Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6561,2,Mod(1,6561)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6561, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6561.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6561 = 3^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6561.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: | \(52.3898487662\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | no (minimal twist has level 81) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6561.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54050 | −1.79641 | −0.898204 | − | 0.439579i | \(-0.855128\pi\) | ||||
−0.898204 | + | 0.439579i | \(0.855128\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.45416 | 2.22708 | ||||||||
\(5\) | 3.18683 | 1.42519 | 0.712597 | − | 0.701573i | \(-0.247519\pi\) | ||||
0.712597 | + | 0.701573i | \(0.247519\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.66066 | −0.627669 | −0.313835 | − | 0.949478i | \(-0.601614\pi\) | ||||
−0.313835 | + | 0.949478i | \(0.601614\pi\) | |||||||
\(8\) | −6.23481 | −2.20434 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.09616 | −2.56023 | ||||||||
\(11\) | −1.96180 | −0.591505 | −0.295753 | − | 0.955265i | \(-0.595570\pi\) | ||||
−0.295753 | + | 0.955265i | \(0.595570\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.88044 | −1.07624 | −0.538121 | − | 0.842868i | \(-0.680866\pi\) | ||||
−0.538121 | + | 0.842868i | \(0.680866\pi\) | |||||||
\(14\) | 4.21891 | 1.12755 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.93125 | 1.73281 | ||||||||
\(17\) | −4.35949 | −1.05733 | −0.528666 | − | 0.848830i | \(-0.677308\pi\) | ||||
−0.528666 | + | 0.848830i | \(0.677308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41661 | 0.324992 | 0.162496 | − | 0.986709i | \(-0.448045\pi\) | ||||
0.162496 | + | 0.986709i | \(0.448045\pi\) | |||||||
\(20\) | 14.1947 | 3.17403 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.98397 | 1.06258 | ||||||||
\(23\) | −2.26830 | −0.472973 | −0.236487 | − | 0.971635i | \(-0.575996\pi\) | ||||
−0.236487 | + | 0.971635i | \(0.575996\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.15590 | 1.03118 | ||||||||
\(26\) | 9.85829 | 1.93337 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.39684 | −1.39787 | ||||||||
\(29\) | 9.44157 | 1.75326 | 0.876628 | − | 0.481169i | \(-0.159788\pi\) | ||||
0.876628 | + | 0.481169i | \(0.159788\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.17854 | −0.750487 | −0.375244 | − | 0.926926i | \(-0.622441\pi\) | ||||
−0.375244 | + | 0.926926i | \(0.622441\pi\) | |||||||
\(32\) | −5.13924 | −0.908498 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.0753 | 1.89940 | ||||||||
\(35\) | −5.29223 | −0.894551 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.84762 | −1.12574 | −0.562871 | − | 0.826545i | \(-0.690303\pi\) | ||||
−0.562871 | + | 0.826545i | \(0.690303\pi\) | |||||||
\(38\) | −3.59890 | −0.583819 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −19.8693 | −3.14161 | ||||||||
\(41\) | 3.56777 | 0.557192 | 0.278596 | − | 0.960408i | \(-0.410131\pi\) | ||||
0.278596 | + | 0.960408i | \(0.410131\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.45581 | 1.13700 | 0.568500 | − | 0.822683i | \(-0.307524\pi\) | ||||
0.568500 | + | 0.822683i | \(0.307524\pi\) | |||||||
\(44\) | −8.73818 | −1.31733 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.76263 | 0.849653 | ||||||||
\(47\) | 6.93565 | 1.01167 | 0.505835 | − | 0.862631i | \(-0.331185\pi\) | ||||
0.505835 | + | 0.862631i | \(0.331185\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.24222 | −0.606032 | ||||||||
\(50\) | −13.0986 | −1.85242 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −17.2841 | −2.39688 | ||||||||
\(53\) | 2.70633 | 0.371743 | 0.185872 | − | 0.982574i | \(-0.440489\pi\) | ||||
0.185872 | + | 0.982574i | \(0.440489\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.25193 | −0.843010 | ||||||||
\(56\) | 10.3539 | 1.38360 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −23.9864 | −3.14956 | ||||||||
\(59\) | 3.53534 | 0.460262 | 0.230131 | − | 0.973160i | \(-0.426085\pi\) | ||||
0.230131 | + | 0.973160i | \(0.426085\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.78995 | −0.357217 | −0.178609 | − | 0.983920i | \(-0.557160\pi\) | ||||
−0.178609 | + | 0.983920i | \(0.557160\pi\) | |||||||
\(62\) | 10.6156 | 1.34818 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.806236 | −0.100779 | ||||||||
\(65\) | −12.3663 | −1.53385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.84415 | −0.225299 | −0.112650 | − | 0.993635i | \(-0.535934\pi\) | ||||
−0.112650 | + | 0.993635i | \(0.535934\pi\) | |||||||
\(68\) | −19.4179 | −2.35477 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 13.4449 | 1.60698 | ||||||||
\(71\) | −2.29664 | −0.272561 | −0.136280 | − | 0.990670i | \(-0.543515\pi\) | ||||
−0.136280 | + | 0.990670i | \(0.543515\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.4402 | −1.33898 | −0.669489 | − | 0.742822i | \(-0.733487\pi\) | ||||
−0.669489 | + | 0.742822i | \(0.733487\pi\) | |||||||
\(74\) | 17.3964 | 2.02229 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.30981 | 0.723785 | ||||||||
\(77\) | 3.25788 | 0.371270 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.96987 | 0.784172 | 0.392086 | − | 0.919929i | \(-0.371754\pi\) | ||||
0.392086 | + | 0.919929i | \(0.371754\pi\) | |||||||
\(80\) | 22.0887 | 2.46959 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.06394 | −1.00094 | ||||||||
\(83\) | 0.107298 | 0.0117775 | 0.00588873 | − | 0.999983i | \(-0.498126\pi\) | ||||
0.00588873 | + | 0.999983i | \(0.498126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.8930 | −1.50690 | ||||||||
\(86\) | −18.9415 | −2.04252 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.2315 | 1.30388 | ||||||||
\(89\) | −5.28583 | −0.560297 | −0.280149 | − | 0.959957i | \(-0.590384\pi\) | ||||
−0.280149 | + | 0.959957i | \(0.590384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.44408 | 0.675524 | ||||||||
\(92\) | −10.1034 | −1.05335 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −17.6201 | −1.81737 | ||||||||
\(95\) | 4.51449 | 0.463177 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.35627 | −0.442312 | −0.221156 | − | 0.975238i | \(-0.570983\pi\) | ||||
−0.221156 | + | 0.975238i | \(0.570983\pi\) | |||||||
\(98\) | 10.7774 | 1.08868 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 22.9652 | 2.29652 | ||||||||
\(101\) | 11.2030 | 1.11474 | 0.557369 | − | 0.830265i | \(-0.311811\pi\) | ||||
0.557369 | + | 0.830265i | \(0.311811\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.02820 | −0.396910 | −0.198455 | − | 0.980110i | \(-0.563592\pi\) | ||||
−0.198455 | + | 0.980110i | \(0.563592\pi\) | |||||||
\(104\) | 24.1939 | 2.37240 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.87545 | −0.667803 | ||||||||
