Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −2.97134 | −1.71551 | −0.857753 | − | 0.514061i | \(-0.828140\pi\) | ||||
−0.857753 | + | 0.514061i | \(0.828140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.343630 | 0.153676 | 0.0768379 | − | 0.997044i | \(-0.475518\pi\) | ||||
0.0768379 | + | 0.997044i | \(0.475518\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.43593 | −0.542732 | −0.271366 | − | 0.962476i | \(-0.587475\pi\) | ||||
−0.271366 | + | 0.962476i | \(0.587475\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.82889 | 1.94296 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.62084 | −1.39324 | −0.696618 | − | 0.717442i | \(-0.745313\pi\) | ||||
−0.696618 | + | 0.717442i | \(0.745313\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0491454 | −0.0136305 | −0.00681524 | − | 0.999977i | \(-0.502169\pi\) | ||||
−0.00681524 | + | 0.999977i | \(0.502169\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.02104 | −0.263632 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.66831 | −0.889695 | −0.444848 | − | 0.895606i | \(-0.646742\pi\) | ||||
−0.444848 | + | 0.895606i | \(0.646742\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.44232 | −1.93680 | −0.968401 | − | 0.249399i | \(-0.919767\pi\) | ||||
−0.968401 | + | 0.249399i | \(0.919767\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.26665 | 0.931060 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.46524 | −1.55661 | −0.778305 | − | 0.627887i | \(-0.783920\pi\) | ||||
−0.778305 | + | 0.627887i | \(0.783920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88192 | −0.976384 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.40561 | −1.61766 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.21104 | 0.410579 | 0.205290 | − | 0.978701i | \(-0.434186\pi\) | ||||
0.205290 | + | 0.978701i | \(0.434186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.764542 | 0.137316 | 0.0686579 | − | 0.997640i | \(-0.478128\pi\) | ||||
0.0686579 | + | 0.997640i | \(0.478128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.7301 | 2.39011 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.493429 | −0.0834047 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.43564 | 0.236018 | 0.118009 | − | 0.993013i | \(-0.462349\pi\) | ||||
0.118009 | + | 0.993013i | \(0.462349\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.146028 | 0.0233832 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.38923 | −0.685482 | −0.342741 | − | 0.939430i | \(-0.611355\pi\) | ||||
−0.342741 | + | 0.939430i | \(0.611355\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.508420 | 0.0775334 | 0.0387667 | − | 0.999248i | \(-0.487657\pi\) | ||||
0.0387667 | + | 0.999248i | \(0.487657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00298 | 0.298587 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.72952 | 0.252276 | 0.126138 | − | 0.992013i | \(-0.459742\pi\) | ||||
0.126138 | + | 0.992013i | \(0.459742\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.93810 | −0.705443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.8998 | 1.52628 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.75864 | −0.378928 | −0.189464 | − | 0.981888i | \(-0.560675\pi\) | ||||
−0.189464 | + | 0.981888i | \(0.560675\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.58786 | −0.214107 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 25.0851 | 3.32260 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.37486 | −0.439370 | −0.219685 | − | 0.975571i | \(-0.570503\pi\) | ||||
−0.219685 | + | 0.975571i | \(0.570503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.47668 | 0.573180 | 0.286590 | − | 0.958053i | \(-0.407478\pi\) | ||||
0.286590 | + | 0.958053i | \(0.407478\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.36989 | −1.05451 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0168878 | −0.00209468 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.03766 | 0.981956 | 0.490978 | − | 0.871172i | \(-0.336640\pi\) | ||||
0.490978 | + | 0.871172i | \(0.336640\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22.1818 | 2.67037 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.02723 | −0.833979 | −0.416989 | − | 0.908911i | \(-0.636915\pi\) | ||||
−0.416989 | + | 0.908911i | \(0.636915\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.2930 | −1.43878 | −0.719392 | − | 0.694605i | \(-0.755579\pi\) | ||||
−0.719392 | + | 0.694605i | \(0.755579\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.5059 | 1.67499 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.63521 | 0.756153 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.4658 | −1.85255 | −0.926275 | − | 0.376847i | \(-0.877008\pi\) | ||||
−0.926275 | + | 0.376847i | \(0.877008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48929 | 0.832143 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.64120 | −0.289909 | −0.144954 | − | 0.989438i | \(-0.546304\pi\) | ||||
−0.144954 | + | 0.989438i | \(0.546304\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.26054 | −0.136725 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.56976 | −0.704352 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.57255 | 0.484690 | 0.242345 | − | 0.970190i | \(-0.422083\pi\) | ||||
0.242345 | + | 0.970190i | \(0.422083\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0705695 | 0.00739769 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.27172 | −0.235566 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.90103 | −0.297640 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.346939 | 0.0352263 | 0.0176131 | − | 0.999845i | \(-0.494393\pi\) | ||||
0.0176131 | + | 0.999845i | \(0.494393\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26.9344 | −2.70701 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1152 | −1.00650 | −0.503249 | − | 0.864141i | \(-0.667862\pi\) | ||||
−0.503249 | + | 0.864141i | \(0.667862\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.76800 | −0.174206 | −0.0871029 | − | 0.996199i | \(-0.527761\pi\) | ||||
−0.0871029 | + | 0.996199i | \(0.527761\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.46615 | 0.143081 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.2387 | 0.989808 | 0.494904 | − | 0.868948i | \(-0.335203\pi\) | ||||
0.494904 | + | 0.868948i | \(0.335203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.77213 | −0.361304 | −0.180652 | − | 0.983547i | \(-0.557821\pi\) | ||||
