Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8624,2,Mod(1,8624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8624.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8624 = 2^{4} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8624.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: | \(68.8629867032\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 34x^{10} + 421x^{8} - 2246x^{6} + 4540x^{4} - 1832x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 4312) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.690446\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8624.1 |
$q$-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 | ||||||||
\(3\) | 0.690446 | 0.398629 | 0.199315 | − | 0.979936i | \(-0.436128\pi\) | ||||
0.199315 | + | 0.979936i | \(0.436128\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.23978 | 1.44887 | 0.724437 | − | 0.689341i | \(-0.242100\pi\) | ||||
0.724437 | + | 0.689341i | \(0.242100\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.52328 | −0.841095 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.83733 | 1.34163 | 0.670817 | − | 0.741623i | \(-0.265944\pi\) | ||||
0.670817 | + | 0.741623i | \(0.265944\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23689 | 0.577564 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.46034 | 1.80940 | 0.904700 | − | 0.426050i | \(-0.140095\pi\) | ||||
0.904700 | + | 0.426050i | \(0.140095\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.88978 | −1.35121 | −0.675604 | − | 0.737265i | \(-0.736117\pi\) | ||||
−0.675604 | + | 0.737265i | \(0.736117\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.20082 | −0.250388 | −0.125194 | − | 0.992132i | \(-0.539955\pi\) | ||||
−0.125194 | + | 0.992132i | \(0.539955\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.49617 | 1.09923 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.81353 | −0.733914 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.24823 | 0.974571 | 0.487286 | − | 0.873243i | \(-0.337987\pi\) | ||||
0.487286 | + | 0.873243i | \(0.337987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.40865 | 1.68984 | 0.844922 | − | 0.534890i | \(-0.179647\pi\) | ||||
0.844922 | + | 0.534890i | \(0.179647\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.690446 | 0.120191 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.03079 | −1.15585 | −0.577927 | − | 0.816088i | \(-0.696138\pi\) | ||||
−0.577927 | + | 0.816088i | \(0.696138\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.33992 | 0.534815 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.05245 | −0.164365 | −0.0821825 | − | 0.996617i | \(-0.526189\pi\) | ||||
−0.0821825 | + | 0.996617i | \(0.526189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.24823 | −0.495350 | −0.247675 | − | 0.968843i | \(-0.579667\pi\) | ||||
−0.247675 | + | 0.968843i | \(0.579667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.17488 | −1.21864 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.87456 | 1.29449 | 0.647244 | − | 0.762283i | \(-0.275922\pi\) | ||||
0.647244 | + | 0.762283i | \(0.275922\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.15097 | 0.721280 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.25517 | −0.721853 | −0.360926 | − | 0.932594i | \(-0.617539\pi\) | ||||
−0.360926 | + | 0.932594i | \(0.617539\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.23978 | 0.436852 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.06658 | −0.538631 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.5428 | 1.89331 | 0.946654 | − | 0.322253i | \(-0.104440\pi\) | ||||
0.946654 | + | 0.322253i | \(0.104440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.7070 | 1.75500 | 0.877499 | − | 0.479578i | \(-0.159210\pi\) | ||||
0.877499 | + | 0.479578i | \(0.159210\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.6719 | 1.94386 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0738 | −1.71939 | −0.859694 | − | 0.510809i | \(-0.829346\pi\) | ||||
−0.859694 | + | 0.510809i | \(0.829346\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.829102 | −0.0998121 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.98456 | −0.947593 | −0.473796 | − | 0.880634i | \(-0.657117\pi\) | ||||
−0.473796 | + | 0.880634i | \(0.657117\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.45687 | −0.989802 | −0.494901 | − | 0.868949i | \(-0.664796\pi\) | ||||
−0.494901 | + | 0.868949i | \(0.664796\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.79481 | 0.438187 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.57819 | 0.290069 | 0.145034 | − | 0.989427i | \(-0.453671\pi\) | ||||
0.145034 | + | 0.989427i | \(0.453671\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.93681 | 0.548535 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.33731 | −0.805375 | −0.402687 | − | 0.915338i | \(-0.631924\pi\) | ||||
−0.402687 | + | 0.915338i | \(0.631924\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.1699 | 2.62159 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.62362 | 0.388493 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.55929 | 0.695283 | 0.347642 | − | 0.937627i | \(-0.386983\pi\) | ||||
0.347642 | + | 0.937627i | \(0.386983\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.49617 | 0.673621 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.0816 | −1.95773 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.20247 | 0.122092 | 0.0610459 | − | 0.998135i | \(-0.480556\pi\) | ||||
0.0610459 | + | 0.998135i | \(0.480556\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.52328 | −0.253600 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3501 | 1.32839 | 0.664193 | − | 0.747561i | \(-0.268775\pi\) | ||||
0.664193 | + | 0.747561i | \(0.268775\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.90500 | 0.286238 | 0.143119 | − | 0.989705i | \(-0.454287\pi\) | ||||
