Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 11x^{7} + 51x^{6} + 25x^{5} - 180x^{4} + 29x^{3} + 119x^{2} - 8x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.71772\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.02880 | −0.907306 | −0.453653 | − | 0.891178i | \(-0.649880\pi\) | ||||
−0.453653 | + | 0.891178i | \(0.649880\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.70084 | −0.642858 | −0.321429 | − | 0.946934i | \(-0.604163\pi\) | ||||
−0.321429 | + | 0.946934i | \(0.604163\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.02880 | 0.641563 | ||||||||
\(11\) | −0.223482 | −0.0673824 | −0.0336912 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336912 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 4.73778 | 1.31402 | 0.657012 | − | 0.753880i | \(-0.271820\pi\) | ||||
0.657012 | + | 0.753880i | \(0.271820\pi\) | |||||||
\(14\) | 1.70084 | 0.454569 | ||||||||
\(15\) | 2.02880 | 0.523834 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.06304 | −0.500361 | −0.250181 | − | 0.968199i | \(-0.580490\pi\) | ||||
−0.250181 | + | 0.968199i | \(0.580490\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.02880 | −0.453653 | ||||||||
\(21\) | 1.70084 | 0.371154 | ||||||||
\(22\) | 0.223482 | 0.0476466 | ||||||||
\(23\) | 4.59214 | 0.957527 | 0.478763 | − | 0.877944i | \(-0.341085\pi\) | ||||
0.478763 | + | 0.877944i | \(0.341085\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −0.883975 | −0.176795 | ||||||||
\(26\) | −4.73778 | −0.929155 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.70084 | −0.321429 | ||||||||
\(29\) | 8.61390 | 1.59956 | 0.799781 | − | 0.600292i | \(-0.204949\pi\) | ||||
0.799781 | + | 0.600292i | \(0.204949\pi\) | |||||||
\(30\) | −2.02880 | −0.370406 | ||||||||
\(31\) | −6.41980 | −1.15303 | −0.576515 | − | 0.817087i | \(-0.695588\pi\) | ||||
−0.576515 | + | 0.817087i | \(0.695588\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.223482 | 0.0389033 | ||||||||
\(34\) | 2.06304 | 0.353809 | ||||||||
\(35\) | 3.45067 | 0.583269 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.05467 | 0.830983 | 0.415492 | − | 0.909597i | \(-0.363610\pi\) | ||||
0.415492 | + | 0.909597i | \(0.363610\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −4.73778 | −0.758652 | ||||||||
\(40\) | 2.02880 | 0.320781 | ||||||||
\(41\) | −5.36854 | −0.838424 | −0.419212 | − | 0.907888i | \(-0.637694\pi\) | ||||
−0.419212 | + | 0.907888i | \(0.637694\pi\) | |||||||
\(42\) | −1.70084 | −0.262446 | ||||||||
\(43\) | −8.67694 | −1.32322 | −0.661611 | − | 0.749847i | \(-0.730127\pi\) | ||||
−0.661611 | + | 0.749847i | \(0.730127\pi\) | |||||||
\(44\) | −0.223482 | −0.0336912 | ||||||||
\(45\) | −2.02880 | −0.302435 | ||||||||
\(46\) | −4.59214 | −0.677074 | ||||||||
\(47\) | 10.7858 | 1.57327 | 0.786633 | − | 0.617421i | \(-0.211822\pi\) | ||||
0.786633 | + | 0.617421i | \(0.211822\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.10714 | −0.586734 | ||||||||
\(50\) | 0.883975 | 0.125013 | ||||||||
\(51\) | 2.06304 | 0.288884 | ||||||||
\(52\) | 4.73778 | 0.657012 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.453401 | 0.0611365 | ||||||||
\(56\) | 1.70084 | 0.227285 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −8.61390 | −1.13106 | ||||||||
\(59\) | 9.34264 | 1.21631 | 0.608154 | − | 0.793819i | \(-0.291910\pi\) | ||||
0.608154 | + | 0.793819i | \(0.291910\pi\) | |||||||
\(60\) | 2.02880 | 0.261917 | ||||||||
\(61\) | −9.93398 | −1.27192 | −0.635958 | − | 0.771724i | \(-0.719395\pi\) | ||||
−0.635958 | + | 0.771724i | \(0.719395\pi\) | |||||||
\(62\) | 6.41980 | 0.815315 | ||||||||
\(63\) | −1.70084 | −0.214286 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.61200 | −1.19222 | ||||||||
\(66\) | −0.223482 | −0.0275088 | ||||||||
\(67\) | −15.8980 | −1.94225 | −0.971127 | − | 0.238561i | \(-0.923324\pi\) | ||||
−0.971127 | + | 0.238561i | \(0.923324\pi\) | |||||||
\(68\) | −2.06304 | −0.250181 | ||||||||
\(69\) | −4.59214 | −0.552828 | ||||||||
\(70\) | −3.45067 | −0.412434 | ||||||||
\(71\) | 7.18427 | 0.852616 | 0.426308 | − | 0.904578i | \(-0.359814\pi\) | ||||
0.426308 | + | 0.904578i | \(0.359814\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −7.93289 | −0.928474 | −0.464237 | − | 0.885711i | \(-0.653671\pi\) | ||||
−0.464237 | + | 0.885711i | \(0.653671\pi\) | |||||||
\(74\) | −5.05467 | −0.587594 | ||||||||
\(75\) | 0.883975 | 0.102073 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0.380108 | 0.0433173 | ||||||||
\(78\) | 4.73778 | 0.536448 | ||||||||
\(79\) | 14.4968 | 1.63101 | 0.815506 | − | 0.578749i | \(-0.196459\pi\) | ||||
0.815506 | + | 0.578749i | \(0.196459\pi\) | |||||||
\(80\) | −2.02880 | −0.226827 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.36854 | 0.592856 | ||||||||
\(83\) | 3.88043 | 0.425932 | 0.212966 | − | 0.977060i | \(-0.431688\pi\) | ||||
0.212966 | + | 0.977060i | \(0.431688\pi\) | |||||||
\(84\) | 1.70084 | 0.185577 | ||||||||
\(85\) | 4.18550 | 0.453981 | ||||||||
\(86\) | 8.67694 | 0.935659 | ||||||||
\(87\) | −8.61390 | −0.923507 | ||||||||
\(88\) | 0.223482 | 0.0238233 | ||||||||
\(89\) | −2.21998 | −0.235317 | −0.117659 | − | 0.993054i | \(-0.537539\pi\) | ||||
−0.117659 | + | 0.993054i | \(0.537539\pi\) | |||||||
\(90\) | 2.02880 | 0.213854 | ||||||||
\(91\) | −8.05822 | −0.844731 | ||||||||
\(92\) | 4.59214 | 0.478763 | ||||||||
\(93\) | 6.41980 | 0.665702 | ||||||||
\(94\) | −10.7858 | −1.11247 | ||||||||
\(95\) | 2.02880 | 0.208150 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −3.71588 | −0.377291 | −0.188645 | − | 0.982045i | \(-0.560410\pi\) | ||||
−0.188645 | + | 0.982045i | \(0.560410\pi\) | |||||||
\(98\) | 4.10714 | 0.414883 | ||||||||
\(99\) | −0.223482 | −0.0224608 | ||||||||
\(100\) | −0.883975 | −0.0883975 | ||||||||
\(101\) | −17.5021 | −1.74153 | −0.870763 | − | 0.491704i | \(-0.836374\pi\) | ||||
−0.870763 | + | 0.491704i | \(0.836374\pi\) | |||||||
\(102\) | −2.06304 | −0.204272 | ||||||||
\(103\) | 6.54700 | 0.645095 | 0.322547 | − | 0.946553i | \(-0.395461\pi\) | ||||
0.322547 | + | 0.946553i | \(0.395461\pi\) | |||||||
\(104\) | −4.73778 | −0.464578 | ||||||||
\(105\) | −3.45067 | −0.336751 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | −8.87172 | −0.857661 | −0.428831 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428831 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −6.30195 | −0.603617 | −0.301809 | − | 0.953369i | \(-0.597590\pi\) | ||||
−0.301809 | + | 0.953369i | \(0.597590\pi\) | |||||||
\(110\) | −0.453401 | −0.0432300 | ||||||||
\(111\) | −5.05467 | −0.479768 | ||||||||
\(112\) | −1.70084 | −0.160714 | ||||||||
\(113\) | −3.08374 | −0.290094 | −0.145047 | − | 0.989425i | \(-0.546333\pi\) | ||||
−0.145047 | + | 0.989425i | \(0.546333\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −9.31652 | −0.868770 | ||||||||
\(116\) | 8.61390 | 0.799781 | ||||||||
\(117\) | 4.73778 | 0.438008 | ||||||||
\(118\) | −9.34264 | −0.860059 | ||||||||
\(119\) | 3.50891 | 0.321661 | ||||||||
\(120\) | −2.02880 | −0.185203 | ||||||||