−0.180652 | + | 0.983547i | \(0.557821\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.26579 | −0.404891 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.6720 | −1.38023 | −0.690113 | − | 0.723701i | \(-0.742439\pi\) | ||||
−0.690113 | + | 0.723701i | \(0.742439\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.56528 | −0.239213 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.286463 | −0.0264835 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.26744 | 0.482866 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3522 | 0.941106 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.0419 | 1.17595 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.39572 | −0.303722 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.81598 | −0.782292 | −0.391146 | − | 0.920329i | \(-0.627921\pi\) | ||||
−0.391146 | + | 0.920329i | \(0.627921\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.51069 | −0.133009 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.16118 | 0.363564 | 0.181782 | − | 0.983339i | \(-0.441813\pi\) | ||||
0.181782 | + | 0.983339i | \(0.441813\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.1226 | 1.05116 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.88842 | −0.248595 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.351303 | 0.0300138 | 0.0150069 | − | 0.999887i | \(-0.495223\pi\) | ||||
0.0150069 | + | 0.999887i | \(0.495223\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.2267 | 1.54597 | 0.772983 | − | 0.634427i | \(-0.218764\pi\) | ||||
0.772983 | + | 0.634427i | \(0.218764\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.13899 | −0.432781 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.227093 | 0.0189905 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.759778 | 0.0630962 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.6728 | 1.21019 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.2338 | −1.00223 | −0.501116 | − | 0.865380i | \(-0.667077\pi\) | ||||
−0.501116 | + | 0.865380i | \(0.667077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1763 | −1.47916 | −0.739582 | − | 0.673067i | \(-0.764977\pi\) | ||||
−0.739582 | + | 0.673067i | \(0.764977\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.3822 | −1.72865 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.262719 | 0.0211021 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.28430 | −0.102499 | −0.0512493 | − | 0.998686i | \(-0.516320\pi\) | ||||
−0.0512493 | + | 0.998686i | \(0.516320\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.19686 | 0.650053 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7196 | 0.844821 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.53430 | 0.511806 | 0.255903 | − | 0.966702i | \(-0.417627\pi\) | ||||
0.255903 | + | 0.966702i | \(0.417627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.71807 | 0.367301 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.4435 | −0.808139 | −0.404070 | − | 0.914728i | \(-0.632405\pi\) | ||||
−0.404070 | + | 0.914728i | \(0.632405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9976 | −0.999814 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −49.2094 | −3.76313 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.5372 | −1.56141 | −0.780706 | − | 0.624899i | \(-0.785140\pi\) | ||||
−0.780706 | + | 0.624899i | \(0.785140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.01011 | 0.529914 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0279 | 0.753742 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.3752 | −0.999708 | −0.499854 | − | 0.866110i | \(-0.666613\pi\) | ||||
−0.499854 | + | 0.866110i | \(0.666613\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.7792 | 1.91615 | 0.958075 | − | 0.286518i | \(-0.0924977\pi\) | ||||
0.958075 | + | 0.286518i | \(0.0924977\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3018 | −0.983294 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.493329 | 0.0362703 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.9507 | 1.23956 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.0699 | 0.877955 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.09149 | 0.368407 | 0.184204 | − | 0.982888i | \(-0.441029\pi\) | ||||
0.184204 | + | 0.982888i | \(0.441029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.05868 | −0.220169 | −0.110084 | − | 0.993922i | \(-0.535112\pi\) | ||||
−0.110084 | + | 0.993922i | \(0.535112\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0501795 | 0.00359343 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.74396 | 0.124252 | 0.0621261 | − | 0.998068i | \(-0.480212\pi\) | ||||
0.0621261 | + | 0.998068i | \(0.480212\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0399 | −0.853489 | −0.426744 | − | 0.904372i | \(-0.640340\pi\) | ||||
−0.426744 | + | 0.904372i | \(0.640340\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.8826 | −1.68455 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.17490 | −0.222834 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50827 | −0.105342 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −43.5140 | −3.02444 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 39.0106 | 2.69842 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.0033 | 1.51477 | 0.757385 | − | 0.652969i | \(-0.226477\pi\) | ||||
0.757385 | + | 0.652969i | \(0.226477\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.8803 | 1.43070 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.174708 | 0.0119150 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.09783 | −0.0745256 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 36.5267 | 2.46824 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.180280 | 0.0121270 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6491 | 0.780083 | 0.390042 | − | 0.920797i | \(-0.372461\pi\) | ||||
0.390042 | + | 0.920797i | \(0.372461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −28.4562 | −1.89708 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.04337 | 0.201996 | 0.100998 | − | 0.994887i | \(-0.467796\pi\) | ||||
0.100998 | + | 0.994887i | \(0.467796\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.59651 | −0.171582 | −0.0857911 | − | 0.996313i | \(-0.527342\pi\) | ||||