0.143119 | + | 0.989705i | \(0.454287\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.76429 | −0.460581 | −0.230290 | − | 0.973122i | \(-0.573968\pi\) | ||||
−0.230290 | + | 0.973122i | \(0.573968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.74167 | −0.933082 | −0.466541 | − | 0.884499i | \(-0.654500\pi\) | ||||
−0.466541 | + | 0.884499i | \(0.654500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.85438 | −0.460758 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.5242 | −1.08411 | −0.542054 | − | 0.840344i | \(-0.682353\pi\) | ||||
−0.542054 | + | 0.840344i | \(0.682353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.89039 | −0.362781 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.2060 | −1.12844 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.726660 | −0.0655208 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.60748 | 0.143778 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6394 | 1.29903 | 0.649516 | − | 0.760348i | \(-0.274971\pi\) | ||||
0.649516 | + | 0.760348i | \(0.274971\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.24273 | −0.197461 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.223108 | 0.0194930 | 0.00974652 | − | 0.999953i | \(-0.496898\pi\) | ||||
0.00974652 | + | 0.999953i | \(0.496898\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.3550 | −1.06335 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0856 | 1.03254 | 0.516270 | − | 0.856426i | \(-0.327320\pi\) | ||||
0.516270 | + | 0.856426i | \(0.327320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0594 | −1.70142 | −0.850709 | − | 0.525637i | \(-0.823827\pi\) | ||||
−0.850709 | + | 0.525637i | \(0.823827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.12741 | 0.516021 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.83733 | 0.404518 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.0031 | 1.41203 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.4186 | 1.34507 | 0.672534 | − | 0.740066i | \(-0.265206\pi\) | ||||
0.672534 | + | 0.740066i | \(0.265206\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.6674 | 1.35638 | 0.678188 | − | 0.734888i | \(-0.262765\pi\) | ||||
0.678188 | + | 0.734888i | \(0.262765\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.8246 | −1.52188 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.4820 | 2.44837 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.80954 | −0.144417 | −0.0722084 | − | 0.997390i | \(-0.523005\pi\) | ||||
−0.0722084 | + | 0.997390i | \(0.523005\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.62841 | −0.287752 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.0045 | −1.41022 | −0.705110 | − | 0.709097i | \(-0.749103\pi\) | ||||
−0.705110 | + | 0.709097i | \(0.749103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.23689 | 0.174142 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.30347 | 0.333013 | 0.166506 | − | 0.986040i | \(-0.446751\pi\) | ||||
0.166506 | + | 0.986040i | \(0.446751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3997 | 0.799981 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.8616 | 1.13649 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.33235 | 0.329382 | 0.164691 | − | 0.986345i | \(-0.447337\pi\) | ||||
0.164691 | + | 0.986345i | \(0.447337\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0410 | 0.754728 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0031 | 1.27087 | 0.635436 | − | 0.772153i | \(-0.280820\pi\) | ||||
0.635436 | + | 0.772153i | \(0.280820\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.67922 | 0.422133 | 0.211066 | − | 0.977472i | \(-0.432306\pi\) | ||||
0.211066 | + | 0.977472i | \(0.432306\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.46393 | 0.699594 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.7782 | −1.67469 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.46034 | 0.545554 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.63159 | −0.335130 | −0.167565 | − | 0.985861i | \(-0.553590\pi\) | ||||
−0.167565 | + | 0.985861i | \(0.553590\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.75627 | −0.486327 | −0.243163 | − | 0.969985i | \(-0.578185\pi\) | ||||
−0.243163 | + | 0.969985i | \(0.578185\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.8206 | 0.774879 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.61781 | 0.685241 | 0.342620 | − | 0.939474i | \(-0.388686\pi\) | ||||
0.342620 | + | 0.939474i | \(0.388686\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7625 | −1.18826 | −0.594132 | − | 0.804368i | \(-0.702504\pi\) | ||||
−0.594132 | + | 0.804368i | \(0.702504\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.71721 | −0.685399 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.40971 | −0.238144 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.03001 | 0.210600 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.88978 | −0.407405 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.4381 | −1.40702 | −0.703508 | − | 0.710687i | \(-0.748384\pi\) | ||||
−0.703508 | + | 0.710687i | \(0.748384\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.51291 | −0.377738 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.5235 | −0.717699 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.83901 | −0.394564 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.0881 | 2.42755 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.24162 | −0.217075 | −0.108538 | − | 0.994092i | \(-0.534617\pi\) | ||||
−0.108538 | + | 0.994092i | \(0.534617\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.8684 | −0.924560 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.0439 | 1.19761 | 0.598807 | − | 0.800893i | \(-0.295641\pi\) | ||||