\(121\) | −10.9501 | −0.995460 | ||||||||
\(122\) | 9.93398 | 0.899380 | ||||||||
\(123\) | 5.36854 | 0.484065 | ||||||||
\(124\) | −6.41980 | −0.576515 | ||||||||
\(125\) | 11.9374 | 1.06771 | ||||||||
\(126\) | 1.70084 | 0.151523 | ||||||||
\(127\) | 4.57655 | 0.406103 | 0.203051 | − | 0.979168i | \(-0.434914\pi\) | ||||
0.203051 | + | 0.979168i | \(0.434914\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.67694 | 0.763962 | ||||||||
\(130\) | 9.61200 | 0.843028 | ||||||||
\(131\) | 14.5165 | 1.26831 | 0.634155 | − | 0.773206i | \(-0.281348\pi\) | ||||
0.634155 | + | 0.773206i | \(0.281348\pi\) | |||||||
\(132\) | 0.223482 | 0.0194516 | ||||||||
\(133\) | 1.70084 | 0.147482 | ||||||||
\(134\) | 15.8980 | 1.37338 | ||||||||
\(135\) | 2.02880 | 0.174611 | ||||||||
\(136\) | 2.06304 | 0.176904 | ||||||||
\(137\) | −2.25805 | −0.192918 | −0.0964591 | − | 0.995337i | \(-0.530752\pi\) | ||||
−0.0964591 | + | 0.995337i | \(0.530752\pi\) | |||||||
\(138\) | 4.59214 | 0.390909 | ||||||||
\(139\) | −2.95933 | −0.251007 | −0.125504 | − | 0.992093i | \(-0.540055\pi\) | ||||
−0.125504 | + | 0.992093i | \(0.540055\pi\) | |||||||
\(140\) | 3.45067 | 0.291635 | ||||||||
\(141\) | −10.7858 | −0.908325 | ||||||||
\(142\) | −7.18427 | −0.602891 | ||||||||
\(143\) | −1.05881 | −0.0885421 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −17.4759 | −1.45129 | ||||||||
\(146\) | 7.93289 | 0.656530 | ||||||||
\(147\) | 4.10714 | 0.338751 | ||||||||
\(148\) | 5.05467 | 0.415492 | ||||||||
\(149\) | −4.29566 | −0.351914 | −0.175957 | − | 0.984398i | \(-0.556302\pi\) | ||||
−0.175957 | + | 0.984398i | \(0.556302\pi\) | |||||||
\(150\) | −0.883975 | −0.0721763 | ||||||||
\(151\) | 8.63019 | 0.702315 | 0.351158 | − | 0.936316i | \(-0.385788\pi\) | ||||
0.351158 | + | 0.936316i | \(0.385788\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −2.06304 | −0.166787 | ||||||||
\(154\) | −0.380108 | −0.0306300 | ||||||||
\(155\) | 13.0245 | 1.04615 | ||||||||
\(156\) | −4.73778 | −0.379326 | ||||||||
\(157\) | 10.1567 | 0.810596 | 0.405298 | − | 0.914185i | \(-0.367168\pi\) | ||||
0.405298 | + | 0.914185i | \(0.367168\pi\) | |||||||
\(158\) | −14.4968 | −1.15330 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | 2.02880 | 0.160391 | ||||||||
\(161\) | −7.81050 | −0.615554 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −18.0373 | −1.41279 | −0.706393 | − | 0.707819i | \(-0.749679\pi\) | ||||
−0.706393 | + | 0.707819i | \(0.749679\pi\) | |||||||
\(164\) | −5.36854 | −0.419212 | ||||||||
\(165\) | −0.453401 | −0.0352972 | ||||||||
\(166\) | −3.88043 | −0.301180 | ||||||||
\(167\) | 5.49247 | 0.425020 | 0.212510 | − | 0.977159i | \(-0.431836\pi\) | ||||
0.212510 | + | 0.977159i | \(0.431836\pi\) | |||||||
\(168\) | −1.70084 | −0.131223 | ||||||||
\(169\) | 9.44656 | 0.726659 | ||||||||
\(170\) | −4.18550 | −0.321013 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −8.67694 | −0.661611 | ||||||||
\(173\) | −5.96211 | −0.453291 | −0.226645 | − | 0.973977i | \(-0.572776\pi\) | ||||
−0.226645 | + | 0.973977i | \(0.572776\pi\) | |||||||
\(174\) | 8.61390 | 0.653018 | ||||||||
\(175\) | 1.50350 | 0.113654 | ||||||||
\(176\) | −0.223482 | −0.0168456 | ||||||||
\(177\) | −9.34264 | −0.702236 | ||||||||
\(178\) | 2.21998 | 0.166394 | ||||||||
\(179\) | −4.27562 | −0.319575 | −0.159788 | − | 0.987151i | \(-0.551081\pi\) | ||||
−0.159788 | + | 0.987151i | \(0.551081\pi\) | |||||||
\(180\) | −2.02880 | −0.151218 | ||||||||
\(181\) | −6.32260 | −0.469955 | −0.234977 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234977 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(182\) | 8.05822 | 0.597315 | ||||||||
\(183\) | 9.93398 | 0.734341 | ||||||||
\(184\) | −4.59214 | −0.338537 | ||||||||
\(185\) | −10.2549 | −0.753956 | ||||||||
\(186\) | −6.41980 | −0.470722 | ||||||||
\(187\) | 0.461053 | 0.0337155 | ||||||||
\(188\) | 10.7858 | 0.786633 | ||||||||
\(189\) | 1.70084 | 0.123718 | ||||||||
\(190\) | −2.02880 | −0.147185 | ||||||||
\(191\) | −5.88433 | −0.425775 | −0.212888 | − | 0.977077i | \(-0.568287\pi\) | ||||
−0.212888 | + | 0.977077i | \(0.568287\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 19.1609 | 1.37923 | 0.689615 | − | 0.724176i | \(-0.257780\pi\) | ||||
0.689615 | + | 0.724176i | \(0.257780\pi\) | |||||||
\(194\) | 3.71588 | 0.266785 | ||||||||
\(195\) | 9.61200 | 0.688330 | ||||||||
\(196\) | −4.10714 | −0.293367 | ||||||||
\(197\) | 4.17039 | 0.297128 | 0.148564 | − | 0.988903i | \(-0.452535\pi\) | ||||
0.148564 | + | 0.988903i | \(0.452535\pi\) | |||||||
\(198\) | 0.223482 | 0.0158822 | ||||||||
\(199\) | 18.9956 | 1.34656 | 0.673280 | − | 0.739388i | \(-0.264885\pi\) | ||||
0.673280 | + | 0.739388i | \(0.264885\pi\) | |||||||
\(200\) | 0.883975 | 0.0625065 | ||||||||
\(201\) | 15.8980 | 1.12136 | ||||||||
\(202\) | 17.5021 | 1.23144 | ||||||||
\(203\) | −14.6509 | −1.02829 | ||||||||
\(204\) | 2.06304 | 0.144442 | ||||||||
\(205\) | 10.8917 | 0.760708 | ||||||||
\(206\) | −6.54700 | −0.456151 | ||||||||
\(207\) | 4.59214 | 0.319176 | ||||||||
\(208\) | 4.73778 | 0.328506 | ||||||||
\(209\) | 0.223482 | 0.0154586 | ||||||||
\(210\) | 3.45067 | 0.238119 | ||||||||
\(211\) | −3.45387 | −0.237775 | −0.118887 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118887 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | −7.18427 | −0.492258 | ||||||||
\(214\) | 8.87172 | 0.606458 | ||||||||
\(215\) | 17.6038 | 1.20057 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 10.9191 | 0.741234 | ||||||||
\(218\) | 6.30195 | 0.426822 | ||||||||
\(219\) | 7.93289 | 0.536055 | ||||||||
\(220\) | 0.453401 | 0.0305683 | ||||||||
\(221\) | −9.77424 | −0.657486 | ||||||||
\(222\) | 5.05467 | 0.339247 | ||||||||
\(223\) | 12.6841 | 0.849392 | 0.424696 | − | 0.905336i | \(-0.360381\pi\) | ||||
0.424696 | + | 0.905336i | \(0.360381\pi\) | |||||||
\(224\) | 1.70084 | 0.113642 | ||||||||
\(225\) | −0.883975 | −0.0589317 | ||||||||
\(226\) | 3.08374 | 0.205127 | ||||||||
\(227\) | 16.5026 | 1.09532 | 0.547658 | − | 0.836702i | \(-0.315520\pi\) | ||||
0.547658 | + | 0.836702i | \(0.315520\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 25.0432 | 1.65490 | 0.827450 | − | 0.561540i | \(-0.189791\pi\) | ||||
0.827450 | + | 0.561540i | \(0.189791\pi\) | |||||||
\(230\) | 9.31652 | 0.614313 | ||||||||
\(231\) | −0.380108 | −0.0250093 | ||||||||
\(232\) | −8.61390 | −0.565530 | ||||||||
\(233\) | 5.73384 | 0.375636 | 0.187818 | − | 0.982204i | \(-0.439858\pi\) | ||||
0.187818 | + | 0.982204i | \(0.439858\pi\) | |||||||
\(234\) | −4.73778 | −0.309718 | ||||||||
\(235\) | −21.8822 | −1.42743 | ||||||||
\(236\) | 9.34264 | 0.608154 | ||||||||
\(237\) | −14.4968 | −0.941665 | ||||||||
\(238\) | −3.50891 | −0.227449 | ||||||||
\(239\) | −1.76355 | −0.114075 | −0.0570373 | − | 0.998372i | \(-0.518165\pi\) | ||||
−0.0570373 | + | 0.998372i | \(0.518165\pi\) | |||||||
\(240\) | 2.02880 | 0.130958 | ||||||||
\(241\) | 20.9874 | 1.35192 | 0.675960 | − | 0.736938i | \(-0.263729\pi\) | ||||
