Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2800,2,Mod(1,2800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2800, 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("2800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2800.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: | \(22.3581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.363328 | −0.209768 | −0.104884 | − | 0.994484i | \(-0.533447\pi\) | ||||
−0.104884 | + | 0.994484i | \(0.533447\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.86799 | −0.955998 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.14134 | −1.55017 | −0.775086 | − | 0.631856i | \(-0.782293\pi\) | ||||
−0.775086 | + | 0.631856i | \(0.782293\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.64600 | −1.28857 | −0.644284 | − | 0.764786i | \(-0.722845\pi\) | ||||
−0.644284 | + | 0.764786i | \(0.722845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.86799 | 0.938126 | 0.469063 | − | 0.883165i | \(-0.344592\pi\) | ||||
0.469063 | + | 0.883165i | \(0.344592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.778008 | 0.178487 | 0.0892436 | − | 0.996010i | \(-0.471555\pi\) | ||||
0.0892436 | + | 0.996010i | \(0.471555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.363328 | 0.0792847 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.00933 | −1.04452 | −0.522259 | − | 0.852787i | \(-0.674910\pi\) | ||||
−0.522259 | + | 0.852787i | \(0.674910\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13201 | 0.410305 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.42401 | 1.74999 | 0.874997 | − | 0.484128i | \(-0.160863\pi\) | ||||
0.874997 | + | 0.484128i | \(0.160863\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.72666 | −0.848933 | −0.424466 | − | 0.905444i | \(-0.639538\pi\) | ||||
−0.424466 | + | 0.905444i | \(0.639538\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.86799 | 0.325176 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.68802 | 0.270300 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00933 | −0.157631 | −0.0788153 | − | 0.996889i | \(-0.525114\pi\) | ||||
−0.0788153 | + | 0.996889i | \(0.525114\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.00933 | 1.06891 | 0.534456 | − | 0.845196i | \(-0.320516\pi\) | ||||
0.534456 | + | 0.845196i | \(0.320516\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4240 | 1.66636 | 0.833181 | − | 0.553000i | \(-0.186517\pi\) | ||||
0.833181 | + | 0.553000i | \(0.186517\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.40535 | −0.196788 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.55602 | 1.03790 | 0.518949 | − | 0.854805i | \(-0.326323\pi\) | ||||
0.518949 | + | 0.854805i | \(0.326323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.282672 | −0.0374409 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.5140 | −1.62918 | −0.814592 | − | 0.580035i | \(-0.803039\pi\) | ||||
−0.814592 | + | 0.580035i | \(0.803039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5047 | 1.47302 | 0.736511 | − | 0.676426i | \(-0.236472\pi\) | ||||
0.736511 | + | 0.676426i | \(0.236472\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.86799 | 0.361333 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7360 | 1.43378 | 0.716889 | − | 0.697187i | \(-0.245565\pi\) | ||||
0.716889 | + | 0.697187i | \(0.245565\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.82003 | 0.219106 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.72666 | −0.323595 | −0.161797 | − | 0.986824i | \(-0.551729\pi\) | ||||
−0.161797 | + | 0.986824i | \(0.551729\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00933 | 0.586298 | 0.293149 | − | 0.956067i | \(-0.405297\pi\) | ||||
0.293149 | + | 0.956067i | \(0.405297\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.14134 | 0.585910 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.68802 | −0.639953 | −0.319976 | − | 0.947426i | \(-0.603675\pi\) | ||||
−0.319976 | + | 0.947426i | \(0.603675\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.82936 | 0.869929 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.67531 | 0.513181 | 0.256591 | − | 0.966520i | \(-0.417401\pi\) | ||||
0.256591 | + | 0.966520i | \(0.417401\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.42401 | −0.367092 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.82936 | −0.299911 | −0.149956 | − | 0.988693i | \(-0.547913\pi\) | ||||
−0.149956 | + | 0.988693i | \(0.547913\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.64600 | 0.487033 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.71733 | 0.178079 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.58532 | −0.160965 | −0.0804824 | − | 0.996756i | \(-0.525646\pi\) | ||||
−0.0804824 | + | 0.996756i | \(0.525646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.7453 | 1.48196 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.06068 | −0.901571 | −0.450786 | − | 0.892632i | \(-0.648856\pi\) | ||||
−0.450786 | + | 0.892632i | \(0.648856\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.14134 | −0.506591 | −0.253295 | − | 0.967389i | \(-0.581514\pi\) | ||||
−0.253295 | + | 0.967389i | \(0.581514\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.97070 | −0.380324 | −0.190162 | − | 0.981753i | \(-0.560901\pi\) | ||||
−0.190162 | + | 0.981753i | \(0.560901\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.17997 | −0.206914 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.54669 | 0.427716 | 0.213858 | − | 0.976865i | \(-0.431397\pi\) | ||||