0.598807 | + | 0.800893i | \(0.295641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.1649 | 1.86119 | 0.930596 | − | 0.366048i | \(-0.119289\pi\) | ||||
0.930596 | + | 0.366048i | \(0.119289\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.6280 | 1.02382 | 0.511911 | − | 0.859038i | \(-0.328938\pi\) | ||||
0.511911 | + | 0.859038i | \(0.328938\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.7516 | 1.87555 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.78010 | 0.115630 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.1835 | −0.658715 | −0.329358 | − | 0.944205i | \(-0.606832\pi\) | ||||
−0.329358 | + | 0.944205i | \(0.606832\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.2225 | −1.88238 | −0.941192 | − | 0.337871i | \(-0.890293\pi\) | ||||
−0.941192 | + | 0.337871i | \(0.890293\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8492 | 0.952577 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.4908 | −1.81283 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.06602 | −0.321046 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9766 | 1.51339 | 0.756694 | − | 0.653770i | \(-0.226813\pi\) | ||||
0.756694 | + | 0.653770i | \(0.226813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.20082 | −0.0754949 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.6880 | 1.04504 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.89151 | 0.367502 | 0.183751 | − | 0.982973i | \(-0.441176\pi\) | ||||
0.183751 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.2428 | −0.819707 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.83597 | −0.236536 | −0.118268 | − | 0.992982i | \(-0.537734\pi\) | ||||
−0.118268 | + | 0.992982i | \(0.537734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.0256 | −1.04587 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.52884 | 0.277160 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.5879 | 0.950414 | 0.475207 | − | 0.879874i | \(-0.342373\pi\) | ||||
0.475207 | + | 0.879874i | \(0.342373\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.37965 | −0.569773 | −0.284887 | − | 0.958561i | \(-0.591956\pi\) | ||||
−0.284887 | + | 0.958561i | \(0.591956\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.49617 | 0.331432 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.9145 | 1.13646 | 0.568232 | − | 0.822868i | \(-0.307628\pi\) | ||||
0.568232 | + | 0.822868i | \(0.307628\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.7407 | −1.42132 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.22633 | −0.550397 | −0.275198 | − | 0.961387i | \(-0.588744\pi\) | ||||
−0.275198 | + | 0.961387i | \(0.588744\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5558 | 0.746367 | 0.373183 | − | 0.927758i | \(-0.378266\pi\) | ||||
0.373183 | + | 0.927758i | \(0.378266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.1748 | −0.780408 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.6567 | 2.27392 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.830238 | 0.0486694 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.81103 | −0.105801 | −0.0529007 | − | 0.998600i | \(-0.516847\pi\) | ||||
−0.0529007 | + | 0.998600i | \(0.516847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 47.1154 | 2.74316 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.81353 | −0.221284 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.80876 | −0.335929 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.21754 | 0.529534 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 44.4076 | 2.54277 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.0084 | −0.799501 | −0.399750 | − | 0.916624i | \(-0.630903\pi\) | ||||
−0.399750 | + | 0.916624i | \(0.630903\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.00575 | 0.114103 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.96620 | −0.395017 | −0.197508 | − | 0.980301i | \(-0.563285\pi\) | ||||
−0.197508 | + | 0.980301i | \(0.563285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0080 | −0.791781 | −0.395890 | − | 0.918298i | \(-0.629564\pi\) | ||||
−0.395890 | + | 0.918298i | \(0.629564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.7650 | −1.67177 | −0.835883 | − | 0.548907i | \(-0.815044\pi\) | ||||
−0.835883 | + | 0.548907i | \(0.815044\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.24823 | 0.293844 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.28948 | −0.183601 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −43.9398 | −2.44487 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.5868 | 1.47477 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.72610 | −0.371954 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.22740 | 0.342289 | 0.171144 | − | 0.985246i | \(-0.445254\pi\) | ||||
0.171144 | + | 0.985246i | \(0.445254\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.7407 | 0.972183 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −45.5960 | −2.49118 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.205750 | 0.0112079 | 0.00560395 | − | 0.999984i | \(-0.498216\pi\) | ||||
0.00560395 | + | 0.999984i | \(0.498216\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.95686 | −0.432157 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.40865 | 0.509507 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.68611 | −0.144615 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.4883 | −1.31460 | −0.657300 | − | 0.753629i | \(-0.728301\pi\) | ||||
−0.657300 | + | 0.753629i | \(0.728301\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.13736 | 0.274997 | 0.137498 | − | 0.990502i | \(-0.456094\pi\) | ||||
0.137498 | + | 0.990502i | \(0.456094\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.4473 | −0.984644 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.49784 | 0.345845 | 0.172923 | − | 0.984935i | \(-0.444679\pi\) | ||||
