Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + \cdots + 3008 \) |
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 | 1.2 | ||
Root | \(-3.49351\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(5\) | −3.49351 | −1.56235 | −0.781173 | − | 0.624315i | \(-0.785378\pi\) | ||||
−0.781173 | + | 0.624315i | \(0.785378\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.58171 | 1.73172 | 0.865862 | − | 0.500283i | \(-0.166771\pi\) | ||||
0.865862 | + | 0.500283i | \(0.166771\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.512480 | 0.154519 | 0.0772593 | − | 0.997011i | \(-0.475383\pi\) | ||||
0.0772593 | + | 0.997011i | \(0.475383\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.325752 | −0.0903473 | −0.0451737 | − | 0.998979i | \(-0.514384\pi\) | ||||
−0.0451737 | + | 0.998979i | \(0.514384\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.49351 | −0.902021 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.49148 | −0.604273 | −0.302136 | − | 0.953265i | \(-0.597700\pi\) | ||||
−0.302136 | + | 0.953265i | \(0.597700\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.26410 | 0.748837 | 0.374418 | − | 0.927260i | \(-0.377842\pi\) | ||||
0.374418 | + | 0.927260i | \(0.377842\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58171 | 0.999812 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00623 | −0.835356 | −0.417678 | − | 0.908595i | \(-0.637156\pi\) | ||||
−0.417678 | + | 0.908595i | \(0.637156\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.20462 | 1.44092 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.72350 | 0.320045 | 0.160023 | − | 0.987113i | \(-0.448843\pi\) | ||||
0.160023 | + | 0.987113i | \(0.448843\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.79709 | 1.04119 | 0.520594 | − | 0.853804i | \(-0.325711\pi\) | ||||
0.520594 | + | 0.853804i | \(0.325711\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.512480 | 0.0892114 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.0063 | −2.70555 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.03510 | 1.15656 | 0.578282 | − | 0.815837i | \(-0.303723\pi\) | ||||
0.578282 | + | 0.815837i | \(0.303723\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.325752 | −0.0521621 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.69446 | 0.264630 | 0.132315 | − | 0.991208i | \(-0.457759\pi\) | ||||
0.132315 | + | 0.991208i | \(0.457759\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.20067 | −1.09809 | −0.549046 | − | 0.835792i | \(-0.685009\pi\) | ||||
−0.549046 | + | 0.835792i | \(0.685009\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.49351 | −0.520782 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.49012 | 0.363222 | 0.181611 | − | 0.983370i | \(-0.441869\pi\) | ||||
0.181611 | + | 0.983370i | \(0.441869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.9921 | 1.99887 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.49148 | −0.348877 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.26872 | 0.311633 | 0.155817 | − | 0.987786i | \(-0.450199\pi\) | ||||
0.155817 | + | 0.987786i | \(0.450199\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.79036 | −0.241411 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.26410 | 0.432341 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.76876 | −0.881218 | −0.440609 | − | 0.897699i | \(-0.645237\pi\) | ||||
−0.440609 | + | 0.897699i | \(0.645237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.57345 | −0.201459 | −0.100730 | − | 0.994914i | \(-0.532118\pi\) | ||||
−0.100730 | + | 0.994914i | \(0.532118\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.58171 | 0.577241 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.13802 | 0.141154 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.691665 | 0.0845003 | 0.0422501 | − | 0.999107i | \(-0.486547\pi\) | ||||
0.0422501 | + | 0.999107i | \(0.486547\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00623 | −0.482293 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4421 | 1.47661 | 0.738304 | − | 0.674468i | \(-0.235627\pi\) | ||||
0.738304 | + | 0.674468i | \(0.235627\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.41218 | 0.399366 | 0.199683 | − | 0.979861i | \(-0.436009\pi\) | ||||
0.199683 | + | 0.979861i | \(0.436009\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.20462 | 0.831918 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.34804 | 0.267584 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.7644 | −1.21110 | −0.605548 | − | 0.795809i | \(-0.707046\pi\) | ||||
−0.605548 | + | 0.795809i | \(0.707046\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.12519 | −0.343035 | −0.171517 | − | 0.985181i | \(-0.554867\pi\) | ||||
−0.171517 | + | 0.985181i | \(0.554867\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.70401 | 0.944083 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.72350 | 0.184778 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.5543 | 1.64876 | 0.824378 | − | 0.566040i | \(-0.191525\pi\) | ||||
0.824378 | + | 0.566040i | \(0.191525\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.49250 | −0.156457 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.79709 | 0.601130 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.4032 | −1.16994 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.68185 | 0.881508 | 0.440754 | − | 0.897628i | \(-0.354711\pi\) | ||||
0.440754 | + | 0.897628i | \(0.354711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.512480 | 0.0515062 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.25125 | −0.423015 | −0.211508 | − | 0.977376i | \(-0.567837\pi\) | ||||
−0.211508 | + | 0.977376i | \(0.567837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.64310 | −0.161899 | −0.0809496 | − | 0.996718i | \(-0.525795\pi\) | ||||
−0.0809496 | + | 0.996718i | \(0.525795\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.0063 | −1.56205 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.3290 | 1.86861 | 0.934305 | − | 0.356475i | \(-0.116022\pi\) | ||||
0.934305 | + | 0.356475i | \(0.116022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.467960 | 0.0448224 | 0.0224112 | − | 0.999749i | \(-0.492866\pi\) | ||||
0.0224112 | + | 0.999749i | \(0.492866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.03510 | 0.667743 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0604 | −0.946405 | −0.473202 | − | 0.880954i | \(-0.656902\pi\) | ||||
