0.575185\pi\) | ||||
−0.234011 | + | 0.972234i | \(0.575185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.1996 | 1.01846 | ||||||||
\(254\) | −1.24549 | −0.0781493 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.1871 | −0.636695 | ||||||||
\(257\) | −16.3544 | −1.02016 | −0.510080 | − | 0.860127i | \(-0.670384\pi\) | ||||
−0.510080 | + | 0.860127i | \(0.670384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.12052 | −0.380310 | ||||||||
\(260\) | 6.20217 | 0.384642 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.6586 | −1.52341 | ||||||||
\(263\) | −4.68637 | −0.288974 | −0.144487 | − | 0.989507i | \(-0.546153\pi\) | ||||
−0.144487 | + | 0.989507i | \(0.546153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.73591 | 0.598072 | ||||||||
\(266\) | 3.11830 | 0.191195 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.31847 | −0.202708 | ||||||||
\(269\) | 14.6818 | 0.895167 | 0.447584 | − | 0.894242i | \(-0.352285\pi\) | ||||
0.447584 | + | 0.894242i | \(0.352285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7458 | −0.652764 | −0.326382 | − | 0.945238i | \(-0.605830\pi\) | ||||
−0.326382 | + | 0.945238i | \(0.605830\pi\) | |||||||
\(272\) | −5.01533 | −0.304099 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.1797 | −0.675388 | ||||||||
\(275\) | 3.89955 | 0.235152 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.856063 | 0.0514358 | 0.0257179 | − | 0.999669i | \(-0.491813\pi\) | ||||
0.0257179 | + | 0.999669i | \(0.491813\pi\) | |||||||
\(278\) | 7.30665 | 0.438224 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.42249 | 0.443578 | ||||||||
\(281\) | −14.3744 | −0.857504 | −0.428752 | − | 0.903422i | \(-0.641047\pi\) | ||||
−0.428752 | + | 0.903422i | \(0.641047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.7855 | 1.11668 | 0.558341 | − | 0.829612i | \(-0.311438\pi\) | ||||
0.558341 | + | 0.829612i | \(0.311438\pi\) | |||||||
\(284\) | 3.42423 | 0.203191 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.8896 | −1.76741 | ||||||||
\(287\) | −4.31444 | −0.254673 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0114 | −0.824203 | ||||||||
\(290\) | −18.0924 | −1.06242 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.38168 | −0.197898 | ||||||||
\(293\) | 14.6548 | 0.856145 | 0.428072 | − | 0.903744i | \(-0.359193\pi\) | ||||
0.428072 | + | 0.903744i | \(0.359193\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.8056 | 2.02646 | ||||||||
\(296\) | −18.6669 | −1.08499 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.8999 | 1.55827 | ||||||||
\(299\) | −21.7715 | −1.25908 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.93422 | −0.284404 | ||||||||
\(302\) | −13.5123 | −0.777548 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.26348 | 0.416589 | ||||||||
\(305\) | 7.83375 | 0.448559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.1328 | −0.635385 | −0.317692 | − | 0.948194i | \(-0.602908\pi\) | ||||
−0.317692 | + | 0.948194i | \(0.602908\pi\) | |||||||
\(308\) | 1.89625 | 0.108049 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.6033 | −0.943004 | ||||||||
\(311\) | 16.8169 | 0.953602 | 0.476801 | − | 0.879011i | \(-0.341796\pi\) | ||||
0.476801 | + | 0.879011i | \(0.341796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4057 | −0.757732 | −0.378866 | − | 0.925451i | \(-0.623686\pi\) | ||||
−0.378866 | + | 0.925451i | \(0.623686\pi\) | |||||||
\(314\) | −4.48160 | −0.252911 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.92953 | 0.389817 | ||||||||
\(317\) | 18.6801 | 1.04918 | 0.524588 | − | 0.851356i | \(-0.324219\pi\) | ||||
0.524588 | + | 0.851356i | \(0.324219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.2224 | −1.41219 | ||||||||
\(320\) | 21.6577 | 1.21070 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.77474 | −0.266086 | ||||||||
\(323\) | −4.32819 | −0.240827 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.24081 | −0.290708 | ||||||||
\(326\) | −7.41530 | −0.410696 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.1586 | −0.726562 | ||||||||
\(329\) | −10.9899 | −0.605893 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.41940 | 0.132982 | 0.0664910 | − | 0.997787i | \(-0.478820\pi\) | ||||
0.0664910 | + | 0.997787i | \(0.478820\pi\) | |||||||
\(332\) | −5.74053 | −0.315053 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.6300 | −1.07411 | ||||||||
\(335\) | 17.9971 | 0.983289 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.2871 | −0.941687 | −0.470844 | − | 0.882217i | \(-0.656050\pi\) | ||||
−0.470844 | + | 0.882217i | \(0.656050\pi\) | |||||||
\(338\) | 23.9788 | 1.30427 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.88796 | −0.102389 | ||||||||
\(341\) | −23.1465 | −1.25345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −15.0489 | −0.811380 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.2313 | 1.14140 | ||||||||