\(107\) | −16.2002 | −1.56614 | −0.783068 | − | 0.621936i | \(-0.786346\pi\) | ||||
−0.783068 | + | 0.621936i | \(0.786346\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8910 | 1.23473 | 0.617365 | − | 0.786677i | \(-0.288200\pi\) | ||||
0.617365 | + | 0.786677i | \(0.288200\pi\) | |||||||
\(110\) | 15.8831 | 1.51439 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.5104 | −1.08763 | ||||||||
\(113\) | 16.1325 | 1.51761 | 0.758807 | − | 0.651315i | \(-0.225782\pi\) | ||||
0.758807 | + | 0.651315i | \(0.225782\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.22869 | −0.674079 | ||||||||
\(116\) | 42.0543 | 3.90464 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.98154 | −0.826818 | ||||||||
\(119\) | 7.23962 | 0.663655 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.15134 | −0.650121 | ||||||||
\(122\) | 7.08789 | 0.641708 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −18.6119 | −1.67140 | ||||||||
\(125\) | 0.496823 | 0.0444372 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.99204 | −0.354236 | −0.177118 | − | 0.984190i | \(-0.556677\pi\) | ||||
−0.177118 | + | 0.984190i | \(0.556677\pi\) | |||||||
\(128\) | 12.3267 | 1.08954 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 31.4167 | 2.75543 | ||||||||
\(131\) | 9.76431 | 0.853111 | 0.426556 | − | 0.904461i | \(-0.359727\pi\) | ||||
0.426556 | + | 0.904461i | \(0.359727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.35250 | −0.203988 | ||||||||
\(134\) | 4.68508 | 0.404729 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.1806 | 2.33072 | ||||||||
\(137\) | 7.42951 | 0.634745 | 0.317373 | − | 0.948301i | \(-0.397199\pi\) | ||||
0.317373 | + | 0.948301i | \(0.397199\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7537 | 1.50585 | 0.752924 | − | 0.658108i | \(-0.228643\pi\) | ||||
0.752924 | + | 0.658108i | \(0.228643\pi\) | |||||||
\(140\) | −23.5725 | −1.99224 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.83462 | 0.489630 | ||||||||
\(143\) | 7.61266 | 0.636603 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.0887 | 2.49873 | ||||||||
\(146\) | 29.0640 | 2.40535 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −30.5004 | −2.50712 | ||||||||
\(149\) | 14.0449 | 1.15061 | 0.575303 | − | 0.817940i | \(-0.304884\pi\) | ||||
0.575303 | + | 0.817940i | \(0.304884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.76578 | 0.225076 | 0.112538 | − | 0.993647i | \(-0.464102\pi\) | ||||
0.112538 | + | 0.993647i | \(0.464102\pi\) | |||||||
\(152\) | −8.83229 | −0.716394 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.27665 | −0.666952 | ||||||||
\(155\) | −13.3163 | −1.06959 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.99735 | 0.398832 | 0.199416 | − | 0.979915i | \(-0.436096\pi\) | ||||
0.199416 | + | 0.979915i | \(0.436096\pi\) | |||||||
\(158\) | −17.7070 | −1.40869 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.3779 | −1.29479 | ||||||||
\(161\) | 3.76687 | 0.296871 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7147 | 0.995894 | 0.497947 | − | 0.867208i | \(-0.334087\pi\) | ||||
0.497947 | + | 0.867208i | \(0.334087\pi\) | |||||||
\(164\) | 15.8914 | 1.24091 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.272591 | −0.0211571 | ||||||||
\(167\) | 20.2459 | 1.56668 | 0.783338 | − | 0.621596i | \(-0.213515\pi\) | ||||
0.783338 | + | 0.621596i | \(0.213515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.05785 | 0.158296 | ||||||||
\(170\) | 35.2952 | 2.70701 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 33.2094 | 2.53219 | ||||||||
\(173\) | 6.79458 | 0.516582 | 0.258291 | − | 0.966067i | \(-0.416841\pi\) | ||||
0.258291 | + | 0.966067i | \(0.416841\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.56218 | −0.647240 | ||||||||
\(176\) | −13.5977 | −1.02497 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.4287 | 1.00652 | ||||||||
\(179\) | 22.4033 | 1.67450 | 0.837252 | − | 0.546817i | \(-0.184161\pi\) | ||||
0.837252 | + | 0.546817i | \(0.184161\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.7104 | −1.68805 | −0.844024 | − | 0.536306i | \(-0.819819\pi\) | ||||
−0.844024 | + | 0.536306i | \(0.819819\pi\) | |||||||
\(182\) | −16.3712 | −1.21352 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.1424 | 1.04259 | ||||||||
\(185\) | −21.8222 | −1.60440 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.55246 | 0.625418 | ||||||||
\(188\) | 30.8925 | 2.25307 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.4691 | −0.832056 | ||||||||
\(191\) | −18.2867 | −1.32318 | −0.661591 | − | 0.749865i | \(-0.730118\pi\) | ||||
−0.661591 | + | 0.749865i | \(0.730118\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.79042 | 0.632748 | 0.316374 | − | 0.948634i | \(-0.397534\pi\) | ||||
0.316374 | + | 0.948634i | \(0.397534\pi\) | |||||||
\(194\) | 11.0671 | 0.794573 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.8955 | −1.34968 | ||||||||
\(197\) | −1.86015 | −0.132530 | −0.0662649 | − | 0.997802i | \(-0.521108\pi\) | ||||
−0.0662649 | + | 0.997802i | \(0.521108\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.3896 | 0.949160 | 0.474580 | − | 0.880212i | \(-0.342600\pi\) | ||||
0.474580 | + | 0.880212i | \(0.342600\pi\) | |||||||
\(200\) | −32.1461 | −2.27307 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −28.4612 | −2.00252 | ||||||||
\(203\) | −15.6792 | −1.10046 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3699 | 0.794107 | ||||||||
\(206\) | 10.2336 | 0.713012 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −26.8963 | −1.86492 | ||||||||
\(209\) | −2.77911 | −0.192235 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3694 | 1.67766 | 0.838831 | − | 0.544392i | \(-0.183240\pi\) | ||||
0.838831 | + | 0.544392i | \(0.183240\pi\) | |||||||
\(212\) | 12.0545 | 0.827903 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 41.1568 | 2.81342 | ||||||||
\(215\) | 23.7604 | 1.62045 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.93911 | 0.471058 | ||||||||
\(218\) | −32.7495 | −2.21808 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −27.8471 | −1.87745 | ||||||||
\(221\) | 16.9168 | 1.13794 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.9499 | −1.93863 | −0.969315 | − | 0.245821i | \(-0.920943\pi\) | ||||
−0.969315 | + | 0.245821i | \(0.920943\pi\) | |||||||
\(224\) | 8.53451 | 0.570236 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −40.9846 | −2.72625 | ||||||||
\(227\) | −5.76469 | −0.382616 | −0.191308 | − | 0.981530i | \(-0.561273\pi\) | ||||
−0.191308 | + | 0.981530i | \(0.561273\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.8731 | −1.51150 | −0.755748 | − | 0.654863i | \(-0.772726\pi\) | ||||
−0.755748 | + | 0.654863i | \(0.772726\pi\) | |||||||
\(230\) | 18.3645 | 1.21092 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −58.8665 | −3.86477 | ||||||||