−0.0857911 | + | 0.996313i | \(0.527342\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.7155 | −1.29719 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.4569 | 1.27466 | 0.637331 | − | 0.770590i | \(-0.280038\pi\) | ||||
0.637331 | + | 0.770590i | \(0.280038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.594314 | 0.0387688 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 48.9257 | 3.17806 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.34917 | 0.151955 | 0.0759776 | − | 0.997110i | \(-0.475792\pi\) | ||||
0.0759776 | + | 0.997110i | \(0.475792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.6402 | 0.943059 | 0.471530 | − | 0.881850i | \(-0.343702\pi\) | ||||
0.471530 | + | 0.881850i | \(0.343702\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.96356 | 0.190113 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.69688 | −0.108409 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.414901 | 0.0263995 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.84791 | 0.497341 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.08850 | −0.321183 | −0.160592 | − | 0.987021i | \(-0.551340\pi\) | ||||
−0.160592 | + | 0.987021i | \(0.551340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.4957 | 2.16872 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.74550 | 0.234552 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.2462 | −1.32530 | −0.662652 | − | 0.748927i | \(-0.730569\pi\) | ||||
−0.662652 | + | 0.748927i | \(0.730569\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.06148 | −0.128094 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.8879 | 0.797741 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.2830 | 1.62068 | 0.810341 | − | 0.585959i | \(-0.199282\pi\) | ||||
0.810341 | + | 0.585959i | \(0.199282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.947949 | −0.0582321 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.5866 | −0.831489 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.75172 | −0.289717 | −0.144859 | − | 0.989452i | \(-0.546273\pi\) | ||||
−0.144859 | + | 0.989452i | \(0.546273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.74968 | 0.167031 | 0.0835156 | − | 0.996506i | \(-0.473385\pi\) | ||||
0.0835156 | + | 0.996506i | \(0.473385\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.209686 | −0.0126908 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.5586 | 1.36033 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7768 | −1.12819 | −0.564094 | − | 0.825711i | \(-0.690774\pi\) | ||||
−0.564094 | + | 0.825711i | \(0.690774\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.45643 | 0.266799 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9396 | 1.12984 | 0.564920 | − | 0.825145i | \(-0.308907\pi\) | ||||
0.564920 | + | 0.825145i | \(0.308907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.580094 | −0.0344830 | −0.0172415 | − | 0.999851i | \(-0.505488\pi\) | ||||
−0.0172415 | + | 0.999851i | \(0.505488\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.61997 | 0.510603 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.30263 | 0.372033 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.54351 | −0.208442 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.03087 | −0.0604309 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.39793 | 0.256930 | 0.128465 | − | 0.991714i | \(-0.458995\pi\) | ||||
0.128465 | + | 0.991714i | \(0.458995\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.15970 | −0.0675205 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 38.8410 | 2.25378 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.366882 | 0.0212173 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.730057 | −0.0420798 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 30.0557 | 1.72666 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.53832 | 0.0880839 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.5154 | −1.57039 | −0.785193 | − | 0.619251i | \(-0.787436\pi\) | ||||
−0.785193 | + | 0.619251i | \(0.787436\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.25332 | 0.298851 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.48920 | −0.254559 | −0.127280 | − | 0.991867i | \(-0.540625\pi\) | ||||
−0.127280 | + | 0.991867i | \(0.540625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.6691 | 0.998719 | 0.499360 | − | 0.866395i | \(-0.333569\pi\) | ||||
0.499360 | + | 0.866395i | \(0.333569\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.87614 | −0.162052 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.6921 | 1.16218 | 0.581092 | − | 0.813838i | \(-0.302626\pi\) | ||||
0.581092 | + | 0.813838i | \(0.302626\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.2169 | −0.572034 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.4226 | −1.69802 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.9690 | 1.72316 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.239924 | 0.0133086 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.2083 | 0.619820 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.48347 | −0.136918 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.44499 | −0.409214 | −0.204607 | − | 0.978844i | \(-0.565592\pi\) | ||||
−0.204607 | + | 0.978844i | \(0.565592\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.36820 | 0.458574 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.76198 | 0.150903 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.7620 | 0.640718 | 0.320359 | − | 0.947296i | \(-0.396197\pi\) | ||||
0.320359 | + | 0.947296i | \(0.396197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.5956 | 2.36779 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.53282 | −0.191313 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.1423 | 0.925597 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.62232 | 0.410372 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.4748 | −1.36756 | −0.683780 | − | 0.729689i | \(-0.739665\pi\) | ||||
−0.683780 | + | 0.729689i | \(0.739665\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.7600 | −1.43243 | −0.716215 | − | 0.697879i | \(-0.754127\pi\) | ||||
−0.716215 | + | 0.697879i | \(0.754127\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.413097 | 0.0220495 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.1096 | 1.23000 | 0.615001 | − | 0.788527i | \(-0.289156\pi\) | ||||