0.675960 | + | 0.736938i | \(0.263729\pi\) | |||||||
\(242\) | 10.9501 | 0.703896 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.93398 | −0.635958 | ||||||||
\(245\) | 8.33255 | 0.532347 | ||||||||
\(246\) | −5.36854 | −0.342285 | ||||||||
\(247\) | −4.73778 | −0.301458 | ||||||||
\(248\) | 6.41980 | 0.407657 | ||||||||
\(249\) | −3.88043 | −0.245912 | ||||||||
\(250\) | −11.9374 | −0.754988 | ||||||||
\(251\) | 14.7483 | 0.930903 | 0.465452 | − | 0.885073i | \(-0.345892\pi\) | ||||
0.465452 | + | 0.885073i | \(0.345892\pi\) | |||||||
\(252\) | −1.70084 | −0.107143 | ||||||||
\(253\) | −1.02626 | −0.0645205 | ||||||||
\(254\) | −4.57655 | −0.287158 | ||||||||
\(255\) | −4.18550 | −0.262106 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.08991 | −0.192743 | −0.0963716 | − | 0.995345i | \(-0.530724\pi\) | ||||
−0.0963716 | + | 0.995345i | \(0.530724\pi\) | |||||||
\(258\) | −8.67694 | −0.540203 | ||||||||
\(259\) | −8.59720 | −0.534204 | ||||||||
\(260\) | −9.61200 | −0.596111 | ||||||||
\(261\) | 8.61390 | 0.533187 | ||||||||
\(262\) | −14.5165 | −0.896830 | ||||||||
\(263\) | −2.74031 | −0.168975 | −0.0844873 | − | 0.996425i | \(-0.526925\pi\) | ||||
−0.0844873 | + | 0.996425i | \(0.526925\pi\) | |||||||
\(264\) | −0.223482 | −0.0137544 | ||||||||
\(265\) | −2.02880 | −0.124628 | ||||||||
\(266\) | −1.70084 | −0.104285 | ||||||||
\(267\) | 2.21998 | 0.135860 | ||||||||
\(268\) | −15.8980 | −0.971127 | ||||||||
\(269\) | 9.03286 | 0.550743 | 0.275372 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275372 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(270\) | −2.02880 | −0.123469 | ||||||||
\(271\) | 0.501586 | 0.0304692 | 0.0152346 | − | 0.999884i | \(-0.495150\pi\) | ||||
0.0152346 | + | 0.999884i | \(0.495150\pi\) | |||||||
\(272\) | −2.06304 | −0.125090 | ||||||||
\(273\) | 8.05822 | 0.487705 | ||||||||
\(274\) | 2.25805 | 0.136414 | ||||||||
\(275\) | 0.197553 | 0.0119129 | ||||||||
\(276\) | −4.59214 | −0.276414 | ||||||||
\(277\) | −16.0326 | −0.963308 | −0.481654 | − | 0.876362i | \(-0.659964\pi\) | ||||
−0.481654 | + | 0.876362i | \(0.659964\pi\) | |||||||
\(278\) | 2.95933 | 0.177489 | ||||||||
\(279\) | −6.41980 | −0.384343 | ||||||||
\(280\) | −3.45067 | −0.206217 | ||||||||
\(281\) | −10.0444 | −0.599201 | −0.299600 | − | 0.954065i | \(-0.596853\pi\) | ||||
−0.299600 | + | 0.954065i | \(0.596853\pi\) | |||||||
\(282\) | 10.7858 | 0.642283 | ||||||||
\(283\) | 4.04982 | 0.240737 | 0.120368 | − | 0.992729i | \(-0.461592\pi\) | ||||
0.120368 | + | 0.992729i | \(0.461592\pi\) | |||||||
\(284\) | 7.18427 | 0.426308 | ||||||||
\(285\) | −2.02880 | −0.120176 | ||||||||
\(286\) | 1.05881 | 0.0626087 | ||||||||
\(287\) | 9.13103 | 0.538988 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −12.7439 | −0.749639 | ||||||||
\(290\) | 17.4759 | 1.02622 | ||||||||
\(291\) | 3.71588 | 0.217829 | ||||||||
\(292\) | −7.93289 | −0.464237 | ||||||||
\(293\) | 18.6011 | 1.08669 | 0.543345 | − | 0.839509i | \(-0.317157\pi\) | ||||
0.543345 | + | 0.839509i | \(0.317157\pi\) | |||||||
\(294\) | −4.10714 | −0.239533 | ||||||||
\(295\) | −18.9543 | −1.10356 | ||||||||
\(296\) | −5.05467 | −0.293797 | ||||||||
\(297\) | 0.223482 | 0.0129678 | ||||||||
\(298\) | 4.29566 | 0.248841 | ||||||||
\(299\) | 21.7565 | 1.25821 | ||||||||
\(300\) | 0.883975 | 0.0510363 | ||||||||
\(301\) | 14.7581 | 0.850643 | ||||||||
\(302\) | −8.63019 | −0.496612 | ||||||||
\(303\) | 17.5021 | 1.00547 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 20.1540 | 1.15402 | ||||||||
\(306\) | 2.06304 | 0.117936 | ||||||||
\(307\) | 32.9887 | 1.88277 | 0.941384 | − | 0.337338i | \(-0.109526\pi\) | ||||
0.941384 | + | 0.337338i | \(0.109526\pi\) | |||||||
\(308\) | 0.380108 | 0.0216587 | ||||||||
\(309\) | −6.54700 | −0.372446 | ||||||||
\(310\) | −13.0245 | −0.739741 | ||||||||
\(311\) | −5.42378 | −0.307554 | −0.153777 | − | 0.988106i | \(-0.549144\pi\) | ||||
−0.153777 | + | 0.988106i | \(0.549144\pi\) | |||||||
\(312\) | 4.73778 | 0.268224 | ||||||||
\(313\) | −6.21772 | −0.351446 | −0.175723 | − | 0.984440i | \(-0.556226\pi\) | ||||
−0.175723 | + | 0.984440i | \(0.556226\pi\) | |||||||
\(314\) | −10.1567 | −0.573178 | ||||||||
\(315\) | 3.45067 | 0.194423 | ||||||||
\(316\) | 14.4968 | 0.815506 | ||||||||
\(317\) | −15.1750 | −0.852313 | −0.426156 | − | 0.904650i | \(-0.640133\pi\) | ||||
−0.426156 | + | 0.904650i | \(0.640133\pi\) | |||||||
\(318\) | 1.00000 | 0.0560772 | ||||||||
\(319\) | −1.92505 | −0.107782 | ||||||||
\(320\) | −2.02880 | −0.113413 | ||||||||
\(321\) | 8.87172 | 0.495171 | ||||||||
\(322\) | 7.81050 | 0.435262 | ||||||||
\(323\) | 2.06304 | 0.114791 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.18808 | −0.232313 | ||||||||
\(326\) | 18.0373 | 0.998991 | ||||||||
\(327\) | 6.30195 | 0.348499 | ||||||||
\(328\) | 5.36854 | 0.296428 | ||||||||
\(329\) | −18.3449 | −1.01139 | ||||||||
\(330\) | 0.453401 | 0.0249589 | ||||||||
\(331\) | −28.0327 | −1.54082 | −0.770408 | − | 0.637552i | \(-0.779947\pi\) | ||||
−0.770408 | + | 0.637552i | \(0.779947\pi\) | |||||||
\(332\) | 3.88043 | 0.212966 | ||||||||
\(333\) | 5.05467 | 0.276994 | ||||||||
\(334\) | −5.49247 | −0.300535 | ||||||||
\(335\) | 32.2539 | 1.76222 | ||||||||
\(336\) | 1.70084 | 0.0927886 | ||||||||
\(337\) | 21.2001 | 1.15484 | 0.577421 | − | 0.816447i | \(-0.304059\pi\) | ||||
0.577421 | + | 0.816447i | \(0.304059\pi\) | |||||||
\(338\) | −9.44656 | −0.513825 | ||||||||
\(339\) | 3.08374 | 0.167486 | ||||||||
\(340\) | 4.18550 | 0.226990 | ||||||||
\(341\) | 1.43471 | 0.0776939 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 18.8915 | 1.02004 | ||||||||
\(344\) | 8.67694 | 0.467829 | ||||||||
\(345\) | 9.31652 | 0.501585 | ||||||||
\(346\) | 5.96211 | 0.320525 | ||||||||
\(347\) | 12.4103 | 0.666218 | 0.333109 | − | 0.942888i | \(-0.391902\pi\) | ||||
0.333109 | + | 0.942888i | \(0.391902\pi\) | |||||||
\(348\) | −8.61390 | −0.461754 | ||||||||
\(349\) | 16.0095 | 0.856969 | 0.428485 | − | 0.903549i | \(-0.359048\pi\) | ||||
0.428485 | + | 0.903549i | \(0.359048\pi\) | |||||||
\(350\) | −1.50350 | −0.0803656 | ||||||||
\(351\) | −4.73778 | −0.252884 | ||||||||
\(352\) | 0.223482 | 0.0119116 | ||||||||
\(353\) | −22.0225 | −1.17214 | −0.586069 | − | 0.810261i | \(-0.699325\pi\) | ||||
−0.586069 | + | 0.810261i | \(0.699325\pi\) | |||||||
\(354\) | 9.34264 | 0.496556 | ||||||||
\(355\) | −14.5754 | −0.773584 | ||||||||
\(356\) | −2.21998 | −0.117659 | ||||||||
\(357\) | −3.50891 | −0.185711 | ||||||||
\(358\) | 4.27562 | 0.225974 | ||||||||
\(359\) | 14.2394 | 0.751526 | 0.375763 | − | 0.926716i | \(-0.377381\pi\) | ||||
0.375763 | + | 0.926716i | \(0.377381\pi\) | |||||||
\(360\) | 2.02880 | 0.106927 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 6.32260 | 0.332308 | ||||||||
\(363\) | 10.9501 | 0.574729 | ||||||||
\(364\) | −8.05822 | −0.422365 | ||||||||
\(365\) | 16.0942 | 0.842410 | ||||||||
\(366\) | −9.93398 | −0.519257 | ||||||||
\(367\) | 33.7719 | 1.76288 | 0.881440 | − | 0.472296i | \(-0.156575\pi\) | ||||