−0.473202 | + | 0.880954i | \(0.656902\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.9958 | 1.30512 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.325752 | −0.0301158 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.4152 | −1.04643 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7374 | −0.976124 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.69446 | 0.152784 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.70186 | −0.688875 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.02371 | 0.623254 | 0.311627 | − | 0.950205i | \(-0.399126\pi\) | ||||
0.311627 | + | 0.950205i | \(0.399126\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.20067 | −0.633984 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.39191 | −0.645834 | −0.322917 | − | 0.946427i | \(-0.604663\pi\) | ||||
−0.322917 | + | 0.946427i | \(0.604663\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.9552 | 1.29678 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.49351 | −0.300674 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.76010 | 0.748426 | 0.374213 | − | 0.927343i | \(-0.377913\pi\) | ||||
0.374213 | + | 0.927343i | \(0.377913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.16611 | 0.268546 | 0.134273 | − | 0.990944i | \(-0.457130\pi\) | ||||
0.134273 | + | 0.990944i | \(0.457130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.49012 | 0.209706 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.166941 | −0.0139603 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.02105 | −0.500021 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.9921 | 1.15405 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.8088 | 0.885488 | 0.442744 | − | 0.896648i | \(-0.354005\pi\) | ||||
0.442744 | + | 0.896648i | \(0.354005\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5677 | 1.18550 | 0.592750 | − | 0.805386i | \(-0.298042\pi\) | ||||
0.592750 | + | 0.805386i | \(0.298042\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.49148 | −0.201424 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.2522 | −1.62670 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.35228 | −0.267541 | −0.133771 | − | 0.991012i | \(-0.542709\pi\) | ||||
−0.133771 | + | 0.991012i | \(0.542709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.26872 | 0.179921 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.3554 | −1.44661 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.58993 | −0.359511 | −0.179756 | − | 0.983711i | \(-0.557531\pi\) | ||||
−0.179756 | + | 0.983711i | \(0.557531\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.79036 | −0.139379 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8939 | −0.991837 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.26410 | 0.249612 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.8765 | 1.28310 | 0.641549 | − | 0.767082i | \(-0.278292\pi\) | ||||
0.641549 | + | 0.767082i | \(0.278292\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 33.0095 | 2.49528 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.76876 | −0.508771 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.6247 | −1.84053 | −0.920266 | − | 0.391292i | \(-0.872028\pi\) | ||||
−0.920266 | + | 0.391292i | \(0.872028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.54891 | 0.115130 | 0.0575648 | − | 0.998342i | \(-0.481666\pi\) | ||||
0.0575648 | + | 0.998342i | \(0.481666\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.57345 | −0.116312 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.5772 | −1.80695 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.27683 | −0.0933714 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.58171 | 0.333271 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.85499 | 0.134222 | 0.0671111 | − | 0.997746i | \(-0.478622\pi\) | ||||
0.0671111 | + | 0.997746i | \(0.478622\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.6759 | 1.41630 | 0.708151 | − | 0.706061i | \(-0.249530\pi\) | ||||
0.708151 | + | 0.706061i | \(0.249530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.13802 | 0.0814952 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.0223 | 1.78276 | 0.891382 | − | 0.453252i | \(-0.149736\pi\) | ||||
0.891382 | + | 0.453252i | \(0.149736\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.2466 | 1.64791 | 0.823953 | − | 0.566659i | \(-0.191764\pi\) | ||||
0.823953 | + | 0.566659i | \(0.191764\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.691665 | 0.0487863 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.89657 | 0.554230 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.91962 | −0.413444 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00623 | −0.278452 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.67279 | 0.115709 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.45455 | −0.582035 | −0.291018 | − | 0.956718i | \(-0.593994\pi\) | ||||
−0.291018 | + | 0.956718i | \(0.593994\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.4421 | 0.852520 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.1556 | 1.71560 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.5606 | 1.80305 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.41218 | 0.230574 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.811605 | 0.0545944 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.8078 | 1.32643 | 0.663215 | − | 0.748429i | \(-0.269191\pi\) | ||||
0.663215 | + | 0.748429i | \(0.269191\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.20462 | 0.480308 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.09680 | −0.0727970 | −0.0363985 | − | 0.999337i | \(-0.511589\pi\) | ||||
−0.0363985 | + | 0.999337i | \(0.511589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0699 | −0.665441 | −0.332720 | − | 0.943026i | \(-0.607967\pi\) | ||||
−0.332720 | + | 0.943026i | \(0.607967\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.34804 | 0.154490 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.01463 | 0.328519 | 0.164260 | − | 0.986417i | \(-0.447477\pi\) | ||||
0.164260 | + | 0.986417i | \(0.447477\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.69927 | −0.567478 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.7644 | −0.699226 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.8946 | 1.09282 | 0.546410 | − | 0.837518i | \(-0.315994\pi\) | ||||
