Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} + \cdots - 208 \) |
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 | 1.1 | ||
Root | \(-4.28632\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.28632 | −1.91690 | −0.958451 | − | 0.285257i | \(-0.907921\pi\) | ||||
−0.958451 | + | 0.285257i | \(0.907921\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.70119 | 0.642988 | 0.321494 | − | 0.946912i | \(-0.395815\pi\) | ||||
0.321494 | + | 0.946912i | \(0.395815\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.51446 | 1.36116 | 0.680581 | − | 0.732673i | \(-0.261728\pi\) | ||||
0.680581 | + | 0.732673i | \(0.261728\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.48859 | −0.412860 | −0.206430 | − | 0.978461i | \(-0.566185\pi\) | ||||
−0.206430 | + | 0.978461i | \(0.566185\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.28632 | 1.10672 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.55072 | −0.376105 | −0.188052 | − | 0.982159i | \(-0.560217\pi\) | ||||
−0.188052 | + | 0.982159i | \(0.560217\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.31263 | −0.301138 | −0.150569 | − | 0.988600i | \(-0.548111\pi\) | ||||
−0.150569 | + | 0.988600i | \(0.548111\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.70119 | −0.371229 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.3726 | 2.67451 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.61274 | −0.469262 | −0.234631 | − | 0.972084i | \(-0.575388\pi\) | ||||
−0.234631 | + | 0.972084i | \(0.575388\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.51446 | −0.785867 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.29183 | −1.23254 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.322680 | −0.0530483 | −0.0265241 | − | 0.999648i | \(-0.508444\pi\) | ||||
−0.0265241 | + | 0.999648i | \(0.508444\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.48859 | 0.238365 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.70149 | −1.20277 | −0.601385 | − | 0.798959i | \(-0.705384\pi\) | ||||
−0.601385 | + | 0.798959i | \(0.705384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.70934 | 0.718168 | 0.359084 | − | 0.933305i | \(-0.383089\pi\) | ||||
0.359084 | + | 0.933305i | \(0.383089\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.28632 | −0.638967 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.0439 | 1.90264 | 0.951322 | − | 0.308199i | \(-0.0997263\pi\) | ||||
0.951322 | + | 0.308199i | \(0.0997263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.10597 | −0.586567 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.55072 | 0.217144 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.24304 | 0.994908 | 0.497454 | − | 0.867490i | \(-0.334268\pi\) | ||||
0.497454 | + | 0.867490i | \(0.334268\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.3504 | −2.60921 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.31263 | 0.173862 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.70167 | 1.26305 | 0.631525 | − | 0.775356i | \(-0.282429\pi\) | ||||
0.631525 | + | 0.775356i | \(0.282429\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.23430 | −0.542146 | −0.271073 | − | 0.962559i | \(-0.587378\pi\) | ||||
−0.271073 | + | 0.962559i | \(0.587378\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.70119 | 0.214329 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.38057 | 0.791412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.71674 | −0.454072 | −0.227036 | − | 0.973886i | \(-0.572903\pi\) | ||||
−0.227036 | + | 0.973886i | \(0.572903\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9916 | 1.42314 | 0.711570 | − | 0.702616i | \(-0.247985\pi\) | ||||
0.711570 | + | 0.702616i | \(0.247985\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7328 | −1.25618 | −0.628092 | − | 0.778139i | \(-0.716164\pi\) | ||||
−0.628092 | + | 0.778139i | \(0.716164\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.3726 | −1.54413 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.67994 | 0.875210 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.6430 | −1.98500 | −0.992498 | − | 0.122262i | \(-0.960985\pi\) | ||||
−0.992498 | + | 0.122262i | \(0.960985\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.1598 | 1.22495 | 0.612473 | − | 0.790491i | \(-0.290175\pi\) | ||||
0.612473 | + | 0.790491i | \(0.290175\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.64689 | 0.720956 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.7972 | −1.88650 | −0.943251 | − | 0.332080i | \(-0.892250\pi\) | ||||
−0.943251 | + | 0.332080i | \(0.892250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.53236 | −0.265464 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.61274 | 0.270929 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.62635 | 0.577252 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.650043 | −0.0660019 | −0.0330009 | − | 0.999455i | \(-0.510506\pi\) | ||||
−0.0330009 | + | 0.999455i | \(0.510506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.51446 | 0.453721 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.9798 | −1.68956 | −0.844778 | − | 0.535117i | \(-0.820267\pi\) | ||||
−0.844778 | + | 0.535117i | \(0.820267\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.0401 | −1.87607 | −0.938037 | − | 0.346535i | \(-0.887358\pi\) | ||||
−0.938037 | + | 0.346535i | \(0.887358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.29183 | 0.711610 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3417 | 0.999766 | 0.499883 | − | 0.866093i | \(-0.333376\pi\) | ||||
0.499883 | + | 0.866093i | \(0.333376\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.48832 | −0.525685 | −0.262843 | − | 0.964839i | \(-0.584660\pi\) | ||||
−0.262843 | + | 0.964839i | \(0.584660\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.322680 | 0.0306274 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.27014 | 0.495773 | 0.247886 | − | 0.968789i | \(-0.420264\pi\) | ||||