\(233\) | −20.4379 | −1.33893 | −0.669464 | − | 0.742844i | \(-0.733476\pi\) | ||||
−0.669464 | + | 0.742844i | \(0.733476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.1028 | 1.44183 | ||||||||
\(236\) | 15.7470 | 1.02504 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.3923 | −1.19219 | ||||||||
\(239\) | 11.6116 | 0.751090 | 0.375545 | − | 0.926804i | \(-0.377455\pi\) | ||||
0.375545 | + | 0.926804i | \(0.377455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.2687 | 0.854710 | 0.427355 | − | 0.904084i | \(-0.359446\pi\) | ||||
0.427355 | + | 0.904084i | \(0.359446\pi\) | |||||||
\(242\) | 18.1680 | 1.16788 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.4269 | −0.795552 | ||||||||
\(245\) | −13.5192 | −0.863713 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.49707 | −0.349770 | ||||||||
\(248\) | 26.0524 | 1.65433 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.26218 | −0.0798274 | ||||||||
\(251\) | 7.29619 | 0.460532 | 0.230266 | − | 0.973128i | \(-0.426040\pi\) | ||||
0.230266 | + | 0.973128i | \(0.426040\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.44996 | 0.279766 | ||||||||
\(254\) | 10.1418 | 0.636352 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.7036 | −1.85648 | ||||||||
\(257\) | 13.6877 | 0.853818 | 0.426909 | − | 0.904295i | \(-0.359603\pi\) | ||||
0.426909 | + | 0.904295i | \(0.359603\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3715 | 0.706594 | ||||||||
\(260\) | −55.0816 | −3.41602 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.8063 | −1.53254 | ||||||||
\(263\) | 0.175949 | 0.0108495 | 0.00542473 | − | 0.999985i | \(-0.498273\pi\) | ||||
0.00542473 | + | 0.999985i | \(0.498273\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.62463 | 0.529807 | ||||||||
\(266\) | 5.97654 | 0.366445 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.21416 | −0.501760 | ||||||||
\(269\) | 8.05183 | 0.490929 | 0.245464 | − | 0.969406i | \(-0.421060\pi\) | ||||
0.245464 | + | 0.969406i | \(0.421060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1488 | 1.16321 | 0.581605 | − | 0.813471i | \(-0.302425\pi\) | ||||
0.581605 | + | 0.813471i | \(0.302425\pi\) | |||||||
\(272\) | −30.2167 | −1.83216 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.8747 | −1.14026 | ||||||||
\(275\) | −10.1148 | −0.609948 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.2874 | 1.27904 | 0.639518 | − | 0.768776i | \(-0.279134\pi\) | ||||
0.639518 | + | 0.768776i | \(0.279134\pi\) | |||||||
\(278\) | −45.1033 | −2.70512 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 32.9961 | 1.97189 | ||||||||
\(281\) | −10.0072 | −0.596977 | −0.298489 | − | 0.954413i | \(-0.596483\pi\) | ||||
−0.298489 | + | 0.954413i | \(0.596483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.5972 | 1.64048 | 0.820241 | − | 0.572019i | \(-0.193840\pi\) | ||||
0.820241 | + | 0.572019i | \(0.193840\pi\) | |||||||
\(284\) | −10.2296 | −0.607015 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19.3400 | −1.14360 | ||||||||
\(287\) | −5.92484 | −0.349732 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.00517 | 0.117951 | ||||||||
\(290\) | −76.4405 | −4.48874 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −50.9567 | −2.98202 | ||||||||
\(293\) | 7.33127 | 0.428298 | 0.214149 | − | 0.976801i | \(-0.431302\pi\) | ||||
0.214149 | + | 0.976801i | \(0.431302\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2665 | 0.655963 | ||||||||
\(296\) | 42.6937 | 2.48152 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −35.6812 | −2.06696 | ||||||||
\(299\) | 8.80201 | 0.509034 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.3815 | −0.713660 | ||||||||
\(302\) | −7.02648 | −0.404328 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.81887 | 0.563151 | ||||||||
\(305\) | −8.89112 | −0.509104 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.82836 | 0.332642 | 0.166321 | − | 0.986072i | \(-0.446811\pi\) | ||||
0.166321 | + | 0.986072i | \(0.446811\pi\) | |||||||
\(308\) | 14.5111 | 0.826848 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 33.8301 | 1.92142 | ||||||||
\(311\) | −9.12122 | −0.517217 | −0.258608 | − | 0.965982i | \(-0.583264\pi\) | ||||
−0.258608 | + | 0.965982i | \(0.583264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.39310 | 0.361359 | 0.180680 | − | 0.983542i | \(-0.442170\pi\) | ||||
0.180680 | + | 0.983542i | \(0.442170\pi\) | |||||||
\(314\) | −12.6958 | −0.716465 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 31.0450 | 1.74642 | ||||||||
\(317\) | −24.7081 | −1.38775 | −0.693873 | − | 0.720097i | \(-0.744097\pi\) | ||||
−0.693873 | + | 0.720097i | \(0.744097\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.5225 | −1.03706 | ||||||||
\(320\) | −2.56934 | −0.143630 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.56975 | −0.533301 | ||||||||
\(323\) | −6.17570 | −0.343625 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.0072 | −1.10980 | ||||||||
\(326\) | −32.3018 | −1.78903 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −22.2444 | −1.22824 | ||||||||
\(329\) | −11.5177 | −0.634993 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.06870 | −0.388531 | −0.194265 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194265 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(332\) | 0.477922 | 0.0262294 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −51.4349 | −2.81439 | ||||||||
\(335\) | −5.87701 | −0.321095 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.489921 | 0.0266877 | 0.0133439 | − | 0.999911i | \(-0.495752\pi\) | ||||
0.0133439 | + | 0.999911i | \(0.495752\pi\) | |||||||
\(338\) | −5.22797 | −0.284364 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −61.8816 | −3.35600 | ||||||||
\(341\) | 8.19746 | 0.443917 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.6695 | 1.00806 | ||||||||
\(344\) | −46.4856 | −2.50634 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.2617 | −0.927993 | ||||||||
\(347\) | 18.8536 | 1.01211 | 0.506057 | − | 0.862500i | \(-0.331103\pi\) | ||||
0.506057 | + | 0.862500i | \(0.331103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.4610 | 1.89818 | 0.949092 | − | 0.314999i | \(-0.102004\pi\) | ||||
0.949092 | + | 0.314999i | \(0.102004\pi\) | |||||||
\(350\) | 21.7522 | 1.16271 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.0822 | 0.537381 | ||||||||
\(353\) | −1.97621 | −0.105183 | −0.0525914 | − | 0.998616i | \(-0.516748\pi\) | ||||
−0.0525914 | + | 0.998616i | \(0.516748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.31900 | −0.388452 | ||||||||
\(356\) | −23.5440 | −1.24783 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −56.9158 | −3.00809 | ||||||||
\(359\) | −8.05736 | −0.425251 | −0.212626 | − | 0.977134i | \(-0.568201\pi\) | ||||