0.213858 | + | 0.976865i | \(0.431397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.3247 | 1.23187 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.86799 | −0.354578 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.4333 | 1.40303 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.366718 | 0.0330658 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.1214 | −1.43054 | −0.715270 | − | 0.698849i | \(-0.753696\pi\) | ||||
−0.715270 | + | 0.698849i | \(0.753696\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.54669 | −0.224223 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0513514 | −0.00448659 | −0.00224330 | − | 0.999997i | \(-0.500714\pi\) | ||||
−0.00224330 | + | 0.999997i | \(0.500714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.778008 | −0.0674618 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.0187 | −1.19769 | −0.598847 | − | 0.800863i | \(-0.704374\pi\) | ||||
−0.598847 | + | 0.800863i | \(0.704374\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.6167 | −1.07013 | −0.535067 | − | 0.844810i | \(-0.679714\pi\) | ||||
−0.535067 | + | 0.844810i | \(0.679714\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.15066 | −0.349549 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.8867 | 1.99750 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.363328 | −0.0299668 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.4533 | −0.938292 | −0.469146 | − | 0.883121i | \(-0.655438\pi\) | ||||
−0.469146 | + | 0.883121i | \(0.655438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.86799 | −0.477530 | −0.238765 | − | 0.971077i | \(-0.576743\pi\) | ||||
−0.238765 | + | 0.971077i | \(0.576743\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.0934 | −0.896846 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.78734 | −0.461880 | −0.230940 | − | 0.972968i | \(-0.574180\pi\) | ||||
−0.230940 | + | 0.972968i | \(0.574180\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.74531 | −0.217718 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.00933 | 0.394790 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.27334 | −0.256388 | −0.128194 | − | 0.991749i | \(-0.540918\pi\) | ||||
−0.128194 | + | 0.991749i | \(0.540918\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.8773 | 1.92506 | 0.962532 | − | 0.271166i | \(-0.0874094\pi\) | ||||
0.962532 | + | 0.271166i | \(0.0874094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.58532 | 0.660409 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.23132 | −0.170633 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.62734 | 0.503868 | 0.251934 | − | 0.967744i | \(-0.418933\pi\) | ||||
0.251934 | + | 0.967744i | \(0.418933\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.54669 | 0.341750 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0187 | 0.748830 | 0.374415 | − | 0.927261i | \(-0.377844\pi\) | ||||
0.374415 | + | 0.927261i | \(0.377844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.78734 | 0.132852 | 0.0664258 | − | 0.997791i | \(-0.478840\pi\) | ||||
0.0664258 | + | 0.997791i | \(0.478840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.17997 | −0.308992 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.8867 | −1.45426 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.13201 | −0.155081 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.59465 | 0.621887 | 0.310943 | − | 0.950428i | \(-0.399355\pi\) | ||||
0.310943 | + | 0.950428i | \(0.399355\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.17064 | −0.372191 | −0.186095 | − | 0.982532i | \(-0.559583\pi\) | ||||
−0.186095 | + | 0.982532i | \(0.559583\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.9160 | 1.70394 | 0.851971 | − | 0.523590i | \(-0.175407\pi\) | ||||
0.851971 | + | 0.523590i | \(0.175407\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.3107 | 1.08534 | 0.542672 | − | 0.839945i | \(-0.317413\pi\) | ||||
0.542672 | + | 0.839945i | \(0.317413\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.26401 | −0.300760 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.42401 | −0.661436 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.3667 | 0.998556 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.03863 | 0.0715025 | 0.0357512 | − | 0.999361i | \(-0.488618\pi\) | ||||
0.0357512 | + | 0.999361i | \(0.488618\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.990671 | 0.0678797 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.72666 | 0.320866 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.82003 | −0.122986 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.9707 | −1.20884 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.86799 | 0.660810 | 0.330405 | − | 0.943839i | \(-0.392815\pi\) | ||||
0.330405 | + | 0.943839i | \(0.392815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.6553 | 1.43731 | 0.718657 | − | 0.695364i | \(-0.244757\pi\) | ||||
0.718657 | + | 0.695364i | \(0.244757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.2313 | 1.33692 | 0.668462 | − | 0.743747i | \(-0.266953\pi\) | ||||
0.668462 | + | 0.743747i | \(0.266953\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.86799 | −0.122905 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.45331 | −0.357258 | −0.178629 | − | 0.983916i | \(-0.557166\pi\) | ||||
−0.178629 | + | 0.983916i | \(0.557166\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.06662 | 0.134241 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.5853 | 0.749392 | 0.374696 | − | 0.927148i | \(-0.377747\pi\) | ||||
0.374696 | + | 0.927148i | \(0.377747\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00933 | −0.322679 | −0.161340 | − | 0.986899i | \(-0.551581\pi\) | ||||