0.881440 | + | 0.472296i | \(0.156575\pi\) | |||||||
\(368\) | 4.59214 | 0.239382 | ||||||||
\(369\) | −5.36854 | −0.279475 | ||||||||
\(370\) | 10.2549 | 0.533128 | ||||||||
\(371\) | −1.70084 | −0.0883033 | ||||||||
\(372\) | 6.41980 | 0.332851 | ||||||||
\(373\) | 21.7568 | 1.12652 | 0.563262 | − | 0.826278i | \(-0.309546\pi\) | ||||
0.563262 | + | 0.826278i | \(0.309546\pi\) | |||||||
\(374\) | −0.461053 | −0.0238405 | ||||||||
\(375\) | −11.9374 | −0.616445 | ||||||||
\(376\) | −10.7858 | −0.556233 | ||||||||
\(377\) | 40.8108 | 2.10186 | ||||||||
\(378\) | −1.70084 | −0.0874819 | ||||||||
\(379\) | −8.08932 | −0.415520 | −0.207760 | − | 0.978180i | \(-0.566617\pi\) | ||||
−0.207760 | + | 0.978180i | \(0.566617\pi\) | |||||||
\(380\) | 2.02880 | 0.104075 | ||||||||
\(381\) | −4.57655 | −0.234464 | ||||||||
\(382\) | 5.88433 | 0.301069 | ||||||||
\(383\) | 5.30508 | 0.271077 | 0.135539 | − | 0.990772i | \(-0.456724\pi\) | ||||
0.135539 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.771163 | −0.0393021 | ||||||||
\(386\) | −19.1609 | −0.975263 | ||||||||
\(387\) | −8.67694 | −0.441074 | ||||||||
\(388\) | −3.71588 | −0.188645 | ||||||||
\(389\) | 11.9606 | 0.606424 | 0.303212 | − | 0.952923i | \(-0.401941\pi\) | ||||
0.303212 | + | 0.952923i | \(0.401941\pi\) | |||||||
\(390\) | −9.61200 | −0.486723 | ||||||||
\(391\) | −9.47377 | −0.479109 | ||||||||
\(392\) | 4.10714 | 0.207442 | ||||||||
\(393\) | −14.5165 | −0.732259 | ||||||||
\(394\) | −4.17039 | −0.210101 | ||||||||
\(395\) | −29.4110 | −1.47983 | ||||||||
\(396\) | −0.223482 | −0.0112304 | ||||||||
\(397\) | −2.38568 | −0.119734 | −0.0598669 | − | 0.998206i | \(-0.519068\pi\) | ||||
−0.0598669 | + | 0.998206i | \(0.519068\pi\) | |||||||
\(398\) | −18.9956 | −0.952161 | ||||||||
\(399\) | −1.70084 | −0.0851486 | ||||||||
\(400\) | −0.883975 | −0.0441988 | ||||||||
\(401\) | 12.3413 | 0.616293 | 0.308146 | − | 0.951339i | \(-0.400291\pi\) | ||||
0.308146 | + | 0.951339i | \(0.400291\pi\) | |||||||
\(402\) | −15.8980 | −0.792922 | ||||||||
\(403\) | −30.4156 | −1.51511 | ||||||||
\(404\) | −17.5021 | −0.870763 | ||||||||
\(405\) | −2.02880 | −0.100812 | ||||||||
\(406\) | 14.6509 | 0.727111 | ||||||||
\(407\) | −1.12963 | −0.0559937 | ||||||||
\(408\) | −2.06304 | −0.102136 | ||||||||
\(409\) | −0.0414247 | −0.00204832 | −0.00102416 | − | 0.999999i | \(-0.500326\pi\) | ||||
−0.00102416 | + | 0.999999i | \(0.500326\pi\) | |||||||
\(410\) | −10.8917 | −0.537902 | ||||||||
\(411\) | 2.25805 | 0.111381 | ||||||||
\(412\) | 6.54700 | 0.322547 | ||||||||
\(413\) | −15.8903 | −0.781913 | ||||||||
\(414\) | −4.59214 | −0.225691 | ||||||||
\(415\) | −7.87261 | −0.386451 | ||||||||
\(416\) | −4.73778 | −0.232289 | ||||||||
\(417\) | 2.95933 | 0.144919 | ||||||||
\(418\) | −0.223482 | −0.0109309 | ||||||||
\(419\) | −22.9342 | −1.12041 | −0.560205 | − | 0.828354i | \(-0.689278\pi\) | ||||
−0.560205 | + | 0.828354i | \(0.689278\pi\) | |||||||
\(420\) | −3.45067 | −0.168375 | ||||||||
\(421\) | −6.38045 | −0.310964 | −0.155482 | − | 0.987839i | \(-0.549693\pi\) | ||||
−0.155482 | + | 0.987839i | \(0.549693\pi\) | |||||||
\(422\) | 3.45387 | 0.168132 | ||||||||
\(423\) | 10.7858 | 0.524422 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | 1.82368 | 0.0884614 | ||||||||
\(426\) | 7.18427 | 0.348079 | ||||||||
\(427\) | 16.8961 | 0.817661 | ||||||||
\(428\) | −8.87172 | −0.428831 | ||||||||
\(429\) | 1.05881 | 0.0511198 | ||||||||
\(430\) | −17.6038 | −0.848929 | ||||||||
\(431\) | −26.9070 | −1.29607 | −0.648033 | − | 0.761613i | \(-0.724408\pi\) | ||||
−0.648033 | + | 0.761613i | \(0.724408\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −0.497344 | −0.0239008 | −0.0119504 | − | 0.999929i | \(-0.503804\pi\) | ||||
−0.0119504 | + | 0.999929i | \(0.503804\pi\) | |||||||
\(434\) | −10.9191 | −0.524132 | ||||||||
\(435\) | 17.4759 | 0.837904 | ||||||||
\(436\) | −6.30195 | −0.301809 | ||||||||
\(437\) | −4.59214 | −0.219672 | ||||||||
\(438\) | −7.93289 | −0.379048 | ||||||||
\(439\) | −17.0256 | −0.812590 | −0.406295 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406295 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(440\) | −0.453401 | −0.0216150 | ||||||||
\(441\) | −4.10714 | −0.195578 | ||||||||
\(442\) | 9.77424 | 0.464913 | ||||||||
\(443\) | 24.4326 | 1.16083 | 0.580414 | − | 0.814322i | \(-0.302891\pi\) | ||||
0.580414 | + | 0.814322i | \(0.302891\pi\) | |||||||
\(444\) | −5.05467 | −0.239884 | ||||||||
\(445\) | 4.50389 | 0.213505 | ||||||||
\(446\) | −12.6841 | −0.600611 | ||||||||
\(447\) | 4.29566 | 0.203178 | ||||||||
\(448\) | −1.70084 | −0.0803572 | ||||||||
\(449\) | 11.6675 | 0.550625 | 0.275313 | − | 0.961355i | \(-0.411219\pi\) | ||||
0.275313 | + | 0.961355i | \(0.411219\pi\) | |||||||
\(450\) | 0.883975 | 0.0416710 | ||||||||
\(451\) | 1.19977 | 0.0564951 | ||||||||
\(452\) | −3.08374 | −0.145047 | ||||||||
\(453\) | −8.63019 | −0.405482 | ||||||||
\(454\) | −16.5026 | −0.774505 | ||||||||
\(455\) | 16.3485 | 0.766430 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 4.47028 | 0.209111 | 0.104555 | − | 0.994519i | \(-0.466658\pi\) | ||||
0.104555 | + | 0.994519i | \(0.466658\pi\) | |||||||
\(458\) | −25.0432 | −1.17019 | ||||||||
\(459\) | 2.06304 | 0.0962945 | ||||||||
\(460\) | −9.31652 | −0.434385 | ||||||||
\(461\) | 17.0418 | 0.793717 | 0.396858 | − | 0.917880i | \(-0.370100\pi\) | ||||
0.396858 | + | 0.917880i | \(0.370100\pi\) | |||||||
\(462\) | 0.380108 | 0.0176842 | ||||||||
\(463\) | −29.2509 | −1.35940 | −0.679702 | − | 0.733488i | \(-0.737891\pi\) | ||||
−0.679702 | + | 0.733488i | \(0.737891\pi\) | |||||||
\(464\) | 8.61390 | 0.399890 | ||||||||
\(465\) | −13.0245 | −0.603996 | ||||||||
\(466\) | −5.73384 | −0.265615 | ||||||||
\(467\) | 28.3787 | 1.31321 | 0.656604 | − | 0.754236i | \(-0.271992\pi\) | ||||
0.656604 | + | 0.754236i | \(0.271992\pi\) | |||||||
\(468\) | 4.73778 | 0.219004 | ||||||||
\(469\) | 27.0401 | 1.24859 | ||||||||
\(470\) | 21.8822 | 1.00935 | ||||||||
\(471\) | −10.1567 | −0.467998 | ||||||||
\(472\) | −9.34264 | −0.430030 | ||||||||
\(473\) | 1.93914 | 0.0891619 | ||||||||
\(474\) | 14.4968 | 0.665858 | ||||||||
\(475\) | 0.883975 | 0.0405596 | ||||||||
\(476\) | 3.50891 | 0.160831 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | 1.76355 | 0.0806629 | ||||||||
\(479\) | −5.30183 | −0.242247 | −0.121123 | − | 0.992637i | \(-0.538650\pi\) | ||||
−0.121123 | + | 0.992637i | \(0.538650\pi\) | |||||||
\(480\) | −2.02880 | −0.0926016 | ||||||||
\(481\) | 23.9479 | 1.09193 | ||||||||
\(482\) | −20.9874 | −0.955952 | ||||||||
\(483\) | 7.81050 | 0.355390 | ||||||||
\(484\) | −10.9501 | −0.497730 | ||||||||
\(485\) | 7.53878 | 0.342318 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −12.5119 | −0.566969 | −0.283484 | − | 0.958977i | \(-0.591490\pi\) | ||||
−0.283484 | + | 0.958977i | \(0.591490\pi\) | |||||||
\(488\) | 9.93398 | 0.449690 | ||||||||
\(489\) | 18.0373 | 0.815673 | ||||||||
\(490\) | −8.33255 | −0.376426 | ||||||||