−0.212626 | + | 0.977134i | \(0.568201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.9932 | −0.894380 | ||||||||
\(362\) | 57.6958 | 3.03242 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 28.7030 | 1.50445 | ||||||||
\(365\) | −36.4581 | −1.90831 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.8111 | 0.929730 | 0.464865 | − | 0.885382i | \(-0.346103\pi\) | ||||
0.464865 | + | 0.885382i | \(0.346103\pi\) | |||||||
\(368\) | −15.7222 | −0.819574 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 55.4395 | 2.88216 | ||||||||
\(371\) | −4.49429 | −0.233332 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.35142 | 0.121752 | 0.0608760 | − | 0.998145i | \(-0.480611\pi\) | ||||
0.0608760 | + | 0.998145i | \(0.480611\pi\) | |||||||
\(374\) | −21.7276 | −1.12351 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −43.2425 | −2.23006 | ||||||||
\(377\) | −36.6375 | −1.88693 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6298 | 0.597382 | 0.298691 | − | 0.954350i | \(-0.403450\pi\) | ||||
0.298691 | + | 0.954350i | \(0.403450\pi\) | |||||||
\(380\) | 20.1083 | 1.03153 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 46.4575 | 2.37697 | ||||||||
\(383\) | −29.9411 | −1.52992 | −0.764958 | − | 0.644080i | \(-0.777240\pi\) | ||||
−0.764958 | + | 0.644080i | \(0.777240\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.3823 | 0.529131 | ||||||||
\(386\) | −22.3321 | −1.13667 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −19.4035 | −0.985065 | ||||||||
\(389\) | 3.41170 | 0.172980 | 0.0864900 | − | 0.996253i | \(-0.472435\pi\) | ||||
0.0864900 | + | 0.996253i | \(0.472435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.88864 | 0.500090 | ||||||||
\(392\) | 26.4495 | 1.33590 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.72571 | 0.238078 | ||||||||
\(395\) | 22.2118 | 1.11760 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.85437 | −0.143257 | −0.0716285 | − | 0.997431i | \(-0.522820\pi\) | ||||
−0.0716285 | + | 0.997431i | \(0.522820\pi\) | |||||||
\(398\) | −34.0162 | −1.70508 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 35.7368 | 1.78684 | ||||||||
\(401\) | 24.8247 | 1.23969 | 0.619843 | − | 0.784726i | \(-0.287196\pi\) | ||||
0.619843 | + | 0.784726i | \(0.287196\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2146 | 0.807705 | ||||||||
\(404\) | 49.8999 | 2.48261 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 39.8331 | 1.97688 | ||||||||
\(407\) | 13.4337 | 0.665883 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.3691 | −0.710506 | −0.355253 | − | 0.934770i | \(-0.615605\pi\) | ||||
−0.355253 | + | 0.934770i | \(0.615605\pi\) | |||||||
\(410\) | −28.8852 | −1.42654 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.9422 | −0.883951 | ||||||||
\(413\) | −5.87098 | −0.288892 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.341940 | 0.0167852 | ||||||||
\(416\) | 19.9425 | 0.977763 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.06033 | 0.345332 | ||||||||
\(419\) | −18.4515 | −0.901415 | −0.450707 | − | 0.892672i | \(-0.648828\pi\) | ||||
−0.450707 | + | 0.892672i | \(0.648828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.7932 | 0.867188 | 0.433594 | − | 0.901108i | \(-0.357245\pi\) | ||||
0.433594 | + | 0.901108i | \(0.357245\pi\) | |||||||
\(422\) | −61.9107 | −3.01377 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.8735 | −0.819449 | ||||||||
\(425\) | −22.4771 | −1.09030 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.63316 | 0.224214 | ||||||||
\(428\) | −72.1585 | −3.48791 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −60.3634 | −2.91098 | ||||||||
\(431\) | −10.8330 | −0.521808 | −0.260904 | − | 0.965365i | \(-0.584021\pi\) | ||||
−0.260904 | + | 0.965365i | \(0.584021\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.1293 | −1.44792 | −0.723962 | − | 0.689840i | \(-0.757681\pi\) | ||||
−0.723962 | + | 0.689840i | \(0.757681\pi\) | |||||||
\(434\) | −17.6288 | −0.846212 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 57.4184 | 2.74984 | ||||||||
\(437\) | −3.21330 | −0.153713 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0736 | 1.33988 | 0.669940 | − | 0.742415i | \(-0.266320\pi\) | ||||
0.669940 | + | 0.742415i | \(0.266320\pi\) | |||||||
\(440\) | 38.9796 | 1.85828 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −42.9771 | −2.04421 | ||||||||
\(443\) | 14.5133 | 0.689546 | 0.344773 | − | 0.938686i | \(-0.387956\pi\) | ||||
0.344773 | + | 0.938686i | \(0.387956\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.8451 | −0.798532 | ||||||||
\(446\) | 73.5474 | 3.48257 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.33888 | 0.0632562 | ||||||||
\(449\) | 7.86431 | 0.371140 | 0.185570 | − | 0.982631i | \(-0.440587\pi\) | ||||
0.185570 | + | 0.982631i | \(0.440587\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.99926 | −0.329582 | ||||||||
\(452\) | 71.8566 | 3.37985 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.6452 | 0.687335 | ||||||||
\(455\) | 20.5362 | 0.962753 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.4437 | 1.19021 | 0.595103 | − | 0.803649i | \(-0.297111\pi\) | ||||
0.595103 | + | 0.803649i | \(0.297111\pi\) | |||||||
\(458\) | 58.1092 | 2.71526 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −32.1978 | −1.50123 | ||||||||
\(461\) | −20.4311 | −0.951570 | −0.475785 | − | 0.879562i | \(-0.657836\pi\) | ||||
−0.475785 | + | 0.879562i | \(0.657836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.6385 | 1.28447 | 0.642236 | − | 0.766507i | \(-0.278007\pi\) | ||||
0.642236 | + | 0.766507i | \(0.278007\pi\) | |||||||
\(464\) | 65.4419 | 3.03806 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 51.9225 | 2.40526 | ||||||||
\(467\) | 9.16496 | 0.424104 | 0.212052 | − | 0.977258i | \(-0.431985\pi\) | ||||
0.212052 | + | 0.977258i | \(0.431985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.06250 | 0.141413 | ||||||||
\(470\) | −56.1522 | −2.59011 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.0422 | −1.01457 | ||||||||
\(473\) | −14.6268 | −0.672542 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.30389 | 0.335126 | ||||||||
\(476\) | 32.2464 | 1.47801 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −29.4993 | −1.34926 | ||||||||
\(479\) | 6.75559 | 0.308671 | 0.154335 | − | 0.988019i | \(-0.450676\pi\) | ||||
0.154335 | + | 0.988019i | \(0.450676\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.5718 | 1.21157 | ||||||||
\(482\) | −33.7091 | −1.53541 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −31.8532 | −1.44787 | ||||||||
\(485\) | −13.8827 | −0.630381 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.6769 | −0.891646 | −0.445823 | − | 0.895121i | \(-0.647089\pi\) | ||||
−0.445823 | + | 0.895121i | \(0.647089\pi\) | |||||||
\(488\) | 17.3949 | 0.787428 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 34.3457 | 1.55158 | ||||||||
\(491\) | −33.2134 | −1.49890 | −0.749449 | − | 0.662062i | \(-0.769681\pi\) | ||||
−0.749449 | + | 0.662062i | \(0.769681\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.1605 | −1.85377 | ||||||||
\(494\) | 13.9653 | 0.628330 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.9625 | −1.30045 | ||||||||
\(497\) | 3.81393 | 0.171078 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.1585 | 1.43961 | 0.719805 | − | 0.694176i | \(-0.244231\pi\) | ||||
0.719805 | + | 0.694176i | \(0.244231\pi\) | |||||||
\(500\) | 2.21293 | 0.0989654 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.5360 | −0.827303 | ||||||||
\(503\) | 17.2428 | 0.768819 | 0.384410 | − | 0.923163i | \(-0.374405\pi\) | ||||
0.384410 | + | 0.923163i | \(0.374405\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.7020 | 1.58872 | ||||||||
\(506\) | −11.3051 | −0.502574 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.7812 | −0.788912 | ||||||||
\(509\) | 32.1700 | 1.42591 | 0.712954 | − | 0.701211i | \(-0.247357\pi\) | ||||
0.712954 | + | 0.701211i | \(0.247357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.9983 | 0.840436 | ||||||||
\(512\) | 50.8088 | 2.24545 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −34.7738 | −1.53380 | ||||||||
\(515\) | −12.8372 | −0.565674 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.6064 | −0.598408 | ||||||||
\(518\) | −28.8895 | −1.26933 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 77.1017 | 3.38113 | ||||||||
\(521\) | 24.6284 | 1.07899 | 0.539495 | − | 0.841989i | \(-0.318615\pi\) | ||||
0.539495 | + | 0.841989i | \(0.318615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.84292 | 0.255493 | 0.127747 | − | 0.991807i | \(-0.459226\pi\) | ||||
0.127747 | + | 0.991807i | \(0.459226\pi\) | |||||||
\(524\) | 43.4918 | 1.89995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.446998 | −0.0194900 | ||||||||
\(527\) | 18.2163 | 0.793514 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.8548 | −0.776296 | ||||||||
\(530\) | −21.9109 | −0.951749 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.4784 | −0.454297 | ||||||||
\(533\) | −13.8445 | −0.599673 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −51.6274 | −2.23205 | ||||||||
\(536\) | 11.4980 | 0.496636 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.4557 | −0.881908 | ||||||||
\(539\) | 8.32239 | 0.358471 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.50279 | −0.365564 | −0.182782 | − | 0.983154i | \(-0.558510\pi\) | ||||
−0.182782 | + | 0.983154i | \(0.558510\pi\) | |||||||
\(542\) | −48.6477 | −2.08960 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.4045 | 0.960584 | ||||||||
\(545\) | 41.0813 | 1.75973 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.9602 | −1.92236 | −0.961179 | − | 0.275925i | \(-0.911016\pi\) | ||||
−0.961179 | + | 0.275925i | \(0.911016\pi\) | |||||||
\(548\) | 33.0922 | 1.41363 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.6968 | 1.09572 | ||||||||
\(551\) | 13.3750 | 0.569795 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.5746 | −0.492201 | ||||||||
\(554\) | −54.0807 | −2.29767 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 79.0778 | 3.35365 | ||||||||
\(557\) | −24.4636 | −1.03656 | −0.518278 | − | 0.855212i | \(-0.673427\pi\) | ||||
−0.518278 | + | 0.855212i | \(0.673427\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.9319 | −1.22369 | ||||||||
\(560\) | −36.6818 | −1.55009 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.4233 | 1.07242 | ||||||||
\(563\) | 6.06992 | 0.255817 | 0.127908 | − | 0.991786i | \(-0.459174\pi\) | ||||
0.127908 | + | 0.991786i | \(0.459174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 51.4114 | 2.16290 | ||||||||
\(566\) | −70.1107 | −2.94697 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.3191 | 0.600817 | ||||||||
\(569\) | 10.6297 | 0.445620 | 0.222810 | − | 0.974862i | \(-0.428477\pi\) | ||||
0.222810 | + | 0.974862i | \(0.428477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.4864 | 1.15027 | 0.575134 | − | 0.818059i | \(-0.304950\pi\) | ||||
0.575134 | + | 0.818059i | \(0.304950\pi\) | |||||||
\(572\) | 33.9080 | 1.41777 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.0521 | 0.628262 | ||||||||
\(575\) | −11.6951 | −0.487721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.93714 | −0.247166 | −0.123583 | − | 0.992334i | \(-0.539439\pi\) | ||||
−0.123583 | + | 0.992334i | \(0.539439\pi\) | |||||||
\(578\) | −5.09415 | −0.211889 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 134.020 | 5.56488 | ||||||||
\(581\) | −0.178185 | −0.00739235 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.30929 | −0.219888 | ||||||||
\(584\) | 71.3278 | 2.95156 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.6251 | −0.769397 | ||||||||
\(587\) | −11.1071 | −0.458440 | −0.229220 | − | 0.973375i | \(-0.573617\pi\) | ||||
−0.229220 | + | 0.973375i | \(0.573617\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.91935 | −0.243903 | ||||||||
\(590\) | −28.6227 | −1.17838 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −47.4626 | −1.95070 | ||||||||
\(593\) | 2.05072 | 0.0842128 | 0.0421064 | − | 0.999113i | \(-0.486593\pi\) | ||||
0.0421064 | + | 0.999113i | \(0.486593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.0714 | 0.945837 | ||||||||
\(596\) | 62.5584 | 2.56249 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.3616 | −0.914432 | ||||||||
\(599\) | 2.80439 | 0.114584 | 0.0572921 | − | 0.998357i | \(-0.481753\pi\) | ||||
0.0572921 | + | 0.998357i | \(0.481753\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.0402 | −1.47011 | −0.735055 | − | 0.678007i | \(-0.762844\pi\) | ||||
−0.735055 | + | 0.678007i | \(0.762844\pi\) | |||||||
\(602\) | 31.4554 | 1.28202 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.3192 | 0.501263 | ||||||||
\(605\) | −22.7901 | −0.926550 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.5142 | 1.56324 | 0.781621 | − | 0.623754i | \(-0.214393\pi\) | ||||
0.781621 | + | 0.623754i | \(0.214393\pi\) | |||||||
\(608\) | −7.28029 | −0.295255 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.5879 | 0.914558 | ||||||||
\(611\) | −26.9134 | −1.08880 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.45973 | 0.0589580 | 0.0294790 | − | 0.999565i | \(-0.490615\pi\) | ||||
0.0294790 | + | 0.999565i | \(0.490615\pi\) | |||||||
\(614\) | −14.8070 | −0.597561 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −20.3123 | −0.818404 | ||||||||
\(617\) | −12.0248 | −0.484102 | −0.242051 | − | 0.970264i | \(-0.577820\pi\) | ||||
−0.242051 | + | 0.970264i | \(0.577820\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.3697 | 1.26085 | 0.630427 | − | 0.776249i | \(-0.282880\pi\) | ||||
0.630427 | + | 0.776249i | \(0.282880\pi\) | |||||||
\(620\) | −59.3129 | −2.38206 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.1725 | 0.929132 | ||||||||
\(623\) | 8.77795 | 0.351681 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.1962 | −0.967848 | ||||||||
\(626\) | −16.2417 | −0.649149 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.2590 | 0.888231 | ||||||||
\(629\) | 29.8522 | 1.19028 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.4483 | −0.694605 | −0.347303 | − | 0.937753i | \(-0.612902\pi\) | ||||
−0.347303 | + | 0.937753i | \(0.612902\pi\) | |||||||
\(632\) | −43.4559 | −1.72858 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 62.7711 | 2.49296 | ||||||||
\(635\) | −12.7219 | −0.504855 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.4617 | 0.652236 | ||||||||
\(638\) | 47.0565 | 1.86298 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 39.2832 | 1.55280 | ||||||||
\(641\) | 9.22820 | 0.364492 | 0.182246 | − | 0.983253i | \(-0.441663\pi\) | ||||
0.182246 | + | 0.983253i | \(0.441663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.30126 | 0.287934 | 0.143967 | − | 0.989583i | \(-0.454014\pi\) | ||||
0.143967 | + | 0.989583i | \(0.454014\pi\) | |||||||
\(644\) | 16.7782 | 0.661156 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.6894 | 0.617291 | ||||||||
\(647\) | 34.3969 | 1.35228 | 0.676142 | − | 0.736772i | \(-0.263651\pi\) | ||||
0.676142 | + | 0.736772i | \(0.263651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.93563 | −0.272247 | ||||||||
\(650\) | 50.8283 | 1.99365 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 56.6335 | 2.21794 | ||||||||
\(653\) | 14.2491 | 0.557612 | 0.278806 | − | 0.960347i | \(-0.410061\pi\) | ||||
0.278806 | + | 0.960347i | \(0.410061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.1172 | 1.21585 | ||||||||
\(656\) | 24.7291 | 0.965509 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 29.2609 | 1.14071 | ||||||||
\(659\) | 44.0929 | 1.71761 | 0.858807 | − | 0.512300i | \(-0.171206\pi\) | ||||
0.858807 | + | 0.512300i | \(0.171206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.63277 | −0.102403 | −0.0512015 | − | 0.998688i | \(-0.516305\pi\) | ||||
−0.0512015 | + | 0.998688i | \(0.516305\pi\) | |||||||
\(662\) | 17.9581 | 0.697960 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.668982 | −0.0259615 | ||||||||
\(665\) | −7.49702 | −0.290722 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.4163 | −0.829244 | ||||||||
\(668\) | 90.1787 | 3.48912 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.9306 | 0.576818 | ||||||||
\(671\) | 5.47334 | 0.211296 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.41710 | −0.131720 | −0.0658598 | − | 0.997829i | \(-0.520979\pi\) | ||||
−0.0658598 | + | 0.997829i | \(0.520979\pi\) | |||||||
\(674\) | −1.24465 | −0.0479420 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.16598 | 0.352538 | ||||||||
\(677\) | 38.8868 | 1.49454 | 0.747271 | − | 0.664520i | \(-0.231364\pi\) | ||||
0.747271 | + | 0.664520i | \(0.231364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.23427 | 0.277626 | ||||||||
\(680\) | 86.6201 | 3.32173 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20.8257 | −0.797456 | ||||||||
\(683\) | 23.1782 | 0.886891 | 0.443445 | − | 0.896301i | \(-0.353756\pi\) | ||||
0.443445 | + | 0.896301i | \(0.353756\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.6766 | 0.904636 | ||||||||
\(686\) | −47.4299 | −1.81088 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 51.6781 | 1.97021 | ||||||||
\(689\) | −10.5018 | −0.400086 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.3931 | 0.661665 | 0.330833 | − | 0.943689i | \(-0.392670\pi\) | ||||
0.330833 | + | 0.943689i | \(0.392670\pi\) | |||||||
\(692\) | 30.2642 | 1.15047 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −47.8976 | −1.81817 | ||||||||
\(695\) | 56.5780 | 2.14613 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.5537 | −0.589137 | ||||||||
\(698\) | −90.0888 | −3.40991 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −38.1373 | −1.44146 | ||||||||
\(701\) | −18.9249 | −0.714785 | −0.357393 | − | 0.933954i | \(-0.616334\pi\) | ||||
−0.357393 | + | 0.933954i | \(0.616334\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.70041 | −0.365858 | ||||||||
\(704\) | 1.58167 | 0.0596116 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.02056 | 0.188951 | ||||||||
\(707\) | −18.6043 | −0.699687 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.7604 | 1.60590 | 0.802951 | − | 0.596045i | \(-0.203262\pi\) | ||||
0.802951 | + | 0.596045i | \(0.203262\pi\) | |||||||
\(710\) | 18.5940 | 0.697819 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 32.9562 | 1.23509 | ||||||||
\(713\) | 9.47818 | 0.354960 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.2603 | 0.907283 | ||||||||
\(716\) | 99.7882 | 3.72926 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.4698 | 0.763924 | ||||||||
\(719\) | 13.0136 | 0.485326 | 0.242663 | − | 0.970111i | \(-0.421979\pi\) | ||||
0.242663 | + | 0.970111i | \(0.421979\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.68945 | 0.249128 | ||||||||
\(722\) | 43.1714 | 1.60667 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −101.156 | −3.75942 | ||||||||
\(725\) | 48.6798 | 1.80792 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.4565 | −1.87133 | −0.935664 | − | 0.352891i | \(-0.885199\pi\) | ||||
−0.935664 | + | 0.352891i | \(0.885199\pi\) | |||||||
\(728\) | −40.1777 | −1.48908 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 92.6220 | 3.42810 | ||||||||
\(731\) | −32.5035 | −1.20219 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.9879 | −0.590527 | −0.295263 | − | 0.955416i | \(-0.595407\pi\) | ||||
−0.295263 | + | 0.955416i | \(0.595407\pi\) | |||||||
\(734\) | −45.2491 | −1.67017 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.6573 | 0.429695 | ||||||||
\(737\) | 3.61786 | 0.133266 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.13598 | −0.262501 | −0.131251 | − | 0.991349i | \(-0.541899\pi\) | ||||
−0.131251 | + | 0.991349i | \(0.541899\pi\) | |||||||
\(740\) | −97.1998 | −3.57313 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.4178 | 0.419159 | ||||||||
\(743\) | −33.9109 | −1.24407 | −0.622036 | − | 0.782989i | \(-0.713694\pi\) | ||||
−0.622036 | + | 0.782989i | \(0.713694\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.7589 | 1.63984 | ||||||||
\(746\) | −5.97380 | −0.218716 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 38.0940 | 1.39286 | ||||||||
\(749\) | 26.9030 | 0.983015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.9333 | −1.53017 | −0.765085 | − | 0.643930i | \(-0.777303\pi\) | ||||
−0.765085 | + | 0.643930i | \(0.777303\pi\) | |||||||
\(752\) | 48.0727 | 1.75303 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 93.0777 | 3.38969 | ||||||||
\(755\) | 8.81408 | 0.320777 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.1805 | 0.951548 | 0.475774 | − | 0.879568i | \(-0.342168\pi\) | ||||