0.546410 | + | 0.837518i | \(0.315994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0016 | 0.901924 | 0.450962 | − | 0.892543i | \(-0.351081\pi\) | ||||
0.450962 | + | 0.892543i | \(0.351081\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −48.8815 | −3.12292 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.06329 | −0.0676554 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.12519 | −0.198051 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.8610 | 1.31673 | 0.658367 | − | 0.752697i | \(-0.271247\pi\) | ||||
0.658367 | + | 0.752697i | \(0.271247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.05311 | −0.129078 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.70401 | 0.545066 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0215 | 0.937018 | 0.468509 | − | 0.883459i | \(-0.344791\pi\) | ||||
0.468509 | + | 0.883459i | \(0.344791\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.2328 | 2.00285 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.72350 | 0.106682 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.66555 | 0.596003 | 0.298002 | − | 0.954565i | \(-0.403680\pi\) | ||||
0.298002 | + | 0.954565i | \(0.403680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.92581 | −0.486879 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.5543 | 0.951909 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.0300 | 0.672510 | 0.336255 | − | 0.941771i | \(-0.390840\pi\) | ||||
0.336255 | + | 0.941771i | \(0.390840\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.3714 | 1.66269 | 0.831347 | − | 0.555754i | \(-0.187570\pi\) | ||||
0.831347 | + | 0.555754i | \(0.187570\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.49250 | −0.0903303 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.69222 | 0.222650 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2246 | −0.854675 | −0.427338 | − | 0.904092i | \(-0.640548\pi\) | ||||
−0.427338 | + | 0.904092i | \(0.640548\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.79709 | 0.347063 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.17980 | 0.428311 | 0.214156 | − | 0.976800i | \(-0.431300\pi\) | ||||
0.214156 | + | 0.976800i | \(0.431300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.49336 | −0.445434 | −0.222717 | − | 0.974883i | \(-0.571493\pi\) | ||||
−0.222717 | + | 0.974883i | \(0.571493\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.4032 | −0.675466 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.76354 | 0.458267 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.7925 | −0.634855 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.68185 | 0.508939 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.4024 | −1.30876 | −0.654380 | − | 0.756166i | \(-0.727070\pi\) | ||||
−0.654380 | + | 0.756166i | \(0.727070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.6467 | 1.37677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.512480 | 0.0297371 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.30504 | 0.0754722 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.9914 | −1.90159 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.25125 | −0.244228 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.49685 | 0.314749 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.30538 | 0.416940 | 0.208470 | − | 0.978029i | \(-0.433152\pi\) | ||||
0.208470 | + | 0.978029i | \(0.433152\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.64310 | −0.0934725 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.7279 | −1.51560 | −0.757800 | − | 0.652487i | \(-0.773726\pi\) | ||||
−0.757800 | + | 0.652487i | \(0.773726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0884 | −1.07894 | −0.539469 | − | 0.842005i | \(-0.681375\pi\) | ||||
−0.539469 | + | 0.842005i | \(0.681375\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.0063 | −0.901851 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.844016 | −0.0474047 | −0.0237023 | − | 0.999719i | \(-0.507545\pi\) | ||||
−0.0237023 | + | 0.999719i | \(0.507545\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.883258 | 0.0494530 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.3290 | 1.07884 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.13245 | −0.452502 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.34692 | −0.130184 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.467960 | 0.0258782 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.4090 | 0.629000 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.805305 | −0.0442636 | −0.0221318 | − | 0.999755i | \(-0.507045\pi\) | ||||
−0.0221318 | + | 0.999755i | \(0.507045\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.03510 | 0.385521 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.41634 | −0.132019 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.49693 | 0.0815429 | 0.0407715 | − | 0.999168i | \(-0.487018\pi\) | ||||
0.0407715 | + | 0.999168i | \(0.487018\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.0604 | −0.546407 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.97089 | 0.160883 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 32.0357 | 1.72977 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.9958 | 0.753509 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.4606 | −1.25943 | −0.629715 | − | 0.776826i | \(-0.716828\pi\) | ||||
−0.629715 | + | 0.776826i | \(0.716828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.0540 | −1.01994 | −0.509970 | − | 0.860192i | \(-0.670343\pi\) | ||||
−0.509970 | + | 0.860192i | \(0.670343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.325752 | −0.0173874 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.1020 | −0.963471 | −0.481735 | − | 0.876317i | \(-0.659993\pi\) | ||||
−0.481735 | + | 0.876317i | \(0.659993\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.4667 | −2.30697 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.4152 | −0.604159 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.02286 | 0.423430 | 0.211715 | − | 0.977331i | \(-0.432095\pi\) | ||||