0.247886 | + | 0.968789i | \(0.420264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.28632 | −0.399702 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.48859 | −0.137620 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.63806 | −0.241831 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.38037 | 0.852761 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.70149 | 0.694420 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −35.8876 | −3.20988 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.46610 | −0.662509 | −0.331255 | − | 0.943541i | \(-0.607472\pi\) | ||||
−0.331255 | + | 0.943541i | \(0.607472\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.70934 | −0.414634 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3089 | 0.988059 | 0.494030 | − | 0.869445i | \(-0.335523\pi\) | ||||
0.494030 | + | 0.869445i | \(0.335523\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.23303 | −0.193628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.28632 | 0.368908 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.30951 | −0.795365 | −0.397683 | − | 0.917523i | \(-0.630186\pi\) | ||||
−0.397683 | + | 0.917523i | \(0.630186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9397 | 1.60645 | 0.803224 | − | 0.595677i | \(-0.203116\pi\) | ||||
0.803224 | + | 0.595677i | \(0.203116\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.0439 | −1.09849 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.72017 | −0.561969 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.28632 | −0.355960 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.10597 | 0.338654 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.200164 | 0.0163981 | 0.00819906 | − | 0.999966i | \(-0.497390\pi\) | ||||
0.00819906 | + | 0.999966i | \(0.497390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.1714 | 1.31601 | 0.658004 | − | 0.753015i | \(-0.271401\pi\) | ||||
0.658004 | + | 0.753015i | \(0.271401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.55072 | −0.125368 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.1991 | 0.899530 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.72841 | −0.536986 | −0.268493 | − | 0.963282i | \(-0.586526\pi\) | ||||
−0.268493 | + | 0.963282i | \(0.586526\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.24304 | −0.574410 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.70119 | 0.134072 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.55383 | −0.200032 | −0.100016 | − | 0.994986i | \(-0.531889\pi\) | ||||
−0.100016 | + | 0.994986i | \(0.531889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.3504 | 1.50643 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.272414 | −0.0210800 | −0.0105400 | − | 0.999944i | \(-0.503355\pi\) | ||||
−0.0105400 | + | 0.999944i | \(0.503355\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7841 | −0.829547 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.31263 | −0.100379 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.0168 | 1.29376 | 0.646881 | − | 0.762591i | \(-0.276073\pi\) | ||||
0.646881 | + | 0.762591i | \(0.276073\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.7492 | 1.71968 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.70167 | −0.729222 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.3164 | −0.920569 | −0.460285 | − | 0.887771i | \(-0.652253\pi\) | ||||
−0.460285 | + | 0.887771i | \(0.652253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.16472 | −0.309561 | −0.154781 | − | 0.987949i | \(-0.549467\pi\) | ||||
−0.154781 | + | 0.987949i | \(0.549467\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.23430 | 0.313008 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.38311 | 0.101688 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.00067 | −0.511939 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.70119 | −0.123743 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.8725 | −1.36557 | −0.682784 | − | 0.730621i | \(-0.739231\pi\) | ||||
−0.682784 | + | 0.730621i | \(0.739231\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.72554 | −0.556097 | −0.278048 | − | 0.960567i | \(-0.589688\pi\) | ||||
−0.278048 | + | 0.960567i | \(0.589688\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.38057 | −0.456922 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.0387 | 1.42770 | 0.713851 | − | 0.700298i | \(-0.246949\pi\) | ||||
0.713851 | + | 0.700298i | \(0.246949\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.1404 | 1.85304 | 0.926520 | − | 0.376244i | \(-0.122785\pi\) | ||||
0.926520 | + | 0.376244i | \(0.122785\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.71674 | 0.262158 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.70119 | 0.119400 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 33.0111 | 2.30559 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.92581 | −0.409897 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.36990 | 0.369679 | 0.184840 | − | 0.982769i | \(-0.440823\pi\) | ||||
0.184840 | + | 0.982769i | \(0.440823\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.9916 | −0.821650 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.1858 | −1.37666 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.44476 | −0.301730 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.7328 | 0.725258 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.30838 | 0.155279 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.2451 | 1.42268 | 0.711339 | − | 0.702849i | \(-0.248089\pi\) | ||||
0.711339 | + | 0.702849i | \(0.248089\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.3726 | 0.891505 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.120251 | 0.00798134 | 0.00399067 | − | 0.999992i | \(-0.498730\pi\) | ||||
0.00399067 | + | 0.999992i | \(0.498730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.2154 | 1.66628 | 0.833141 | − | 0.553060i | \(-0.186540\pi\) | ||||
0.833141 | + | 0.553060i | \(0.186540\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.67994 | −0.505303 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.5036 | 1.01567 | 0.507837 | − | 0.861453i | \(-0.330445\pi\) | ||||
0.507837 | + | 0.861453i | \(0.330445\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −55.9102 | −3.64718 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.6430 | 1.14604 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.11436 | −0.266136 | −0.133068 | − | 0.991107i | \(-0.542483\pi\) | ||||