\(347\) | 20.7673 | 1.11485 | 0.557424 | − | 0.830228i | \(-0.311790\pi\) | ||||
0.557424 | + | 0.830228i | \(0.311790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.6254 | 1.26464 | 0.632318 | − | 0.774709i | \(-0.282103\pi\) | ||||
0.632318 | + | 0.774709i | \(0.282103\pi\) | |||||||
\(350\) | −1.14937 | −0.0614363 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.5069 | 0.560019 | ||||||||
\(353\) | 15.5597 | 0.828161 | 0.414080 | − | 0.910240i | \(-0.364103\pi\) | ||||
0.414080 | + | 0.910240i | \(0.364103\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.5707 | −0.985632 | ||||||||
\(356\) | 1.74375 | 0.0924184 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.32462 | −0.439970 | ||||||||
\(359\) | 7.03515 | 0.371301 | 0.185651 | − | 0.982616i | \(-0.440561\pi\) | ||||
0.185651 | + | 0.982616i | \(0.440561\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.7317 | −0.670088 | ||||||||
\(362\) | 16.4181 | 0.862919 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.54847 | −0.133576 | ||||||||
\(365\) | 18.3400 | 0.959957 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.6265 | 1.49429 | 0.747145 | − | 0.664661i | \(-0.231424\pi\) | ||||
0.747145 | + | 0.664661i | \(0.231424\pi\) | |||||||
\(368\) | −11.1219 | −0.579767 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.5521 | 0.964480 | ||||||||
\(371\) | −4.00048 | −0.207695 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.75654 | 0.194506 | 0.0972531 | − | 0.995260i | \(-0.468994\pi\) | ||||
0.0972531 | + | 0.995260i | \(0.468994\pi\) | |||||||
\(374\) | 9.09849 | 0.470472 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33.5181 | −1.72856 | ||||||||
\(377\) | 33.8978 | 1.74582 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.7800 | 1.06740 | 0.533699 | − | 0.845675i | \(-0.320802\pi\) | ||||
0.533699 | + | 0.845675i | \(0.320802\pi\) | |||||||
\(380\) | 2.73425 | 0.140264 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.7056 | −1.11056 | ||||||||
\(383\) | −17.6927 | −0.904054 | −0.452027 | − | 0.892004i | \(-0.649299\pi\) | ||||
−0.452027 | + | 0.892004i | \(0.649299\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2840 | −0.524120 | ||||||||
\(386\) | 10.9838 | 0.559058 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.90422 | −0.0966722 | ||||||||
\(389\) | −27.3076 | −1.38455 | −0.692275 | − | 0.721634i | \(-0.743391\pi\) | ||||
−0.692275 | + | 0.721634i | \(0.743391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.62733 | 0.335159 | ||||||||
\(392\) | −3.04990 | −0.154043 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 27.9482 | 1.40801 | ||||||||
\(395\) | −37.5811 | −1.89091 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.7728 | −0.641046 | −0.320523 | − | 0.947241i | \(-0.603859\pi\) | ||||
−0.320523 | + | 0.947241i | \(0.603859\pi\) | |||||||
\(398\) | 7.97275 | 0.399638 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.67723 | −0.133862 | ||||||||
\(401\) | −10.4514 | −0.521919 | −0.260960 | − | 0.965350i | \(-0.584039\pi\) | ||||
−0.260960 | + | 0.965350i | \(0.584039\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.1078 | 1.54959 | ||||||||
\(404\) | −7.81711 | −0.388916 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.43416 | 0.368951 | ||||||||
\(407\) | 25.8634 | 1.28200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0572 | −0.497297 | −0.248648 | − | 0.968594i | \(-0.579986\pi\) | ||||
−0.248648 | + | 0.968594i | \(0.579986\pi\) | |||||||
\(410\) | 13.0777 | 0.645860 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.98681 | 0.0978832 | ||||||||
\(413\) | −14.3016 | −0.703736 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31.1328 | 1.52825 | ||||||||
\(416\) | −14.1208 | −0.692328 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.1769 | −0.644505 | ||||||||
\(419\) | 4.78230 | 0.233631 | 0.116815 | − | 0.993154i | \(-0.462731\pi\) | ||||
0.116815 | + | 0.993154i | \(0.462731\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.2705 | −0.646766 | −0.323383 | − | 0.946268i | \(-0.604820\pi\) | ||||
−0.323383 | + | 0.946268i | \(0.604820\pi\) | |||||||
\(422\) | 21.2979 | 1.03676 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.2011 | −0.592536 | ||||||||
\(425\) | 1.59532 | 0.0773844 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.21888 | −0.155773 | ||||||||
\(428\) | −2.56633 | −0.124048 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.9563 | 0.721258 | ||||||||
\(431\) | 21.8535 | 1.05264 | 0.526322 | − | 0.850285i | \(-0.323571\pi\) | ||||
0.526322 | + | 0.850285i | \(0.323571\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.0481 | −1.34791 | −0.673953 | − | 0.738774i | \(-0.735405\pi\) | ||||
−0.673953 | + | 0.738774i | \(0.735405\pi\) | |||||||
\(434\) | 6.82229 | 0.327480 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.53832 | −0.313129 | ||||||||