0.172923 | + | 0.984935i | \(0.444679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.8682 | −1.37294 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.1704 | 1.01178 | 0.505888 | − | 0.862599i | \(-0.331165\pi\) | ||||
0.505888 | + | 0.862599i | \(0.331165\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.6895 | 0.825763 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.690446 | 0.0362390 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.3984 | −1.43410 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.2232 | 0.846846 | 0.423423 | − | 0.905932i | \(-0.360828\pi\) | ||||
0.423423 | + | 0.905932i | \(0.360828\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.65563 | 0.138247 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.2301 | −1.40992 | −0.704959 | − | 0.709248i | \(-0.749035\pi\) | ||||
−0.704959 | + | 0.709248i | \(0.749035\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.10988 | 0.0573139 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.3874 | 1.30752 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.3000 | 1.60777 | 0.803886 | − | 0.594784i | \(-0.202762\pi\) | ||||
0.803886 | + | 0.594784i | \(0.202762\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.1077 | 0.517833 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.3001 | 0.832896 | 0.416448 | − | 0.909160i | \(-0.363275\pi\) | ||||
0.416448 | + | 0.909160i | \(0.363275\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.19620 | 0.416636 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.934263 | 0.0473690 | 0.0236845 | − | 0.999719i | \(-0.492460\pi\) | ||||
0.0236845 | + | 0.999719i | \(0.492460\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.95853 | −0.453052 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.154044 | 0.00777050 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.35276 | 0.420273 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5452 | −0.629627 | −0.314813 | − | 0.949154i | \(-0.601942\pi\) | ||||
−0.314813 | + | 0.949154i | \(0.601942\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.75162 | −0.387098 | −0.193549 | − | 0.981091i | \(-0.562000\pi\) | ||||
−0.193549 | + | 0.981091i | \(0.562000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45.5127 | 2.26715 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.9942 | 0.794757 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.03079 | −0.348503 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.96185 | −0.443135 | −0.221567 | − | 0.975145i | \(-0.571117\pi\) | ||||
−0.221567 | + | 0.975145i | \(0.571117\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.34444 | 0.411601 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.7713 | −1.16689 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.8500 | −0.678235 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.83951 | −0.431838 | −0.215919 | − | 0.976411i | \(-0.569275\pi\) | ||||
−0.215919 | + | 0.976411i | \(0.569275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8380 | 1.01558 | 0.507790 | − | 0.861481i | \(-0.330463\pi\) | ||||
0.507790 | + | 0.861481i | \(0.330463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.3930 | −1.08879 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 41.0033 | 1.98895 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.33992 | 0.161253 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.13151 | 0.150840 | 0.0754198 | − | 0.997152i | \(-0.475970\pi\) | ||||
0.0754198 | + | 0.997152i | \(0.475970\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1331 | −0.583082 | −0.291541 | − | 0.956558i | \(-0.594168\pi\) | ||||
−0.291541 | + | 0.956558i | \(0.594168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.7397 | 0.562877 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.07256 | 0.338327 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.34989 | −0.303064 | −0.151532 | − | 0.988452i | \(-0.548421\pi\) | ||||
−0.151532 | + | 0.988452i | \(0.548421\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.1521 | −0.672389 | −0.336194 | − | 0.941793i | \(-0.609140\pi\) | ||||
−0.336194 | + | 0.941793i | \(0.609140\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.2506 | 1.00738 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.3362 | 0.536184 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.4313 | 1.05860 | 0.529299 | − | 0.848435i | \(-0.322455\pi\) | ||||
0.529299 | + | 0.848435i | \(0.322455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.05245 | −0.0495579 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.5080 | 0.540691 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.2993 | 1.13667 | 0.568336 | − | 0.822796i | \(-0.307587\pi\) | ||||
0.568336 | + | 0.822796i | \(0.307587\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28.4503 | −1.32794 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.0811 | −1.86676 | −0.933381 | − | 0.358887i | \(-0.883156\pi\) | ||||
−0.933381 | + | 0.358887i | \(0.883156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1554 | −1.16907 | −0.584535 | − | 0.811369i | \(-0.698723\pi\) | ||||
−0.584535 | + | 0.811369i | \(0.698723\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.0462 | 0.975992 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.7091 | 0.912028 | 0.456014 | − | 0.889973i | \(-0.349277\pi\) | ||||
0.456014 | + | 0.889973i | \(0.349277\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.24939 | −0.0575688 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.24823 | −0.149354 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.3712 | −1.48529 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.2603 | 0.607147 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.4428 | 0.477145 | 0.238572 | − | 0.971125i | \(-0.423321\pi\) | ||||