−0.161340 | + | 0.986899i | \(0.551581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.24065 | −0.592788 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.61462 | −0.229993 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.69867 | −0.107649 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.4206 | 1.47830 | 0.739148 | − | 0.673543i | \(-0.235228\pi\) | ||||
0.739148 | + | 0.673543i | \(0.235228\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.7546 | 1.61918 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.0093 | 0.811500 | 0.405750 | − | 0.913984i | \(-0.367010\pi\) | ||||
0.405750 | + | 0.913984i | \(0.367010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.0280 | −1.67299 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.01866 | −0.371126 | −0.185563 | − | 0.982632i | \(-0.559411\pi\) | ||||
−0.185563 | + | 0.982632i | \(0.559411\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.02799 | 0.0629117 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.24065 | 0.197586 | 0.0987929 | − | 0.995108i | \(-0.468502\pi\) | ||||
0.0987929 | + | 0.995108i | \(0.468502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.1307 | 1.76956 | 0.884782 | − | 0.466006i | \(-0.154307\pi\) | ||||
0.884782 | + | 0.466006i | \(0.154307\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.68802 | −0.102164 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.44398 | −0.267013 | −0.133507 | − | 0.991048i | \(-0.542624\pi\) | ||||
−0.133507 | + | 0.991048i | \(0.542624\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.5560 | 0.811577 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.6974 | −1.47332 | −0.736660 | − | 0.676263i | \(-0.763598\pi\) | ||||
−0.736660 | + | 0.676263i | \(0.763598\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.73937 | −0.460058 | −0.230029 | − | 0.973184i | \(-0.573882\pi\) | ||||
−0.230029 | + | 0.973184i | \(0.573882\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.00933 | 0.0595788 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.03863 | −0.119920 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.575992 | 0.0337652 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.1086 | 1.46686 | 0.733431 | − | 0.679764i | \(-0.237918\pi\) | ||||
0.733431 | + | 0.679764i | \(0.237918\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.9614 | −0.636043 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.2733 | 1.34593 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.00933 | −0.404011 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.29200 | 0.189121 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.9193 | 1.93588 | 0.967940 | − | 0.251183i | \(-0.0808196\pi\) | ||||
0.967940 | + | 0.251183i | \(0.0808196\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.86799 | 0.106266 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.565344 | −0.0320577 | −0.0160289 | − | 0.999872i | \(-0.505102\pi\) | ||||
−0.0160289 | + | 0.999872i | \(0.505102\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.3400 | −1.54535 | −0.772673 | − | 0.634804i | \(-0.781081\pi\) | ||||
−0.772673 | + | 0.634804i | \(0.781081\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.7267 | 1.27646 | 0.638228 | − | 0.769847i | \(-0.279668\pi\) | ||||
0.638228 | + | 0.769847i | \(0.279668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −48.4520 | −2.71279 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00933 | 0.167444 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.44267 | 0.0797796 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.4240 | −0.629826 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.462642 | −0.0254291 | −0.0127145 | − | 0.999919i | \(-0.504047\pi\) | ||||
−0.0127145 | + | 0.999919i | \(0.504047\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.2080 | −0.942990 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.5653 | −0.575531 | −0.287765 | − | 0.957701i | \(-0.592912\pi\) | ||||
−0.287765 | + | 0.957701i | \(0.592912\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.65194 | −0.0897211 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.3013 | 1.31599 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.8760 | −1.71119 | −0.855597 | − | 0.517643i | \(-0.826810\pi\) | ||||
−0.855597 | + | 0.517643i | \(0.826810\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.62602 | −0.515269 | −0.257635 | − | 0.966242i | \(-0.582943\pi\) | ||||
−0.257635 | + | 0.966242i | \(0.582943\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.90531 | −0.528706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.2534 | −1.39733 | −0.698663 | − | 0.715451i | \(-0.746221\pi\) | ||||
−0.698663 | + | 0.715451i | \(0.746221\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.40535 | 0.0743791 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.56534 | 0.240950 | 0.120475 | − | 0.992716i | \(-0.461558\pi\) | ||||
0.120475 | + | 0.992716i | \(0.461558\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3947 | −0.968142 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.60737 | −0.294310 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.79073 | −0.197874 | −0.0989371 | − | 0.995094i | \(-0.531544\pi\) | ||||
−0.0989371 | + | 0.995094i | \(0.531544\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.89475 | 0.150695 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.55602 | −0.392289 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.7453 | 1.07415 | 0.537076 | − | 0.843534i | \(-0.319529\pi\) | ||||
0.537076 | + | 0.843534i | \(0.319529\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −43.7839 | −2.25499 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.00933 | −0.154579 | −0.0772894 | − | 0.997009i | \(-0.524627\pi\) | ||||
