Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.239123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | −0.288675 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288675 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.521753 | 0.233335 | 0.116668 | − | 0.993171i | \(-0.462779\pi\) | ||||
0.116668 | + | 0.993171i | \(0.462779\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.478247 | 0.132642 | 0.0663209 | − | 0.997798i | \(-0.478874\pi\) | ||||
0.0663209 | + | 0.997798i | \(0.478874\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.521753 | −0.134716 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.52175 | −0.578530 | −0.289265 | − | 0.957249i | \(-0.593411\pi\) | ||||
−0.289265 | + | 0.957249i | \(0.593411\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.88564 | 1.22724 | 0.613620 | − | 0.789601i | \(-0.289713\pi\) | ||||
0.613620 | + | 0.789601i | \(0.289713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.72777 | −0.945555 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.47825 | −0.274503 | −0.137252 | − | 0.990536i | \(-0.543827\pi\) | ||||
−0.137252 | + | 0.990536i | \(0.543827\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.84213 | 1.22888 | 0.614442 | − | 0.788962i | \(-0.289381\pi\) | ||||
0.614442 | + | 0.788962i | \(0.289381\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.521753 | 0.0881924 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.32038 | 1.20346 | 0.601732 | − | 0.798698i | \(-0.294478\pi\) | ||||
0.601732 | + | 0.798698i | \(0.294478\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.478247 | −0.0765807 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.52175 | −0.393832 | −0.196916 | − | 0.980420i | \(-0.563093\pi\) | ||||
−0.196916 | + | 0.980420i | \(0.563093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.84213 | 0.433421 | 0.216711 | − | 0.976236i | \(-0.430467\pi\) | ||||
0.216711 | + | 0.976236i | \(0.430467\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.04351 | −0.155557 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.88564 | −1.44197 | −0.720984 | − | 0.692951i | \(-0.756310\pi\) | ||||
−0.720984 | + | 0.692951i | \(0.756310\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.72777 | −0.786770 | −0.393385 | − | 0.919374i | \(-0.628696\pi\) | ||||
−0.393385 | + | 0.919374i | \(0.628696\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.04351 | −0.140706 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.52175 | 0.334014 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.47825 | −0.317307 | −0.158653 | − | 0.987334i | \(-0.550715\pi\) | ||||
−0.158653 | + | 0.987334i | \(0.550715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.00000 | −0.251976 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.249527 | 0.0309500 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.7713 | −1.68243 | −0.841215 | − | 0.540701i | \(-0.818159\pi\) | ||||
−0.841215 | + | 0.540701i | \(0.818159\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.88564 | −0.708548 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.7278 | −1.51051 | −0.755254 | − | 0.655432i | \(-0.772487\pi\) | ||||
−0.755254 | + | 0.655432i | \(0.772487\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.72777 | 0.545916 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00000 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.32038 | 0.364459 | 0.182230 | − | 0.983256i | \(-0.441669\pi\) | ||||
0.182230 | + | 0.983256i | \(0.441669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.521753 | 0.0565921 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.47825 | 0.158485 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.84213 | 0.937264 | 0.468632 | − | 0.883393i | \(-0.344747\pi\) | ||||
0.468632 | + | 0.883393i | \(0.344747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.478247 | 0.0501339 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.84213 | −0.709496 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.31573 | −0.134991 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.20602 | 0.731660 | 0.365830 | − | 0.930682i | \(-0.380785\pi\) | ||||
0.365830 | + | 0.930682i | \(0.380785\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.592606 | −0.0589665 | −0.0294833 | − | 0.999565i | \(-0.509386\pi\) | ||||
−0.0294833 | + | 0.999565i | \(0.509386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.2930 | −1.90100 | −0.950500 | − | 0.310726i | \(-0.899428\pi\) | ||||
−0.950500 | + | 0.310726i | \(0.899428\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.521753 | −0.0509179 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.04351 | 0.197553 | 0.0987766 | − | 0.995110i | \(-0.468507\pi\) | ||||
0.0987766 | + | 0.995110i | \(0.468507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.7713 | 1.70218 | 0.851090 | − | 0.525020i | \(-0.175942\pi\) | ||||
0.851090 | + | 0.525020i | \(0.175942\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.32038 | −0.694820 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2930 | 1.06236 | 0.531180 | − | 0.847259i | \(-0.321749\pi\) | ||||
0.531180 | + | 0.847259i | \(0.321749\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.07085 | 0.286359 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.956493 | −0.0884278 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.52175 | 0.227379 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.07550 | −0.453966 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.56526 | 0.671308 | 0.335654 | − | 0.941985i | \(-0.391043\pi\) | ||||
0.335654 | + | 0.941985i | \(0.391043\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.84213 | −0.250236 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.6843 | −1.89456 | −0.947282 | − | 0.320402i | \(-0.896182\pi\) | ||||
−0.947282 | + | 0.320402i | \(0.896182\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.52175 | −0.218664 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.60877 | 0.224527 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.04351 | 0.516332 | 0.258166 | − | 0.966101i | \(-0.416882\pi\) | ||||