0.238572 | + | 0.971125i | \(0.423321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.0102 | −1.55073 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.89572 | 0.176896 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.9371 | 1.13001 | 0.565003 | − | 0.825089i | \(-0.308875\pi\) | ||||
0.565003 | + | 0.825089i | \(0.308875\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.4311 | −0.562156 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.5461 | −0.521067 | −0.260533 | − | 0.965465i | \(-0.583898\pi\) | ||||
−0.260533 | + | 0.965465i | \(0.583898\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.1536 | 1.76339 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.17488 | −0.367434 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.25144 | 0.414151 | 0.207076 | − | 0.978325i | \(-0.433605\pi\) | ||||
0.207076 | + | 0.978325i | \(0.433605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.97132 | 0.132749 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.392850 | −0.0175163 | −0.00875815 | − | 0.999962i | \(-0.502788\pi\) | ||||
−0.00875815 | + | 0.999962i | \(0.502788\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.2514 | 1.92466 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.18047 | 0.318896 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.2792 | −0.721564 | −0.360782 | − | 0.932650i | \(-0.617490\pi\) | ||||
−0.360782 | + | 0.932650i | \(0.617490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.4609 | 0.991671 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.41156 | 0.414723 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.87456 | 0.390303 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.99126 | 0.131302 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.19158 | −0.402690 | −0.201345 | − | 0.979520i | \(-0.564531\pi\) | ||||
−0.201345 | + | 0.979520i | \(0.564531\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.9443 | −1.57174 | −0.785868 | − | 0.618394i | \(-0.787783\pi\) | ||||
−0.785868 | + | 0.618394i | \(0.787783\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 70.1918 | 3.05760 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5580 | −0.937306 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.6955 | −1.59245 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.09105 | −0.220518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.4352 | −0.667323 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.7397 | 0.506607 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0737 | −0.433101 | −0.216551 | − | 0.976271i | \(-0.569481\pi\) | ||||
−0.216551 | + | 0.976271i | \(0.569481\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.92120 | 0.168275 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −31.5609 | −1.35192 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.98320 | −0.298580 | −0.149290 | − | 0.988793i | \(-0.547699\pi\) | ||||
−0.149290 | + | 0.988793i | \(0.547699\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −34.5866 | −1.47612 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.9109 | −1.31685 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.7271 | −0.667579 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.13637 | −0.0905207 | −0.0452604 | − | 0.998975i | \(-0.514412\pi\) | ||||
−0.0452604 | + | 0.998975i | \(0.514412\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.7127 | −0.664578 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.15097 | 0.217474 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.8092 | −0.666277 | −0.333138 | − | 0.942878i | \(-0.608108\pi\) | ||||
−0.333138 | + | 0.942878i | \(0.608108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.3360 | −1.57074 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.0199 | −0.755432 | −0.377716 | − | 0.925922i | \(-0.623290\pi\) | ||||
−0.377716 | + | 0.925922i | \(0.623290\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.11815 | 0.381583 | 0.190791 | − | 0.981631i | \(-0.438895\pi\) | ||||
0.190791 | + | 0.981631i | \(0.438895\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.19787 | −0.133593 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.59991 | −0.275235 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.51169 | −0.104563 | −0.0522816 | − | 0.998632i | \(-0.516649\pi\) | ||||
−0.0522816 | + | 0.998632i | \(0.516649\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.66484 | −0.193864 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.25517 | −0.217647 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −39.5446 | −1.63497 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.79430 | 0.362980 | 0.181490 | − | 0.983393i | \(-0.441908\pi\) | ||||
0.181490 | + | 0.983393i | \(0.441908\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −55.4149 | −2.28333 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.64058 | 0.273157 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.1082 | −1.11320 | −0.556601 | − | 0.830780i | \(-0.687895\pi\) | ||||
−0.556601 | + | 0.830780i | \(0.687895\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.5736 | −0.473677 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.4506 | −1.57105 | −0.785525 | − | 0.618830i | \(-0.787607\pi\) | ||||
−0.785525 | + | 0.618830i | \(0.787607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.13995 | −0.332035 | −0.166018 | − | 0.986123i | \(-0.553091\pi\) | ||||
−0.166018 | + | 0.986123i | \(0.553091\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35.5122 | 1.44617 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.23978 | 0.131716 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.8138 | −0.438917 | −0.219458 | − | 0.975622i | \(-0.570429\pi\) | ||||
−0.219458 | + | 0.975622i | \(0.570429\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.9291 | 1.73673 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.8676 | −1.40829 | −0.704144 | − | 0.710057i | \(-0.748669\pi\) | ||||