\(437\) | −9.59808 | −0.459138 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.864598 | −0.0412650 | −0.0206325 | − | 0.999787i | \(-0.506568\pi\) | ||||
−0.0206325 | + | 0.999787i | \(0.506568\pi\) | |||||||
\(440\) | −31.3651 | −1.49527 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.2279 | −0.581624 | ||||||||
\(443\) | −17.3136 | −0.822592 | −0.411296 | − | 0.911502i | \(-0.634924\pi\) | ||||
−0.411296 | + | 0.911502i | \(0.634924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.45691 | −0.448301 | ||||||||
\(446\) | −4.42460 | −0.209511 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.89913 | −0.420444 | ||||||||
\(449\) | −8.34805 | −0.393969 | −0.196985 | − | 0.980407i | \(-0.563115\pi\) | ||||
−0.196985 | + | 0.980407i | \(0.563115\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.2315 | 0.858486 | ||||||||
\(452\) | 2.65325 | 0.124798 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.575369 | 0.0270034 | ||||||||
\(455\) | 13.8212 | 0.647947 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.6135 | 1.47882 | 0.739408 | − | 0.673258i | \(-0.235106\pi\) | ||||
0.739408 | + | 0.673258i | \(0.235106\pi\) | |||||||
\(458\) | 28.4759 | 1.33059 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.18669 | −0.195205 | ||||||||
\(461\) | −14.9040 | −0.694148 | −0.347074 | − | 0.937838i | \(-0.612825\pi\) | ||||
−0.347074 | + | 0.937838i | \(0.612825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.32576 | −0.293983 | −0.146992 | − | 0.989138i | \(-0.546959\pi\) | ||||
−0.146992 | + | 0.989138i | \(0.546959\pi\) | |||||||
\(464\) | 17.3165 | 0.803896 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.81303 | −0.130311 | ||||||||
\(467\) | 25.5517 | 1.18239 | 0.591196 | − | 0.806528i | \(-0.298656\pi\) | ||||
0.591196 | + | 0.806528i | \(0.298656\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.39502 | −0.341470 | ||||||||
\(470\) | 33.3120 | 1.53657 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −43.6184 | −2.00770 | ||||||||
\(473\) | 20.8505 | 0.958705 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.31043 | −0.106010 | ||||||||
\(476\) | 0.775763 | 0.0355570 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 35.5704 | 1.62695 | ||||||||
\(479\) | 5.61743 | 0.256667 | 0.128333 | − | 0.991731i | \(-0.459037\pi\) | ||||
0.128333 | + | 0.991731i | \(0.459037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.7592 | −1.58488 | ||||||||
\(482\) | −17.0516 | −0.776677 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.07676 | −0.139853 | ||||||||
\(485\) | 10.3272 | 0.468935 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1524 | 1.13976 | 0.569881 | − | 0.821727i | \(-0.306989\pi\) | ||||
0.569881 | + | 0.821727i | \(0.306989\pi\) | |||||||
\(488\) | −9.81726 | −0.444407 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.03114 | 0.136933 | ||||||||
\(491\) | 30.3800 | 1.37103 | 0.685515 | − | 0.728058i | \(-0.259577\pi\) | ||||
0.685515 | + | 0.728058i | \(0.259577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3186 | −0.464726 | ||||||||
\(494\) | 17.7092 | 0.796774 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.8912 | 0.713537 | ||||||||
\(497\) | 7.63071 | 0.342284 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.6191 | −1.28116 | −0.640582 | − | 0.767889i | \(-0.721307\pi\) | ||||
−0.640582 | + | 0.767889i | \(0.721307\pi\) | |||||||
\(500\) | 4.45269 | 0.199130 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.23518 | −0.412186 | ||||||||
\(503\) | −13.1761 | −0.587493 | −0.293746 | − | 0.955883i | \(-0.594902\pi\) | ||||
−0.293746 | + | 0.955883i | \(0.594902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.3948 | 1.88654 | ||||||||
\(506\) | 20.1766 | 0.896957 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.448744 | 0.0199098 | ||||||||
\(509\) | 31.0674 | 1.37704 | 0.688518 | − | 0.725219i | \(-0.258262\pi\) | ||||
0.688518 | + | 0.725219i | \(0.258262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.53588 | −0.333368 | ||||||||
\(512\) | −24.9099 | −1.10087 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20.3693 | −0.898452 | ||||||||
\(515\) | −10.7751 | −0.474809 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.4399 | 2.04242 | ||||||||
\(518\) | −7.62307 | −0.334939 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 42.1532 | 1.84854 | ||||||||
\(521\) | −21.6092 | −0.946714 | −0.473357 | − | 0.880871i | \(-0.656958\pi\) | ||||
−0.473357 | + | 0.880871i | \(0.656958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.8477 | −0.518063 | −0.259032 | − | 0.965869i | \(-0.583403\pi\) | ||||
−0.259032 | + | 0.965869i | \(0.583403\pi\) | |||||||
\(524\) | 8.88433 | 0.388114 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.83685 | −0.254499 | ||||||||
\(527\) | −9.46932 | −0.412490 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.30341 | −0.361018 | ||||||||