0.258166 | + | 0.966101i | \(0.416882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7278 | −1.07956 | −0.539778 | − | 0.841808i | \(-0.681492\pi\) | ||||
−0.539778 | + | 0.841808i | \(0.681492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.88564 | 0.832521 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.956493 | −0.0799860 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.771280 | −0.0640513 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.00000 | 0.494872 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.52175 | −0.452360 | −0.226180 | − | 0.974086i | \(-0.572624\pi\) | ||||
−0.226180 | + | 0.974086i | \(0.572624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.3639 | −1.33167 | −0.665837 | − | 0.746097i | \(-0.731925\pi\) | ||||
−0.665837 | + | 0.746097i | \(0.731925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.56991 | 0.286742 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.20602 | 0.734720 | 0.367360 | − | 0.930079i | \(-0.380262\pi\) | ||||
0.367360 | + | 0.930079i | \(0.380262\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.72777 | 0.454242 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.88564 | 0.463853 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8148 | 1.16038 | 0.580192 | − | 0.814480i | \(-0.302978\pi\) | ||||
0.580192 | + | 0.814480i | \(0.302978\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.04351 | 0.0812369 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.7713 | −1.14304 | −0.571518 | − | 0.820590i | \(-0.693645\pi\) | ||||
−0.571518 | + | 0.820590i | \(0.693645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7713 | −0.982406 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.04351 | 0.385687 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.24953 | −0.171028 | −0.0855142 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855142 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.72777 | −0.357386 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.47825 | −0.633694 | −0.316847 | − | 0.948477i | \(-0.602624\pi\) | ||||
−0.316847 | + | 0.948477i | \(0.602624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.9338 | −1.70466 | −0.852328 | − | 0.523008i | \(-0.824810\pi\) | ||||
−0.852328 | + | 0.523008i | \(0.824810\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.47825 | 0.183197 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.81943 | 0.280810 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | −0.146254 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.00000 | 0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7986 | −0.998434 | −0.499217 | − | 0.866477i | \(-0.666379\pi\) | ||||
−0.499217 | + | 0.866477i | \(0.666379\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.434740 | −0.0312932 | −0.0156466 | − | 0.999878i | \(-0.504981\pi\) | ||||
−0.0156466 | + | 0.999878i | \(0.504981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.249527 | −0.0178690 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.4991 | −1.60299 | −0.801496 | − | 0.598001i | \(-0.795962\pi\) | ||||
−0.801496 | + | 0.598001i | \(0.795962\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.72777 | 0.122479 | 0.0612393 | − | 0.998123i | \(-0.480495\pi\) | ||||
0.0612393 | + | 0.998123i | \(0.480495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.7713 | 0.971351 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.47825 | −0.103753 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.31573 | −0.0918948 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.7713 | −0.818161 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.04351 | 0.348867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.92915 | −0.477022 | −0.238511 | − | 0.971140i | \(-0.576659\pi\) | ||||
−0.238511 | + | 0.971140i | \(0.576659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.7278 | 0.872093 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.48289 | 0.101132 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.84213 | 0.464474 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.478247 | 0.0321703 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.6843 | −1.71995 | −0.859973 | − | 0.510340i | \(-0.829520\pi\) | ||||
−0.859973 | + | 0.510340i | \(0.829520\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.45555 | 0.630370 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.4074 | 1.55360 | 0.776802 | − | 0.629745i | \(-0.216841\pi\) | ||||
0.776802 | + | 0.629745i | \(0.216841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.09166 | 0.600794 | 0.300397 | − | 0.953814i | \(-0.402881\pi\) | ||||
0.300397 | + | 0.953814i | \(0.402881\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.00000 | 0.131590 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.2769 | −0.804285 | −0.402142 | − | 0.915577i | \(-0.631734\pi\) | ||||
−0.402142 | + | 0.915577i | \(0.631734\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.15787 | −0.336462 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.00000 | 0.324785 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.52175 | −0.292488 | −0.146244 | − | 0.989249i | \(-0.546718\pi\) | ||||
−0.146244 | + | 0.989249i | \(0.546718\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.5653 | −1.00265 | −0.501323 | − | 0.865260i | \(-0.667153\pi\) | ||||
−0.501323 | + | 0.865260i | \(0.667153\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.13052 | −0.200002 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.20602 | −0.0767372 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.32038 | −0.210421 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.1625 | 0.830810 | 0.415405 | − | 0.909636i | \(-0.363640\pi\) | ||||
0.415405 | + | 0.909636i | \(0.363640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.7713 | −0.740054 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.521753 | −0.0326735 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.6843 | 1.16549 | 0.582746 | − | 0.812654i | \(-0.301978\pi\) | ||||