0.615001 | + | 0.788527i | \(0.289156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.41476 | −0.128162 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.6514 | −0.828359 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1174 | −0.586752 | −0.293376 | − | 0.955997i | \(-0.594779\pi\) | ||||
−0.293376 | + | 0.955997i | \(0.594779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.2728 | 2.75120 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.7598 | −1.61447 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.22423 | −0.221106 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.9175 | 1.45728 | 0.728641 | − | 0.684896i | \(-0.240152\pi\) | ||||
0.728641 | + | 0.684896i | \(0.240152\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.5843 | −1.33187 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.96121 | 0.205656 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.21823 | −0.477302 | −0.238651 | − | 0.971105i | \(-0.576705\pi\) | ||||
−0.238651 | + | 0.971105i | \(0.576705\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.0899 | 0.521038 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.108662 | −0.00559639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3495 | 0.942550 | 0.471275 | − | 0.881986i | \(-0.343794\pi\) | ||||
0.471275 | + | 0.881986i | \(0.343794\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.1953 | 1.34203 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.6447 | 0.952698 | 0.476349 | − | 0.879256i | \(-0.341960\pi\) | ||||
0.476349 | + | 0.879256i | \(0.341960\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.28006 | 0.116202 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.96353 | 0.150644 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.8384 | −0.650931 | −0.325465 | − | 0.945554i | \(-0.605521\pi\) | ||||
−0.325465 | + | 0.945554i | \(0.605521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.3848 | 1.38491 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.3643 | −0.623696 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.65815 | −0.284692 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.04334 | −0.102552 | −0.0512761 | − | 0.998685i | \(-0.516329\pi\) | ||||
−0.0512761 | + | 0.998685i | \(0.516329\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −36.0204 | −1.80328 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.7641 | −1.73604 | −0.868019 | − | 0.496531i | \(-0.834607\pi\) | ||||
−0.868019 | + | 0.496531i | \(0.834607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0375737 | −0.00187168 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.57354 | 0.127880 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.63387 | −0.328829 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.4640 | −1.06133 | −0.530664 | − | 0.847582i | \(-0.678057\pi\) | ||||
−0.530664 | + | 0.847582i | \(0.678057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.04384 | −0.0514889 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.84607 | 0.238460 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.907594 | −0.0445520 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −54.1577 | −2.65212 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8700 | 0.824155 | 0.412078 | − | 0.911149i | \(-0.364803\pi\) | ||||
0.412078 | + | 0.911149i | \(0.364803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8430 | 1.06456 | 0.532281 | − | 0.846568i | \(-0.321335\pi\) | ||||
0.532281 | + | 0.846568i | \(0.321335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.0812 | 0.490163 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.9084 | 0.868684 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.42821 | −0.311083 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.674771 | −0.0325783 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.2561 | −1.02387 | −0.511936 | − | 0.859024i | \(-0.671072\pi\) | ||||
−0.511936 | + | 0.859024i | \(0.671072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.83699 | 0.376622 | 0.188311 | − | 0.982109i | \(-0.439699\pi\) | ||||
0.188311 | + | 0.982109i | \(0.439699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.25756 | −0.108242 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 63.0239 | 3.01484 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2921 | −0.634396 | −0.317198 | − | 0.948359i | \(-0.602742\pi\) | ||||
−0.317198 | + | 0.948359i | \(0.602742\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −28.7836 | −1.37065 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.8426 | 1.46537 | 0.732687 | − | 0.680566i | \(-0.238266\pi\) | ||||
0.732687 | + | 0.680566i | \(0.238266\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.57127 | 0.0744851 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.3508 | 1.71934 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.6520 | −1.21059 | −0.605296 | − | 0.796001i | \(-0.706945\pi\) | ||||
−0.605296 | + | 0.796001i | \(0.706945\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.2819 | 0.955038 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 54.0079 | 2.53751 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0242498 | 0.00113685 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.31909 | −0.295595 | −0.147797 | − | 0.989018i | \(-0.547218\pi\) | ||||
−0.147797 | + | 0.989018i | \(0.547218\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 30.8344 | 1.43922 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5015 | 0.815128 | 0.407564 | − | 0.913177i | \(-0.366378\pi\) | ||||
0.407564 | + | 0.913177i | \(0.366378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.3125 | 1.12990 | 0.564948 | − | 0.825127i | \(-0.308896\pi\) | ||||
0.564948 | + | 0.825127i | \(0.308896\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.780629 | −0.0362008 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.1917 | −1.53593 | −0.767964 | − | 0.640493i | \(-0.778730\pi\) | ||||
−0.767964 | + | 0.640493i | \(0.778730\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.5415 | −0.532938 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.81611 | 0.175837 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.34933 | −0.108022 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41.2147 | 1.89106 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.0798 | −0.736243 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.9888 | −1.87283 | −0.936414 | − | 0.350898i | \(-0.885876\pi\) | ||||