0.211715 | + | 0.977331i | \(0.432095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.34562 | −0.439243 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.7374 | −0.563565 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.9205 | −0.623948 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.45266 | −0.336826 | −0.168413 | − | 0.985716i | \(-0.553864\pi\) | ||||
−0.168413 | + | 0.985716i | \(0.553864\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.69446 | 0.0882101 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3946 | 0.539663 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.68132 | 0.345946 | 0.172973 | − | 0.984927i | \(-0.444663\pi\) | ||||
0.172973 | + | 0.984927i | \(0.444663\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.70186 | −0.397722 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.561432 | −0.0289152 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.6658 | −1.67793 | −0.838966 | − | 0.544184i | \(-0.816839\pi\) | ||||
−0.838966 | + | 0.544184i | \(0.816839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.02371 | 0.359836 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.4445 | 0.635884 | 0.317942 | − | 0.948110i | \(-0.397008\pi\) | ||||
0.317942 | + | 0.948110i | \(0.397008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.20289 | −0.418058 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.20067 | −0.366031 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.21421 | 0.0615628 | 0.0307814 | − | 0.999526i | \(-0.490200\pi\) | ||||
0.0307814 | + | 0.999526i | \(0.490200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.98144 | 0.504783 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.39191 | −0.372873 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.6057 | 1.89215 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2956 | 0.918231 | 0.459116 | − | 0.888376i | \(-0.348166\pi\) | ||||
0.459116 | + | 0.888376i | \(0.348166\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.9552 | 0.748696 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.88106 | −0.243748 | −0.121874 | − | 0.992546i | \(-0.538890\pi\) | ||||
−0.121874 | + | 0.992546i | \(0.538890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.88841 | −0.0940686 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.49351 | −0.173594 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.60535 | 0.178711 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.2838 | −0.557947 | −0.278973 | − | 0.960299i | \(-0.589994\pi\) | ||||
−0.278973 | + | 0.960299i | \(0.589994\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.76010 | 0.432104 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.0125 | −1.52603 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.9179 | 0.535939 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.16611 | 0.155045 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.7280 | 1.11034 | 0.555168 | − | 0.831738i | \(-0.312654\pi\) | ||||
0.555168 | + | 0.831738i | \(0.312654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.9399 | −0.971810 | −0.485905 | − | 0.874012i | \(-0.661510\pi\) | ||||
−0.485905 | + | 0.874012i | \(0.661510\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.49012 | 0.121074 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.9502 | −0.870711 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.20907 | −0.348872 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.166941 | −0.00806001 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.4845 | −0.649525 | −0.324763 | − | 0.945796i | \(-0.605284\pi\) | ||||
−0.324763 | + | 0.945796i | \(0.605284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.6652 | −1.47368 | −0.736839 | − | 0.676068i | \(-0.763682\pi\) | ||||
−0.736839 | + | 0.676068i | \(0.763682\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.02105 | −0.288687 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.0767 | −0.625546 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.49335 | −0.357638 | −0.178819 | − | 0.983882i | \(-0.557228\pi\) | ||||
−0.178819 | + | 0.983882i | \(0.557228\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.9921 | 0.666290 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.21514 | 0.295290 | 0.147645 | − | 0.989040i | \(-0.452831\pi\) | ||||
0.147645 | + | 0.989040i | \(0.452831\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −54.3392 | −2.57593 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.8088 | 0.511237 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3577 | 0.866354 | 0.433177 | − | 0.901309i | \(-0.357393\pi\) | ||||
0.433177 | + | 0.901309i | \(0.357393\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.868378 | 0.0408903 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.5677 | 0.684449 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.21407 | 0.244439 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.7113 | −1.38984 | −0.694918 | − | 0.719089i | \(-0.744559\pi\) | ||||
−0.694918 | + | 0.719089i | \(0.744559\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.49148 | −0.116292 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.4413 | −0.486301 | −0.243150 | − | 0.969989i | \(-0.578181\pi\) | ||||
−0.243150 | + | 0.969989i | \(0.578181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.4434 | 0.578295 | 0.289147 | − | 0.957285i | \(-0.406628\pi\) | ||||
0.289147 | + | 0.957285i | \(0.406628\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.2522 | −0.939173 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.8612 | −0.733969 | −0.366985 | − | 0.930227i | \(-0.619610\pi\) | ||||
−0.366985 | + | 0.930227i | \(0.619610\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.16901 | 0.146331 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.35228 | −0.154465 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.69020 | −0.169676 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.5166 | 1.07902 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.26872 | 0.103878 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.6120 | 0.804712 | 0.402356 | − | 0.915483i | \(-0.368191\pi\) | ||||
0.402356 | + | 0.915483i | \(0.368191\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.29170 | −0.104492 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.3554 | −0.835199 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30.3301 | −1.37722 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9871 | 0.588499 | 0.294250 | − | 0.955729i | \(-0.404930\pi\) | ||||