0.582746 | + | 0.812654i | \(0.301978\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.32038 | 0.454866 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.95649 | 0.183002 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.521753 | −0.0321727 | −0.0160863 | − | 0.999871i | \(-0.505121\pi\) | ||||
−0.0160863 | + | 0.999871i | \(0.505121\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.98849 | −0.183581 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.84213 | −0.541130 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.1352 | −0.617952 | −0.308976 | − | 0.951070i | \(-0.599986\pi\) | ||||
−0.308976 | + | 0.951070i | \(0.599986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0208 | 0.790958 | 0.395479 | − | 0.918475i | \(-0.370579\pi\) | ||||
0.395479 | + | 0.918475i | \(0.370579\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.478247 | −0.0289448 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.45555 | 0.570191 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.47825 | 0.569493 | 0.284746 | − | 0.958603i | \(-0.408091\pi\) | ||||
0.284746 | + | 0.958603i | \(0.408091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.6843 | −0.819256 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.1833 | −1.62162 | −0.810810 | − | 0.585309i | \(-0.800973\pi\) | ||||
−0.810810 | + | 0.585309i | \(0.800973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.9773 | 1.24697 | 0.623486 | − | 0.781835i | \(-0.285716\pi\) | ||||
0.623486 | + | 0.781835i | \(0.285716\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.31573 | 0.0779373 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.52175 | −0.148854 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.20602 | −0.422424 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.8583 | −1.45224 | −0.726119 | − | 0.687570i | \(-0.758678\pi\) | ||||
−0.726119 | + | 0.687570i | \(0.758678\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.521753 | −0.0303777 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.0000 | −0.580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.81479 | 0.162783 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.84213 | 0.163818 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.592606 | 0.0340444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.29303 | −0.0740389 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.2060 | 1.60980 | 0.804901 | − | 0.593409i | \(-0.202218\pi\) | ||||
0.804901 | + | 0.593409i | \(0.202218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.2930 | 1.09754 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | −0.850572 | −0.425286 | − | 0.905059i | \(-0.639826\pi\) | ||||
−0.425286 | + | 0.905059i | \(0.639826\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.4782 | 0.592266 | 0.296133 | − | 0.955147i | \(-0.404303\pi\) | ||||
0.296133 | + | 0.955147i | \(0.404303\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.04351 | −0.0587950 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.8148 | 0.944413 | 0.472206 | − | 0.881488i | \(-0.343458\pi\) | ||||
0.472206 | + | 0.881488i | \(0.343458\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.95649 | 0.165532 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.04351 | −0.114057 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.52175 | −0.140314 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.26104 | −0.125420 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.7713 | −0.982754 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.88564 | −0.545013 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.5218 | −1.23791 | −0.618954 | − | 0.785427i | \(-0.712443\pi\) | ||||
−0.618954 | + | 0.785427i | \(0.712443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.6408 | −0.802309 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.18521 | −0.392570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.6408 | −0.579639 | −0.289820 | − | 0.957081i | \(-0.593595\pi\) | ||||
−0.289820 | + | 0.957081i | \(0.593595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.2930 | −0.613353 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.6843 | −0.741045 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.07085 | −0.165329 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35.8194 | −1.92289 | −0.961444 | − | 0.275001i | \(-0.911322\pi\) | ||||
−0.961444 | + | 0.275001i | \(0.911322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.40739 | −0.289451 | −0.144726 | − | 0.989472i | \(-0.546230\pi\) | ||||
−0.144726 | + | 0.989472i | \(0.546230\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.39123 | 0.127635 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.27687 | 0.440533 | 0.220267 | − | 0.975440i | \(-0.429307\pi\) | ||||
0.220267 | + | 0.975440i | \(0.429307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.64076 | −0.352455 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.00000 | −0.0529256 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.2495 | −0.804839 | −0.402420 | − | 0.915455i | \(-0.631831\pi\) | ||||
−0.402420 | + | 0.915455i | \(0.631831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.6408 | −0.665303 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.04351 | 0.0546196 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.8194 | 0.825768 | 0.412884 | − | 0.910784i | \(-0.364522\pi\) | ||||
0.412884 | + | 0.910784i | \(0.364522\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.04351 | 0.262554 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.72777 | −0.297371 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.72777 | 0.348351 | 0.174175 | − | 0.984715i | \(-0.444274\pi\) | ||||
0.174175 | + | 0.984715i | \(0.444274\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.07550 | 0.262098 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.706966 | −0.0364106 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0870 | −0.672235 | −0.336117 | − | 0.941820i | \(-0.609114\pi\) | ||||