−0.133068 | + | 0.991107i | \(0.542483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.29590 | 0.534386 | 0.267193 | − | 0.963643i | \(-0.413904\pi\) | ||||
0.267193 | + | 0.963643i | \(0.413904\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.5995 | 1.12439 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.95396 | 0.124328 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.1598 | −0.707223 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.4531 | 1.54347 | 0.771733 | − | 0.635946i | \(-0.219390\pi\) | ||||
0.771733 | + | 0.635946i | \(0.219390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.51446 | 0.283822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.64689 | −0.416244 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.87202 | −0.428665 | −0.214332 | − | 0.976761i | \(-0.568758\pi\) | ||||
−0.214332 | + | 0.976761i | \(0.568758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.548939 | −0.0341094 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.2428 | 0.878246 | 0.439123 | − | 0.898427i | \(-0.355289\pi\) | ||||
0.439123 | + | 0.898427i | \(0.355289\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.0460 | −1.90714 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.7972 | 1.08917 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.4638 | −1.43061 | −0.715306 | − | 0.698811i | \(-0.753713\pi\) | ||||
−0.715306 | + | 0.698811i | \(0.753713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3651 | 1.29784 | 0.648918 | − | 0.760859i | \(-0.275222\pi\) | ||||
0.648918 | + | 0.760859i | \(0.275222\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.53236 | 0.153266 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 60.3700 | 3.64045 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.2990 | −1.21965 | −0.609824 | − | 0.792537i | \(-0.708760\pi\) | ||||
−0.609824 | + | 0.792537i | \(0.708760\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.61274 | −0.156421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9991 | 0.835117 | 0.417558 | − | 0.908650i | \(-0.362886\pi\) | ||||
0.417558 | + | 0.908650i | \(0.362886\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.4813 | 1.39582 | 0.697909 | − | 0.716186i | \(-0.254114\pi\) | ||||
0.697909 | + | 0.716186i | \(0.254114\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.62635 | −0.333276 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.1017 | −0.773367 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.5953 | −0.858545 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.650043 | 0.0381062 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.87158 | 0.401442 | 0.200721 | − | 0.979648i | \(-0.435672\pi\) | ||||
0.200721 | + | 0.979648i | \(0.435672\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −41.5845 | −2.42114 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.51446 | −0.261956 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.48859 | −0.0860872 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.01147 | 0.461773 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.9798 | 0.975465 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.1496 | 1.03924 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.69689 | 0.325139 | 0.162569 | − | 0.986697i | \(-0.448022\pi\) | ||||
0.162569 | + | 0.986697i | \(0.448022\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.0401 | 1.08315 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.45195 | −0.479266 | −0.239633 | − | 0.970864i | \(-0.577027\pi\) | ||||
−0.239633 | + | 0.970864i | \(0.577027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.2225 | −1.65175 | −0.825877 | − | 0.563850i | \(-0.809319\pi\) | ||||
−0.825877 | + | 0.563850i | \(0.809319\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.29183 | −0.410848 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.03917 | −0.170697 | −0.0853485 | − | 0.996351i | \(-0.527200\pi\) | ||||
−0.0853485 | + | 0.996351i | \(0.527200\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.51446 | 0.252761 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3417 | −0.577215 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.03552 | 0.113259 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.9062 | −1.10420 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.48832 | 0.303505 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.1900 | 1.22338 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.0230 | 1.81511 | 0.907555 | − | 0.419933i | \(-0.137946\pi\) | ||||
0.907555 | + | 0.419933i | \(0.137946\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.322680 | −0.0176828 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.9311 | 0.870411 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.0649 | 1.80116 | 0.900580 | − | 0.434690i | \(-0.143142\pi\) | ||||
0.900580 | + | 0.434690i | \(0.143142\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.27014 | −0.286235 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.7951 | −0.638742 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8933 | −1.02014 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.28632 | 0.230768 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.7918 | 1.43826 | 0.719130 | − | 0.694875i | \(-0.244540\pi\) | ||||
0.719130 | + | 0.694875i | \(0.244540\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.6622 | −0.677790 | −0.338895 | − | 0.940824i | \(-0.610053\pi\) | ||||
−0.338895 | + | 0.940824i | \(0.610053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.48859 | 0.0794549 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.30737 | 0.122809 | 0.0614046 | − | 0.998113i | \(-0.480442\pi\) | ||||
0.0614046 | + | 0.998113i | \(0.480442\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −51.3998 | −2.72802 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.63806 | 0.139621 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.5132 | 1.61043 | 0.805213 | − | 0.592986i | \(-0.202051\pi\) | ||||
0.805213 | + | 0.592986i | \(0.202051\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2770 | −0.909316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.38037 | −0.492342 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 46.0044 | 2.40798 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.40674 | −0.438828 | −0.219414 | − | 0.975632i | \(-0.570415\pi\) | ||||