\(530\) | 12.1260 | 0.526721 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.12350 | −0.0487100 | ||||||||
\(533\) | −24.5022 | −1.06131 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.9181 | 0.601730 | ||||||||
\(536\) | −22.5540 | −0.974186 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.2861 | 0.788372 | ||||||||
\(539\) | 4.22568 | 0.182013 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3103 | −0.572253 | −0.286126 | − | 0.958192i | \(-0.592368\pi\) | ||||
−0.286126 | + | 0.958192i | \(0.592368\pi\) | |||||||
\(542\) | −13.3839 | −0.574887 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.29841 | 0.184293 | ||||||||
\(545\) | 35.4595 | 1.51892 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.103601 | 0.00442966 | 0.00221483 | − | 0.999998i | \(-0.499295\pi\) | ||||
0.00221483 | + | 0.999998i | \(0.499295\pi\) | |||||||
\(548\) | 4.02796 | 0.172066 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.85686 | 0.207097 | ||||||||
\(551\) | 14.9440 | 0.636635 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.4421 | 0.656664 | ||||||||
\(554\) | 1.06622 | 0.0452994 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.63254 | −0.111645 | ||||||||
\(557\) | −3.49486 | −0.148082 | −0.0740410 | − | 0.997255i | \(-0.523590\pi\) | ||||
−0.0740410 | + | 0.997255i | \(0.523590\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.0220 | −1.18521 | ||||||||
\(560\) | 7.06046 | 0.298359 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.9032 | −0.755202 | ||||||||
\(563\) | 35.0406 | 1.47679 | 0.738393 | − | 0.674370i | \(-0.235585\pi\) | ||||
0.738393 | + | 0.674370i | \(0.235585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.3894 | −0.605368 | ||||||||
\(566\) | 23.3972 | 0.983459 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.2729 | 0.976508 | ||||||||
\(569\) | −9.51641 | −0.398949 | −0.199474 | − | 0.979903i | \(-0.563923\pi\) | ||||
−0.199474 | + | 0.979903i | \(0.563923\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.7756 | −1.74825 | −0.874127 | − | 0.485697i | \(-0.838566\pi\) | ||||
−0.874127 | + | 0.485697i | \(0.838566\pi\) | |||||||
\(572\) | 10.7690 | 0.450275 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.37361 | −0.224290 | ||||||||
\(575\) | 3.53774 | 0.147534 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.2875 | −0.761320 | −0.380660 | − | 0.924715i | \(-0.624303\pi\) | ||||
−0.380660 | + | 0.924715i | \(0.624303\pi\) | |||||||
\(578\) | −17.4512 | −0.725873 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.51858 | 0.270669 | ||||||||
\(581\) | −12.7925 | −0.530720 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.9048 | 0.700124 | ||||||||
\(584\) | −22.9837 | −0.951070 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.2525 | 0.754005 | ||||||||
\(587\) | −2.18408 | −0.0901465 | −0.0450732 | − | 0.998984i | \(-0.514352\pi\) | ||||
−0.0450732 | + | 0.998984i | \(0.514352\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.7140 | 0.565076 | ||||||||
\(590\) | 43.3502 | 1.78470 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.7565 | −0.729787 | ||||||||
\(593\) | 31.5402 | 1.29520 | 0.647600 | − | 0.761981i | \(-0.275773\pi\) | ||||
0.647600 | + | 0.761981i | \(0.275773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.20722 | −0.172479 | ||||||||
\(596\) | −9.69186 | −0.396994 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −27.1163 | −1.10887 | ||||||||
\(599\) | 42.0406 | 1.71773 | 0.858866 | − | 0.512200i | \(-0.171169\pi\) | ||||
0.858866 | + | 0.512200i | \(0.171169\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4807 | −0.549891 | −0.274945 | − | 0.961460i | \(-0.588660\pi\) | ||||
−0.274945 | + | 0.961460i | \(0.588660\pi\) | |||||||
\(602\) | −6.14555 | −0.250474 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.86841 | 0.198093 | ||||||||
\(605\) | 16.6863 | 0.678395 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.69701 | −0.271823 | −0.135912 | − | 0.990721i | \(-0.543396\pi\) | ||||
−0.135912 | + | 0.990721i | \(0.543396\pi\) | |||||||
\(608\) | −6.22520 | −0.252465 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.75689 | 0.395045 | ||||||||
\(611\) | −62.4130 | −2.52496 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.2623 | −1.46462 | −0.732311 | − | 0.680970i | \(-0.761558\pi\) | ||||
−0.732311 | + | 0.680970i | \(0.761558\pi\) | |||||||
\(614\) | −13.8659 | −0.559582 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.8879 | 0.519268 | ||||||||
\(617\) | −38.6679 | −1.55671 | −0.778356 | − | 0.627823i | \(-0.783946\pi\) | ||||
−0.778356 | + | 0.627823i | \(0.783946\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.11816 | −0.326296 | −0.163148 | − | 0.986602i | \(-0.552165\pi\) | ||||
−0.163148 | + | 0.986602i | \(0.552165\pi\) | |||||||
\(620\) | 5.98206 | 0.240245 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.9454 | 0.839835 | ||||||||