−0.336117 | + | 0.941820i | \(0.609114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.56526 | −0.387580 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.4991 | 0.843062 | 0.421531 | − | 0.906814i | \(-0.361493\pi\) | ||||
0.421531 | + | 0.906814i | \(0.361493\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.04351 | −0.0531820 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.68427 | −0.288948 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.6843 | −0.795224 | −0.397612 | − | 0.917554i | \(-0.630161\pi\) | ||||
−0.397612 | + | 0.917554i | \(0.630161\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.88564 | 0.297650 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.6843 | 1.09383 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.60877 | −0.131261 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.9773 | 1.75546 | 0.877730 | − | 0.479155i | \(-0.159057\pi\) | ||||
0.877730 | + | 0.479155i | \(0.159057\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.52175 | 0.126246 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2495 | −1.01121 | −0.505607 | − | 0.862764i | \(-0.668731\pi\) | ||||
−0.505607 | + | 0.862764i | \(0.668731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.27223 | 0.163001 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.521753 | 0.0259261 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.6408 | −0.725716 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.2495 | 1.19906 | 0.599531 | − | 0.800352i | \(-0.295354\pi\) | ||||
0.599531 | + | 0.800352i | \(0.295354\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.04351 | −0.298104 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.00000 | −0.0492068 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.73242 | 0.0850411 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.7278 | 0.623282 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.2060 | −1.62222 | −0.811110 | − | 0.584893i | \(-0.801136\pi\) | ||||
−0.811110 | + | 0.584893i | \(0.801136\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.3412 | 1.52748 | 0.763738 | − | 0.645526i | \(-0.223362\pi\) | ||||
0.763738 | + | 0.645526i | \(0.223362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.7713 | 0.961313 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.72777 | −0.229331 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.47825 | −0.119931 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.956493 | 0.0461799 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2287 | 0.589037 | 0.294518 | − | 0.955646i | \(-0.404841\pi\) | ||||
0.294518 | + | 0.955646i | \(0.404841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.6843 | −1.28236 | −0.641182 | − | 0.767389i | \(-0.721556\pi\) | ||||
−0.641182 | + | 0.767389i | \(0.721556\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.771280 | 0.0369801 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.8421 | −0.709996 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.72777 | 0.225644 | 0.112822 | − | 0.993615i | \(-0.464011\pi\) | ||||
0.112822 | + | 0.993615i | \(0.464011\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.7551 | 0.986105 | 0.493053 | − | 0.869999i | \(-0.335881\pi\) | ||||
0.493053 | + | 0.869999i | \(0.335881\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.61341 | 0.218697 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.52175 | 0.261170 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.9773 | −0.659630 | −0.329815 | − | 0.944046i | \(-0.606986\pi\) | ||||
−0.329815 | + | 0.944046i | \(0.606986\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.04351 | 0.237489 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.3639 | 0.768842 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.249527 | 0.0116980 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.81014 | 0.0846748 | 0.0423374 | − | 0.999103i | \(-0.486520\pi\) | ||||
0.0423374 | + | 0.999103i | \(0.486520\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.00000 | 0.233380 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.6843 | 1.66198 | 0.830991 | − | 0.556286i | \(-0.187774\pi\) | ||||
0.830991 | + | 0.556286i | \(0.187774\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0597 | −0.467512 | −0.233756 | − | 0.972295i | \(-0.575102\pi\) | ||||
−0.233756 | + | 0.972295i | \(0.575102\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.56991 | −0.165550 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.04351 | 0.418484 | 0.209242 | − | 0.977864i | \(-0.432900\pi\) | ||||
0.209242 | + | 0.977864i | \(0.432900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.7713 | −0.635899 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.20602 | −0.424191 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.68427 | −0.261363 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.9223 | 0.547032 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.4555 | 0.524513 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.5973 | −1.07819 | −0.539093 | − | 0.842246i | \(-0.681233\pi\) | ||||
−0.539093 | + | 0.842246i | \(0.681233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.50095 | 0.159629 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.88564 | −0.267806 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.75977 | 0.170722 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.2268 | −1.64159 | −0.820797 | − | 0.571220i | \(-0.806470\pi\) | ||||
−0.820797 | + | 0.571220i | \(0.806470\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.8148 | −0.669948 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.07550 | −0.229054 | −0.114527 | − | 0.993420i | \(-0.536535\pi\) | ||||
−0.114527 | + | 0.993420i | \(0.536535\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.47825 | −0.0665769 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.08701 | 0.0938043 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.7278 | −0.570919 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7713 | 0.661253 | 0.330627 | − | 0.943762i | \(-0.392740\pi\) | ||||