−0.936414 | + | 0.350898i | \(0.885876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0705552 | −0.00321704 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −31.8516 | −1.44930 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.119218 | 0.00541343 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.843153 | 0.0382069 | 0.0191035 | − | 0.999818i | \(-0.493919\pi\) | ||||
0.0191035 | + | 0.999818i | \(0.493919\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.4157 | −0.878007 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.9217 | −0.944185 | −0.472092 | − | 0.881549i | \(-0.656501\pi\) | ||||
−0.472092 | + | 0.881549i | \(0.656501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.11077 | −0.365291 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.25545 | −0.416001 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.0906 | 0.452627 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.6333 | −1.10274 | −0.551370 | − | 0.834261i | \(-0.685895\pi\) | ||||
−0.551370 | + | 0.834261i | \(0.685895\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.0311 | 1.38637 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.6987 | −0.521619 | −0.260810 | − | 0.965390i | \(-0.583989\pi\) | ||||
−0.260810 | + | 0.965390i | \(0.583989\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.47588 | −0.154675 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.6203 | 1.71519 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.1721 | 1.60330 | 0.801651 | − | 0.597793i | \(-0.203955\pi\) | ||||
0.801651 | + | 0.597793i | \(0.203955\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.6519 | 0.780873 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 70.9628 | 3.13309 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.607536 | −0.0267712 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.99183 | −0.351480 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 61.0230 | 2.67861 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5527 | 0.944241 | 0.472121 | − | 0.881534i | \(-0.343489\pi\) | ||||
0.472121 | + | 0.881534i | \(0.343489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.50799 | −0.284574 | −0.142287 | − | 0.989825i | \(-0.545446\pi\) | ||||
−0.142287 | + | 0.989825i | \(0.545446\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −20.8294 | −0.909071 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.80457 | −0.122169 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.7298 | 1.42303 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.6717 | −0.853679 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.215710 | 0.00934345 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.51831 | 0.152110 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 39.7423 | 1.71501 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.8182 | 0.982848 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.8108 | −0.808737 | −0.404369 | − | 0.914596i | \(-0.632509\pi\) | ||||
−0.404369 | + | 0.914596i | \(0.632509\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −76.5988 | −3.28717 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.29621 | −0.0555237 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.91680 | 0.167470 | 0.0837352 | − | 0.996488i | \(-0.473315\pi\) | ||||
0.0837352 | + | 0.996488i | \(0.473315\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.0941 | 1.11367 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.6663 | −0.795211 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.6438 | 1.00544 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.46585 | −0.0622219 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.41115 | 0.314021 | 0.157010 | − | 0.987597i | \(-0.449814\pi\) | ||||
0.157010 | + | 0.987597i | \(0.449814\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0249865 | −0.00105682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −50.3663 | −2.12647 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.38055 | 0.353198 | 0.176599 | − | 0.984283i | \(-0.443490\pi\) | ||||
0.176599 | + | 0.984283i | \(0.443490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.04174 | −0.212108 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.7541 | −0.451630 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.2279 | −1.51875 | −0.759377 | − | 0.650651i | \(-0.774496\pi\) | ||||
−0.759377 | + | 0.650651i | \(0.774496\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.71890 | −0.0719337 | −0.0359668 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359668 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.1286 | −0.632005 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.4447 | 1.51985 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.6396 | 0.984129 | 0.492065 | − | 0.870559i | \(-0.336242\pi\) | ||||
0.492065 | + | 0.870559i | \(0.336242\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.08840 | 0.377701 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.79258 | 0.157343 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.7472 | 0.527936 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0984372 | −0.00406988 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.35858 | 0.0560748 | 0.0280374 | − | 0.999607i | \(-0.491074\pi\) | ||||
0.0280374 | + | 0.999607i | \(0.491074\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.45451 | −0.265953 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.18192 | −0.213156 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.33616 | 0.260195 | 0.130097 | − | 0.991501i | \(-0.458471\pi\) | ||||
0.130097 | + | 0.991501i | \(0.458471\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.81005 | 0.0742048 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 35.7748 | 1.46417 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.3985 | −1.56892 | −0.784460 | − | 0.620179i | \(-0.787060\pi\) | ||||
−0.784460 | + | 0.620179i | \(0.787060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.1092 | −0.861062 | −0.430531 | − | 0.902576i | \(-0.641674\pi\) | ||||
−0.430531 | + | 0.902576i | \(0.641674\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 46.8506 | 1.90790 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.55731 | 0.144625 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.3475 | 1.11000 | 0.555000 | − | 0.831850i | \(-0.312718\pi\) | ||||