0.294250 | + | 0.955729i | \(0.404930\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.58993 | −0.207564 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.0244 | −1.08420 | −0.542102 | − | 0.840313i | \(-0.682371\pi\) | ||||
−0.542102 | + | 0.840313i | \(0.682371\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.29406 | −0.193395 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.79036 | −0.0804705 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 57.0062 | 2.55708 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.3018 | −1.62509 | −0.812545 | − | 0.582899i | \(-0.801918\pi\) | ||||
−0.812545 | + | 0.582899i | \(0.801918\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.7818 | −1.72920 | −0.864598 | − | 0.502464i | \(-0.832427\pi\) | ||||
−0.864598 | + | 0.502464i | \(0.832427\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.8518 | 0.660896 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8939 | −0.572638 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.7197 | −1.62757 | −0.813786 | − | 0.581165i | \(-0.802597\pi\) | ||||
−0.813786 | + | 0.581165i | \(0.802597\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.6336 | 0.691592 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.26410 | 0.144114 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.74018 | 0.252942 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.27614 | 0.0561245 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.8765 | 0.740797 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.85756 | 0.431867 | 0.215934 | − | 0.976408i | \(-0.430720\pi\) | ||||
0.215934 | + | 0.976408i | \(0.430720\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.4813 | 1.37658 | 0.688290 | − | 0.725435i | \(-0.258362\pi\) | ||||
0.688290 | + | 0.725435i | \(0.258362\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 33.0095 | 1.44065 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.4433 | −0.629161 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.95013 | −0.302180 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.76876 | −0.293739 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.551974 | −0.0239087 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −67.5262 | −2.91941 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.6247 | −1.06263 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.17067 | 0.308863 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.6002 | 0.498729 | 0.249365 | − | 0.968410i | \(-0.419778\pi\) | ||||
0.249365 | + | 0.968410i | \(0.419778\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.54891 | 0.0664701 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.63482 | −0.0700281 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.64269 | 0.326778 | 0.163389 | − | 0.986562i | \(-0.447757\pi\) | ||||
0.163389 | + | 0.986562i | \(0.447757\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.57345 | −0.0671530 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.62567 | 0.239662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.3196 | −2.09728 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.5772 | −1.04324 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.11952 | 0.344035 | 0.172018 | − | 0.985094i | \(-0.444971\pi\) | ||||
0.172018 | + | 0.985094i | \(0.444971\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.34563 | 0.0992097 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.27683 | −0.0539080 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.6113 | −0.868663 | −0.434332 | − | 0.900753i | \(-0.643015\pi\) | ||||
−0.434332 | + | 0.900753i | \(0.643015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.1462 | 1.47861 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.58171 | 0.192414 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.2528 | 0.513664 | 0.256832 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256832 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.0736 | −1.42593 | −0.712967 | − | 0.701197i | \(-0.752649\pi\) | ||||
−0.712967 | + | 0.701197i | \(0.752649\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.85499 | 0.0774932 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.8633 | −1.20368 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.05077 | 0.0853745 | 0.0426873 | − | 0.999088i | \(-0.486408\pi\) | ||||
0.0426873 | + | 0.999088i | \(0.486408\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.6759 | 0.817702 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.3187 | −0.594041 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.16268 | 0.0481531 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.13802 | 0.0470513 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.2048 | 1.12286 | 0.561430 | − | 0.827524i | \(-0.310251\pi\) | ||||
0.561430 | + | 0.827524i | \(0.310251\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.9223 | 0.779680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.0223 | 1.02928 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.2090 | −0.542429 | −0.271215 | − | 0.962519i | \(-0.587425\pi\) | ||||
−0.271215 | + | 0.962519i | \(0.587425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.8793 | 1.63489 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.2466 | 0.951419 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.8049 | −1.38123 | −0.690614 | − | 0.723223i | \(-0.742660\pi\) | ||||
−0.690614 | + | 0.723223i | \(0.742660\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.52887 | 0.388691 | 0.194345 | − | 0.980933i | \(-0.437742\pi\) | ||||
0.194345 | + | 0.980933i | \(0.437742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.691665 | 0.0281668 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 37.5111 | 1.52504 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.2279 | −0.699258 | −0.349629 | − | 0.936888i | \(-0.613692\pi\) | ||||
−0.349629 | + | 0.936888i | \(0.613692\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.89657 | 0.319985 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.811162 | −0.0328161 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.0981 | −1.78111 | −0.890553 | − | 0.454880i | \(-0.849682\pi\) | ||||