−0.704144 | + | 0.710057i | \(0.748669\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.35422 | −0.0949313 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.9755 | −0.562631 | −0.281315 | − | 0.959615i | \(-0.590771\pi\) | ||||
−0.281315 | + | 0.959615i | \(0.590771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.7624 | −1.35703 | −0.678513 | − | 0.734588i | \(-0.737375\pi\) | ||||
−0.678513 | + | 0.734588i | \(0.737375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.57936 | 0.183764 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.2730 | −0.890919 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.06658 | −0.162403 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.4521 | −2.09140 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.5141 | −0.458370 | −0.229185 | − | 0.973383i | \(-0.573606\pi\) | ||||
−0.229185 | + | 0.973383i | \(0.573606\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.1114 | −0.560878 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 47.4283 | 1.88213 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.1473 | 0.797015 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.0001 | 1.30343 | 0.651713 | − | 0.758466i | \(-0.274051\pi\) | ||||
0.651713 | + | 0.758466i | \(0.274051\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.8502 | 0.861689 | 0.430844 | − | 0.902426i | \(-0.358216\pi\) | ||||
0.430844 | + | 0.902426i | \(0.358216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.26594 | −0.286096 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.0568 | 1.49617 | 0.748083 | − | 0.663605i | \(-0.230974\pi\) | ||||
0.748083 | + | 0.663605i | \(0.230974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.5428 | 0.570854 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.71234 | 0.380073 | 0.190037 | − | 0.981777i | \(-0.439139\pi\) | ||||
0.190037 | + | 0.981777i | \(0.439139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.722821 | 0.0282430 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.3391 | 0.832517 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.0625 | −0.664660 | −0.332330 | − | 0.943163i | \(-0.607835\pi\) | ||||
−0.332330 | + | 0.943163i | \(0.607835\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6190 | 0.529717 | 0.264859 | − | 0.964287i | \(-0.414675\pi\) | ||||
0.264859 | + | 0.964287i | \(0.414675\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.9169 | 0.967693 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.30218 | −0.244021 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.23817 | −0.0865326 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.7070 | 0.529152 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.8358 | 1.41992 | 0.709958 | − | 0.704244i | \(-0.248714\pi\) | ||||
0.709958 | + | 0.704244i | \(0.248714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.9598 | −0.806744 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.803164 | −0.0308681 | −0.0154340 | − | 0.999881i | \(-0.504913\pi\) | ||||
−0.0154340 | + | 0.999881i | \(0.504913\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.4583 | 0.477405 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.6356 | 0.904391 | 0.452195 | − | 0.891919i | \(-0.350641\pi\) | ||||
0.452195 | + | 0.891919i | \(0.350641\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.1546 | 1.49602 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.4464 | 0.741926 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.4210 | −0.968462 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.71270 | −0.331447 | −0.165723 | − | 0.986172i | \(-0.552996\pi\) | ||||
−0.165723 | + | 0.986172i | \(0.552996\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −64.9881 | −2.46514 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.85164 | −0.297402 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.7903 | 0.408126 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.1289 | 0.798026 | 0.399013 | − | 0.916945i | \(-0.369353\pi\) | ||||
0.399013 | + | 0.916945i | \(0.369353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.4098 | 1.56180 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.8514 | 0.747649 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.5069 | −1.85927 | −0.929634 | − | 0.368483i | \(-0.879877\pi\) | ||||
−0.929634 | + | 0.368483i | \(0.879877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.50550 | −0.243975 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.2981 | −0.423117 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.6719 | 0.586095 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.03115 | −0.262583 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.5388 | 1.10161 | 0.550806 | − | 0.834634i | \(-0.314321\pi\) | ||||
0.550806 | + | 0.834634i | \(0.314321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.1765 | −0.750374 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.8451 | 1.07128 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0948 | −0.819450 | −0.409725 | − | 0.912209i | \(-0.634375\pi\) | ||||
−0.409725 | + | 0.912209i | \(0.634375\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.55786 | −0.168810 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.2329 | −0.896286 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.27897 | 0.305791 | 0.152895 | − | 0.988242i | \(-0.451140\pi\) | ||||
0.152895 | + | 0.988242i | \(0.451140\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.0738 | −0.518415 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.7989 | 0.397243 | 0.198621 | − | 0.980076i | \(-0.436354\pi\) | ||||
0.198621 | + | 0.980076i | \(0.436354\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.6714 | −0.722646 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.82131 | 0.250250 | 0.125125 | − | 0.992141i | \(-0.460067\pi\) | ||||