\(623\) | 3.88584 | 0.155683 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.7625 | −1.15050 | ||||||||
\(626\) | −16.6967 | −0.667333 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.61469 | 0.0644332 | ||||||||
\(629\) | 10.5808 | 0.421884 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.4072 | −0.772587 | −0.386293 | − | 0.922376i | \(-0.626245\pi\) | ||||
−0.386293 | + | 0.922376i | \(0.626245\pi\) | |||||||
\(632\) | 47.0967 | 1.87341 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.2659 | 0.924007 | ||||||||
\(635\) | −2.43368 | −0.0965778 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.67912 | −0.225015 | ||||||||
\(638\) | −31.4144 | −1.24371 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.8721 | 0.587871 | ||||||||
\(641\) | −11.5636 | −0.456736 | −0.228368 | − | 0.973575i | \(-0.573339\pi\) | ||||
−0.228368 | + | 0.973575i | \(0.573339\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.96147 | −0.235098 | −0.117549 | − | 0.993067i | \(-0.537504\pi\) | ||||
−0.117549 | + | 0.993067i | \(0.537504\pi\) | |||||||
\(644\) | 1.72031 | 0.0677897 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.39074 | −0.212096 | ||||||||
\(647\) | 50.1845 | 1.97296 | 0.986478 | − | 0.163892i | \(-0.0524050\pi\) | ||||
0.986478 | + | 0.163892i | \(0.0524050\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 60.4341 | 2.37224 | ||||||||
\(650\) | −6.52740 | −0.256026 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.67169 | 0.104631 | ||||||||
\(653\) | −7.04866 | −0.275835 | −0.137918 | − | 0.990444i | \(-0.544041\pi\) | ||||
−0.137918 | + | 0.990444i | \(0.544041\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.1826 | −1.88265 | ||||||||
\(656\) | −12.5168 | −0.488699 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.6879 | −0.533609 | ||||||||
\(659\) | 48.8016 | 1.90104 | 0.950521 | − | 0.310660i | \(-0.100550\pi\) | ||||
0.950521 | + | 0.310660i | \(0.100550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.03546 | −0.273648 | −0.136824 | − | 0.990595i | \(-0.543689\pi\) | ||||
−0.136824 | + | 0.990595i | \(0.543689\pi\) | |||||||
\(662\) | 3.01334 | 0.117117 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −39.0156 | −1.51410 | ||||||||
\(665\) | 6.09313 | 0.236281 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.8822 | −0.886004 | ||||||||
\(668\) | 7.07257 | 0.273646 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 22.4153 | 0.865980 | ||||||||
\(671\) | 13.6020 | 0.525099 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.0452 | −1.85201 | −0.926004 | − | 0.377514i | \(-0.876779\pi\) | ||||
−0.926004 | + | 0.377514i | \(0.876779\pi\) | |||||||
\(674\) | −21.5310 | −0.829342 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.63939 | −0.332284 | ||||||||
\(677\) | −8.31499 | −0.319571 | −0.159786 | − | 0.987152i | \(-0.551080\pi\) | ||||
−0.159786 | + | 0.987152i | \(0.551080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.24345 | −0.162849 | ||||||||
\(680\) | −12.8316 | −0.492068 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28.8288 | −1.10391 | ||||||||
\(683\) | −5.68344 | −0.217471 | −0.108735 | − | 0.994071i | \(-0.534680\pi\) | ||||
−0.108735 | + | 0.994071i | \(0.534680\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.8450 | −0.834653 | ||||||||
\(686\) | −1.24549 | −0.0475532 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.3149 | −0.545750 | ||||||||
\(689\) | −22.7192 | −0.865533 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.26192 | 0.238215 | 0.119107 | − | 0.992881i | \(-0.461997\pi\) | ||||
0.119107 | + | 0.992881i | \(0.461997\pi\) | |||||||
\(692\) | −7.64950 | −0.290790 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.8656 | 0.981844 | ||||||||
\(695\) | 14.2771 | 0.541562 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.45856 | 0.282513 | ||||||||
\(698\) | 29.4253 | 1.11376 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.414110 | 0.0156519 | ||||||||
\(701\) | −9.37500 | −0.354089 | −0.177044 | − | 0.984203i | \(-0.556654\pi\) | ||||
−0.177044 | + | 0.984203i | \(0.556654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.3237 | −0.577945 | ||||||||
\(704\) | 37.6049 | 1.41729 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.3796 | 0.729359 | ||||||||
\(707\) | −17.4200 | −0.655146 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.9615 | −1.31301 | −0.656504 | − | 0.754323i | \(-0.727965\pi\) | ||||
−0.656504 | + | 0.754323i | \(0.727965\pi\) | |||||||
\(710\) | −23.1297 | −0.868044 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.8514 | 0.444151 | ||||||||
\(713\) | −20.9989 | −0.786415 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −58.4039 | −2.18418 | ||||||||
\(716\) | 2.99931 | 0.112089 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.76224 | 0.327004 | ||||||||