\(491\) | −42.2114 | −1.90497 | −0.952487 | − | 0.304580i | \(-0.901484\pi\) | ||||
−0.952487 | + | 0.304580i | \(0.901484\pi\) | |||||||
\(492\) | 5.36854 | 0.242032 | ||||||||
\(493\) | −17.7708 | −0.800358 | ||||||||
\(494\) | 4.73778 | 0.213163 | ||||||||
\(495\) | 0.453401 | 0.0203788 | ||||||||
\(496\) | −6.41980 | −0.288257 | ||||||||
\(497\) | −12.2193 | −0.548111 | ||||||||
\(498\) | 3.88043 | 0.173886 | ||||||||
\(499\) | −0.579520 | −0.0259429 | −0.0129714 | − | 0.999916i | \(-0.504129\pi\) | ||||
−0.0129714 | + | 0.999916i | \(0.504129\pi\) | |||||||
\(500\) | 11.9374 | 0.533857 | ||||||||
\(501\) | −5.49247 | −0.245386 | ||||||||
\(502\) | −14.7483 | −0.658248 | ||||||||
\(503\) | 33.0715 | 1.47459 | 0.737293 | − | 0.675573i | \(-0.236104\pi\) | ||||
0.737293 | + | 0.675573i | \(0.236104\pi\) | |||||||
\(504\) | 1.70084 | 0.0757615 | ||||||||
\(505\) | 35.5083 | 1.58010 | ||||||||
\(506\) | 1.02626 | 0.0456229 | ||||||||
\(507\) | −9.44656 | −0.419537 | ||||||||
\(508\) | 4.57655 | 0.203051 | ||||||||
\(509\) | −2.70935 | −0.120090 | −0.0600448 | − | 0.998196i | \(-0.519124\pi\) | ||||
−0.0600448 | + | 0.998196i | \(0.519124\pi\) | |||||||
\(510\) | 4.18550 | 0.185337 | ||||||||
\(511\) | 13.4926 | 0.596877 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 3.08991 | 0.136290 | ||||||||
\(515\) | −13.2825 | −0.585299 | ||||||||
\(516\) | 8.67694 | 0.381981 | ||||||||
\(517\) | −2.41043 | −0.106010 | ||||||||
\(518\) | 8.59720 | 0.377739 | ||||||||
\(519\) | 5.96211 | 0.261708 | ||||||||
\(520\) | 9.61200 | 0.421514 | ||||||||
\(521\) | 7.25875 | 0.318012 | 0.159006 | − | 0.987278i | \(-0.449171\pi\) | ||||
0.159006 | + | 0.987278i | \(0.449171\pi\) | |||||||
\(522\) | −8.61390 | −0.377020 | ||||||||
\(523\) | 33.8400 | 1.47972 | 0.739860 | − | 0.672761i | \(-0.234892\pi\) | ||||
0.739860 | + | 0.672761i | \(0.234892\pi\) | |||||||
\(524\) | 14.5165 | 0.634155 | ||||||||
\(525\) | −1.50350 | −0.0656182 | ||||||||
\(526\) | 2.74031 | 0.119483 | ||||||||
\(527\) | 13.2443 | 0.576931 | ||||||||
\(528\) | 0.223482 | 0.00972582 | ||||||||
\(529\) | −1.91228 | −0.0831427 | ||||||||
\(530\) | 2.02880 | 0.0881254 | ||||||||
\(531\) | 9.34264 | 0.405436 | ||||||||
\(532\) | 1.70084 | 0.0737409 | ||||||||
\(533\) | −25.4349 | −1.10171 | ||||||||
\(534\) | −2.21998 | −0.0960679 | ||||||||
\(535\) | 17.9989 | 0.778162 | ||||||||
\(536\) | 15.8980 | 0.686691 | ||||||||
\(537\) | 4.27562 | 0.184507 | ||||||||
\(538\) | −9.03286 | −0.389434 | ||||||||
\(539\) | 0.917872 | 0.0395355 | ||||||||
\(540\) | 2.02880 | 0.0873056 | ||||||||
\(541\) | 9.47507 | 0.407365 | 0.203683 | − | 0.979037i | \(-0.434709\pi\) | ||||
0.203683 | + | 0.979037i | \(0.434709\pi\) | |||||||
\(542\) | −0.501586 | −0.0215450 | ||||||||
\(543\) | 6.32260 | 0.271329 | ||||||||
\(544\) | 2.06304 | 0.0884522 | ||||||||
\(545\) | 12.7854 | 0.547666 | ||||||||
\(546\) | −8.05822 | −0.344860 | ||||||||
\(547\) | 25.5433 | 1.09215 | 0.546076 | − | 0.837736i | \(-0.316121\pi\) | ||||
0.546076 | + | 0.837736i | \(0.316121\pi\) | |||||||
\(548\) | −2.25805 | −0.0964591 | ||||||||
\(549\) | −9.93398 | −0.423972 | ||||||||
\(550\) | −0.197553 | −0.00842368 | ||||||||
\(551\) | −8.61390 | −0.366965 | ||||||||
\(552\) | 4.59214 | 0.195454 | ||||||||
\(553\) | −24.6567 | −1.04851 | ||||||||
\(554\) | 16.0326 | 0.681161 | ||||||||
\(555\) | 10.2549 | 0.435297 | ||||||||
\(556\) | −2.95933 | −0.125504 | ||||||||
\(557\) | 32.8585 | 1.39226 | 0.696130 | − | 0.717916i | \(-0.254904\pi\) | ||||
0.696130 | + | 0.717916i | \(0.254904\pi\) | |||||||
\(558\) | 6.41980 | 0.271772 | ||||||||
\(559\) | −41.1095 | −1.73874 | ||||||||
\(560\) | 3.45067 | 0.145817 | ||||||||
\(561\) | −0.461053 | −0.0194657 | ||||||||
\(562\) | 10.0444 | 0.423699 | ||||||||
\(563\) | 25.5273 | 1.07585 | 0.537923 | − | 0.842994i | \(-0.319209\pi\) | ||||
0.537923 | + | 0.842994i | \(0.319209\pi\) | |||||||
\(564\) | −10.7858 | −0.454163 | ||||||||
\(565\) | 6.25629 | 0.263204 | ||||||||
\(566\) | −4.04982 | −0.170227 | ||||||||
\(567\) | −1.70084 | −0.0714287 | ||||||||
\(568\) | −7.18427 | −0.301445 | ||||||||
\(569\) | −3.30396 | −0.138509 | −0.0692547 | − | 0.997599i | \(-0.522062\pi\) | ||||
−0.0692547 | + | 0.997599i | \(0.522062\pi\) | |||||||
\(570\) | 2.02880 | 0.0849770 | ||||||||
\(571\) | 39.3805 | 1.64802 | 0.824011 | − | 0.566574i | \(-0.191731\pi\) | ||||
0.824011 | + | 0.566574i | \(0.191731\pi\) | |||||||
\(572\) | −1.05881 | −0.0442711 | ||||||||
\(573\) | 5.88433 | 0.245821 | ||||||||
\(574\) | −9.13103 | −0.381122 | ||||||||
\(575\) | −4.05934 | −0.169286 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −10.1944 | −0.424397 | −0.212199 | − | 0.977227i | \(-0.568062\pi\) | ||||
−0.212199 | + | 0.977227i | \(0.568062\pi\) | |||||||
\(578\) | 12.7439 | 0.530075 | ||||||||
\(579\) | −19.1609 | −0.796299 | ||||||||
\(580\) | −17.4759 | −0.725646 | ||||||||
\(581\) | −6.60000 | −0.273814 | ||||||||
\(582\) | −3.71588 | −0.154028 | ||||||||
\(583\) | −0.223482 | −0.00925569 | ||||||||
\(584\) | 7.93289 | 0.328265 | ||||||||
\(585\) | −9.61200 | −0.397407 | ||||||||
\(586\) | −18.6011 | −0.768406 | ||||||||
\(587\) | 21.5564 | 0.889729 | 0.444864 | − | 0.895598i | \(-0.353252\pi\) | ||||
0.444864 | + | 0.895598i | \(0.353252\pi\) | |||||||
\(588\) | 4.10714 | 0.169375 | ||||||||
\(589\) | 6.41980 | 0.264523 | ||||||||
\(590\) | 18.9543 | 0.780337 | ||||||||
\(591\) | −4.17039 | −0.171547 | ||||||||
\(592\) | 5.05467 | 0.207746 | ||||||||
\(593\) | 21.0705 | 0.865263 | 0.432632 | − | 0.901571i | \(-0.357585\pi\) | ||||
0.432632 | + | 0.901571i | \(0.357585\pi\) | |||||||
\(594\) | −0.223482 | −0.00916959 | ||||||||
\(595\) | −7.11887 | −0.291845 | ||||||||
\(596\) | −4.29566 | −0.175957 | ||||||||
\(597\) | −18.9956 | −0.777436 | ||||||||
\(598\) | −21.7565 | −0.889691 | ||||||||
\(599\) | 29.3944 | 1.20102 | 0.600511 | − | 0.799616i | \(-0.294964\pi\) | ||||
0.600511 | + | 0.799616i | \(0.294964\pi\) | |||||||
\(600\) | −0.883975 | −0.0360881 | ||||||||
\(601\) | −27.4704 | −1.12054 | −0.560270 | − | 0.828310i | \(-0.689303\pi\) | ||||
−0.560270 | + | 0.828310i | \(0.689303\pi\) | |||||||
\(602\) | −14.7581 | −0.601496 | ||||||||
\(603\) | −15.8980 | −0.647418 | ||||||||
\(604\) | 8.63019 | 0.351158 | ||||||||
\(605\) | 22.2155 | 0.903187 | ||||||||
\(606\) | −17.5021 | −0.710975 | ||||||||
\(607\) | 24.1580 | 0.980544 | 0.490272 | − | 0.871569i | \(-0.336897\pi\) | ||||
0.490272 | + | 0.871569i | \(0.336897\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 14.6509 | 0.593684 | ||||||||
\(610\) | −20.1540 | −0.816013 | ||||||||
\(611\) | 51.1006 | 2.06731 | ||||||||
\(612\) | −2.06304 | −0.0833935 | ||||||||
\(613\) | −12.7610 | −0.515413 | −0.257707 | − | 0.966223i | \(-0.582967\pi\) | ||||
−0.257707 | + | 0.966223i | \(0.582967\pi\) | |||||||
\(614\) | −32.9887 | −1.33132 | ||||||||
\(615\) | −10.8917 | −0.439195 | ||||||||
\(616\) | −0.380108 | −0.0153150 | ||||||||
\(617\) | −18.5230 | −0.745706 | −0.372853 | − | 0.927890i | \(-0.621620\pi\) | ||||