−0.890553 | + | 0.454880i | \(0.849682\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.91962 | −0.238702 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.7800 | 1.27941 | 0.639706 | − | 0.768619i | \(-0.279056\pi\) | ||||
0.639706 | + | 0.768619i | \(0.279056\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00109 | 0.0804307 | 0.0402153 | − | 0.999191i | \(-0.487196\pi\) | ||||
0.0402153 | + | 0.999191i | \(0.487196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00623 | −0.160764 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 71.2655 | 2.85519 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.11657 | −0.364663 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.67279 | 0.0668048 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.5278 | −0.698880 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.1185 | 1.67671 | 0.838355 | − | 0.545125i | \(-0.183518\pi\) | ||||
0.838355 | + | 0.545125i | \(0.183518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.45455 | −0.336038 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.5374 | −0.973737 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.55795 | −0.180593 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.4421 | 0.492203 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.22836 | 0.325001 | 0.162500 | − | 0.986708i | \(-0.448044\pi\) | ||||
0.162500 | + | 0.986708i | \(0.448044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.04621 | 0.277876 | 0.138938 | − | 0.990301i | \(-0.455631\pi\) | ||||
0.138938 | + | 0.990301i | \(0.455631\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.1556 | 0.990502 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.5212 | −1.78962 | −0.894812 | − | 0.446444i | \(-0.852690\pi\) | ||||
−0.894812 | + | 0.446444i | \(0.852690\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.46886 | −0.136165 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.5606 | 1.04099 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.4865 | 1.15389 | 0.576947 | − | 0.816782i | \(-0.304244\pi\) | ||||
0.576947 | + | 0.816782i | \(0.304244\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.8237 | 1.00902 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.41218 | 0.133122 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.5112 | −1.03273 | −0.516364 | − | 0.856369i | \(-0.672715\pi\) | ||||
−0.516364 | + | 0.856369i | \(0.672715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.4928 | −0.641494 | −0.320747 | − | 0.947165i | \(-0.603934\pi\) | ||||
−0.320747 | + | 0.947165i | \(0.603934\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.811605 | 0.0315201 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −52.2461 | −2.02602 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.90472 | −0.267352 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.8078 | 0.765815 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.806360 | −0.0311292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.9616 | 1.73314 | 0.866571 | − | 0.499054i | \(-0.166319\pi\) | ||||
0.866571 | + | 0.499054i | \(0.166319\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.20462 | 0.277306 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.9435 | −1.07396 | −0.536978 | − | 0.843596i | \(-0.680434\pi\) | ||||
−0.536978 | + | 0.843596i | \(0.680434\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.7777 | 1.52653 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.09680 | −0.0420293 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.1762 | −1.07813 | −0.539067 | − | 0.842263i | \(-0.681223\pi\) | ||||
−0.539067 | + | 0.842263i | \(0.681223\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.6035 | −1.16930 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.0699 | −0.384192 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.739041 | −0.0281552 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4670 | −0.968810 | −0.484405 | − | 0.874844i | \(-0.660964\pi\) | ||||
−0.484405 | + | 0.874844i | \(0.660964\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.34804 | 0.0891946 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.0608 | −0.419561 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.22172 | −0.159909 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.01463 | 0.189671 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.60309 | −0.0983174 | −0.0491587 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491587 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.9633 | 0.866078 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.69927 | −0.327633 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.4780 | −0.732546 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.4907 | 0.994878 | 0.497439 | − | 0.867499i | \(-0.334274\pi\) | ||||
0.497439 | + | 0.867499i | \(0.334274\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.7644 | −0.403698 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.2245 | −0.869763 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.583212 | 0.0218109 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.8946 | 0.630939 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 53.1883 | 1.98359 | 0.991794 | − | 0.127850i | \(-0.0408076\pi\) | ||||
0.991794 | + | 0.127850i | \(0.0408076\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.52819 | −0.280365 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.0016 | 0.520726 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.4171 | 0.461161 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.2624 | −1.49325 | −0.746625 | − | 0.665245i | \(-0.768327\pi\) | ||||
−0.746625 | + | 0.665245i | \(0.768327\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.9403 | 0.663547 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2660 | 0.600798 | 0.300399 | − | 0.953814i | \(-0.402880\pi\) | ||||
0.300399 | + | 0.953814i | \(0.402880\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −48.8815 | −1.80302 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.354465 | 0.0130569 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.4651 | −1.52532 | −0.762660 | − | 0.646800i | \(-0.776107\pi\) | ||||
−0.762660 | + | 0.646800i | \(0.776107\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.06329 | −0.0390609 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.6758 | −1.34551 | −0.672753 | − | 0.739867i | \(-0.734888\pi\) | ||||