−0.219414 | + | 0.975632i | \(0.570415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.70149 | −0.400923 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.3218 | 0.639714 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.9437 | 0.721977 | 0.360988 | − | 0.932570i | \(-0.382439\pi\) | ||||
0.360988 | + | 0.932570i | \(0.382439\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 35.8876 | 1.85323 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.48859 | −0.0766661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7324 | 1.52725 | 0.763624 | − | 0.645661i | \(-0.223418\pi\) | ||||
0.763624 | + | 0.645661i | \(0.223418\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.46610 | 0.382500 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.87971 | 0.300439 | 0.150219 | − | 0.988653i | \(-0.452002\pi\) | ||||
0.150219 | + | 0.988653i | \(0.452002\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −32.9187 | −1.67769 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.70934 | 0.239389 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.17532 | −0.160995 | −0.0804976 | − | 0.996755i | \(-0.525651\pi\) | ||||
−0.0804976 | + | 0.996755i | \(0.525651\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.55072 | −0.0784233 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.3089 | −0.570456 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 75.6237 | 3.80504 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.94465 | 0.248165 | 0.124082 | − | 0.992272i | \(-0.460401\pi\) | ||||
0.124082 | + | 0.992272i | \(0.460401\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.23303 | 0.111791 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.4870 | 1.62232 | 0.811161 | − | 0.584823i | \(-0.198836\pi\) | ||||
0.811161 | + | 0.584823i | \(0.198836\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.88929 | 0.193739 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.28632 | −0.212989 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.45673 | −0.0722073 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.19666 | −0.306405 | −0.153202 | − | 0.988195i | \(-0.548959\pi\) | ||||
−0.153202 | + | 0.988195i | \(0.548959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.30951 | 0.459204 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.5043 | 0.812125 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −47.8345 | −2.34810 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.9397 | −0.927483 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.8722 | 1.41050 | 0.705250 | − | 0.708959i | \(-0.250835\pi\) | ||||
0.705250 | + | 0.708959i | \(0.250835\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.9336 | 1.80003 | 0.900016 | − | 0.435857i | \(-0.143554\pi\) | ||||
0.900016 | + | 0.435857i | \(0.143554\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.0439 | 0.634215 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.7371 | −1.00590 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.20332 | −0.348593 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.72017 | 0.324453 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.7749 | −0.904354 | −0.452177 | − | 0.891928i | \(-0.649353\pi\) | ||||
−0.452177 | + | 0.891928i | \(0.649353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.2249 | 1.21223 | 0.606116 | − | 0.795377i | \(-0.292727\pi\) | ||||
0.606116 | + | 0.795377i | \(0.292727\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.28632 | 0.205514 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.31263 | −0.0627916 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.5690 | 1.17261 | 0.586306 | − | 0.810090i | \(-0.300582\pi\) | ||||
0.586306 | + | 0.810090i | \(0.300582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.10597 | −0.195522 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.7431 | −1.12807 | −0.564034 | − | 0.825752i | \(-0.690751\pi\) | ||||
−0.564034 | + | 0.825752i | \(0.690751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 76.2847 | 3.61624 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.200164 | −0.00946745 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.8149 | 1.31266 | 0.656332 | − | 0.754472i | \(-0.272107\pi\) | ||||
0.656332 | + | 0.754472i | \(0.272107\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.7681 | −1.63716 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.1714 | −0.759797 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.8545 | 0.508868 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 41.9187 | 1.96088 | 0.980438 | − | 0.196829i | \(-0.0630644\pi\) | ||||
0.980438 | + | 0.196829i | \(0.0630644\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.55072 | 0.0723814 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.48238 | 0.208765 | 0.104383 | − | 0.994537i | \(-0.466713\pi\) | ||||
0.104383 | + | 0.994537i | \(0.466713\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.4327 | 0.996064 | 0.498032 | − | 0.867159i | \(-0.334056\pi\) | ||||
0.498032 | + | 0.867159i | \(0.334056\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.1991 | −0.519344 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.7109 | −1.09721 | −0.548605 | − | 0.836081i | \(-0.684841\pi\) | ||||
−0.548605 | + | 0.836081i | \(0.684841\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.32286 | −0.291962 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.72841 | 0.310029 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.2601 | 0.977543 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.5532 | −0.805397 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.24304 | 0.331636 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.90312 | −0.361103 | −0.180551 | − | 0.983566i | \(-0.557788\pi\) | ||||
−0.180551 | + | 0.983566i | \(0.557788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.480337 | 0.0219015 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.70119 | −0.0774066 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.78629 | 0.126519 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.5725 | −1.83852 | −0.919259 | − | 0.393654i | \(-0.871211\pi\) | ||||