0.125125 | + | 0.992141i | \(0.460067\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.1928 | 1.94883 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.5141 | 0.677396 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.0702 | 1.20675 | 0.603375 | − | 0.797458i | \(-0.293822\pi\) | ||||
0.603375 | + | 0.797458i | \(0.293822\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.5545 | 0.603281 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 53.9988 | 1.96522 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.2962 | −0.955750 | −0.477875 | − | 0.878428i | \(-0.658593\pi\) | ||||
−0.477875 | + | 0.878428i | \(0.658593\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.829102 | −0.0300945 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.00551 | −0.290199 | −0.145100 | − | 0.989417i | \(-0.546350\pi\) | ||||
−0.145100 | + | 0.989417i | \(0.546350\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −60.9874 | −2.20501 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 70.3482 | 2.54012 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.1416 | −0.906631 | −0.453315 | − | 0.891350i | \(-0.649759\pi\) | ||||
−0.453315 | + | 0.891350i | \(0.649759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.06777 | 0.146497 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.3735 | 1.45213 | 0.726066 | − | 0.687625i | \(-0.241347\pi\) | ||||
0.726066 | + | 0.687625i | \(0.241347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51.7116 | 1.85753 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.19870 | 0.222091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.98456 | −0.285710 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.0143 | −0.715252 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.86250 | −0.209242 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.6762 | 1.41430 | 0.707152 | − | 0.707062i | \(-0.249980\pi\) | ||||
0.707152 | + | 0.707062i | \(0.249980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.64853 | −0.0942901 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66.3052 | 2.35457 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.7553 | −0.416916 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.0208 | −0.638330 | −0.319165 | − | 0.947699i | \(-0.603402\pi\) | ||||
−0.319165 | + | 0.947699i | \(0.603402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 66.2072 | 2.34224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.5509 | −0.584799 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.45687 | −0.298436 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.7626 | 0.378863 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.69414 | −0.340828 | −0.170414 | − | 0.985373i | \(-0.554510\pi\) | ||||
−0.170414 | + | 0.985373i | \(0.554510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.7050 | 0.621707 | 0.310853 | − | 0.950458i | \(-0.399385\pi\) | ||||
0.310853 | + | 0.950458i | \(0.399385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.47615 | −0.227128 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −58.3306 | −2.04323 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.1313 | 0.669321 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6472 | 0.685691 | 0.342845 | − | 0.939392i | \(-0.388609\pi\) | ||||
0.342845 | + | 0.939392i | \(0.388609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.2983 | −0.986417 | −0.493208 | − | 0.869911i | \(-0.664176\pi\) | ||||
−0.493208 | + | 0.869911i | \(0.664176\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.79481 | 0.132118 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.9716 | 0.381520 | 0.190760 | − | 0.981637i | \(-0.438905\pi\) | ||||
0.190760 | + | 0.981637i | \(0.438905\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.8823 | −0.690542 | −0.345271 | − | 0.938503i | \(-0.612213\pi\) | ||||
−0.345271 | + | 0.938503i | \(0.612213\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.0595 | 0.453028 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.9423 | 0.482493 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −35.8802 | −1.24020 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47.0348 | 1.62382 | 0.811910 | − | 0.583782i | \(-0.198428\pi\) | ||||
0.811910 | + | 0.583782i | \(0.198428\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.45611 | −0.0502107 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.37028 | −0.219404 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33.6929 | 1.15907 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.66913 | 0.297524 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.44271 | 0.289412 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.2276 | −0.761060 | −0.380530 | − | 0.924769i | \(-0.624258\pi\) | ||||
−0.380530 | + | 0.924769i | \(0.624258\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 48.1482 | 1.64664 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 56.9269 | 1.94459 | 0.972293 | − | 0.233767i | \(-0.0751053\pi\) | ||||
0.972293 | + | 0.233767i | \(0.0751053\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.7962 | 0.402482 | 0.201241 | − | 0.979542i | \(-0.435503\pi\) | ||||
0.201241 | + | 0.979542i | \(0.435503\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.0584 | −0.614717 | −0.307358 | − | 0.951594i | \(-0.599445\pi\) | ||||
−0.307358 | + | 0.951594i | \(0.599445\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0359 | 0.477233 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.6904 | 0.906453 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.57819 | 0.0874590 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −68.0796 | −2.30679 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.03416 | −0.102691 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.81033 | 0.229969 | 0.114984 | − | 0.993367i | \(-0.463318\pi\) | ||||