0.555000 | + | 0.831850i | \(0.312718\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.43373 | 0.382274 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0849978 | −0.00343864 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.809174 | −0.0326822 | −0.0163411 | − | 0.999866i | \(-0.505202\pi\) | ||||
−0.0163411 | + | 0.999866i | \(0.505202\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.48159 | 0.180715 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.7264 | 0.592863 | 0.296432 | − | 0.955054i | \(-0.404203\pi\) | ||||
0.296432 | + | 0.955054i | \(0.404203\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.84706 | −0.235013 | −0.117507 | − | 0.993072i | \(-0.537490\pi\) | ||||
−0.117507 | + | 0.993072i | \(0.537490\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 62.7499 | 2.51806 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.56588 | −0.263056 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2427 | 0.929709 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −115.914 | −4.62916 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.26638 | −0.209984 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.1832 | −1.04234 | −0.521168 | − | 0.853454i | \(-0.674503\pi\) | ||||
−0.521168 | + | 0.853454i | \(0.674503\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −65.3794 | −2.59860 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.02943 | −0.120219 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.242685 | 0.00961552 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.9609 | −1.62039 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.6223 | −0.696037 | −0.348019 | − | 0.937488i | \(-0.613145\pi\) | ||||
−0.348019 | + | 0.937488i | \(0.613145\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.9812 | −0.472494 | −0.236247 | − | 0.971693i | \(-0.575917\pi\) | ||||
−0.236247 | + | 0.971693i | \(0.575917\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.519119 | −0.0204403 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.1539 | −0.556446 | −0.278223 | − | 0.960517i | \(-0.589745\pi\) | ||||
−0.278223 | + | 0.960517i | \(0.589745\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.5947 | 0.612145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.26203 | 0.127849 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.58530 | 0.375102 | 0.187551 | − | 0.982255i | \(-0.439945\pi\) | ||||
0.187551 | + | 0.982255i | \(0.439945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.42990 | 0.0558710 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −71.6544 | −2.79550 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.36439 | −0.0921035 | −0.0460517 | − | 0.998939i | \(-0.514664\pi\) | ||||
−0.0460517 | + | 0.998939i | \(0.514664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5947 | 0.412085 | 0.206043 | − | 0.978543i | \(-0.433941\pi\) | ||||
0.206043 | + | 0.978543i | \(0.433941\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.535675 | −0.0208039 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.16569 | 0.161538 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.5059 | −0.639112 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.6136 | −1.33824 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.6860 | −0.798574 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.2357 | −0.471652 | −0.235826 | − | 0.971795i | \(-0.575779\pi\) | ||||
−0.235826 | + | 0.971795i | \(0.575779\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 41.0355 | 1.57946 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.7430 | 1.29685 | 0.648424 | − | 0.761279i | \(-0.275428\pi\) | ||||
0.648424 | + | 0.761279i | \(0.275428\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.498181 | −0.0191184 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.04290 | −0.346525 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.0033 | 1.03325 | 0.516626 | − | 0.856211i | \(-0.327188\pi\) | ||||
0.516626 | + | 0.856211i | \(0.327188\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.120718 | 0.00461240 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.71513 | 0.294350 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.135574 | 0.00516497 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.194869 | −0.00741317 | −0.00370659 | − | 0.999993i | \(-0.501180\pi\) | ||||
−0.00370659 | + | 0.999993i | \(0.501180\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 38.6759 | 1.46918 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.26323 | 0.237578 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.1010 | 0.609870 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −57.8131 | −2.18669 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.2430 | −0.689029 | −0.344515 | − | 0.938781i | \(-0.611957\pi\) | ||||
−0.344515 | + | 0.938781i | \(0.611957\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.1201 | −0.457120 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.76591 | −0.0665081 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.5247 | 0.546259 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.4184 | 1.10483 | 0.552416 | − | 0.833568i | \(-0.313706\pi\) | ||||
0.552416 | + | 0.833568i | \(0.313706\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −95.9775 | −3.59944 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.70748 | −0.213747 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0780359 | 0.00291838 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.98020 | −0.260680 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.3065 | 1.50318 | 0.751590 | − | 0.659631i | \(-0.229287\pi\) | ||||
0.751590 | + | 0.659631i | \(0.229287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.53872 | 0.0945470 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −43.5011 | −1.61782 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.7941 | −0.400883 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.8581 | 1.55243 | 0.776216 | − | 0.630467i | \(-0.217136\pi\) | ||||
0.776216 | + | 0.630467i | \(0.217136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31.2736 | −1.15828 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.86504 | −0.0689811 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.9611 | 0.737282 | 0.368641 | − | 0.929572i | \(-0.379823\pi\) | ||||
0.368641 | + | 0.929572i | \(0.379823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.04201 | 0.185977 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37.1407 | −1.36810 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.0715 | 1.21655 | 0.608277 | − | 0.793725i | \(-0.291861\pi\) | ||||