0.330627 | + | 0.943762i | \(0.392740\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.7713 | 0.659932 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −43.0046 | −1.91748 | −0.958741 | − | 0.284280i | \(-0.908245\pi\) | ||||
−0.958741 | + | 0.284280i | \(0.908245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.309194 | −0.0137590 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.7713 | 0.567192 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.60877 | 0.248604 | 0.124302 | − | 0.992244i | \(-0.460331\pi\) | ||||
0.124302 | + | 0.992244i | \(0.460331\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.6088 | −0.556691 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.0662 | −0.443570 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.7713 | 0.869540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.24953 | 0.0987433 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.6843 | 0.862383 | 0.431192 | − | 0.902260i | \(-0.358093\pi\) | ||||
0.431192 | + | 0.902260i | \(0.358093\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.0643 | −1.75189 | −0.875945 | − | 0.482411i | \(-0.839761\pi\) | ||||
−0.875945 | + | 0.482411i | \(0.839761\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.72777 | 0.206337 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.84213 | 0.298048 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.6408 | 0.506120 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.00000 | 0.0867926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.20602 | −0.0522385 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.06621 | 0.0460961 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.47825 | 0.365863 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0000 | 0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.0255 | 1.76382 | 0.881911 | − | 0.471416i | \(-0.156257\pi\) | ||||
0.881911 | + | 0.471416i | \(0.156257\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.9338 | 0.984183 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.27223 | 0.397179 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | 0.171028 | 0.0855138 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855138 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.95649 | 0.211538 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.72777 | 0.158808 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | −0.212622 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.81943 | −0.162126 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.8695 | 0.587669 | 0.293834 | − | 0.955856i | \(-0.405069\pi\) | ||||
0.293834 | + | 0.955856i | \(0.405069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.35924 | 0.0574897 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.00000 | 0.0844401 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.6843 | −0.576723 | −0.288362 | − | 0.957522i | \(-0.593110\pi\) | ||||
−0.288362 | + | 0.957522i | \(0.593110\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.89218 | 0.247886 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.8194 | 1.50163 | 0.750814 | − | 0.660513i | \(-0.229661\pi\) | ||||
0.750814 | + | 0.660513i | \(0.229661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.3185 | −1.43618 | −0.718092 | − | 0.695948i | \(-0.754984\pi\) | ||||
−0.718092 | + | 0.695948i | \(0.754984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.7986 | 0.576446 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.8260 | −1.16042 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.0000 | 1.04076 | 0.520382 | − | 0.853934i | \(-0.325790\pi\) | ||||
0.520382 | + | 0.853934i | \(0.325790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.434740 | 0.0180672 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.32038 | 0.137753 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.4555 | 0.474440 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.499054 | −0.0206333 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.7004 | 1.26714 | 0.633571 | − | 0.773684i | \(-0.281588\pi\) | ||||
0.633571 | + | 0.773684i | \(0.281588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.2542 | −0.710946 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.4991 | 0.925487 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.2703 | −1.44838 | −0.724190 | − | 0.689601i | \(-0.757786\pi\) | ||||
−0.724190 | + | 0.689601i | \(0.757786\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.521753 | 0.0213898 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.72777 | −0.0707131 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.9773 | −0.979686 | −0.489843 | − | 0.871811i | \(-0.662946\pi\) | ||||
−0.489843 | + | 0.871811i | \(0.662946\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.6731 | 1.33276 | 0.666381 | − | 0.745611i | \(-0.267842\pi\) | ||||
0.666381 | + | 0.745611i | \(0.267842\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.5426 | 1.12162 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.65227 | −0.148486 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.6296 | 1.56793 | 0.783963 | − | 0.620808i | \(-0.213195\pi\) | ||||
0.783963 | + | 0.620808i | \(0.213195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.47825 | 0.0599016 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.72777 | −0.191265 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.24488 | −0.373397 | −0.186699 | − | 0.982417i | \(-0.559779\pi\) | ||||
−0.186699 | + | 0.982417i | \(0.559779\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.31573 | 0.0530555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.97730 | 0.321154 | 0.160577 | − | 0.987023i | \(-0.448665\pi\) | ||||
0.160577 | + | 0.987023i | \(0.448665\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.8148 | 0.957197 | 0.478599 | − | 0.878034i | \(-0.341145\pi\) | ||||