−0.372853 | + | 0.927890i | \(0.621620\pi\) | |||||||
\(618\) | 6.54700 | 0.263359 | ||||||||
\(619\) | −35.1184 | −1.41153 | −0.705764 | − | 0.708447i | \(-0.749396\pi\) | ||||
−0.705764 | + | 0.708447i | \(0.749396\pi\) | |||||||
\(620\) | 13.0245 | 0.523076 | ||||||||
\(621\) | −4.59214 | −0.184276 | ||||||||
\(622\) | 5.42378 | 0.217474 | ||||||||
\(623\) | 3.77583 | 0.151276 | ||||||||
\(624\) | −4.73778 | −0.189663 | ||||||||
\(625\) | −19.7987 | −0.791948 | ||||||||
\(626\) | 6.21772 | 0.248510 | ||||||||
\(627\) | −0.223482 | −0.00892502 | ||||||||
\(628\) | 10.1567 | 0.405298 | ||||||||
\(629\) | −10.4280 | −0.415792 | ||||||||
\(630\) | −3.45067 | −0.137478 | ||||||||
\(631\) | 30.7829 | 1.22545 | 0.612724 | − | 0.790297i | \(-0.290074\pi\) | ||||
0.612724 | + | 0.790297i | \(0.290074\pi\) | |||||||
\(632\) | −14.4968 | −0.576650 | ||||||||
\(633\) | 3.45387 | 0.137279 | ||||||||
\(634\) | 15.1750 | 0.602676 | ||||||||
\(635\) | −9.28490 | −0.368460 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | −19.4587 | −0.770982 | ||||||||
\(638\) | 1.92505 | 0.0762136 | ||||||||
\(639\) | 7.18427 | 0.284205 | ||||||||
\(640\) | 2.02880 | 0.0801953 | ||||||||
\(641\) | 33.7703 | 1.33385 | 0.666924 | − | 0.745126i | \(-0.267611\pi\) | ||||
0.666924 | + | 0.745126i | \(0.267611\pi\) | |||||||
\(642\) | −8.87172 | −0.350139 | ||||||||
\(643\) | 15.9466 | 0.628871 | 0.314435 | − | 0.949279i | \(-0.398185\pi\) | ||||
0.314435 | + | 0.949279i | \(0.398185\pi\) | |||||||
\(644\) | −7.81050 | −0.307777 | ||||||||
\(645\) | −17.6038 | −0.693148 | ||||||||
\(646\) | −2.06304 | −0.0811693 | ||||||||
\(647\) | 23.3905 | 0.919574 | 0.459787 | − | 0.888029i | \(-0.347926\pi\) | ||||
0.459787 | + | 0.888029i | \(0.347926\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −2.08791 | −0.0819578 | ||||||||
\(650\) | 4.18808 | 0.164270 | ||||||||
\(651\) | −10.9191 | −0.427952 | ||||||||
\(652\) | −18.0373 | −0.706393 | ||||||||
\(653\) | 15.9056 | 0.622433 | 0.311217 | − | 0.950339i | \(-0.399264\pi\) | ||||
0.311217 | + | 0.950339i | \(0.399264\pi\) | |||||||
\(654\) | −6.30195 | −0.246426 | ||||||||
\(655\) | −29.4510 | −1.15074 | ||||||||
\(656\) | −5.36854 | −0.209606 | ||||||||
\(657\) | −7.93289 | −0.309491 | ||||||||
\(658\) | 18.3449 | 0.715158 | ||||||||
\(659\) | 3.30773 | 0.128851 | 0.0644255 | − | 0.997923i | \(-0.479479\pi\) | ||||
0.0644255 | + | 0.997923i | \(0.479479\pi\) | |||||||
\(660\) | −0.453401 | −0.0176486 | ||||||||
\(661\) | −6.39916 | −0.248898 | −0.124449 | − | 0.992226i | \(-0.539716\pi\) | ||||
−0.124449 | + | 0.992226i | \(0.539716\pi\) | |||||||
\(662\) | 28.0327 | 1.08952 | ||||||||
\(663\) | 9.77424 | 0.379600 | ||||||||
\(664\) | −3.88043 | −0.150590 | ||||||||
\(665\) | −3.45067 | −0.133811 | ||||||||
\(666\) | −5.05467 | −0.195865 | ||||||||
\(667\) | 39.5562 | 1.53162 | ||||||||
\(668\) | 5.49247 | 0.212510 | ||||||||
\(669\) | −12.6841 | −0.490397 | ||||||||
\(670\) | −32.2539 | −1.24608 | ||||||||
\(671\) | 2.22007 | 0.0857048 | ||||||||
\(672\) | −1.70084 | −0.0656114 | ||||||||
\(673\) | 17.0437 | 0.656986 | 0.328493 | − | 0.944506i | \(-0.393459\pi\) | ||||
0.328493 | + | 0.944506i | \(0.393459\pi\) | |||||||
\(674\) | −21.2001 | −0.816596 | ||||||||
\(675\) | 0.883975 | 0.0340242 | ||||||||
\(676\) | 9.44656 | 0.363329 | ||||||||
\(677\) | 11.2277 | 0.431516 | 0.215758 | − | 0.976447i | \(-0.430778\pi\) | ||||
0.215758 | + | 0.976447i | \(0.430778\pi\) | |||||||
\(678\) | −3.08374 | −0.118430 | ||||||||
\(679\) | 6.32013 | 0.242544 | ||||||||
\(680\) | −4.18550 | −0.160506 | ||||||||
\(681\) | −16.5026 | −0.632381 | ||||||||
\(682\) | −1.43471 | −0.0549379 | ||||||||
\(683\) | −4.10099 | −0.156920 | −0.0784600 | − | 0.996917i | \(-0.525000\pi\) | ||||
−0.0784600 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 4.58113 | 0.175036 | ||||||||
\(686\) | −18.8915 | −0.721280 | ||||||||
\(687\) | −25.0432 | −0.955457 | ||||||||
\(688\) | −8.67694 | −0.330805 | ||||||||
\(689\) | 4.73778 | 0.180495 | ||||||||
\(690\) | −9.31652 | −0.354674 | ||||||||
\(691\) | 7.45659 | 0.283662 | 0.141831 | − | 0.989891i | \(-0.454701\pi\) | ||||
0.141831 | + | 0.989891i | \(0.454701\pi\) | |||||||
\(692\) | −5.96211 | −0.226645 | ||||||||
\(693\) | 0.380108 | 0.0144391 | ||||||||
\(694\) | −12.4103 | −0.471087 | ||||||||
\(695\) | 6.00389 | 0.227741 | ||||||||
\(696\) | 8.61390 | 0.326509 | ||||||||
\(697\) | 11.0755 | 0.419515 | ||||||||
\(698\) | −16.0095 | −0.605969 | ||||||||
\(699\) | −5.73384 | −0.216874 | ||||||||
\(700\) | 1.50350 | 0.0568271 | ||||||||
\(701\) | 11.7003 | 0.441914 | 0.220957 | − | 0.975284i | \(-0.429082\pi\) | ||||
0.220957 | + | 0.975284i | \(0.429082\pi\) | |||||||
\(702\) | 4.73778 | 0.178816 | ||||||||
\(703\) | −5.05467 | −0.190641 | ||||||||
\(704\) | −0.223482 | −0.00842280 | ||||||||
\(705\) | 21.8822 | 0.824130 | ||||||||
\(706\) | 22.0225 | 0.828827 | ||||||||
\(707\) | 29.7683 | 1.11955 | ||||||||
\(708\) | −9.34264 | −0.351118 | ||||||||
\(709\) | −11.6337 | −0.436914 | −0.218457 | − | 0.975847i | \(-0.570102\pi\) | ||||
−0.218457 | + | 0.975847i | \(0.570102\pi\) | |||||||
\(710\) | 14.5754 | 0.547007 | ||||||||
\(711\) | 14.4968 | 0.543671 | ||||||||
\(712\) | 2.21998 | 0.0831972 | ||||||||
\(713\) | −29.4806 | −1.10406 | ||||||||
\(714\) | 3.50891 | 0.131318 | ||||||||
\(715\) | 2.14811 | 0.0803348 | ||||||||
\(716\) | −4.27562 | −0.159788 | ||||||||
\(717\) | 1.76355 | 0.0658610 | ||||||||
\(718\) | −14.2394 | −0.531409 | ||||||||
\(719\) | 46.1040 | 1.71939 | 0.859694 | − | 0.510809i | \(-0.170654\pi\) | ||||
0.859694 | + | 0.510809i | \(0.170654\pi\) | |||||||
\(720\) | −2.02880 | −0.0756089 | ||||||||
\(721\) | −11.1354 | −0.414704 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −20.9874 | −0.780531 | ||||||||
\(724\) | −6.32260 | −0.234977 | ||||||||
\(725\) | −7.61448 | −0.282795 | ||||||||
\(726\) | −10.9501 | −0.406395 | ||||||||
\(727\) | 17.1220 | 0.635019 | 0.317510 | − | 0.948255i | \(-0.397153\pi\) | ||||
0.317510 | + | 0.948255i | \(0.397153\pi\) | |||||||
\(728\) | 8.05822 | 0.298657 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −16.0942 | −0.595674 | ||||||||
\(731\) | 17.9009 | 0.662088 | ||||||||
\(732\) | 9.93398 | 0.367170 | ||||||||
\(733\) | 5.23908 | 0.193510 | 0.0967549 | − | 0.995308i | \(-0.469154\pi\) | ||||
0.0967549 | + | 0.995308i | \(0.469154\pi\) | |||||||
\(734\) | −33.7719 | −1.24654 | ||||||||
\(735\) | −8.33255 | −0.307351 | ||||||||
\(736\) | −4.59214 | −0.169268 | ||||||||
\(737\) | 3.55293 | 0.130874 | ||||||||
\(738\) | 5.36854 | 0.197619 | ||||||||
\(739\) | −2.05156 | −0.0754678 | −0.0377339 | − | 0.999288i | \(-0.512014\pi\) | ||||
−0.0377339 | + | 0.999288i | \(0.512014\pi\) | |||||||
\(740\) | −10.2549 | −0.376978 | ||||||||
\(741\) | 4.73778 | 0.174047 | ||||||||
\(742\) | 1.70084 | 0.0624399 | ||||||||
\(743\) | −21.0817 | −0.773412 | −0.386706 | − | 0.922203i | \(-0.626387\pi\) | ||||
−0.386706 | + | 0.922203i | \(0.626387\pi\) | |||||||
\(744\) | −6.41980 | −0.235361 | ||||||||