−0.672753 | + | 0.739867i | \(0.734888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.7605 | −1.38344 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.12519 | −0.114345 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 88.5601 | 3.23592 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.0394 | 1.24212 | 0.621058 | − | 0.783765i | \(-0.286703\pi\) | ||||
0.621058 | + | 0.783765i | \(0.286703\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.8610 | 0.760217 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −50.8923 | −1.85216 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.5338 | −1.18246 | −0.591231 | − | 0.806503i | \(-0.701358\pi\) | ||||
−0.591231 | + | 0.806503i | \(0.701358\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.05311 | −0.0745233 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.8709 | −0.430319 | −0.215159 | − | 0.976579i | \(-0.569027\pi\) | ||||
−0.215159 | + | 0.976579i | \(0.569027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.14406 | 0.0776201 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.70401 | 0.314694 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.20494 | 0.0796157 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.7830 | 0.569149 | 0.284574 | − | 0.958654i | \(-0.408148\pi\) | ||||
0.284574 | + | 0.958654i | \(0.408148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0215 | 0.540987 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.1698 | 1.19304 | 0.596518 | − | 0.802600i | \(-0.296551\pi\) | ||||
0.596518 | + | 0.802600i | \(0.296551\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.7658 | 1.50027 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.2328 | 1.15635 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.53090 | 0.198165 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.37634 | 0.228164 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.72350 | 0.0615927 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.7112 | 0.417992 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.27019 | 0.294800 | 0.147400 | − | 0.989077i | \(-0.452909\pi\) | ||||
0.147400 | + | 0.989077i | \(0.452909\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.66555 | 0.344103 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.0940 | −1.63891 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.512553 | 0.0182013 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.92581 | −0.281099 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.7455 | 0.628578 | 0.314289 | − | 0.949327i | \(-0.398234\pi\) | ||||
0.314289 | + | 0.949327i | \(0.398234\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.20409 | −0.219485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.5543 | 0.549585 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.74868 | 0.0617095 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 64.1247 | 2.26010 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.0300 | 0.388274 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.8874 | −1.57816 | −0.789079 | − | 0.614292i | \(-0.789442\pi\) | ||||
−0.789079 | + | 0.614292i | \(0.789442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.5750 | 1.88127 | 0.940636 | − | 0.339418i | \(-0.110230\pi\) | ||||
0.940636 | + | 0.339418i | \(0.110230\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.3714 | 0.959956 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.0350 | 0.561681 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.5037 | −0.822292 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.49250 | −0.0521522 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.2612 | −0.986321 | −0.493161 | − | 0.869938i | \(-0.664158\pi\) | ||||
−0.493161 | + | 0.869938i | \(0.664158\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.5821 | −1.06603 | −0.533013 | − | 0.846107i | \(-0.678940\pi\) | ||||
−0.533013 | + | 0.846107i | \(0.678940\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.69222 | 0.128547 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.0995 | 0.907567 | 0.453784 | − | 0.891112i | \(-0.350074\pi\) | ||||
0.453784 | + | 0.891112i | \(0.350074\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.79496 | 0.305462 | 0.152731 | − | 0.988268i | \(-0.451193\pi\) | ||||
0.152731 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2246 | −0.493447 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.8610 | −1.20786 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.49351 | −0.120898 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.79709 | 0.200377 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.6667 | 0.851591 | 0.425795 | − | 0.904820i | \(-0.359994\pi\) | ||||
0.425795 | + | 0.904820i | \(0.359994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0296 | −0.897571 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.17980 | 0.247286 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.0449 | 1.54959 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −49.1955 | −1.69038 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.49336 | −0.257172 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.1842 | −0.966143 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.7504 | −0.368088 | −0.184044 | − | 0.982918i | \(-0.558919\pi\) | ||||
−0.184044 | + | 0.982918i | \(0.558919\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.4032 | −0.389981 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.67868 | 0.296458 | 0.148229 | − | 0.988953i | \(-0.452643\pi\) | ||||
0.148229 | + | 0.988953i | \(0.452643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.1922 | 0.484232 | 0.242116 | − | 0.970247i | \(-0.422159\pi\) | ||||
0.242116 | + | 0.970247i | \(0.422159\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.76354 | 0.264581 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.4638 | −1.24124 | −0.620622 | − | 0.784110i | \(-0.713120\pi\) | ||||
−0.620622 | + | 0.784110i | \(0.713120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −58.9583 | −2.00464 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.7925 | −0.366533 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.51657 | −0.187137 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.225311 | −0.00763438 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.68185 | 0.293836 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.2877 | −1.19294 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.68456 | 0.225722 | 0.112861 | − | 0.993611i | \(-0.463999\pi\) | ||||