0.478599 | + | 0.878034i | \(0.341145\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.4282 | 1.18091 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.84213 | 0.354253 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.9907 | 0.839628 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.04351 | −0.201418 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.32038 | 0.291883 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.2268 | 1.00426 | 0.502132 | − | 0.864791i | \(-0.332549\pi\) | ||||
0.502132 | + | 0.864791i | \(0.332549\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.92915 | 0.275409 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.94720 | 0.156640 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.86948 | −0.113693 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.4555 | 1.00701 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.4120 | 1.59618 | 0.798090 | − | 0.602539i | \(-0.205844\pi\) | ||||
0.798090 | + | 0.602539i | \(0.205844\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.0528 | −1.81615 | −0.908073 | − | 0.418813i | \(-0.862446\pi\) | ||||
−0.908073 | + | 0.418813i | \(0.862446\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.48289 | −0.0583888 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.3800 | −1.19436 | −0.597181 | − | 0.802106i | \(-0.703713\pi\) | ||||
−0.597181 | + | 0.802106i | \(0.703713\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.00000 | 0.0785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.84213 | −0.268164 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.69578 | −0.262026 | −0.131013 | − | 0.991381i | \(-0.541823\pi\) | ||||
−0.131013 | + | 0.991381i | \(0.541823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.3138 | −0.442068 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.2657 | 1.14003 | 0.570015 | − | 0.821635i | \(-0.306938\pi\) | ||||
0.570015 | + | 0.821635i | \(0.306938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5973 | 0.412185 | 0.206093 | − | 0.978532i | \(-0.433925\pi\) | ||||
0.206093 | + | 0.978532i | \(0.433925\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.478247 | −0.0185736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.31573 | −0.0510220 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.70043 | −0.336882 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.6843 | 0.993011 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.95649 | 0.191343 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.1560 | 1.54790 | 0.773950 | − | 0.633247i | \(-0.218278\pi\) | ||||
0.773950 | + | 0.633247i | \(0.218278\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.6389 | −0.909860 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.4991 | −1.47964 | −0.739819 | − | 0.672805i | \(-0.765089\pi\) | ||||
−0.739819 | + | 0.672805i | \(0.765089\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.20602 | 0.276542 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.4074 | −0.896973 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.6616 | 0.790593 | 0.395296 | − | 0.918554i | \(-0.370642\pi\) | ||||
0.395296 | + | 0.918554i | \(0.370642\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.15322 | 0.120478 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.09166 | −0.346868 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.73929 | −0.104359 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.2542 | −0.960714 | −0.480357 | − | 0.877073i | \(-0.659493\pi\) | ||||
−0.480357 | + | 0.877073i | \(0.659493\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000 | 0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.64076 | −0.251898 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.52175 | −0.0955182 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.2769 | 0.464354 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.2977 | 1.37094 | 0.685472 | − | 0.728099i | \(-0.259596\pi\) | ||||
0.685472 | + | 0.728099i | \(0.259596\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.4602 | −0.696239 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.15787 | 0.194257 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.592606 | −0.0222873 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.7505 | 0.553966 | 0.276983 | − | 0.960875i | \(-0.410665\pi\) | ||||
0.276983 | + | 0.960875i | \(0.410665\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.2703 | 1.50814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.499054 | −0.0186635 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.52175 | 0.168868 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.73929 | 0.176746 | 0.0883728 | − | 0.996087i | \(-0.471833\pi\) | ||||
0.0883728 | + | 0.996087i | \(0.471833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.2930 | −0.718510 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.5653 | 0.578878 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.98881 | 0.259558 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.4991 | 0.760268 | 0.380134 | − | 0.924931i | \(-0.375878\pi\) | ||||
0.380134 | + | 0.924931i | \(0.375878\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.84213 | 0.105120 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.1833 | −1.48420 | −0.742102 | − | 0.670287i | \(-0.766171\pi\) | ||||
−0.742102 | + | 0.670287i | \(0.766171\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.13052 | 0.115471 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.5426 | 1.01454 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.8791 | 1.24626 | 0.623131 | − | 0.782117i | \(-0.285860\pi\) | ||||
0.623131 | + | 0.782117i | \(0.285860\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.20602 | 0.0443042 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.36853 | 0.123579 | 0.0617897 | − | 0.998089i | \(-0.480319\pi\) | ||||
0.0617897 | + | 0.998089i | \(0.480319\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.88099 | −0.105551 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.64076 | −0.242973 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.04351 | 0.0746681 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.6843 | −1.44810 | −0.724050 | − | 0.689748i | \(-0.757721\pi\) | ||||