0.475774 | + | 0.879568i | \(0.342168\pi\) | |||||||
\(758\) | −29.5455 | −1.07314 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −28.1470 | −1.02100 | ||||||||
\(761\) | −46.8751 | −1.69922 | −0.849610 | − | 0.527411i | \(-0.823163\pi\) | ||||
−0.849610 | + | 0.527411i | \(0.823163\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.4074 | −0.775001 | ||||||||
\(764\) | −81.4521 | −2.94683 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 76.0654 | 2.74835 | ||||||||
\(767\) | −13.7187 | −0.495353 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.7103 | −0.494407 | −0.247203 | − | 0.968964i | \(-0.579512\pi\) | ||||
−0.247203 | + | 0.968964i | \(0.579512\pi\) | |||||||
\(770\) | −26.3763 | −0.950536 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 39.1540 | 1.40918 | ||||||||
\(773\) | 15.2517 | 0.548566 | 0.274283 | − | 0.961649i | \(-0.411559\pi\) | ||||
0.274283 | + | 0.961649i | \(0.411559\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.5441 | −0.773887 | ||||||||
\(776\) | 27.1605 | 0.975006 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.66743 | −0.310743 | ||||||||
\(779\) | 5.05414 | 0.181083 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.50555 | 0.161221 | ||||||||
\(782\) | −25.1221 | −0.898366 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −29.4039 | −1.05014 | ||||||||
\(785\) | 15.9257 | 0.568413 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.0003 | −0.748580 | −0.374290 | − | 0.927312i | \(-0.622114\pi\) | ||||
−0.374290 | + | 0.927312i | \(0.622114\pi\) | |||||||
\(788\) | −8.28539 | −0.295155 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −56.4292 | −2.00766 | ||||||||
\(791\) | −26.7905 | −0.952560 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.8263 | 0.384452 | ||||||||
\(794\) | 7.25155 | 0.257348 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 59.6393 | 2.11386 | ||||||||
\(797\) | 46.1575 | 1.63498 | 0.817491 | − | 0.575941i | \(-0.195364\pi\) | ||||
0.817491 | + | 0.575941i | \(0.195364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.2359 | −1.06967 | ||||||||
\(800\) | −26.4974 | −0.936824 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −63.0672 | −2.22698 | ||||||||
\(803\) | 22.4435 | 0.792013 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0044 | 0.423099 | ||||||||
\(806\) | −41.1932 | −1.45097 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −69.8485 | −2.45726 | ||||||||
\(809\) | 15.0049 | 0.527545 | 0.263772 | − | 0.964585i | \(-0.415033\pi\) | ||||
0.263772 | + | 0.964585i | \(0.415033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.0448 | 1.65197 | 0.825983 | − | 0.563695i | \(-0.190621\pi\) | ||||
0.825983 | + | 0.563695i | \(0.190621\pi\) | |||||||
\(812\) | −69.8378 | −2.45082 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −34.1283 | −1.19620 | ||||||||
\(815\) | 40.5197 | 1.41934 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5620 | 0.369516 | ||||||||
\(818\) | 36.5047 | 1.27636 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 50.6433 | 1.76854 | ||||||||
\(821\) | 1.52951 | 0.0533801 | 0.0266901 | − | 0.999644i | \(-0.491503\pi\) | ||||
0.0266901 | + | 0.999644i | \(0.491503\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.16425 | 0.0754410 | 0.0377205 | − | 0.999288i | \(-0.487990\pi\) | ||||
0.0377205 | + | 0.999288i | \(0.487990\pi\) | |||||||
\(824\) | 25.1151 | 0.874924 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.9153 | 0.518968 | ||||||||
\(827\) | −40.8370 | −1.42004 | −0.710020 | − | 0.704181i | \(-0.751314\pi\) | ||||
−0.710020 | + | 0.704181i | \(0.751314\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.1117 | 0.594316 | 0.297158 | − | 0.954828i | \(-0.403961\pi\) | ||||
0.297158 | + | 0.954828i | \(0.403961\pi\) | |||||||
\(830\) | −0.868701 | −0.0301530 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.12855 | 0.108463 | ||||||||
\(833\) | 18.4939 | 0.640777 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.5204 | 2.23282 | ||||||||
\(836\) | −12.3786 | −0.428122 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 46.8761 | 1.61931 | ||||||||
\(839\) | −18.3623 | −0.633937 | −0.316969 | − | 0.948436i | \(-0.602665\pi\) | ||||
−0.316969 | + | 0.948436i | \(0.602665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.1433 | 2.07391 | ||||||||
\(842\) | −45.2037 | −1.55782 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 108.546 | 3.73629 | ||||||||
\(845\) | 6.55801 | 0.225602 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.8759 | 0.408061 | ||||||||
\(848\) | 18.7583 | 0.644162 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 57.1032 | 1.95862 | ||||||||
\(851\) | 15.5325 | 0.532446 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5086 | 0.531005 | 0.265503 | − | 0.964110i | \(-0.414462\pi\) | ||||
0.265503 | + | 0.964110i | \(0.414462\pi\) | |||||||
\(854\) | −11.7706 | −0.402780 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 101.005 | 3.45229 | ||||||||
\(857\) | 19.0971 | 0.652344 | 0.326172 | − | 0.945310i | \(-0.394241\pi\) | ||||
0.326172 | + | 0.945310i | \(0.394241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.83131 | 0.0966032 | 0.0483016 | − | 0.998833i | \(-0.484619\pi\) | ||||
0.0483016 | + | 0.998833i | \(0.484619\pi\) | |||||||
\(860\) | 105.833 | 3.60887 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.5213 | 0.937380 | ||||||||
\(863\) | 3.01216 | 0.102535 | 0.0512675 | − | 0.998685i | \(-0.483674\pi\) | ||||
0.0512675 | + | 0.998685i | \(0.483674\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.6532 | 0.736231 | ||||||||
\(866\) | 76.5437 | 2.60106 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 30.9079 | 1.04908 | ||||||||
\(869\) | −13.6735 | −0.463842 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.15613 | 0.242476 | ||||||||
\(872\) | −80.3727 | −2.72176 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.16339 | 0.276131 | ||||||||
\(875\) | −0.825053 | −0.0278919 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.5173 | 0.490214 | 0.245107 | − | 0.969496i | \(-0.421177\pi\) | ||||
0.245107 | + | 0.969496i | \(0.421177\pi\) | |||||||
\(878\) | −71.3212 | −2.40697 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −43.3337 | −1.46078 | ||||||||
\(881\) | 6.48384 | 0.218446 | 0.109223 | − | 0.994017i | \(-0.465164\pi\) | ||||
0.109223 | + | 0.994017i | \(0.465164\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.3933 | 0.854554 | 0.427277 | − | 0.904121i | \(-0.359473\pi\) | ||||
0.427277 | + | 0.904121i | \(0.359473\pi\) | |||||||
\(884\) | 75.3500 | 2.53430 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.8710 | −1.23871 | ||||||||
\(887\) | 0.107021 | 0.00359341 | 0.00179671 | − | 0.999998i | \(-0.499428\pi\) | ||||
0.00179671 | + | 0.999998i | \(0.499428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.62940 | 0.222343 | ||||||||