0.608277 | + | 0.793725i | \(0.291861\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23281 | −0.0452886 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.9789 | −1.06313 | −0.531567 | − | 0.847017i | \(-0.678396\pi\) | ||||
−0.531567 | + | 0.847017i | \(0.678396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.20390 | −0.154019 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.3952 | −0.563283 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.7020 | −0.537200 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.1197 | 0.550992 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.24590 | −0.227312 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.0900 | −0.766530 | −0.383265 | − | 0.923638i | \(-0.625200\pi\) | ||||
−0.383265 | + | 0.923638i | \(0.625200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −102.499 | −3.72046 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.54644 | −0.128558 | −0.0642791 | − | 0.997932i | \(-0.520475\pi\) | ||||
−0.0642791 | + | 0.997932i | \(0.520475\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.41652 | 0.196091 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.34755 | −0.265651 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.165859 | 0.00598882 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.73837 | −0.351175 | −0.175587 | − | 0.984464i | \(-0.556182\pi\) | ||||
−0.175587 | + | 0.984464i | \(0.556182\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 63.1299 | 2.27357 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.7194 | −0.961030 | −0.480515 | − | 0.876987i | \(-0.659550\pi\) | ||||
−0.480515 | + | 0.876987i | \(0.659550\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.73243 | −0.134073 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.12538 | 0.219747 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.0553 | 1.32764 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.4717 | 1.16193 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.5851 | −0.664178 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.441325 | −0.0157516 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6834 | 0.986807 | 0.493403 | − | 0.869801i | \(-0.335753\pi\) | ||||
0.493403 | + | 0.869801i | \(0.335753\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −78.0960 | −2.78029 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.0680 | 0.749092 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.220008 | −0.00781271 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.81668 | 0.0998975 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.8043 | −1.51621 | −0.758104 | − | 0.652134i | \(-0.773874\pi\) | ||||
−0.758104 | + | 0.652134i | \(0.773874\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.34440 | −0.224449 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.6529 | 0.941735 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56.8038 | 2.00456 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.68357 | 0.129829 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.1190 | 0.497012 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.2810 | 1.27557 | 0.637785 | − | 0.770214i | \(-0.279851\pi\) | ||||
0.637785 | + | 0.770214i | \(0.279851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.2274 | 0.394249 | 0.197125 | − | 0.980378i | \(-0.436840\pi\) | ||||
0.197125 | + | 0.980378i | \(0.436840\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.17025 | −0.286543 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.24538 | 0.0786523 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.29225 | −0.150167 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.411342 | 0.0143734 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.2557 | −1.43983 | −0.719917 | − | 0.694061i | \(-0.755820\pi\) | ||||
−0.719917 | + | 0.694061i | \(0.755820\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.5150 | −1.16826 | −0.584129 | − | 0.811661i | \(-0.698564\pi\) | ||||
−0.584129 | + | 0.811661i | \(0.698564\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −67.0293 | −2.33366 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.2127 | 0.876730 | 0.438365 | − | 0.898797i | \(-0.355558\pi\) | ||||
0.438365 | + | 0.898797i | \(0.355558\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.1710 | −1.15208 | −0.576038 | − | 0.817423i | \(-0.695402\pi\) | ||||
−0.576038 | + | 0.817423i | \(0.695402\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 55.7923 | 1.93541 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.1145 | 0.627629 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.58868 | −0.124192 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.42644 | −0.222130 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.3377 | 0.598562 | 0.299281 | − | 0.954165i | \(-0.403253\pi\) | ||||
0.299281 | + | 0.954165i | \(0.403253\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1113 | −0.831425 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −56.2760 | −1.93825 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.46636 | −0.153647 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.8650 | −0.510768 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.72366 | 0.0591559 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.7174 | −0.367388 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.8869 | 1.57114 | 0.785568 | − | 0.618775i | \(-0.212371\pi\) | ||||
0.785568 | + | 0.618775i | \(0.212371\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.9098 | −0.578303 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0723 | 0.651496 | 0.325748 | − | 0.945457i | \(-0.394384\pi\) | ||||
0.325748 | + | 0.945457i | \(0.394384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.41099 | 0.218740 | 0.109370 | − | 0.994001i | \(-0.465117\pi\) | ||||
0.109370 | + | 0.994001i | \(0.465117\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.7273 | −0.638225 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.48469 | −0.322863 | −0.161431 | − | 0.986884i | \(-0.551611\pi\) | ||||
−0.161431 | + | 0.986884i | \(0.551611\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.05718 | −0.239951 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.5290 | 0.357584 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 76.0860 | 2.58104 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.395014 | −0.0133845 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.02227 | 0.0684434 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.87603 | 0.164840 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0781 | 0.340313 | 0.170156 | − | 0.985417i | \(-0.445573\pi\) | ||||
0.170156 | + | 0.985417i | \(0.445573\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.0678 | −0.440765 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.7601 | 0.935262 | 0.467631 | − | 0.883924i | \(-0.345108\pi\) | ||||
0.467631 | + | 0.883924i | \(0.345108\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.2389 | −0.344567 | −0.172283 | − | 0.985047i | \(-0.555114\pi\) | ||||
−0.172283 | + | 0.985047i | \(0.555114\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.44588 | 0.115832 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 54.6655 | 1.83549 | 0.917745 | − | 0.397171i | \(-0.130008\pi\) | ||||
0.917745 | + | 0.397171i | \(0.130008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.6591 | 0.424574 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.6068 | −1.15937 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.6011 | −0.488609 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.59611 | −0.153631 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.09013 | −0.0363985 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.69043 | 0.0563790 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.1195 | 0.337130 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.16925 | 0.0721882 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.85849 | 0.294466 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.3279 | −0.840998 | −0.420499 | − | 0.907293i | \(-0.638145\pi\) | ||||
−0.420499 | + | 0.907293i | \(0.638145\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −58.9603 | −1.95559 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.9288 | −1.09098 | −0.545491 | − | 0.838117i | \(-0.683657\pi\) | ||||
−0.545491 | + | 0.838117i | \(0.683657\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.2045 | 0.403912 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.57088 | −0.151109 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.97517 | −0.197318 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.265854 | 0.00876971 | 0.00438485 | − | 0.999990i | \(-0.498604\pi\) | ||||
0.00438485 | + | 0.999990i | \(0.498604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 81.7577 | 2.69401 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.345356 | 0.0113675 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00869 | −0.230444 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.3055 | −0.338475 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.426009 | 0.0139769 | 0.00698844 | − | 0.999976i | \(-0.497775\pi\) | ||||
0.00698844 | + | 0.999976i | \(0.497775\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.6890 | 1.36630 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.3390 | 0.436698 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.82475 | 0.190490 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.7808 | 0.842222 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −52.5011 | −1.71331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.4944 | 0.700697 | 0.350348 | − | 0.936619i | \(-0.386063\pi\) | ||||
0.350348 | + | 0.936619i | \(0.386063\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.7666 | 1.06703 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.14757 | 0.134921 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.1488 | 1.59712 | 0.798560 | − | 0.601915i | \(-0.205595\pi\) | ||||
0.798560 | + | 0.601915i | \(0.205595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.604143 | 0.0196113 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −61.4833 | −1.99373 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.2774 | −0.980781 | −0.490391 | − | 0.871503i | \(-0.663146\pi\) | ||||
−0.490391 | + | 0.871503i | \(0.663146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.74959 | 0.0566153 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.3578 | 0.981328 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.504447 | −0.0162894 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4155 | −0.981144 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 59.6800 | 1.92316 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.05105 | −0.0338346 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.0631 | −0.838132 | −0.419066 | − | 0.907956i | \(-0.637642\pi\) | ||||
−0.419066 | + | 0.907956i | \(0.637642\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −92.0197 | −2.95610 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.6428 | −1.65730 | −0.828648 | − | 0.559770i | \(-0.810890\pi\) | ||||
−0.828648 | + | 0.559770i | \(0.810890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.1723 | −0.839045 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.712896 | −0.0228310 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.61973 | 0.275770 | 0.137885 | − | 0.990448i | \(-0.455970\pi\) | ||||
0.137885 | + | 0.990448i | \(0.455970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.1290 | −0.675287 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.9873 | −0.702001 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.8716 | −0.793281 | −0.396641 | − | 0.917974i | \(-0.629824\pi\) | ||||
−0.396641 | + | 0.917974i | \(0.629824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.599278 | 0.0190946 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.37925 | 0.234884 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.79548 | −0.120689 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.5601 | −0.494283 | −0.247142 | − | 0.968979i | \(-0.579491\pi\) | ||||
−0.247142 | + | 0.968979i | \(0.579491\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.1216 | 0.702009 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.13728 | −0.131161 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.3009 | −0.579595 | −0.289797 | − | 0.957088i | \(-0.593588\pi\) | ||||
−0.289797 | + | 0.957088i | \(0.593588\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.0674 | −0.381797 |
(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 | 6008.2.a.e.1.3 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.3 | ✓ | 50 | 1.1 | even | 1 | trivial |