\(745\) | 8.71503 | 0.319294 | ||||||||
\(746\) | −21.7568 | −0.796573 | ||||||||
\(747\) | 3.88043 | 0.141977 | ||||||||
\(748\) | 0.461053 | 0.0168578 | ||||||||
\(749\) | 15.0894 | 0.551354 | ||||||||
\(750\) | 11.9374 | 0.435892 | ||||||||
\(751\) | 50.6645 | 1.84877 | 0.924387 | − | 0.381456i | \(-0.124577\pi\) | ||||
0.924387 | + | 0.381456i | \(0.124577\pi\) | |||||||
\(752\) | 10.7858 | 0.393316 | ||||||||
\(753\) | −14.7483 | −0.537457 | ||||||||
\(754\) | −40.8108 | −1.48624 | ||||||||
\(755\) | −17.5089 | −0.637215 | ||||||||
\(756\) | 1.70084 | 0.0618590 | ||||||||
\(757\) | 21.2177 | 0.771172 | 0.385586 | − | 0.922672i | \(-0.373999\pi\) | ||||
0.385586 | + | 0.922672i | \(0.373999\pi\) | |||||||
\(758\) | 8.08932 | 0.293817 | ||||||||
\(759\) | 1.02626 | 0.0372509 | ||||||||
\(760\) | −2.02880 | −0.0735923 | ||||||||
\(761\) | 17.6053 | 0.638193 | 0.319096 | − | 0.947722i | \(-0.396621\pi\) | ||||
0.319096 | + | 0.947722i | \(0.396621\pi\) | |||||||
\(762\) | 4.57655 | 0.165791 | ||||||||
\(763\) | 10.7186 | 0.388040 | ||||||||
\(764\) | −5.88433 | −0.212888 | ||||||||
\(765\) | 4.18550 | 0.151327 | ||||||||
\(766\) | −5.30508 | −0.191680 | ||||||||
\(767\) | 44.2634 | 1.59826 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −24.0275 | −0.866452 | −0.433226 | − | 0.901285i | \(-0.642625\pi\) | ||||
−0.433226 | + | 0.901285i | \(0.642625\pi\) | |||||||
\(770\) | 0.771163 | 0.0277908 | ||||||||
\(771\) | 3.08991 | 0.111280 | ||||||||
\(772\) | 19.1609 | 0.689615 | ||||||||
\(773\) | −5.20207 | −0.187105 | −0.0935527 | − | 0.995614i | \(-0.529822\pi\) | ||||
−0.0935527 | + | 0.995614i | \(0.529822\pi\) | |||||||
\(774\) | 8.67694 | 0.311886 | ||||||||
\(775\) | 5.67494 | 0.203850 | ||||||||
\(776\) | 3.71588 | 0.133392 | ||||||||
\(777\) | 8.59720 | 0.308423 | ||||||||
\(778\) | −11.9606 | −0.428807 | ||||||||
\(779\) | 5.36854 | 0.192348 | ||||||||
\(780\) | 9.61200 | 0.344165 | ||||||||
\(781\) | −1.60556 | −0.0574514 | ||||||||
\(782\) | 9.47377 | 0.338781 | ||||||||
\(783\) | −8.61390 | −0.307836 | ||||||||
\(784\) | −4.10714 | −0.146683 | ||||||||
\(785\) | −20.6060 | −0.735459 | ||||||||
\(786\) | 14.5165 | 0.517785 | ||||||||
\(787\) | −7.79610 | −0.277901 | −0.138951 | − | 0.990299i | \(-0.544373\pi\) | ||||
−0.138951 | + | 0.990299i | \(0.544373\pi\) | |||||||
\(788\) | 4.17039 | 0.148564 | ||||||||
\(789\) | 2.74031 | 0.0975576 | ||||||||
\(790\) | 29.4110 | 1.04640 | ||||||||
\(791\) | 5.24496 | 0.186489 | ||||||||
\(792\) | 0.223482 | 0.00794110 | ||||||||
\(793\) | −47.0650 | −1.67133 | ||||||||
\(794\) | 2.38568 | 0.0846646 | ||||||||
\(795\) | 2.02880 | 0.0719541 | ||||||||
\(796\) | 18.9956 | 0.673280 | ||||||||
\(797\) | 31.1103 | 1.10198 | 0.550992 | − | 0.834511i | \(-0.314250\pi\) | ||||
0.550992 | + | 0.834511i | \(0.314250\pi\) | |||||||
\(798\) | 1.70084 | 0.0602092 | ||||||||
\(799\) | −22.2515 | −0.787201 | ||||||||
\(800\) | 0.883975 | 0.0312533 | ||||||||
\(801\) | −2.21998 | −0.0784391 | ||||||||
\(802\) | −12.3413 | −0.435785 | ||||||||
\(803\) | 1.77286 | 0.0625628 | ||||||||
\(804\) | 15.8980 | 0.560681 | ||||||||
\(805\) | 15.8459 | 0.558496 | ||||||||
\(806\) | 30.4156 | 1.07134 | ||||||||
\(807\) | −9.03286 | −0.317972 | ||||||||
\(808\) | 17.5021 | 0.615722 | ||||||||
\(809\) | 3.95472 | 0.139040 | 0.0695202 | − | 0.997581i | \(-0.477853\pi\) | ||||
0.0695202 | + | 0.997581i | \(0.477853\pi\) | |||||||
\(810\) | 2.02880 | 0.0712847 | ||||||||
\(811\) | 7.90285 | 0.277507 | 0.138753 | − | 0.990327i | \(-0.455690\pi\) | ||||
0.138753 | + | 0.990327i | \(0.455690\pi\) | |||||||
\(812\) | −14.6509 | −0.514145 | ||||||||
\(813\) | −0.501586 | −0.0175914 | ||||||||
\(814\) | 1.12963 | 0.0395935 | ||||||||
\(815\) | 36.5940 | 1.28183 | ||||||||
\(816\) | 2.06304 | 0.0722209 | ||||||||
\(817\) | 8.67694 | 0.303568 | ||||||||
\(818\) | 0.0414247 | 0.00144838 | ||||||||
\(819\) | −8.05822 | −0.281577 | ||||||||
\(820\) | 10.8917 | 0.380354 | ||||||||
\(821\) | 8.33085 | 0.290749 | 0.145374 | − | 0.989377i | \(-0.453561\pi\) | ||||
0.145374 | + | 0.989377i | \(0.453561\pi\) | |||||||
\(822\) | −2.25805 | −0.0787585 | ||||||||
\(823\) | 1.02874 | 0.0358598 | 0.0179299 | − | 0.999839i | \(-0.494292\pi\) | ||||
0.0179299 | + | 0.999839i | \(0.494292\pi\) | |||||||
\(824\) | −6.54700 | −0.228075 | ||||||||
\(825\) | −0.197553 | −0.00687791 | ||||||||
\(826\) | 15.8903 | 0.552896 | ||||||||
\(827\) | 4.57843 | 0.159208 | 0.0796038 | − | 0.996827i | \(-0.474634\pi\) | ||||
0.0796038 | + | 0.996827i | \(0.474634\pi\) | |||||||
\(828\) | 4.59214 | 0.159588 | ||||||||
\(829\) | −50.9301 | −1.76887 | −0.884437 | − | 0.466660i | \(-0.845457\pi\) | ||||
−0.884437 | + | 0.466660i | \(0.845457\pi\) | |||||||
\(830\) | 7.87261 | 0.273262 | ||||||||
\(831\) | 16.0326 | 0.556166 | ||||||||
\(832\) | 4.73778 | 0.164253 | ||||||||
\(833\) | 8.47319 | 0.293579 | ||||||||
\(834\) | −2.95933 | −0.102473 | ||||||||
\(835\) | −11.1431 | −0.385624 | ||||||||
\(836\) | 0.223482 | 0.00772930 | ||||||||
\(837\) | 6.41980 | 0.221901 | ||||||||
\(838\) | 22.9342 | 0.792249 | ||||||||
\(839\) | −27.6799 | −0.955618 | −0.477809 | − | 0.878464i | \(-0.658569\pi\) | ||||
−0.477809 | + | 0.878464i | \(0.658569\pi\) | |||||||
\(840\) | 3.45067 | 0.119059 | ||||||||
\(841\) | 45.1993 | 1.55860 | ||||||||
\(842\) | 6.38045 | 0.219885 | ||||||||
\(843\) | 10.0444 | 0.345949 | ||||||||
\(844\) | −3.45387 | −0.118887 | ||||||||
\(845\) | −19.1652 | −0.659302 | ||||||||
\(846\) | −10.7858 | −0.370822 | ||||||||
\(847\) | 18.6243 | 0.639939 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | −4.04982 | −0.138989 | ||||||||
\(850\) | −1.82368 | −0.0625516 | ||||||||
\(851\) | 23.2117 | 0.795688 | ||||||||
\(852\) | −7.18427 | −0.246129 | ||||||||
\(853\) | −11.3815 | −0.389694 | −0.194847 | − | 0.980834i | \(-0.562421\pi\) | ||||
−0.194847 | + | 0.980834i | \(0.562421\pi\) | |||||||
\(854\) | −16.8961 | −0.578174 | ||||||||
\(855\) | 2.02880 | 0.0693835 | ||||||||
\(856\) | 8.87172 | 0.303229 | ||||||||
\(857\) | −48.1413 | −1.64448 | −0.822238 | − | 0.569144i | \(-0.807275\pi\) | ||||
−0.822238 | + | 0.569144i | \(0.807275\pi\) | |||||||
\(858\) | −1.05881 | −0.0361472 | ||||||||
\(859\) | 36.9543 | 1.26087 | 0.630433 | − | 0.776244i | \(-0.282877\pi\) | ||||
0.630433 | + | 0.776244i | \(0.282877\pi\) | |||||||
\(860\) | 17.6038 | 0.600284 | ||||||||
\(861\) | −9.13103 | −0.311185 | ||||||||
\(862\) | 26.9070 | 0.916457 | ||||||||
\(863\) | 15.8799 | 0.540557 | 0.270278 | − | 0.962782i | \(-0.412884\pi\) | ||||
0.270278 | + | 0.962782i | \(0.412884\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 12.0959 | 0.411274 | ||||||||
\(866\) | 0.497344 | 0.0169004 | ||||||||
\(867\) | 12.7439 | 0.432804 | ||||||||
\(868\) | 10.9191 | 0.370617 | ||||||||
\(869\) | −3.23977 | −0.109902 | ||||||||
\(870\) | −17.4759 | −0.592488 | ||||||||
\(871\) | −75.3214 | −2.55217 | ||||||||
\(872\) | 6.30195 | 0.213411 | ||||||||
\(873\) | −3.71588 | −0.125764 | ||||||||
\(874\) | 4.59214 | 0.155331 | ||||||||
\(875\) | −20.3036 | −0.686388 | ||||||||
\(876\) | 7.93289 | 0.268027 | ||||||||
\(877\) | 36.0829 | 1.21843 | 0.609216 | − | 0.793004i | \(-0.291484\pi\) | ||||
0.609216 | + | 0.793004i | \(0.291484\pi\) | |||||||
\(878\) | 17.0256 | 0.574588 | ||||||||
\(879\) | −18.6011 | −0.627401 | ||||||||
\(880\) | 0.453401 | 0.0152841 | ||||||||
\(881\) | 14.1218 | 0.475774 | 0.237887 | − | 0.971293i | \(-0.423545\pi\) | ||||
0.237887 | + | 0.971293i | \(0.423545\pi\) | |||||||
\(882\) | 4.10714 | 0.138294 | ||||||||
\(883\) | 10.0116 | 0.336918 | 0.168459 | − | 0.985709i | \(-0.446121\pi\) | ||||
0.168459 | + | 0.985709i | \(0.446121\pi\) | |||||||
\(884\) | −9.77424 | −0.328743 | ||||||||
\(885\) | 18.9543 | 0.637143 | ||||||||
\(886\) | −24.4326 | −0.820829 | ||||||||
\(887\) | 24.9380 | 0.837338 | 0.418669 | − | 0.908139i | \(-0.362497\pi\) | ||||
0.418669 | + | 0.908139i | \(0.362497\pi\) | |||||||
\(888\) | 5.05467 | 0.169624 | ||||||||
\(889\) | −7.78399 | −0.261067 | ||||||||
\(890\) | −4.50389 | −0.150971 | ||||||||
\(891\) | −0.223482 | −0.00748694 | ||||||||
\(892\) | 12.6841 | 0.424696 | ||||||||
\(893\) | −10.7858 | −0.360932 | ||||||||
\(894\) | −4.29566 | −0.143668 | ||||||||
\(895\) | 8.67438 | 0.289953 | ||||||||
\(896\) | 1.70084 | 0.0568212 | ||||||||
\(897\) | −21.7565 | −0.726430 | ||||||||
\(898\) | −11.6675 | −0.389351 | ||||||||
\(899\) | −55.2995 | −1.84434 | ||||||||
\(900\) | −0.883975 | −0.0294658 | ||||||||
\(901\) | −2.06304 | −0.0687299 | ||||||||
\(902\) | −1.19977 | −0.0399481 | ||||||||
\(903\) | −14.7581 | −0.491119 | ||||||||
\(904\) | 3.08374 | 0.102564 | ||||||||
\(905\) | 12.8273 | 0.426393 | ||||||||
\(906\) | 8.63019 | 0.286719 | ||||||||
\(907\) | −0.977827 | −0.0324682 | −0.0162341 | − | 0.999868i | \(-0.505168\pi\) | ||||
−0.0162341 | + | 0.999868i | \(0.505168\pi\) | |||||||
\(908\) | 16.5026 | 0.547658 | ||||||||
\(909\) | −17.5021 | −0.580508 | ||||||||
\(910\) | −16.3485 | −0.541948 | ||||||||
\(911\) | −36.6570 | −1.21450 | −0.607251 | − | 0.794510i | \(-0.707728\pi\) | ||||
−0.607251 | + | 0.794510i | \(0.707728\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −0.867207 | −0.0287004 | ||||||||
\(914\) | −4.47028 | −0.147864 | ||||||||
\(915\) | −20.1540 | −0.666272 | ||||||||
\(916\) | 25.0432 | 0.827450 | ||||||||
\(917\) | −24.6902 | −0.815343 | ||||||||
\(918\) | −2.06304 | −0.0680905 | ||||||||
\(919\) | −46.4054 | −1.53077 | −0.765387 | − | 0.643570i | \(-0.777452\pi\) | ||||
−0.765387 | + | 0.643570i | \(0.777452\pi\) | |||||||
\(920\) | 9.31652 | 0.307157 | ||||||||
\(921\) | −32.9887 | −1.08702 | ||||||||
\(922\) | −17.0418 | −0.561242 | ||||||||
\(923\) | 34.0375 | 1.12036 | ||||||||
\(924\) | −0.380108 | −0.0125046 | ||||||||
\(925\) | −4.46821 | −0.146914 | ||||||||
\(926\) | 29.2509 | 0.961244 | ||||||||
\(927\) | 6.54700 | 0.215032 | ||||||||
\(928\) | −8.61390 | −0.282765 | ||||||||
\(929\) | −40.7275 | −1.33623 | −0.668113 | − | 0.744060i | \(-0.732898\pi\) | ||||
−0.668113 | + | 0.744060i | \(0.732898\pi\) | |||||||
\(930\) | 13.0245 | 0.427089 | ||||||||
\(931\) | 4.10714 | 0.134606 | ||||||||
\(932\) | 5.73384 | 0.187818 | ||||||||
\(933\) | 5.42378 | 0.177567 | ||||||||
\(934\) | −28.3787 | −0.928578 | ||||||||
\(935\) | −0.935384 | −0.0305903 | ||||||||
\(936\) | −4.73778 | −0.154859 | ||||||||
\(937\) | −33.1944 | −1.08441 | −0.542207 | − | 0.840245i | \(-0.682411\pi\) | ||||
−0.542207 | + | 0.840245i | \(0.682411\pi\) | |||||||
\(938\) | −27.0401 | −0.882889 | ||||||||
\(939\) | 6.21772 | 0.202908 | ||||||||
\(940\) | −21.8822 | −0.713717 | ||||||||
\(941\) | −27.4054 | −0.893391 | −0.446695 | − | 0.894686i | \(-0.647399\pi\) | ||||
−0.446695 | + | 0.894686i | \(0.647399\pi\) | |||||||
\(942\) | 10.1567 | 0.330925 | ||||||||
\(943\) | −24.6531 | −0.802814 | ||||||||
\(944\) | 9.34264 | 0.304077 | ||||||||
\(945\) | −3.45067 | −0.112250 | ||||||||
\(946\) | −1.93914 | −0.0630470 | ||||||||
\(947\) | 30.2622 | 0.983389 | 0.491694 | − | 0.870768i | \(-0.336378\pi\) | ||||
0.491694 | + | 0.870768i | \(0.336378\pi\) | |||||||
\(948\) | −14.4968 | −0.470833 | ||||||||
\(949\) | −37.5843 | −1.22004 | ||||||||
\(950\) | −0.883975 | −0.0286800 | ||||||||
\(951\) | 15.1750 | 0.492083 | ||||||||
\(952\) | −3.50891 | −0.113724 | ||||||||
\(953\) | −1.25115 | −0.0405287 | −0.0202643 | − | 0.999795i | \(-0.506451\pi\) | ||||
−0.0202643 | + | 0.999795i | \(0.506451\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | 11.9381 | 0.386309 | ||||||||
\(956\) | −1.76355 | −0.0570373 | ||||||||
\(957\) | 1.92505 | 0.0622282 | ||||||||
\(958\) | 5.30183 | 0.171294 | ||||||||
\(959\) | 3.84059 | 0.124019 | ||||||||
\(960\) | 2.02880 | 0.0654792 | ||||||||
\(961\) | 10.2138 | 0.329477 | ||||||||
\(962\) | −23.9479 | −0.772112 | ||||||||
\(963\) | −8.87172 | −0.285887 | ||||||||
\(964\) | 20.9874 | 0.675960 | ||||||||
\(965\) | −38.8736 | −1.25138 | ||||||||
\(966\) | −7.81050 | −0.251299 | ||||||||
\(967\) | −8.68626 | −0.279331 | −0.139666 | − | 0.990199i | \(-0.544603\pi\) | ||||
−0.139666 | + | 0.990199i | \(0.544603\pi\) | |||||||
\(968\) | 10.9501 | 0.351948 | ||||||||
\(969\) | −2.06304 | −0.0662744 | ||||||||
\(970\) | −7.53878 | −0.242056 | ||||||||
\(971\) | −24.2896 | −0.779490 | −0.389745 | − | 0.920923i | \(-0.627437\pi\) | ||||
−0.389745 | + | 0.920923i | \(0.627437\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 5.03336 | 0.161362 | ||||||||
\(974\) | 12.5119 | 0.400908 | ||||||||
\(975\) | 4.18808 | 0.134126 | ||||||||
\(976\) | −9.93398 | −0.317979 | ||||||||
\(977\) | −22.0269 | −0.704703 | −0.352352 | − | 0.935868i | \(-0.614618\pi\) | ||||
−0.352352 | + | 0.935868i | \(0.614618\pi\) | |||||||
\(978\) | −18.0373 | −0.576768 | ||||||||
\(979\) | 0.496126 | 0.0158562 | ||||||||
\(980\) | 8.33255 | 0.266174 | ||||||||
\(981\) | −6.30195 | −0.201206 | ||||||||
\(982\) | 42.2114 | 1.34702 | ||||||||
\(983\) | 7.37854 | 0.235339 | 0.117669 | − | 0.993053i | \(-0.462458\pi\) | ||||
0.117669 | + | 0.993053i | \(0.462458\pi\) | |||||||
\(984\) | −5.36854 | −0.171143 | ||||||||
\(985\) | −8.46088 | −0.269586 | ||||||||
\(986\) | 17.7708 | 0.565939 | ||||||||
\(987\) | 18.3449 | 0.583924 | ||||||||
\(988\) | −4.73778 | −0.150729 | ||||||||
\(989\) | −39.8457 | −1.26702 | ||||||||
\(990\) | −0.453401 | −0.0144100 | ||||||||
\(991\) | −46.2751 | −1.46998 | −0.734988 | − | 0.678080i | \(-0.762812\pi\) | ||||
−0.734988 | + | 0.678080i | \(0.762812\pi\) | |||||||
\(992\) | 6.41980 | 0.203829 | ||||||||
\(993\) | 28.0327 | 0.889590 | ||||||||
\(994\) | 12.2193 | 0.387573 | ||||||||
\(995\) | −38.5382 | −1.22174 | ||||||||
\(996\) | −3.88043 | −0.122956 | ||||||||
\(997\) | 12.7776 | 0.404670 | 0.202335 | − | 0.979316i | \(-0.435147\pi\) | ||||
0.202335 | + | 0.979316i | \(0.435147\pi\) | |||||||
\(998\) | 0.579520 | 0.0183444 | ||||||||
\(999\) | −5.05467 | −0.159923 |
(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 | 6042.2.a.z.1.3 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.z.1.3 | ✓ | 9 | 1.1 | even | 1 | trivial |