−0.919259 | + | 0.393654i | \(0.871211\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.55383 | 0.115488 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.5970 | 1.47108 | 0.735541 | − | 0.677480i | \(-0.236928\pi\) | ||||
0.735541 | + | 0.677480i | \(0.236928\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.55072 | −0.0698409 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.3504 | −0.869738 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.3999 | 0.915061 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.3779 | 0.733177 | 0.366589 | − | 0.930383i | \(-0.380526\pi\) | ||||
0.366589 | + | 0.930383i | \(0.380526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.272414 | 0.0121706 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.6217 | −1.72206 | −0.861028 | − | 0.508557i | \(-0.830179\pi\) | ||||
−0.861028 | + | 0.508557i | \(0.830179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 72.7810 | 3.23871 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.7841 | 0.478939 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.7904 | 0.655571 | 0.327786 | − | 0.944752i | \(-0.393698\pi\) | ||||
0.327786 | + | 0.944752i | \(0.393698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.2585 | −0.807711 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.31263 | 0.0579540 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 81.6119 | 3.59625 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 58.8860 | 2.58981 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.0168 | −0.746954 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.4435 | 0.764212 | 0.382106 | − | 0.924119i | \(-0.375199\pi\) | ||||
0.382106 | + | 0.924119i | \(0.375199\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.98273 | 0.130426 | 0.0652129 | − | 0.997871i | \(-0.479227\pi\) | ||||
0.0652129 | + | 0.997871i | \(0.479227\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.7492 | −0.992858 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.05163 | 0.176492 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.70167 | 0.421016 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.4643 | 0.496575 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −44.3277 | −1.91645 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.3164 | 0.531491 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.5362 | −0.798412 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.89722 | −0.167554 | −0.0837772 | − | 0.996485i | \(-0.526698\pi\) | ||||
−0.0837772 | + | 0.996485i | \(0.526698\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.16472 | 0.178725 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.5247 | 1.00769 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.3710 | −1.08479 | −0.542393 | − | 0.840125i | \(-0.682482\pi\) | ||||
−0.542393 | + | 0.840125i | \(0.682482\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.23430 | −0.180715 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.31263 | −0.0559199 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.0141 | −1.27633 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.38311 | −0.0587098 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.5331 | −0.827646 | −0.413823 | − | 0.910357i | \(-0.635807\pi\) | ||||
−0.413823 | + | 0.910357i | \(0.635807\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.01027 | −0.296503 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.00067 | 0.295568 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.8534 | 1.17388 | 0.586939 | − | 0.809631i | \(-0.300333\pi\) | ||||
0.586939 | + | 0.809631i | \(0.300333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5895 | −0.950348 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.70119 | 0.0714431 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.4536 | 0.773617 | 0.386808 | − | 0.922160i | \(-0.373578\pi\) | ||||
0.386808 | + | 0.922160i | \(0.373578\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.9586 | 0.960789 | 0.480394 | − | 0.877053i | \(-0.340494\pi\) | ||||
0.480394 | + | 0.877053i | \(0.340494\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.8725 | 0.788411 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.3726 | 0.557675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.2346 | −0.675854 | −0.337927 | − | 0.941172i | \(-0.609726\pi\) | ||||
−0.337927 | + | 0.941172i | \(0.609726\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.72554 | 0.321063 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.9849 | 0.787626 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.6984 | 1.35423 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.38057 | 0.263804 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.1911 | 0.750828 | 0.375414 | − | 0.926857i | \(-0.377500\pi\) | ||||
0.375414 | + | 0.926857i | \(0.377500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.42956 | 0.141313 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.0387 | −0.824284 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.8123 | −1.79915 | −0.899577 | − | 0.436762i | \(-0.856125\pi\) | ||||
−0.899577 | + | 0.436762i | \(0.856125\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.3076 | 0.463566 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.1404 | −1.06985 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.0723 | −1.22872 | −0.614359 | − | 0.789026i | \(-0.710586\pi\) | ||||
−0.614359 | + | 0.789026i | \(0.710586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.69148 | −0.191370 | −0.0956848 | − | 0.995412i | \(-0.530504\pi\) | ||||
−0.0956848 | + | 0.995412i | \(0.530504\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.71674 | −0.151357 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40.2073 | −1.63466 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.04644 | −0.0830626 | −0.0415313 | − | 0.999137i | \(-0.513224\pi\) | ||||
−0.0415313 | + | 0.999137i | \(0.513224\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.70119 | −0.0689355 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.4169 | −0.785525 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.0994 | −0.973368 | −0.486684 | − | 0.873578i | \(-0.661794\pi\) | ||||