−0.0772894 | + | 0.997009i | \(0.524627\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.85735 | 0.300081 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.00933 | −0.358160 | −0.179080 | − | 0.983835i | \(-0.557312\pi\) | ||||
−0.179080 | + | 0.983835i | \(0.557312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.1027 | −1.02188 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.7653 | −1.00214 | −0.501070 | − | 0.865407i | \(-0.667060\pi\) | ||||
−0.501070 | + | 0.865407i | \(0.667060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.3760 | −0.979889 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0186574 | 0.000941142 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.37266 | −0.470400 | −0.235200 | − | 0.971947i | \(-0.575575\pi\) | ||||
−0.235200 | + | 0.971947i | \(0.575575\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.282672 | 0.0141513 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.1507 | −0.806526 | −0.403263 | − | 0.915084i | \(-0.632124\pi\) | ||||
−0.403263 | + | 0.915084i | \(0.632124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.9600 | 1.09391 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −30.8480 | −1.52908 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.2920 | 0.756141 | 0.378070 | − | 0.925777i | \(-0.376588\pi\) | ||||
0.378070 | + | 0.925777i | \(0.376588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.09337 | 0.251238 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.5140 | 0.615773 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.58400 | 0.224480 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.1820 | 1.62105 | 0.810524 | − | 0.585705i | \(-0.199182\pi\) | ||||
0.810524 | + | 0.585705i | \(0.199182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8094 | 1.35535 | 0.677673 | − | 0.735363i | \(-0.262988\pi\) | ||||
0.677673 | + | 0.735363i | \(0.262988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −32.7640 | −1.59304 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.5047 | −0.556750 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.67869 | −0.419011 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.5454 | 1.03780 | 0.518902 | − | 0.854834i | \(-0.326341\pi\) | ||||
0.518902 | + | 0.854834i | \(0.326341\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.0187 | −1.73095 | −0.865473 | − | 0.500955i | \(-0.832982\pi\) | ||||
−0.865473 | + | 0.500955i | \(0.832982\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.89730 | −0.186433 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1893 | 1.01131 | 0.505655 | − | 0.862736i | \(-0.331251\pi\) | ||||
0.505655 | + | 0.862736i | \(0.331251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.86799 | −0.136571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.1120 | 0.527949 | 0.263974 | − | 0.964530i | \(-0.414967\pi\) | ||||
0.263974 | + | 0.964530i | \(0.414967\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.16131 | 0.196823 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.961367 | 0.0453697 | 0.0226848 | − | 0.999743i | \(-0.492779\pi\) | ||||
0.0226848 | + | 0.999743i | \(0.492779\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.18930 | 0.244355 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.13201 | 0.100170 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2241 | 1.32027 | 0.660133 | − | 0.751149i | \(-0.270500\pi\) | ||||
0.660133 | + | 0.751149i | \(0.270500\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.24659 | 0.384918 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.0887 | 1.21507 | 0.607535 | − | 0.794293i | \(-0.292158\pi\) | ||||
0.607535 | + | 0.794293i | \(0.292158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.90663 | 0.135082 | 0.0675412 | − | 0.997716i | \(-0.478485\pi\) | ||||
0.0675412 | + | 0.997716i | \(0.478485\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.2020 | −0.564642 | −0.282321 | − | 0.959320i | \(-0.591104\pi\) | ||||
−0.282321 | + | 0.959320i | \(0.591104\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.7360 | −0.541917 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.10270 | 0.0968874 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −36.0373 | −1.65700 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.6706 | −0.992228 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.6519 | 0.806538 | 0.403269 | − | 0.915082i | \(-0.367874\pi\) | ||||
0.403269 | + | 0.915082i | \(0.367874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.8760 | −1.27104 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.82003 | −0.0828143 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.57467 | 0.0713553 | 0.0356776 | − | 0.999363i | \(-0.488641\pi\) | ||||
0.0356776 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.18930 | 0.0537819 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.26270 | 0.147243 | 0.0736217 | − | 0.997286i | \(-0.476544\pi\) | ||||
0.0736217 | + | 0.997286i | \(0.476544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.4520 | 1.64172 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.72666 | 0.122307 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −42.5293 | −1.90387 | −0.951936 | − | 0.306298i | \(-0.900910\pi\) | ||||
−0.951936 | + | 0.306298i | \(0.900910\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.03863 | −0.403816 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.6974 | 0.833674 | 0.416837 | − | 0.908981i | \(-0.363139\pi\) | ||||