0.114984 | + | 0.993367i | \(0.463318\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.25042 | −0.0421755 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.2096 | 1.18624 | 0.593121 | − | 0.805114i | \(-0.297896\pi\) | ||||
0.593121 | + | 0.805114i | \(0.297896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.9739 | −1.27792 | −0.638961 | − | 0.769239i | \(-0.720636\pi\) | ||||
−0.638961 | + | 0.769239i | \(0.720636\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.5306 | 1.09351 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.5460 | 1.29425 | 0.647123 | − | 0.762385i | \(-0.275972\pi\) | ||||
0.647123 | + | 0.762385i | \(0.275972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.93681 | 0.165389 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −52.2692 | −1.74912 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55.0864 | 1.84133 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.01064 | −0.133911 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 49.3787 | 1.64687 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.2054 | −1.30612 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.3994 | 0.611617 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.94237 | −0.164109 | −0.0820543 | − | 0.996628i | \(-0.526148\pi\) | ||||
−0.0820543 | + | 0.996628i | \(0.526148\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.6861 | −1.11730 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.5995 | −0.616230 | −0.308115 | − | 0.951349i | \(-0.599698\pi\) | ||||
−0.308115 | + | 0.951349i | \(0.599698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.33731 | −0.242830 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.6611 | 1.01362 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.68091 | −0.0884350 | −0.0442175 | − | 0.999022i | \(-0.514079\pi\) | ||||
−0.0442175 | + | 0.999022i | \(0.514079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.67204 | −0.318705 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38.6239 | −1.27132 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38.6424 | −1.27055 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.33014 | −0.240753 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.9386 | 0.555737 | 0.277868 | − | 0.960619i | \(-0.410372\pi\) | ||||
0.277868 | + | 0.960619i | \(0.410372\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.80979 | −0.157465 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.1699 | 0.790439 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.6124 | −0.869388 | −0.434694 | − | 0.900578i | \(-0.643143\pi\) | ||||
−0.434694 | + | 0.900578i | \(0.643143\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.67180 | −0.315627 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.4031 | 1.05631 | 0.528155 | − | 0.849148i | \(-0.322884\pi\) | ||||
0.528155 | + | 0.849148i | \(0.322884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.26380 | 0.0411551 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.2924 | 1.66678 | 0.833390 | − | 0.552686i | \(-0.186397\pi\) | ||||
0.833390 | + | 0.552686i | \(0.186397\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.9087 | −1.32795 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.5511 | −0.666415 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.5251 | 0.502907 | 0.251454 | − | 0.967869i | \(-0.419091\pi\) | ||||
0.251454 | + | 0.967869i | \(0.419091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0053 | −0.485561 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.62362 | 0.117135 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.5227 | 1.85557 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0216 | 0.387392 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.8888 | −0.704626 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.1696 | −1.06666 | −0.533330 | − | 0.845907i | \(-0.679060\pi\) | ||||
−0.533330 | + | 0.845907i | \(0.679060\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −30.3381 | −0.974599 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.8348 | 0.829077 | 0.414538 | − | 0.910032i | \(-0.363943\pi\) | ||||
0.414538 | + | 0.910032i | \(0.363943\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.3567 | 0.587886 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.7828 | 0.568922 | 0.284461 | − | 0.958688i | \(-0.408185\pi\) | ||||
0.284461 | + | 0.958688i | \(0.408185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.55929 | 0.209636 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.5810 | 0.784811 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.2639 | −0.710107 | −0.355054 | − | 0.934846i | \(-0.615537\pi\) | ||||
−0.355054 | + | 0.934846i | \(0.615537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.1596 | 0.992827 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.90054 | 0.124030 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.20110 | −0.101686 | −0.0508432 | − | 0.998707i | \(-0.516191\pi\) | ||||
−0.0508432 | + | 0.998707i | \(0.516191\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.29968 | 0.136446 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −54.3069 | −1.72164 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.12241 | −0.0355471 | −0.0177736 | − | 0.999842i | \(-0.505658\pi\) | ||||
−0.0177736 | + | 0.999842i | \(0.505658\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.8121 | 0.848298 |
(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 | 8624.2.a.dg.1.8 | 12 | ||
4.3 | odd | 2 | 4312.2.a.bj.1.5 | ✓ | 12 | ||
7.6 | odd | 2 | inner | 8624.2.a.dg.1.5 | 12 | ||
28.27 | even | 2 | 4312.2.a.bj.1.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4312.2.a.bj.1.5 | ✓ | 12 | 4.3 | odd | 2 | ||
4312.2.a.bj.1.8 | yes | 12 | 28.27 | even | 2 | ||
8624.2.a.dg.1.5 | 12 | 7.6 | odd | 2 | inner | ||
8624.2.a.dg.1.8 | 12 | 1.1 | even | 1 | trivial |