−0.486684 | + | 0.873578i | \(0.661794\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −33.0111 | −1.33113 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.8902 | −1.44488 | −0.722442 | − | 0.691431i | \(-0.756980\pi\) | ||||
−0.722442 | + | 0.691431i | \(0.756980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.8832 | −0.839368 | −0.419684 | − | 0.907670i | \(-0.637859\pi\) | ||||
−0.419684 | + | 0.907670i | \(0.637859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.2764 | −1.21300 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 86.9628 | 3.47851 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.92581 | 0.236654 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.500387 | 0.0199517 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.5474 | −1.13645 | −0.568226 | − | 0.822872i | \(-0.692370\pi\) | ||||
−0.568226 | + | 0.822872i | \(0.692370\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.36990 | −0.213434 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.0021 | 1.26997 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.11209 | 0.242170 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.9916 | 0.474380 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.2128 | 1.03534 | 0.517672 | − | 0.855579i | \(-0.326799\pi\) | ||||
0.517672 | + | 0.855579i | \(0.326799\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.7568 | −1.41011 | −0.705055 | − | 0.709153i | \(-0.749078\pi\) | ||||
−0.705055 | + | 0.709153i | \(0.749078\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.1858 | 0.794814 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.4374 | −1.03936 | −0.519681 | − | 0.854360i | \(-0.673949\pi\) | ||||
−0.519681 | + | 0.854360i | \(0.673949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.7978 | 1.71921 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.44476 | 0.174204 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.1035 | −0.512780 | −0.256390 | − | 0.966573i | \(-0.582533\pi\) | ||||
−0.256390 | + | 0.966573i | \(0.582533\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.4734 | −1.89401 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.7328 | −0.418728 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.19408 | −0.319196 | −0.159598 | − | 0.987182i | \(-0.551020\pi\) | ||||
−0.159598 | + | 0.987182i | \(0.551020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1152 | −0.393434 | −0.196717 | − | 0.980460i | \(-0.563028\pi\) | ||||
−0.196717 | + | 0.980460i | \(0.563028\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.30838 | −0.0896501 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.57147 | 0.371166 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.2451 | −0.821383 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.1156 | −0.737948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.4242 | 1.21132 | 0.605658 | − | 0.795725i | \(-0.292910\pi\) | ||||
0.605658 | + | 0.795725i | \(0.292910\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.3726 | −0.514711 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.4259 | −1.39996 | −0.699980 | − | 0.714162i | \(-0.746808\pi\) | ||||
−0.699980 | + | 0.714162i | \(0.746808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.10584 | −0.0424384 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.120251 | −0.00460803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.6658 | −1.13513 | −0.567566 | − | 0.823328i | \(-0.692115\pi\) | ||||
−0.567566 | + | 0.823328i | \(0.692115\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.9036 | 1.52464 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.2154 | −0.962029 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.7819 | −0.410758 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1234 | 1.18399 | 0.591996 | − | 0.805941i | \(-0.298340\pi\) | ||||
0.591996 | + | 0.805941i | \(0.298340\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.67994 | 0.291737 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −81.1818 | −3.07940 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.9429 | 0.452368 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.5036 | −0.586400 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0718 | 0.795870 | 0.397935 | − | 0.917414i | \(-0.369727\pi\) | ||||
0.397935 | + | 0.917414i | \(0.369727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.423559 | 0.0159748 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 55.9102 | 2.10570 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.8858 | −1.08636 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.39042 | −0.164886 | −0.0824429 | − | 0.996596i | \(-0.526272\pi\) | ||||
−0.0824429 | + | 0.996596i | \(0.526272\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.6430 | −0.661665 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.61274 | −0.0978479 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.8048 | 1.07724 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.11436 | 0.153653 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.6811 | 1.14421 | 0.572106 | − | 0.820180i | \(-0.306127\pi\) | ||||
0.572106 | + | 0.820180i | \(0.306127\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.3907 | −1.20629 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.29590 | −0.308528 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.3726 | 0.496645 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.9250 | −0.738976 | −0.369488 | − | 0.929236i | \(-0.620467\pi\) | ||||
−0.369488 | + | 0.929236i | \(0.620467\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.30287 | −0.270106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.5753 | −0.759965 | −0.379982 | − | 0.924994i | \(-0.624070\pi\) | ||||
−0.379982 | + | 0.924994i | \(0.624070\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.5995 | −0.649167 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.7791 | −0.618065 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.8600 | −0.730560 | −0.365280 | − | 0.930898i | \(-0.619027\pi\) | ||||
−0.365280 | + | 0.930898i | \(0.619027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.95396 | −0.0717806 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.3852 | 0.491056 | 0.245528 | − | 0.969389i | \(-0.421039\pi\) | ||||
0.245528 | + | 0.969389i | \(0.421039\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.857970 | −0.0314336 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.1598 | 0.408315 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.5931 | 0.642837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.0496 | −0.950565 | −0.475282 | − | 0.879833i | \(-0.657654\pi\) | ||||
−0.475282 | + | 0.879833i | \(0.657654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.4531 | −0.891121 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −69.3157 | −2.52266 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.7077 | −1.04340 | −0.521700 | − | 0.853129i | \(-0.674702\pi\) | ||||
−0.521700 | + | 0.853129i | \(0.674702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.51446 | −0.163865 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.9034 | 0.395247 | 0.197624 | − | 0.980278i | \(-0.436678\pi\) | ||||
0.197624 | + | 0.980278i | \(0.436678\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.33665 | −0.338009 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.64689 | 0.240319 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.4418 | −0.521462 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.0411 | −1.26361 | −0.631807 | − | 0.775126i | \(-0.717686\pi\) | ||||
−0.631807 | + | 0.775126i | \(0.717686\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.87202 | 0.247490 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.19141 | −0.114787 | −0.0573936 | − | 0.998352i | \(-0.518279\pi\) | ||||
−0.0573936 | + | 0.998352i | \(0.518279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.9391 | −1.25505 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.548939 | 0.0196931 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.1092 | 0.362200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.1356 | 1.93712 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.8402 | 1.02935 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.29740 | 0.188832 | 0.0944160 | − | 0.995533i | \(-0.469902\pi\) | ||||
0.0944160 | + | 0.995533i | \(0.469902\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.2428 | −0.507056 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.96549 | 0.318776 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.30312 | 0.223830 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31.0460 | 1.10109 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.2239 | 0.362150 | 0.181075 | − | 0.983469i | \(-0.442042\pi\) | ||||
0.181075 | + | 0.983469i | \(0.442042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.2274 | −0.715594 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.7972 | −0.628834 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.4530 | −1.70987 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.29183 | −0.257003 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.4638 | 0.825964 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.0830 | 1.54988 | 0.774939 | − | 0.632036i | \(-0.217781\pi\) | ||||
0.774939 | + | 0.632036i | \(0.217781\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.5966 | 1.03928 | 0.519638 | − | 0.854387i | \(-0.326067\pi\) | ||||
0.519638 | + | 0.854387i | \(0.326067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.3651 | −0.749306 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.9466 | 0.383441 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.18162 | −0.216267 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.53236 | −0.0884879 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.314106 | 0.0109624 | 0.00548119 | − | 0.999985i | \(-0.498255\pi\) | ||||
0.00548119 | + | 0.999985i | \(0.498255\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.68347 | 0.0586819 | 0.0293410 | − | 0.999569i | \(-0.490659\pi\) | ||||
0.0293410 | + | 0.999569i | \(0.490659\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −60.3700 | −2.10181 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.8277 | −1.10676 | −0.553379 | − | 0.832930i | \(-0.686662\pi\) | ||||
−0.553379 | + | 0.832930i | \(0.686662\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.0120 | 1.45914 | 0.729568 | − | 0.683908i | \(-0.239721\pi\) | ||||
0.729568 | + | 0.683908i | \(0.239721\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.2990 | 0.704164 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.36721 | 0.220611 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.16766 | 0.0404084 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.61274 | 0.0903095 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.5412 | 1.05440 | 0.527200 | − | 0.849742i | \(-0.323242\pi\) | ||||
0.527200 | + | 0.849742i | \(0.323242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.9991 | −0.482155 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 46.2242 | 1.59016 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.9577 | 0.548315 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.4813 | −0.805876 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.322680 | −0.0110613 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3151 | −0.353181 | −0.176591 | − | 0.984284i | \(-0.556507\pi\) | ||||
−0.176591 | + | 0.984284i | \(0.556507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.62635 | 0.192417 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.7351 | 0.981571 | 0.490786 | − | 0.871280i | \(-0.336710\pi\) | ||||
0.490786 | + | 0.871280i | \(0.336710\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6931 | 0.774278 | 0.387139 | − | 0.922021i | \(-0.373463\pi\) | ||||
0.387139 | + | 0.922021i | \(0.373463\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.1017 | 0.446503 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.0771 | 0.887676 | 0.443838 | − | 0.896107i | \(-0.353617\pi\) | ||||
0.443838 | + | 0.896107i | \(0.353617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72.9395 | −2.48002 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.5953 | 0.495681 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −79.6488 | −2.70190 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.53268 | 0.187468 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.650043 | −0.0220006 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −61.0514 | −2.06391 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.89634 | −0.334176 | −0.167088 | − | 0.985942i | \(-0.553436\pi\) | ||||
−0.167088 | + | 0.985942i | \(0.553436\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.87158 | −0.231773 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.1270 | 1.45298 | 0.726492 | − | 0.687175i | \(-0.241149\pi\) | ||||
0.726492 | + | 0.687175i | \(0.241149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.1136 | −1.45089 | −0.725445 | − | 0.688280i | \(-0.758366\pi\) | ||||
−0.725445 | + | 0.688280i | \(0.758366\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 41.5845 | 1.39785 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.2874 | −0.681185 | −0.340593 | − | 0.940211i | \(-0.610628\pi\) | ||||
−0.340593 | + | 0.940211i | \(0.610628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.7012 | −0.425985 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.51446 | 0.151240 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.1218 | −0.572958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.7920 | 1.76464 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.48859 | 0.0497025 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.61274 | −0.0871398 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.2319 | −0.374190 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.01147 | −0.266605 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.8513 | 0.593398 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.56974 | 0.118531 | 0.0592656 | − | 0.998242i | \(-0.481124\pi\) | ||||
0.0592656 | + | 0.998242i | \(0.481124\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.9798 | −0.563185 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.8315 | 0.557651 | 0.278826 | − | 0.960342i | \(-0.410055\pi\) | ||||
0.278826 | + | 0.960342i | \(0.410055\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.3805 | 1.66735 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.1496 | −0.600006 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.2385 | 0.635310 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.69555 | 0.253853 | 0.126926 | − | 0.991912i | \(-0.459489\pi\) | ||||
0.126926 | + | 0.991912i | \(0.459489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.69689 | −0.187719 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.8505 | −0.587557 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.31506 | −0.141878 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.0401 | −0.625358 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.4882 | 1.16433 | 0.582165 | − | 0.813071i | \(-0.302206\pi\) | ||||
0.582165 | + | 0.813071i | \(0.302206\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.38961 | 0.176637 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.45195 | 0.276704 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.0071 | 0.981338 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.7653 | 1.03773 | 0.518864 | − | 0.854857i | \(-0.326355\pi\) | ||||
0.518864 | + | 0.854857i | \(0.326355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.2225 | 0.953640 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.4539 | 1.57955 | 0.789777 | − | 0.613394i | \(-0.210196\pi\) | ||||
0.789777 | + | 0.613394i | \(0.210196\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.70149 | −0.250795 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.29183 | 0.237203 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.5567 | 1.31792 | 0.658958 | − | 0.752180i | \(-0.270997\pi\) | ||||
0.658958 | + | 0.752180i | \(0.270997\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.9768 | 0.518628 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.03917 | 0.0985520 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.7158 | −0.606263 | −0.303131 | − | 0.952949i | \(-0.598032\pi\) | ||||
−0.303131 | + | 0.952949i | \(0.598032\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 80.8937 | 2.61766 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.51446 | −0.145932 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.8372 | −0.511410 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.1736 | −0.779793 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.3417 | 0.333255 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.1142 | 1.06598 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.1539 | −0.712421 | −0.356210 | − | 0.934406i | \(-0.615931\pi\) | ||||
−0.356210 | + | 0.934406i | \(0.615931\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.03552 | −0.0653903 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.2222 | −0.392228 | −0.196114 | − | 0.980581i | \(-0.562832\pi\) | ||||
−0.196114 | + | 0.980581i | \(0.562832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.2200 | 1.03293 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.9062 | 0.637510 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.0812 | −0.930391 | −0.465196 | − | 0.885208i | \(-0.654016\pi\) | ||||
−0.465196 | + | 0.885208i | \(0.654016\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −80.3449 | −2.56783 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.48832 | −0.175228 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.2793 | 1.25281 | 0.626407 | − | 0.779496i | \(-0.284525\pi\) | ||||
0.626407 | + | 0.779496i | \(0.284525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −85.8926 | −2.73676 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.1900 | −0.706317 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.70934 | 0.149748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.4921 | 0.746250 | 0.373125 | − | 0.927781i | \(-0.378286\pi\) | ||||
0.373125 | + | 0.927781i | \(0.378286\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.0230 | −1.04795 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −112.046 | −3.55210 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.0294 | 1.45777 | 0.728883 | − | 0.684638i | \(-0.240040\pi\) | ||||
0.728883 | + | 0.684638i | \(0.240040\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.322680 | 0.0102091 |
(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 | 8004.2.a.i.1.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.i.1.1 | ✓ | 16 | 1.1 | even | 1 | trivial |