0.416837 | + | 0.908981i | \(0.363139\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.11929 | −0.138533 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.2313 | 0.896738 | 0.448369 | − | 0.893849i | \(-0.352005\pi\) | ||||
0.448369 | + | 0.893849i | \(0.352005\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.00933 | −0.221600 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.65872 | 0.0732342 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58.7347 | −2.58315 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.40790 | −0.105695 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.8387 | 0.956770 | 0.478385 | − | 0.878150i | \(-0.341222\pi\) | ||||
0.478385 | + | 0.878150i | \(0.341222\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.4554 | 0.894451 | 0.447226 | − | 0.894421i | \(-0.352412\pi\) | ||||
0.447226 | + | 0.894421i | \(0.352412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.2827 | −0.796406 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.09337 | 0.0910163 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.8900 | 1.55750 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.68934 | 0.203118 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.64006 | −0.157080 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.14134 | −0.221453 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.3400 | 1.17544 | 0.587718 | − | 0.809066i | \(-0.300026\pi\) | ||||
0.587718 | + | 0.809066i | \(0.300026\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.649390 | −0.0278680 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.6867 | 0.970013 | 0.485007 | − | 0.874510i | \(-0.338817\pi\) | ||||
0.485007 | + | 0.874510i | \(0.338817\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −32.9953 | −1.40820 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.33195 | 0.312352 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.68802 | 0.241879 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.7453 | −0.540036 | −0.270018 | − | 0.962855i | \(-0.587030\pi\) | ||||
−0.270018 | + | 0.962855i | \(0.587030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.5653 | −1.37737 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.22538 | 0.305056 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.20333 | 0.219294 | 0.109647 | − | 0.993971i | \(-0.465028\pi\) | ||||
0.109647 | + | 0.993971i | \(0.465028\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.82936 | −0.328802 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.37605 | −0.309220 | −0.154610 | − | 0.987976i | \(-0.549412\pi\) | ||||
−0.154610 | + | 0.987976i | \(0.549412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8973 | −0.665281 | −0.332641 | − | 0.943054i | \(-0.607940\pi\) | ||||
−0.332641 | + | 0.943054i | \(0.607940\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.12268 | −0.130452 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.9707 | −0.831391 | −0.415695 | − | 0.909504i | \(-0.636462\pi\) | ||||
−0.415695 | + | 0.909504i | \(0.636462\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.87864 | 0.0780736 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.67531 | −0.193964 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −38.8480 | −1.60892 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.8060 | 0.569834 | 0.284917 | − | 0.958552i | \(-0.408034\pi\) | ||||
0.284917 | + | 0.958552i | \(0.408034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.67738 | −0.151524 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.68934 | −0.357432 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.0666 | 0.824037 | 0.412019 | − | 0.911175i | \(-0.364824\pi\) | ||||
0.412019 | + | 0.911175i | \(0.364824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.56279 | −0.227670 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.0267 | −1.88060 | −0.940299 | − | 0.340349i | \(-0.889455\pi\) | ||||
−0.940299 | + | 0.340349i | \(0.889455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.37605 | −0.0561301 | −0.0280651 | − | 0.999606i | \(-0.508935\pi\) | ||||
−0.0280651 | + | 0.999606i | \(0.508935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.6587 | −1.37069 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7933 | −0.762796 | −0.381398 | − | 0.924411i | \(-0.624557\pi\) | ||||
−0.381398 | + | 0.924411i | \(0.624557\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.42401 | 0.138748 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.0759 | −2.14722 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.8480 | 1.00360 | 0.501801 | − | 0.864983i | \(-0.332671\pi\) | ||||
0.501801 | + | 0.864983i | \(0.332671\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.1680 | 1.73788 | 0.868939 | − | 0.494919i | \(-0.164802\pi\) | ||||
0.868939 | + | 0.494919i | \(0.164802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.9486 | −1.28412 | −0.642062 | − | 0.766652i | \(-0.721921\pi\) | ||||
−0.642062 | + | 0.766652i | \(0.721921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.6799 | −0.428571 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.82936 | 0.113356 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.45331 | 0.0580397 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.2080 | 0.925362 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.59465 | 0.342148 | 0.171074 | − | 0.985258i | \(-0.445276\pi\) | ||||
0.171074 | + | 0.985258i | \(0.445276\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.377365 | −0.0149989 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.64600 | −0.184081 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.82003 | 0.309356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.2266 | 1.31237 | 0.656186 | − | 0.754599i | \(-0.272169\pi\) | ||||