−0.724050 | + | 0.689748i | \(0.757721\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.1625 | −0.479669 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.53791 | −0.310727 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.8148 | −1.66517 | −0.832583 | − | 0.553900i | \(-0.813139\pi\) | ||||
−0.832583 | + | 0.553900i | \(0.813139\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.7713 | 0.427270 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.2268 | 0.950722 | 0.475361 | − | 0.879791i | \(-0.342318\pi\) | ||||
0.475361 | + | 0.879791i | \(0.342318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.7713 | 0.643364 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.04351 | −0.0377281 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.478247 | −0.0172685 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.52175 | 0.343363 | 0.171682 | − | 0.985152i | \(-0.445080\pi\) | ||||
0.171682 | + | 0.985152i | \(0.445080\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.6843 | −0.672897 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.5907 | 0.920434 | 0.460217 | − | 0.887806i | \(-0.347772\pi\) | ||||
0.460217 | + | 0.887806i | \(0.347772\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.3481 | −1.16198 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.32038 | −0.262617 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.35924 | 0.227843 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.4555 | 0.910871 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.39123 | −0.264141 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.80327 | 0.171436 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.49905 | 0.160374 | 0.0801870 | − | 0.996780i | \(-0.474448\pi\) | ||||
0.0801870 | + | 0.996780i | \(0.474448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.521753 | 0.0185749 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.2930 | 0.401534 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.18521 | −0.0420881 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.98849 | 0.105991 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.0755 | −0.356892 | −0.178446 | − | 0.983950i | \(-0.557107\pi\) | ||||
−0.178446 | + | 0.983950i | \(0.557107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.88564 | −0.349729 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.6843 | −0.624843 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.00000 | −0.141157 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.07085 | 0.108233 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.1352 | 0.356775 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.8629 | 1.22572 | 0.612858 | − | 0.790193i | \(-0.290020\pi\) | ||||
0.612858 | + | 0.790193i | \(0.290020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.6889 | 0.937174 | 0.468587 | − | 0.883417i | \(-0.344763\pi\) | ||||
0.468587 | + | 0.883417i | \(0.344763\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.0208 | −0.456660 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.72967 | 0.270758 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.16716 | −0.250747 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.956493 | −0.0334226 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0482 | −0.350683 | −0.175341 | − | 0.984508i | \(-0.556103\pi\) | ||||
−0.175341 | + | 0.984508i | \(0.556103\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.2060 | 1.36664 | 0.683318 | − | 0.730121i | \(-0.260536\pi\) | ||||
0.683318 | + | 0.730121i | \(0.260536\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.45555 | −0.329200 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.8148 | −0.793348 | −0.396674 | − | 0.917960i | \(-0.629836\pi\) | ||||
−0.396674 | + | 0.917960i | \(0.629836\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0963 | −0.802168 | −0.401084 | − | 0.916041i | \(-0.631366\pi\) | ||||
−0.401084 | + | 0.916041i | \(0.631366\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.47825 | −0.328797 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.00000 | −0.207888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.70697 | −0.266711 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.2107 | 1.18249 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.5491 | −0.467767 | −0.233883 | − | 0.972265i | \(-0.575143\pi\) | ||||
−0.233883 | + | 0.972265i | \(0.575143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8148 | −0.924648 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.1833 | 0.936243 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.66346 | −0.229230 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | −0.240523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.9773 | −0.719939 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.0851 | 1.47694 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.0320 | 0.822840 | 0.411420 | − | 0.911446i | \(-0.365033\pi\) | ||||
0.411420 | + | 0.911446i | \(0.365033\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.63147 | 0.0899943 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.5699 | 1.14673 | 0.573363 | − | 0.819301i | \(-0.305638\pi\) | ||||
0.573363 | + | 0.819301i | \(0.305638\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.4717 | 1.10792 | 0.553960 | − | 0.832543i | \(-0.313116\pi\) | ||||
0.553960 | + | 0.832543i | \(0.313116\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.52175 | 0.0859411 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.50095 | 0.0510928 | 0.0255464 | − | 0.999674i | \(-0.491867\pi\) | ||||
0.0255464 | + | 0.999674i | \(0.491867\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.17370 | −0.0399069 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0000 | 0.339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.58607 | −0.223160 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.4120 | −0.487774 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.07550 | −0.171583 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.61995 | 0.0547019 | 0.0273510 | − | 0.999626i | \(-0.491293\pi\) | ||||