\(719\) | 36.7725 | 1.37138 | 0.685691 | − | 0.727893i | \(-0.259500\pi\) | ||||
0.685691 | + | 0.727893i | \(0.259500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.42750 | 0.164889 | ||||||||
\(722\) | −15.8572 | −0.590145 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.91535 | −0.219842 | ||||||||
\(725\) | −5.50817 | −0.204568 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.14372 | −0.339122 | −0.169561 | − | 0.985520i | \(-0.554235\pi\) | ||||
−0.169561 | + | 0.985520i | \(0.554235\pi\) | |||||||
\(728\) | −17.3207 | −0.641949 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 22.8423 | 0.845432 | ||||||||
\(731\) | 8.53000 | 0.315494 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.1847 | 1.07796 | 0.538981 | − | 0.842318i | \(-0.318809\pi\) | ||||
0.538981 | + | 0.842318i | \(0.318809\pi\) | |||||||
\(734\) | 35.6541 | 1.31602 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.53204 | 0.351356 | ||||||||
\(737\) | 31.2490 | 1.15107 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.392476 | −0.0144375 | −0.00721873 | − | 0.999974i | \(-0.502298\pi\) | ||||
−0.00721873 | + | 0.999974i | \(0.502298\pi\) | |||||||
\(740\) | −6.68422 | −0.245717 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.98258 | −0.182916 | ||||||||
\(743\) | 1.15399 | 0.0423359 | 0.0211680 | − | 0.999776i | \(-0.493262\pi\) | ||||
0.0211680 | + | 0.999776i | \(0.493262\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 52.5622 | 1.92573 | ||||||||
\(746\) | 4.67875 | 0.171301 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.27813 | −0.119860 | ||||||||
\(749\) | −5.71893 | −0.208965 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.0457 | 1.75321 | 0.876607 | − | 0.481208i | \(-0.159802\pi\) | ||||
0.876607 | + | 0.481208i | \(0.159802\pi\) | |||||||
\(752\) | −31.8833 | −1.16266 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 42.2195 | 1.53754 | ||||||||
\(755\) | −26.4030 | −0.960903 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.4145 | 1.46889 | 0.734445 | − | 0.678668i | \(-0.237443\pi\) | ||||
0.734445 | + | 0.678668i | \(0.237443\pi\) | |||||||
\(758\) | 25.8814 | 0.940054 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.5834 | 0.674091 | ||||||||
\(761\) | 26.8626 | 0.973769 | 0.486884 | − | 0.873466i | \(-0.338133\pi\) | ||||
0.486884 | + | 0.873466i | \(0.338133\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.5703 | −0.527480 | ||||||||
\(764\) | 7.82040 | 0.282932 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.0362 | −0.796199 | ||||||||
\(767\) | −81.2205 | −2.93270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.9143 | −1.33117 | −0.665583 | − | 0.746324i | \(-0.731817\pi\) | ||||
−0.665583 | + | 0.746324i | \(0.731817\pi\) | |||||||
\(770\) | −12.8086 | −0.461591 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.95737 | −0.142429 | ||||||||
\(773\) | −35.0570 | −1.26091 | −0.630457 | − | 0.776224i | \(-0.717132\pi\) | ||||
−0.630457 | + | 0.776224i | \(0.717132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.05482 | −0.181574 | ||||||||
\(776\) | −12.9421 | −0.464594 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.0114 | −1.21937 | ||||||||
\(779\) | −10.8019 | −0.387018 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.2450 | −1.15382 | ||||||||
\(782\) | 8.25431 | 0.295173 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.90114 | −0.103612 | ||||||||
\(785\) | −8.75700 | −0.312551 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.03988 | 0.144006 | 0.0720031 | − | 0.997404i | \(-0.477061\pi\) | ||||
0.0720031 | + | 0.997404i | \(0.477061\pi\) | |||||||
\(788\) | −10.0696 | −0.358713 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −46.8071 | −1.66532 | ||||||||
\(791\) | 5.91261 | 0.210228 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.2804 | −0.649157 | ||||||||
\(794\) | −15.9084 | −0.564568 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.87253 | −0.101814 | ||||||||
\(797\) | −21.3487 | −0.756208 | −0.378104 | − | 0.925763i | \(-0.623424\pi\) | ||||
−0.378104 | + | 0.925763i | \(0.623424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.9987 | 0.672127 | ||||||||
\(800\) | 2.29454 | 0.0811241 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.0172 | −0.459653 | ||||||||
\(803\) | 31.8442 | 1.12376 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.32981 | −0.328832 | ||||||||
\(806\) | 38.7446 | 1.36472 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −53.1292 | −1.86908 | ||||||||
\(809\) | 26.7700 | 0.941182 | 0.470591 | − | 0.882352i | \(-0.344041\pi\) | ||||
0.470591 | + | 0.882352i | \(0.344041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1435 | 0.777563 | 0.388781 | − | 0.921330i | \(-0.372896\pi\) | ||||
0.388781 | + | 0.921330i | \(0.372896\pi\) | |||||||
\(812\) | −2.67848 | −0.0939962 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 32.2127 | 1.12905 | ||||||||