0.656186 | + | 0.754599i | \(0.272169\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4940 | −0.689897 | −0.344948 | − | 0.938622i | \(-0.612104\pi\) | ||||
−0.344948 | + | 0.938622i | \(0.612104\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.91595 | −0.389836 | −0.194918 | − | 0.980820i | \(-0.562444\pi\) | ||||
−0.194918 | + | 0.980820i | \(0.562444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 64.3386 | 2.52551 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.71733 | −0.0673074 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.6240 | 0.572280 | 0.286140 | − | 0.958188i | \(-0.407628\pi\) | ||||
0.286140 | + | 0.958188i | \(0.407628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.3667 | −0.560499 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.2534 | −0.788959 | −0.394480 | − | 0.918905i | \(-0.629075\pi\) | ||||
−0.394480 | + | 0.918905i | \(0.629075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4299 | −0.483469 | −0.241734 | − | 0.970342i | \(-0.577716\pi\) | ||||
−0.241734 | + | 0.970342i | \(0.577716\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.52926 | 0.253575 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −47.2080 | −1.82790 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.58532 | −0.138616 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −59.1493 | −2.28344 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.6774 | −1.83783 | −0.918914 | − | 0.394458i | \(-0.870932\pi\) | ||||
−0.918914 | + | 0.394458i | \(0.870932\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00339 | 0.230729 | 0.115364 | − | 0.993323i | \(-0.463196\pi\) | ||||
0.115364 | + | 0.993323i | \(0.463196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.58532 | 0.0608390 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.86799 | −0.301502 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.5653 | 1.09302 | 0.546511 | − | 0.837452i | \(-0.315956\pi\) | ||||
0.546511 | + | 0.837452i | \(0.315956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.35061 | −0.280443 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.1053 | −1.33740 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.8247 | −1.81934 | −0.909668 | − | 0.415337i | \(-0.863664\pi\) | ||||
−0.909668 | + | 0.415337i | \(0.863664\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.7453 | −0.560128 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.90408 | −0.147877 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.98134 | 0.0749413 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.80005 | −0.181296 | −0.0906478 | − | 0.995883i | \(-0.528894\pi\) | ||||
−0.0906478 | + | 0.995883i | \(0.528894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.66805 | 0.176059 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.06068 | 0.340762 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.7653 | 0.441855 | 0.220927 | − | 0.975290i | \(-0.429092\pi\) | ||||
0.220927 | + | 0.975290i | \(0.429092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.3132 | 0.611793 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.6774 | 0.886725 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.20927 | −0.157198 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.7640 | 1.52024 | 0.760120 | − | 0.649783i | \(-0.225140\pi\) | ||||
0.760120 | + | 0.649783i | \(0.225140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.14134 | 0.191473 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.82003 | 0.0676877 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.1214 | −0.820436 | −0.410218 | − | 0.911988i | \(-0.634547\pi\) | ||||
−0.410218 | + | 0.911988i | \(0.634547\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.1307 | −0.745581 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.1120 | 1.00277 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0500 | 0.482014 | 0.241007 | − | 0.970523i | \(-0.422522\pi\) | ||||
0.241007 | + | 0.970523i | \(0.422522\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −60.3386 | −2.22260 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.5734 | 1.27180 | 0.635901 | − | 0.771771i | \(-0.280629\pi\) | ||||
0.635901 | + | 0.771771i | \(0.280629\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.31330 | 0.0482451 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.55602 | 0.130458 | 0.0652288 | − | 0.997870i | \(-0.479222\pi\) | ||||
0.0652288 | + | 0.997870i | \(0.479222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.4087 | −0.490600 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.6226 | 0.862002 | 0.431001 | − | 0.902351i | \(-0.358161\pi\) | ||||
0.431001 | + | 0.902351i | \(0.358161\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.50937 | −0.310099 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.1893 | 0.552064 | 0.276032 | − | 0.961148i | \(-0.410980\pi\) | ||||
0.276032 | + | 0.961148i | \(0.410980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.35739 | −0.339652 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.4626 | 1.24927 | 0.624635 | − | 0.780917i | \(-0.285248\pi\) | ||||
0.624635 | + | 0.780917i | \(0.285248\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.97070 | 0.143749 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.1400 | 2.09931 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.3854 | 1.45633 | 0.728167 | − | 0.685400i | \(-0.240373\pi\) | ||||
0.728167 | + | 0.685400i | \(0.240373\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.72666 | −0.170226 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.7674 | −0.387275 | −0.193638 | − | 0.981073i | \(-0.562029\pi\) | ||||