0.112861 | + | 0.993611i | \(0.463999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.4024 | −0.755613 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.97149 | −0.0664211 | −0.0332105 | − | 0.999448i | \(-0.510573\pi\) | ||||
−0.0332105 | + | 0.999448i | \(0.510573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.9784 | −1.34538 | −0.672690 | − | 0.739925i | \(-0.734861\pi\) | ||||
−0.672690 | + | 0.739925i | \(0.734861\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.6467 | 0.794877 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.6633 | −1.06315 | −0.531574 | − | 0.847012i | \(-0.678399\pi\) | ||||
−0.531574 | + | 0.847012i | \(0.678399\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.1806 | 1.07930 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.512480 | 0.0171687 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.12802 | 0.271994 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 86.0265 | 2.87555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.30504 | 0.0435739 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.99126 | 0.333227 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.65248 | −0.188311 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.9914 | −1.09789 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.41113 | −0.179872 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.86210 | 0.128239 | 0.0641195 | − | 0.997942i | \(-0.479576\pi\) | ||||
0.0641195 | + | 0.997942i | \(0.479576\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.25125 | −0.141005 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.0805 | 0.599035 | 0.299518 | − | 0.954091i | \(-0.403174\pi\) | ||||
0.299518 | + | 0.954091i | \(0.403174\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.60160 | −0.0530052 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.49685 | 0.181720 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.8676 | −1.11841 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.7072 | 0.551118 | 0.275559 | − | 0.961284i | \(-0.411137\pi\) | ||||
0.275559 | + | 0.961284i | \(0.411137\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.30538 | 0.240720 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.05305 | −0.133408 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.6852 | 1.66652 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.64310 | −0.0539664 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.5918 | −1.33178 | −0.665888 | − | 0.746052i | \(-0.731947\pi\) | ||||
−0.665888 | + | 0.746052i | \(0.731947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.6716 | 1.49683 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.7279 | −0.875032 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.46064 | 0.145878 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.3223 | 1.15393 | 0.576965 | − | 0.816769i | \(-0.304237\pi\) | ||||
0.576965 | + | 0.816769i | \(0.304237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.0884 | −0.622925 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.9506 | −0.682971 | −0.341485 | − | 0.939887i | \(-0.610930\pi\) | ||||
−0.341485 | + | 0.939887i | \(0.610930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.78840 | −0.221061 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.0063 | −0.520684 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.6755 | −1.25678 | −0.628392 | − | 0.777897i | \(-0.716287\pi\) | ||||
−0.628392 | + | 0.777897i | \(0.716287\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.11153 | −0.0360817 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.844016 | −0.0273691 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.98349 | −0.0966446 | −0.0483223 | − | 0.998832i | \(-0.515387\pi\) | ||||
−0.0483223 | + | 0.998832i | \(0.515387\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.48042 | −0.209701 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.883258 | 0.0285517 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.1363 | 1.29607 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.60624 | 0.0840723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.3290 | 0.622870 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −68.7379 | −2.21275 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.7366 | 0.409580 | 0.204790 | − | 0.978806i | \(-0.434349\pi\) | ||||
0.204790 | + | 0.978806i | \(0.434349\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.13245 | −0.261252 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.6633 | 0.855668 | 0.427834 | − | 0.903857i | \(-0.359277\pi\) | ||||
0.427834 | + | 0.903857i | \(0.359277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.5062 | 0.465047 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.34692 | −0.0751615 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.7975 | −0.345443 | −0.172721 | − | 0.984971i | \(-0.555256\pi\) | ||||
−0.172721 | + | 0.984971i | \(0.555256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.97129 | 0.254763 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.467960 | 0.0149408 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.3650 | −0.394383 | −0.197192 | − | 0.980365i | \(-0.563182\pi\) | ||||
−0.197192 | + | 0.980365i | \(0.563182\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −87.4157 | −2.78529 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.4090 | 0.363153 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.8475 | 0.917299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.4354 | 0.649151 | 0.324576 | − | 0.945860i | \(-0.394779\pi\) | ||||
0.324576 | + | 0.945860i | \(0.394779\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.805305 | −0.0255556 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −81.2121 | −2.57460 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.1561 | 1.05006 | 0.525032 | − | 0.851083i | \(-0.324053\pi\) | ||||
0.525032 | + | 0.851083i | \(0.324053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.03510 | 0.222581 |
(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 | 4008.2.a.l.1.2 | ✓ | 12 | |
4.3 | odd | 2 | 8016.2.a.bf.1.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8016.2.a.bf.1.2 | 12 | 4.3 | odd | 2 |