\(815\) | −14.4894 | −0.507543 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.3536 | −0.432199 | ||||||||
\(818\) | −12.5262 | −0.437968 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.71180 | −0.164543 | ||||||||
\(821\) | −9.39267 | −0.327806 | −0.163903 | − | 0.986476i | \(-0.552408\pi\) | ||||
−0.163903 | + | 0.986476i | \(0.552408\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.914372 | −0.0318730 | −0.0159365 | − | 0.999873i | \(-0.505073\pi\) | ||||
−0.0159365 | + | 0.999873i | \(0.505073\pi\) | |||||||
\(824\) | 13.5034 | 0.470414 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.8126 | −0.619779 | ||||||||
\(827\) | −39.0657 | −1.35845 | −0.679224 | − | 0.733931i | \(-0.737683\pi\) | ||||
−0.679224 | + | 0.733931i | \(0.737683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.1117 | 1.21948 | 0.609741 | − | 0.792601i | \(-0.291274\pi\) | ||||
0.609741 | + | 0.792601i | \(0.291274\pi\) | |||||||
\(830\) | 38.7757 | 1.34592 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −50.5392 | −1.75213 | ||||||||
\(833\) | 1.72874 | 0.0598974 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.3569 | −1.32740 | ||||||||
\(836\) | 4.74757 | 0.164198 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.95632 | 0.205758 | ||||||||
\(839\) | 38.3771 | 1.32492 | 0.662462 | − | 0.749096i | \(-0.269512\pi\) | ||||
0.662462 | + | 0.749096i | \(0.269512\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.62708 | 0.228520 | ||||||||
\(842\) | −16.5284 | −0.569605 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.67348 | −0.264132 | ||||||||
\(845\) | 46.8543 | 1.61184 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.85640 | −0.235589 | ||||||||
\(848\) | −11.6060 | −0.398550 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.98696 | 0.0681522 | ||||||||
\(851\) | 23.4637 | 0.804325 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.6670 | 1.59785 | 0.798924 | − | 0.601432i | \(-0.205403\pi\) | ||||
0.798924 | + | 0.601432i | \(0.205403\pi\) | |||||||
\(854\) | −4.00910 | −0.137189 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.4421 | −0.596160 | ||||||||
\(857\) | −13.5444 | −0.462670 | −0.231335 | − | 0.972874i | \(-0.574309\pi\) | ||||
−0.231335 | + | 0.972874i | \(0.574309\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.2410 | −0.417658 | −0.208829 | − | 0.977952i | \(-0.566965\pi\) | ||||
−0.208829 | + | 0.977952i | \(0.566965\pi\) | |||||||
\(860\) | −5.38867 | −0.183752 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.2184 | 0.927061 | ||||||||
\(863\) | −31.6870 | −1.07864 | −0.539318 | − | 0.842102i | \(-0.681318\pi\) | ||||
−0.539318 | + | 0.842102i | \(0.681318\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.4858 | 1.41056 | ||||||||
\(866\) | −34.9338 | −1.18710 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.45803 | −0.0834308 | ||||||||
\(869\) | −65.2533 | −2.21357 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.9972 | −1.42302 | ||||||||
\(872\) | −44.4379 | −1.50486 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.9544 | −0.404362 | ||||||||
\(875\) | 9.92257 | 0.335444 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.1129 | 1.15191 | 0.575955 | − | 0.817481i | \(-0.304630\pi\) | ||||
0.575955 | + | 0.817481i | \(0.304630\pi\) | |||||||
\(878\) | −1.07685 | −0.0363420 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −29.8353 | −1.00575 | ||||||||
\(881\) | 23.3863 | 0.787905 | 0.393952 | − | 0.919131i | \(-0.371107\pi\) | ||||
0.393952 | + | 0.919131i | \(0.371107\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.39758 | 0.215296 | 0.107648 | − | 0.994189i | \(-0.465668\pi\) | ||||
0.107648 | + | 0.994189i | \(0.465668\pi\) | |||||||
\(884\) | 4.40565 | 0.148178 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.5640 | −0.724455 | ||||||||
\(887\) | −16.3462 | −0.548851 | −0.274425 | − | 0.961608i | \(-0.588488\pi\) | ||||
−0.274425 | + | 0.961608i | \(0.588488\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −11.7785 | −0.394817 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.59416 | 0.0533763 | ||||||||
\(893\) | −27.5150 | −0.920755 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.2662 | −0.543720 | ||||||||
\(896\) | −6.11094 | −0.204152 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.3975 | −0.346968 | ||||||||
\(899\) | 32.6948 | 1.09043 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.91581 | 0.230399 | ||||||||
\(902\) | 22.7072 | 0.756066 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.0329 | 0.599764 | ||||||||
\(905\) | 32.0809 | 1.06641 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.0928 | −0.401534 | −0.200767 | − | 0.979639i | \(-0.564343\pi\) | ||||
−0.200767 | + | 0.979639i | \(0.564343\pi\) | |||||||
\(908\) | −0.207302 | −0.00687955 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.2142 | 0.570645 | ||||||||
\(911\) | 6.38071 | 0.211402 | 0.105701 | − | 0.994398i | \(-0.466291\pi\) | ||||
0.105701 | + | 0.994398i | \(0.466291\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54.0568 | 1.78902 | ||||||||
\(914\) | 39.3744 | 1.30239 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.2597 | −0.338989 | ||||||||
\(917\) | 19.7982 | 0.653795 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.8878 | −0.359156 | −0.179578 | − | 0.983744i | \(-0.557473\pi\) | ||||
−0.179578 | + | 0.983744i | \(0.557473\pi\) | |||||||
\(920\) | −28.4549 | −0.938132 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.5628 | −0.611334 | ||||||||
\(923\) | 43.3357 | 1.42641 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.64814 | 0.185710 | ||||||||
\(926\) | −7.87870 | −0.258910 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14.8412 | −0.487185 | ||||||||
\(929\) | 15.7838 | 0.517851 | 0.258925 | − | 0.965897i | \(-0.416632\pi\) | ||||
0.258925 | + | 0.965897i | \(0.416632\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.50366 | −0.0820543 | ||||||||
\(932\) | 1.01351 | 0.0331988 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.8245 | 1.04133 | ||||||||
\(935\) | 17.7784 | 0.581415 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.4718 | −0.930134 | −0.465067 | − | 0.885275i | \(-0.653970\pi\) | ||||
−0.465067 | + | 0.885275i | \(0.653970\pi\) | |||||||
\(938\) | −9.21045 | −0.300732 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0021 | −0.391465 | ||||||||
\(941\) | −47.9062 | −1.56170 | −0.780849 | − | 0.624720i | \(-0.785213\pi\) | ||||
−0.780849 | + | 0.624720i | \(0.785213\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.5399 | 0.538613 | ||||||||
\(944\) | −41.4910 | −1.35042 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.9691 | 0.844329 | ||||||||
\(947\) | −13.1474 | −0.427233 | −0.213617 | − | 0.976918i | \(-0.568524\pi\) | ||||
−0.213617 | + | 0.976918i | \(0.568524\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.7972 | −1.38925 | ||||||||
\(950\) | −2.87763 | −0.0933626 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.27249 | 0.170882 | ||||||||
\(953\) | −4.75915 | −0.154164 | −0.0770820 | − | 0.997025i | \(-0.524560\pi\) | ||||
−0.0770820 | + | 0.997025i | \(0.524560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.4126 | −1.37244 | ||||||||
\(956\) | −12.8158 | −0.414492 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.99648 | 0.226046 | ||||||||
\(959\) | 8.97609 | 0.289853 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.996189 | −0.0321351 | ||||||||
\(962\) | −43.2923 | −1.39580 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.14356 | 0.197871 | ||||||||
\(965\) | 21.4621 | 0.690891 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.6017 | −0.469558 | −0.234779 | − | 0.972049i | \(-0.575437\pi\) | ||||
−0.234779 | + | 0.972049i | \(0.575437\pi\) | |||||||
\(968\) | −20.9113 | −0.672115 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.8625 | 0.412990 | ||||||||
\(971\) | −2.56019 | −0.0821603 | −0.0410801 | − | 0.999156i | \(-0.513080\pi\) | ||||
−0.0410801 | + | 0.999156i | \(0.513080\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.86647 | −0.188070 | ||||||||
\(974\) | 31.3271 | 1.00379 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.33844 | −0.298916 | ||||||||
\(977\) | −20.9064 | −0.668856 | −0.334428 | − | 0.942421i | \(-0.608543\pi\) | ||||
−0.334428 | + | 0.942421i | \(0.608543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.4203 | −0.524796 | ||||||||
\(980\) | −1.09210 | −0.0348859 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 37.8381 | 1.20746 | ||||||||
\(983\) | 0.0609831 | 0.00194506 | 0.000972530 | − | 1.00000i | \(-0.499690\pi\) | ||||
0.000972530 | 1.00000i | \(0.499690\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 54.6105 | 1.74004 | ||||||||
\(986\) | −12.8518 | −0.409283 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.38051 | −0.202991 | ||||||||
\(989\) | 18.9159 | 0.601491 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.39312 | 0.203084 | 0.101542 | − | 0.994831i | \(-0.467622\pi\) | ||||
0.101542 | + | 0.994831i | \(0.467622\pi\) | |||||||
\(992\) | −13.6196 | −0.432424 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.50400 | 0.301449 | ||||||||
\(995\) | 15.5787 | 0.493877 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.1091 | 1.04858 | 0.524288 | − | 0.851541i | \(-0.324332\pi\) | ||||
0.524288 | + | 0.851541i | \(0.324332\pi\) | |||||||
\(998\) | −35.6449 | −1.12832 | ||||||||
\(999\) | 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.t.1.11 | 16 | ||
3.2 | odd | 2 | 889.2.a.c.1.6 | ✓ | 16 | ||
21.20 | even | 2 | 6223.2.a.k.1.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.c.1.6 | ✓ | 16 | 3.2 | odd | 2 | ||
6223.2.a.k.1.6 | 16 | 21.20 | even | 2 | |||
8001.2.a.t.1.11 | 16 | 1.1 | even | 1 | trivial |