−0.193638 | + | 0.981073i | \(0.562029\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.17997 | 0.0782060 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.785266 | −0.0281351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0187 | 0.501627 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.0921 | 0.718031 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.19269 | 0.327684 | 0.163842 | − | 0.986487i | \(-0.447611\pi\) | ||||
0.163842 | + | 0.986487i | \(0.447611\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.18675 | 0.0778503 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.54669 | −0.161662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.4507 | −1.89809 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.1086 | 0.747706 | 0.373853 | − | 0.927488i | \(-0.378036\pi\) | ||||
0.373853 | + | 0.927488i | \(0.378036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.1880 | 1.56326 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.11458 | 0.286715 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.7546 | −0.908862 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.17742 | −0.0414471 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.8280 | −0.978382 | −0.489191 | − | 0.872177i | \(-0.662708\pi\) | ||||
−0.489191 | + | 0.872177i | \(0.662708\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0607 | 0.388393 | 0.194197 | − | 0.980963i | \(-0.437790\pi\) | ||||
0.194197 | + | 0.980963i | \(0.437790\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.5840 | −0.371197 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.45331 | 0.190787 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.3247 | −0.465603 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.8867 | −0.624248 | −0.312124 | − | 0.950041i | \(-0.601041\pi\) | ||||
−0.312124 | + | 0.950041i | \(0.601041\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −52.8667 | −1.84282 | −0.921408 | − | 0.388596i | \(-0.872960\pi\) | ||||
−0.921408 | + | 0.388596i | \(0.872960\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.3013 | −1.26232 | −0.631160 | − | 0.775652i | \(-0.717421\pi\) | ||||
−0.631160 | + | 0.775652i | \(0.717421\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.759350 | −0.0263733 | −0.0131867 | − | 0.999913i | \(-0.504198\pi\) | ||||
−0.0131867 | + | 0.999913i | \(0.504198\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.61462 | 0.0560107 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.86799 | 0.134018 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0773 | −0.348321 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.3107 | 1.49525 | 0.747625 | − | 0.664121i | \(-0.231194\pi\) | ||||
0.747625 | + | 0.664121i | \(0.231194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.8119 | 2.06248 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.97325 | 0.309055 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.4333 | −0.530296 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.81193 | 0.0965053 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.0560 | −1.03031 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.3713 | −1.38229 | −0.691144 | − | 0.722717i | \(-0.742893\pi\) | ||||
−0.691144 | + | 0.722717i | \(0.742893\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.4720 | 0.460194 | 0.230097 | − | 0.973168i | \(-0.426096\pi\) | ||||
0.230097 | + | 0.973168i | \(0.426096\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.7313 | 1.18502 | 0.592508 | − | 0.805565i | \(-0.298138\pi\) | ||||
0.592508 | + | 0.805565i | \(0.298138\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.366718 | −0.0124977 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.2454 | 0.484918 | 0.242459 | − | 0.970162i | \(-0.422046\pi\) | ||||
0.242459 | + | 0.970162i | \(0.422046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.740693 | 0.0251553 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.2440 | 0.992036 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.5254 | −1.84752 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.54669 | 0.153882 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.7546 | 0.667067 | 0.333533 | − | 0.942738i | \(-0.391759\pi\) | ||||
0.333533 | + | 0.942738i | \(0.391759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.12268 | −0.307700 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.53058 | −0.321093 | −0.160547 | − | 0.987028i | \(-0.551326\pi\) | ||||
−0.160547 | + | 0.987028i | \(0.551326\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.1867 | −1.72257 | −0.861284 | − | 0.508124i | \(-0.830339\pi\) | ||||
−0.861284 | + | 0.508124i | \(0.830339\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.4626 | −0.821375 | −0.410688 | − | 0.911776i | \(-0.634711\pi\) | ||||
−0.410688 | + | 0.911776i | \(0.634711\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.1214 | 0.540693 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.2534 | −1.34854 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.88797 | 0.297425 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.45586 | −0.282333 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −44.5441 | −1.48563 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.2266 | 0.973680 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.54669 | 0.0847484 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.09592 | 0.268821 | 0.134410 | − | 0.990926i | \(-0.457086\pi\) | ||||
0.134410 | + | 0.990926i | \(0.457086\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.9860 | 0.861900 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 59.5093 | 1.97163 | 0.985815 | − | 0.167834i | \(-0.0536772\pi\) | ||||
0.985815 | + | 0.167834i | \(0.0536772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0373 | −0.795519 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0513514 | 0.00169577 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.7067 | −1.70565 | −0.852823 | − | 0.522200i | \(-0.825111\pi\) | ||||
−0.852823 | + | 0.522200i | \(0.825111\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.3239 | −0.406085 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.6680 | 0.416974 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.7453 | 0.484300 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.76142 | −0.123408 | −0.0617041 | − | 0.998094i | \(-0.519654\pi\) | ||||
−0.0617041 | + | 0.998094i | \(0.519654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.778008 | 0.0254982 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.205406 | 0.00672468 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.1014 | 0.689352 | 0.344676 | − | 0.938722i | \(-0.387989\pi\) | ||||
0.344676 | + | 0.938722i | \(0.387989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.93338 | 0.324164 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.72873 | −0.0563549 | −0.0281775 | − | 0.999603i | \(-0.508970\pi\) | ||||
−0.0281775 | + | 0.999603i | \(0.508970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.05606 | 0.164648 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.7267 | 0.803508 | 0.401754 | − | 0.915748i | \(-0.368401\pi\) | ||||
0.401754 | + | 0.915748i | \(0.368401\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.2733 | −0.755485 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.25724 | −0.267759 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.18930 | 0.0385251 | 0.0192626 | − | 0.999814i | \(-0.493868\pi\) | ||||
0.0192626 | + | 0.999814i | \(0.493868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.6040 | 0.569056 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.0187 | 0.452686 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.65872 | −0.279314 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3293 | 0.750220 | 0.375110 | − | 0.926980i | \(-0.377605\pi\) | ||||
0.375110 | + | 0.926980i | \(0.377605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.09337 | −0.0351242 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.61670 | 0.148157 | 0.0740784 | − | 0.997252i | \(-0.476398\pi\) | ||||
0.0740784 | + | 0.997252i | \(0.476398\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.6167 | 0.404473 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.1120 | −0.611448 | −0.305724 | − | 0.952120i | \(-0.598898\pi\) | ||||
−0.305724 | + | 0.952120i | \(0.598898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.5467 | 0.464914 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3879 | 0.363588 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.6506 | 1.67929 | 0.839647 | − | 0.543132i | \(-0.182762\pi\) | ||||
0.839647 | + | 0.543132i | \(0.182762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.15066 | 0.132117 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.1120 | −1.11650 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.4227 | −1.66526 | −0.832631 | − | 0.553828i | \(-0.813166\pi\) | ||||
−0.832631 | + | 0.553828i | \(0.813166\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.168091 | 0.00533420 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.7580 | 0.625743 | 0.312872 | − | 0.949795i | \(-0.398709\pi\) | ||||
0.312872 | + | 0.949795i | \(0.398709\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.7920 | 0.404722 |
(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 | 2800.2.a.br.1.2 | 3 | ||
4.3 | odd | 2 | 1400.2.a.s.1.2 | 3 | |||
5.2 | odd | 4 | 560.2.g.f.449.4 | 6 | |||
5.3 | odd | 4 | 560.2.g.f.449.3 | 6 | |||
5.4 | even | 2 | 2800.2.a.bq.1.2 | 3 | |||
15.2 | even | 4 | 5040.2.t.y.1009.5 | 6 | |||
15.8 | even | 4 | 5040.2.t.y.1009.6 | 6 | |||
20.3 | even | 4 | 280.2.g.b.169.4 | yes | 6 | ||
20.7 | even | 4 | 280.2.g.b.169.3 | ✓ | 6 | ||
20.19 | odd | 2 | 1400.2.a.t.1.2 | 3 | |||
28.27 | even | 2 | 9800.2.a.cg.1.2 | 3 | |||
40.3 | even | 4 | 2240.2.g.l.449.3 | 6 | |||
40.13 | odd | 4 | 2240.2.g.m.449.4 | 6 | |||
40.27 | even | 4 | 2240.2.g.l.449.4 | 6 | |||
40.37 | odd | 4 | 2240.2.g.m.449.3 | 6 | |||
60.23 | odd | 4 | 2520.2.t.g.1009.6 | 6 | |||
60.47 | odd | 4 | 2520.2.t.g.1009.5 | 6 | |||
140.27 | odd | 4 | 1960.2.g.c.1569.4 | 6 | |||
140.83 | odd | 4 | 1960.2.g.c.1569.3 | 6 | |||
140.139 | even | 2 | 9800.2.a.cd.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.g.b.169.3 | ✓ | 6 | 20.7 | even | 4 | ||
280.2.g.b.169.4 | yes | 6 | 20.3 | even | 4 | ||
560.2.g.f.449.3 | 6 | 5.3 | odd | 4 | |||
560.2.g.f.449.4 | 6 | 5.2 | odd | 4 | |||
1400.2.a.s.1.2 | 3 | 4.3 | odd | 2 | |||
1400.2.a.t.1.2 | 3 | 20.19 | odd | 2 | |||
1960.2.g.c.1569.3 | 6 | 140.83 | odd | 4 | |||
1960.2.g.c.1569.4 | 6 | 140.27 | odd | 4 | |||
2240.2.g.l.449.3 | 6 | 40.3 | even | 4 | |||
2240.2.g.l.449.4 | 6 | 40.27 | even | 4 | |||
2240.2.g.m.449.3 | 6 | 40.37 | odd | 4 | |||
2240.2.g.m.449.4 | 6 | 40.13 | odd | 4 | |||
2520.2.t.g.1009.5 | 6 | 60.47 | odd | 4 | |||
2520.2.t.g.1009.6 | 6 | 60.23 | odd | 4 | |||
2800.2.a.bq.1.2 | 3 | 5.4 | even | 2 | |||
2800.2.a.br.1.2 | 3 | 1.1 | even | 1 | trivial | ||
5040.2.t.y.1009.5 | 6 | 15.2 | even | 4 | |||
5040.2.t.y.1009.6 | 6 | 15.8 | even | 4 | |||
9800.2.a.cd.1.2 | 3 | 140.139 | even | 2 | |||
9800.2.a.cg.1.2 | 3 | 28.27 | even | 2 |