\(890\) | 42.7950 | 1.43449 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −128.948 | −4.31749 | ||||||||
\(893\) | 9.82511 | 0.328785 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71.3957 | 2.38650 | ||||||||
\(896\) | −20.4705 | −0.683870 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.9793 | −0.666718 | ||||||||
\(899\) | −39.4519 | −1.31580 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.7982 | −0.393056 | ||||||||
\(902\) | 17.7816 | 0.592064 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −100.583 | −3.34534 | ||||||||
\(905\) | −72.3741 | −2.40580 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.5972 | 1.44762 | 0.723810 | − | 0.689999i | \(-0.242389\pi\) | ||||
0.723810 | + | 0.689999i | \(0.242389\pi\) | |||||||
\(908\) | −25.6769 | −0.852118 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −52.1723 | −1.72950 | ||||||||
\(911\) | 55.4124 | 1.83590 | 0.917948 | − | 0.396702i | \(-0.129845\pi\) | ||||
0.917948 | + | 0.396702i | \(0.129845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.210497 | −0.00696644 | ||||||||
\(914\) | −64.6399 | −2.13810 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −101.880 | −3.36622 | ||||||||
\(917\) | −16.2152 | −0.535472 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.9441 | −1.35062 | −0.675311 | − | 0.737533i | \(-0.735990\pi\) | ||||
−0.675311 | + | 0.737533i | \(0.735990\pi\) | |||||||
\(920\) | 45.0696 | 1.48590 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 51.9053 | 1.70941 | ||||||||
\(923\) | 8.91198 | 0.293341 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.3057 | −1.16084 | ||||||||
\(926\) | −70.2159 | −2.30744 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −48.5225 | −1.59283 | ||||||||
\(929\) | −32.3050 | −1.05989 | −0.529947 | − | 0.848031i | \(-0.677788\pi\) | ||||
−0.529947 | + | 0.848031i | \(0.677788\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00957 | −0.196956 | ||||||||
\(932\) | −91.0336 | −2.98190 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.2836 | −0.761863 | ||||||||
\(935\) | 27.2552 | 0.891342 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.06200 | −0.296043 | −0.148021 | − | 0.988984i | \(-0.547290\pi\) | ||||
−0.148021 | + | 0.988984i | \(0.547290\pi\) | |||||||
\(938\) | −7.78031 | −0.254036 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 98.4493 | 3.21106 | ||||||||
\(941\) | 23.9044 | 0.779263 | 0.389631 | − | 0.920971i | \(-0.372602\pi\) | ||||
0.389631 | + | 0.920971i | \(0.372602\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.09278 | −0.263537 | ||||||||
\(944\) | 24.5043 | 0.797547 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 37.1595 | 1.20816 | ||||||||
\(947\) | 8.23165 | 0.267493 | 0.133746 | − | 0.991016i | \(-0.457299\pi\) | ||||
0.133746 | + | 0.991016i | \(0.457299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.3932 | 1.44106 | ||||||||
\(950\) | −18.5556 | −0.602022 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −45.1377 | −1.46292 | ||||||||
\(953\) | −17.0755 | −0.553129 | −0.276564 | − | 0.960995i | \(-0.589196\pi\) | ||||
−0.276564 | + | 0.960995i | \(0.589196\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −58.2768 | −1.88579 | ||||||||
\(956\) | 51.7199 | 1.67274 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.1626 | −0.554498 | ||||||||
\(959\) | −12.3379 | −0.398410 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5398 | −0.436769 | ||||||||
\(962\) | −67.5058 | −2.17648 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 59.1008 | 1.90351 | ||||||||
\(965\) | 28.0136 | 0.901790 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.3524 | 0.493698 | 0.246849 | − | 0.969054i | \(-0.420605\pi\) | ||||
0.246849 | + | 0.969054i | \(0.420605\pi\) | |||||||
\(968\) | 44.5873 | 1.43309 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 35.2691 | 1.13242 | ||||||||
\(971\) | −10.5213 | −0.337645 | −0.168822 | − | 0.985646i | \(-0.553996\pi\) | ||||
−0.168822 | + | 0.985646i | \(0.553996\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.4828 | −0.945174 | ||||||||
\(974\) | 49.9893 | 1.60176 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.3379 | −0.618990 | ||||||||
\(977\) | 23.0942 | 0.738850 | 0.369425 | − | 0.929261i | \(-0.379555\pi\) | ||||
0.369425 | + | 0.929261i | \(0.379555\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3698 | 0.331419 | ||||||||
\(980\) | −60.2169 | −1.92356 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 84.3787 | 2.69263 | ||||||||
\(983\) | 1.19718 | 0.0381843 | 0.0190921 | − | 0.999818i | \(-0.493922\pi\) | ||||
0.0190921 | + | 0.999818i | \(0.493922\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.92797 | −0.188881 | ||||||||
\(986\) | 104.568 | 3.33013 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.4849 | −0.778967 | ||||||||
\(989\) | −16.9120 | −0.537771 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.7076 | −0.689565 | −0.344783 | − | 0.938683i | \(-0.612047\pi\) | ||||
−0.344783 | + | 0.938683i | \(0.612047\pi\) | |||||||
\(992\) | 21.4745 | 0.681816 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.68930 | −0.307326 | ||||||||
\(995\) | 42.6703 | 1.35274 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.5063 | −1.09282 | −0.546412 | − | 0.837516i | \(-0.684007\pi\) | ||||
−0.546412 | + | 0.837516i | \(0.684007\pi\) | |||||||
\(998\) | −81.6987 | −2.58613 | ||||||||
\(999\) | 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 | 6561.2.a.d.1.3 | 72 | ||
3.2 | odd | 2 | 6561.2.a.c.1.70 | 72 | |||
81.4 | even | 27 | 729.2.g.a.136.1 | 144 | |||
81.7 | even | 27 | 243.2.g.a.37.8 | 144 | |||
81.20 | odd | 54 | 729.2.g.d.595.8 | 144 | |||
81.23 | odd | 54 | 81.2.g.a.43.1 | ✓ | 144 | ||
81.31 | even | 27 | 729.2.g.b.622.8 | 144 | |||
81.34 | even | 27 | 729.2.g.b.109.8 | 144 | |||
81.47 | odd | 54 | 729.2.g.c.109.1 | 144 | |||
81.50 | odd | 54 | 729.2.g.c.622.1 | 144 | |||
81.58 | even | 27 | 243.2.g.a.46.8 | 144 | |||
81.61 | even | 27 | 729.2.g.a.595.1 | 144 | |||
81.74 | odd | 54 | 81.2.g.a.49.1 | yes | 144 | ||
81.77 | odd | 54 | 729.2.g.d.136.8 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.43.1 | ✓ | 144 | 81.23 | odd | 54 | ||
81.2.g.a.49.1 | yes | 144 | 81.74 | odd | 54 | ||
243.2.g.a.37.8 | 144 | 81.7 | even | 27 | |||
243.2.g.a.46.8 | 144 | 81.58 | even | 27 | |||
729.2.g.a.136.1 | 144 | 81.4 | even | 27 | |||
729.2.g.a.595.1 | 144 | 81.61 | even | 27 | |||
729.2.g.b.109.8 | 144 | 81.34 | even | 27 | |||
729.2.g.b.622.8 | 144 | 81.31 | even | 27 | |||
729.2.g.c.109.1 | 144 | 81.47 | odd | 54 | |||
729.2.g.c.622.1 | 144 | 81.50 | odd | 54 | |||
729.2.g.d.136.8 | 144 | 81.77 | odd | 54 | |||
729.2.g.d.595.8 | 144 | 81.20 | odd | 54 | |||
6561.2.a.c.1.70 | 72 | 3.2 | odd | 2 | |||
6561.2.a.d.1.3 | 72 | 1.1 | even | 1 | trivial |