0.0273510 | + | 0.999626i | \(0.491293\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.8583 | 0.838449 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.2657 | −1.05337 | −0.526684 | − | 0.850061i | \(-0.676565\pi\) | ||||
−0.526684 | + | 0.850061i | \(0.676565\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.6616 | 0.459748 | 0.229874 | − | 0.973220i | \(-0.426169\pi\) | ||||
0.229874 | + | 0.973220i | \(0.426169\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.521753 | 0.0175386 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.90180 | −0.231740 | −0.115870 | − | 0.993264i | \(-0.536966\pi\) | ||||
−0.115870 | + | 0.993264i | \(0.536966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.56526 | 0.253731 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.9291 | 0.834222 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.42355 | −0.147863 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.81479 | −0.0939830 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.1144 | −0.337333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.72777 | −0.190820 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.84213 | −0.0945803 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.9658 | −0.397756 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.9130 | 0.827222 | 0.413611 | − | 0.910454i | \(-0.364267\pi\) | ||||
0.413611 | + | 0.910454i | \(0.364267\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.18521 | 0.0393110 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.4444 | 1.37311 | 0.686556 | − | 0.727076i | \(-0.259121\pi\) | ||||
0.686556 | + | 0.727076i | \(0.259121\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.64076 | −0.219777 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.29303 | 0.0427464 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.6843 | −0.716078 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.180567 | 0.00595634 | 0.00297817 | − | 0.999996i | \(-0.499052\pi\) | ||||
0.00297817 | + | 0.999996i | \(0.499052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.2060 | −0.929420 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.08701 | −0.200356 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.6091 | −1.13794 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.5861 | 1.26733 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.3592 | −0.503920 | −0.251960 | − | 0.967738i | \(-0.581075\pi\) | ||||
−0.251960 | + | 0.967738i | \(0.581075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.1305 | 0.495883 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.0000 | 0.491078 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.04351 | −0.0341263 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.26104 | 0.0738650 | 0.0369325 | − | 0.999318i | \(-0.488241\pi\) | ||||
0.0369325 | + | 0.999318i | \(0.488241\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.4782 | −0.341945 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.5310 | −0.832288 | −0.416144 | − | 0.909299i | \(-0.636619\pi\) | ||||
−0.416144 | + | 0.909299i | \(0.636619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.8421 | −0.483326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.60877 | 0.0848632 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.1305 | −0.329198 | −0.164599 | − | 0.986361i | \(-0.552633\pi\) | ||||
−0.164599 | + | 0.986361i | \(0.552633\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.956493 | 0.0310491 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.8148 | −0.545257 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.2268 | −1.78897 | −0.894486 | − | 0.447096i | \(-0.852458\pi\) | ||||
−0.894486 | + | 0.447096i | \(0.852458\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.19948 | −0.232970 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.95649 | −0.0955698 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.04351 | 0.195155 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.8148 | 0.510154 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.08701 | −0.131702 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.226827 | −0.00730182 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.1787 | 1.06695 | 0.533477 | − | 0.845815i | \(-0.320885\pi\) | ||||
0.533477 | + | 0.845815i | \(0.320885\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.52175 | 0.0810104 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.97730 | −0.191821 | −0.0959103 | − | 0.995390i | \(-0.530576\pi\) | ||||
−0.0959103 | + | 0.995390i | \(0.530576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7278 | −0.408034 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.26104 | 0.0724113 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.7874 | −1.43288 | −0.716439 | − | 0.697650i | \(-0.754229\pi\) | ||||
−0.716439 | + | 0.697650i | \(0.754229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.6843 | −0.565192 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −35.5426 | −1.13479 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.9018 | 0.602874 | 0.301437 | − | 0.953486i | \(-0.402534\pi\) | ||||
0.301437 | + | 0.953486i | \(0.402534\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.7390 | −0.374034 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.88564 | 0.314663 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.7278 | 0.531912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4509 | 0.840241 | 0.420120 | − | 0.907468i | \(-0.361988\pi\) | ||||
0.420120 | + | 0.907468i | \(0.361988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.5218 | 0.714706 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.901472 | 0.0285786 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.21721 | −0.101890 | −0.0509450 | − | 0.998701i | \(-0.516223\pi\) | ||||
−0.0509450 | + | 0.998701i | \(0.516223\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.6019 | 1.15803 |
(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 | 4012.2.a.f.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.f.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |