Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | 0.0547853 | 0.0316303 | 0.0158152 | − | 0.999875i | \(-0.494966\pi\) | ||||
0.0158152 | + | 0.999875i | \(0.494966\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.87235 | 1.46361 | 0.731806 | − | 0.681513i | \(-0.238678\pi\) | ||||
0.731806 | + | 0.681513i | \(0.238678\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99700 | −0.999000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.25314 | 0.980858 | 0.490429 | − | 0.871481i | \(-0.336840\pi\) | ||||
0.490429 | + | 0.871481i | \(0.336840\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.91309 | −1.91735 | −0.958674 | − | 0.284508i | \(-0.908170\pi\) | ||||
−0.958674 | + | 0.284508i | \(0.908170\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0547853 | −0.0141455 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.379841 | 0.0921251 | 0.0460625 | − | 0.998939i | \(-0.485333\pi\) | ||||
0.0460625 | + | 0.998939i | \(0.485333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.37288 | 1.00321 | 0.501603 | − | 0.865098i | \(-0.332744\pi\) | ||||
0.501603 | + | 0.865098i | \(0.332744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.212148 | 0.0462945 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.01656 | 0.211967 | 0.105983 | − | 0.994368i | \(-0.466201\pi\) | ||||
0.105983 | + | 0.994368i | \(0.466201\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.328547 | −0.0632290 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.37707 | −0.627106 | −0.313553 | − | 0.949571i | \(-0.601519\pi\) | ||||
−0.313553 | + | 0.949571i | \(0.601519\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.22792 | −1.11857 | −0.559284 | − | 0.828976i | \(-0.688924\pi\) | ||||
−0.559284 | + | 0.828976i | \(0.688924\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.178224 | 0.0310248 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.87235 | −0.654547 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.791545 | −0.130129 | −0.0650646 | − | 0.997881i | \(-0.520725\pi\) | ||||
−0.0650646 | + | 0.997881i | \(0.520725\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.378736 | −0.0606463 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.36327 | 0.369080 | 0.184540 | − | 0.982825i | \(-0.440920\pi\) | ||||
0.184540 | + | 0.982825i | \(0.440920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.241812 | 0.0368760 | 0.0184380 | − | 0.999830i | \(-0.494131\pi\) | ||||
0.0184380 | + | 0.999830i | \(0.494131\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.99700 | 0.446766 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.57722 | −0.959386 | −0.479693 | − | 0.877436i | \(-0.659252\pi\) | ||||
−0.479693 | + | 0.877436i | \(0.659252\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.99512 | 1.14216 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0208097 | 0.00291394 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.52720 | 1.30866 | 0.654331 | − | 0.756208i | \(-0.272950\pi\) | ||||
0.654331 | + | 0.756208i | \(0.272950\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.25314 | −0.438653 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.239569 | 0.0317317 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.22289 | 0.159207 | 0.0796034 | − | 0.996827i | \(-0.474635\pi\) | ||||
0.0796034 | + | 0.996827i | \(0.474635\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.03747 | −1.15713 | −0.578565 | − | 0.815636i | \(-0.696387\pi\) | ||||
−0.578565 | + | 0.815636i | \(0.696387\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.6054 | −1.46215 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.91309 | 0.857464 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.4260 | −1.51807 | −0.759036 | − | 0.651048i | \(-0.774330\pi\) | ||||
−0.759036 | + | 0.651048i | \(0.774330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0556924 | 0.00670458 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.8150 | −1.40219 | −0.701093 | − | 0.713070i | \(-0.747304\pi\) | ||||
−0.701093 | + | 0.713070i | \(0.747304\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.03700 | −0.121372 | −0.0606861 | − | 0.998157i | \(-0.519329\pi\) | ||||
−0.0606861 | + | 0.998157i | \(0.519329\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0547853 | 0.00632606 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.5973 | 1.43560 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.42411 | 0.160225 | 0.0801124 | − | 0.996786i | \(-0.474472\pi\) | ||||
0.0801124 | + | 0.996786i | \(0.474472\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.97300 | 0.997000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0097 | 1.09871 | 0.549356 | − | 0.835588i | \(-0.314873\pi\) | ||||
0.549356 | + | 0.835588i | \(0.314873\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.379841 | −0.0411996 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.185014 | −0.0198356 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.256993 | −0.0272412 | −0.0136206 | − | 0.999907i | \(-0.504336\pi\) | ||||
−0.0136206 | + | 0.999907i | \(0.504336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.7699 | −2.80625 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.341199 | −0.0353807 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.37288 | −0.448648 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.05385 | 0.411606 | 0.205803 | − | 0.978593i | \(-0.434019\pi\) | ||||
0.205803 | + | 0.978593i | \(0.434019\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.74965 | −0.979876 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.29284 | −0.128642 | −0.0643211 | − | 0.997929i | \(-0.520488\pi\) | ||||
−0.0643211 | + | 0.997929i | \(0.520488\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.69720 | 0.462828 | 0.231414 | − | 0.972855i | \(-0.425665\pi\) | ||||
0.231414 | + | 0.972855i | \(0.425665\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.212148 | −0.0207035 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.90373 | 0.280714 | 0.140357 | − | 0.990101i | \(-0.455175\pi\) | ||||
0.140357 | + | 0.990101i | \(0.455175\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.52516 | −0.337649 | −0.168824 | − | 0.985646i | \(-0.553997\pi\) | ||||
−0.168824 | + | 0.985646i | \(0.553997\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0433650 | −0.00411603 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.53383 | −0.426507 | −0.213253 | − | 0.976997i | \(-0.568406\pi\) | ||||
−0.213253 | + | 0.976997i | \(0.568406\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.01656 | −0.0947945 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.7185 | 1.91543 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.47088 | 0.134835 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.417101 | −0.0379183 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.129472 | 0.0116741 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.8505 | −1.22903 | −0.614514 | − | 0.788906i | \(-0.710648\pi\) | ||||
−0.614514 | + | 0.788906i | \(0.710648\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0132477 | 0.00116640 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4760 | −1.00267 | −0.501333 | − | 0.865255i | \(-0.667157\pi\) | ||||
−0.501333 | + | 0.865255i | \(0.667157\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.9333 | 1.46831 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.328547 | 0.0282769 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.2569 | −1.13262 | −0.566308 | − | 0.824194i | \(-0.691629\pi\) | ||||
−0.566308 | + | 0.824194i | \(0.691629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.87929 | −0.244218 | −0.122109 | − | 0.992517i | \(-0.538966\pi\) | ||||
−0.122109 | + | 0.992517i | \(0.538966\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.360335 | −0.0303457 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.4892 | −1.88064 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.37707 | 0.280450 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.438015 | 0.0361269 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.39273 | 0.441790 | 0.220895 | − | 0.975298i | \(-0.429102\pi\) | ||||
0.220895 | + | 0.975298i | \(0.429102\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.42119 | −0.197033 | −0.0985167 | − | 0.995135i | \(-0.531410\pi\) | ||||
−0.0985167 | + | 0.995135i | \(0.531410\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.13838 | −0.0920329 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.22792 | 0.500239 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.904608 | 0.0721956 | 0.0360978 | − | 0.999348i | \(-0.488507\pi\) | ||||
0.0360978 | + | 0.999348i | \(0.488507\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.521951 | 0.0413934 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.93647 | 0.310237 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.73871 | 0.527817 | 0.263908 | − | 0.964548i | \(-0.414988\pi\) | ||||
0.263908 | + | 0.964548i | \(0.414988\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.178224 | −0.0138747 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.2600 | −1.56777 | −0.783885 | − | 0.620907i | \(-0.786765\pi\) | ||||
−0.783885 | + | 0.620907i | \(0.786765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.7909 | 2.67622 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.1055 | −1.00220 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.63353 | −0.428309 | −0.214155 | − | 0.976800i | \(-0.568700\pi\) | ||||
−0.214155 | + | 0.976800i | \(0.568700\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.87235 | 0.292722 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0669965 | 0.00503576 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.2014 | 1.06147 | 0.530733 | − | 0.847539i | \(-0.321917\pi\) | ||||
0.530733 | + | 0.847539i | \(0.321917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.5197 | −1.52522 | −0.762608 | − | 0.646860i | \(-0.776082\pi\) | ||||
−0.762608 | + | 0.646860i | \(0.776082\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.495121 | −0.0366004 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.791545 | 0.0581955 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.23568 | 0.0903616 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.27225 | −0.0925427 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.5800 | −1.56147 | −0.780736 | − | 0.624861i | \(-0.785156\pi\) | ||||
−0.780736 | + | 0.624861i | \(0.785156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.6158 | 0.980090 | 0.490045 | − | 0.871697i | \(-0.336980\pi\) | ||||
0.490045 | + | 0.871697i | \(0.336980\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.378736 | 0.0271218 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.2022 | −1.22561 | −0.612804 | − | 0.790235i | \(-0.709958\pi\) | ||||
−0.612804 | + | 0.790235i | \(0.709958\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.4704 | 1.38022 | 0.690109 | − | 0.723705i | \(-0.257562\pi\) | ||||
0.690109 | + | 0.723705i | \(0.257562\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.680760 | −0.0480171 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.0772 | −0.917840 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.36327 | −0.165058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.04662 | −0.211755 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.2256 | 0.984003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7402 | −0.877072 | −0.438536 | − | 0.898714i | \(-0.644503\pi\) | ||||
−0.438536 | + | 0.898714i | \(0.644503\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.647290 | −0.0443516 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.241812 | −0.0164914 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.1167 | −1.63715 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0568126 | −0.00383904 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.62588 | −0.176636 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.58615 | −0.173181 | −0.0865906 | − | 0.996244i | \(-0.527597\pi\) | ||||
−0.0865906 | + | 0.996244i | \(0.527597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.99700 | −0.199800 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.8804 | 1.05402 | 0.527009 | − | 0.849860i | \(-0.323313\pi\) | ||||
0.527009 | + | 0.849860i | \(0.323313\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.44561 | −0.293774 | −0.146887 | − | 0.989153i | \(-0.546925\pi\) | ||||
−0.146887 | + | 0.989153i | \(0.546925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.690147 | 0.0454083 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.1850 | −0.929292 | −0.464646 | − | 0.885497i | \(-0.653818\pi\) | ||||
−0.464646 | + | 0.885497i | \(0.653818\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.57722 | 0.429051 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.0780202 | 0.00506796 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.56239 | −0.489170 | −0.244585 | − | 0.969628i | \(-0.578652\pi\) | ||||
−0.244585 | + | 0.969628i | \(0.578652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.87453 | 0.636074 | 0.318037 | − | 0.948078i | \(-0.396976\pi\) | ||||
0.318037 | + | 0.948078i | \(0.396976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.47723 | 0.0947644 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.99512 | −0.510789 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.2301 | −1.92350 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.548387 | 0.0347526 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.0552 | −1.39211 | −0.696056 | − | 0.717988i | \(-0.745063\pi\) | ||||
−0.696056 | + | 0.717988i | \(0.745063\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.30700 | 0.207909 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0208097 | −0.00130316 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.3588 | 1.08281 | 0.541405 | − | 0.840762i | \(-0.317892\pi\) | ||||
0.541405 | + | 0.840762i | \(0.317892\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.06514 | −0.190459 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.1211 | 0.626478 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.2110 | −1.12294 | −0.561468 | − | 0.827498i | \(-0.689763\pi\) | ||||
−0.561468 | + | 0.827498i | \(0.689763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.52720 | −0.585251 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0140795 | −0.000861648 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.83629 | 0.294874 | 0.147437 | − | 0.989071i | \(-0.452898\pi\) | ||||
0.147437 | + | 0.989071i | \(0.452898\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0413 | 0.852949 | 0.426474 | − | 0.904500i | \(-0.359755\pi\) | ||||
0.426474 | + | 0.904500i | \(0.359755\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.46660 | −0.0887626 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.25314 | 0.196172 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.8843 | −1.01448 | −0.507238 | − | 0.861806i | \(-0.669334\pi\) | ||||
−0.507238 | + | 0.861806i | \(0.669334\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.6651 | 1.11745 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.8389 | −1.06418 | −0.532091 | − | 0.846687i | \(-0.678593\pi\) | ||||
−0.532091 | + | 0.846687i | \(0.678593\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.4099 | 1.74824 | 0.874119 | − | 0.485711i | \(-0.161439\pi\) | ||||
0.874119 | + | 0.485711i | \(0.161439\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.239569 | −0.0141909 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.15141 | 0.540191 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8557 | −0.991513 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.222091 | 0.0130192 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.2205 | −0.655507 | −0.327754 | − | 0.944763i | \(-0.606292\pi\) | ||||
−0.327754 | + | 0.944763i | \(0.606292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.22289 | −0.0711995 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.06881 | −0.0620186 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.02756 | −0.406414 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.936382 | 0.0539722 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.0708285 | −0.00406899 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.03747 | 0.517484 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0714 | 0.917244 | 0.458622 | − | 0.888631i | \(-0.348343\pi\) | ||||
0.458622 | + | 0.888631i | \(0.348343\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.257337 | 0.0146394 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.5345 | −1.33452 | −0.667259 | − | 0.744825i | \(-0.732533\pi\) | ||||
−0.667259 | + | 0.744825i | \(0.732533\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.46325 | −0.139231 | −0.0696155 | − | 0.997574i | \(-0.522177\pi\) | ||||
−0.0696155 | + | 0.997574i | \(0.522177\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.6054 | 0.653892 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.74184 | 0.153997 | 0.0769984 | − | 0.997031i | \(-0.475466\pi\) | ||||
0.0769984 | + | 0.997031i | \(0.475466\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.9861 | −0.615102 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.159082 | 0.00887908 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.66100 | 0.0924205 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.91309 | −0.383469 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.193127 | −0.0106799 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.4693 | −1.40417 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.1919 | 1.10985 | 0.554924 | − | 0.831901i | \(-0.312747\pi\) | ||||
0.554924 | + | 0.831901i | \(0.312747\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.37226 | 0.129999 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.4260 | 0.678903 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.5295 | 1.44516 | 0.722578 | − | 0.691290i | \(-0.242957\pi\) | ||||
0.722578 | + | 0.691290i | \(0.242957\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.248387 | −0.0134905 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.2603 | −1.09716 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.85346 | 0.208067 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0556924 | −0.00299838 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.16729 | −0.0626634 | −0.0313317 | − | 0.999509i | \(-0.509975\pi\) | ||||
−0.0313317 | + | 0.999509i | \(0.509975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6879 | 0.732698 | 0.366349 | − | 0.930477i | \(-0.380608\pi\) | ||||
0.366349 | + | 0.930477i | \(0.380608\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.27128 | 0.121232 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.960426 | −0.0511183 | −0.0255591 | − | 0.999673i | \(-0.508137\pi\) | ||||
−0.0255591 | + | 0.999673i | \(0.508137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.8150 | 0.627077 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0805826 | 0.00426488 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.7589 | 1.09561 | 0.547807 | − | 0.836605i | \(-0.315463\pi\) | ||||
0.547807 | + | 0.836605i | \(0.315463\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.122051 | 0.00642376 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0228510 | −0.00119937 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.03700 | 0.0542793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1120 | −1.20643 | −0.603217 | − | 0.797577i | \(-0.706115\pi\) | ||||
−0.603217 | + | 0.797577i | \(0.706115\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.08271 | −0.368711 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 36.8927 | 1.91537 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.77344 | −0.0918255 | −0.0459127 | − | 0.998945i | \(-0.514620\pi\) | ||||
−0.0459127 | + | 0.998945i | \(0.514620\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.0547853 | −0.00282910 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.3460 | 1.20238 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.4511 | −0.639572 | −0.319786 | − | 0.947490i | \(-0.603611\pi\) | ||||
−0.319786 | + | 0.947490i | \(0.603611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.758801 | −0.0388746 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.6751 | −0.596569 | −0.298284 | − | 0.954477i | \(-0.596414\pi\) | ||||
−0.298284 | + | 0.954477i | \(0.596414\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.5973 | −0.642018 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.724711 | −0.0368391 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.6275 | 1.14726 | 0.573629 | − | 0.819115i | \(-0.305535\pi\) | ||||
0.573629 | + | 0.819115i | \(0.305535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.386131 | 0.0195275 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.628718 | −0.0317146 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.42411 | −0.0716547 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7266 | 1.04024 | 0.520118 | − | 0.854094i | \(-0.325888\pi\) | ||||
0.520118 | + | 0.854094i | \(0.325888\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.927697 | 0.0464430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 43.0542 | 2.14468 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.97300 | −0.445872 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.57500 | −0.127638 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.5502 | −0.719461 | −0.359730 | − | 0.933056i | \(-0.617131\pi\) | ||||
−0.359730 | + | 0.933056i | \(0.617131\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.726285 | −0.0358250 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.73547 | 0.233017 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0097 | −0.491359 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.157743 | −0.00772469 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.495617 | 0.0242125 | 0.0121062 | − | 0.999927i | \(-0.496146\pi\) | ||||
0.0121062 | + | 0.999927i | \(0.496146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.0564 | −1.75728 | −0.878640 | − | 0.477486i | \(-0.841548\pi\) | ||||
−0.878640 | + | 0.477486i | \(0.841548\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.7119 | 0.958427 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.379841 | 0.0184250 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.9963 | −1.69359 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.23208 | −0.0594854 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.2202 | 1.21481 | 0.607406 | − | 0.794391i | \(-0.292210\pi\) | ||||
0.607406 | + | 0.794391i | \(0.292210\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8649 | 0.570193 | 0.285096 | − | 0.958499i | \(-0.407974\pi\) | ||||
0.285096 | + | 0.958499i | \(0.407974\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.185014 | 0.00887073 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.44528 | 0.212647 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7449 | 0.799191 | 0.399595 | − | 0.916692i | \(-0.369151\pi\) | ||||
0.399595 | + | 0.916692i | \(0.369151\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23.9614 | −1.14102 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.4045 | 0.826912 | 0.413456 | − | 0.910524i | \(-0.364322\pi\) | ||||
0.413456 | + | 0.910524i | \(0.364322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.256993 | 0.0121826 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.295443 | 0.0139740 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.06051 | −0.191627 | −0.0958136 | − | 0.995399i | \(-0.530545\pi\) | ||||
−0.0958136 | + | 0.995399i | \(0.530545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.68803 | 0.362015 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.132645 | −0.00623223 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.7699 | 1.25499 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.7234 | −1.10973 | −0.554867 | − | 0.831939i | \(-0.687231\pi\) | ||||
−0.554867 | + | 0.831939i | \(0.687231\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.124796 | −0.00582497 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.02394 | 0.0942642 | 0.0471321 | − | 0.998889i | \(-0.484992\pi\) | ||||
0.0471321 | + | 0.998889i | \(0.484992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4483 | −0.578520 | −0.289260 | − | 0.957251i | \(-0.593409\pi\) | ||||
−0.289260 | + | 0.957251i | \(0.593409\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.341199 | 0.0158227 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.4461 | −0.992406 | −0.496203 | − | 0.868206i | \(-0.665273\pi\) | ||||
−0.496203 | + | 0.868206i | \(0.665273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −48.1177 | −2.22187 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0495592 | 0.00228357 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.786648 | 0.0361701 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.37288 | 0.200641 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.5530 | −1.30735 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.3565 | −1.43271 | −0.716357 | − | 0.697734i | \(-0.754192\pi\) | ||||
−0.716357 | + | 0.697734i | \(0.754192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.47202 | 0.249503 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.215661 | 0.00981290 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.05385 | −0.184076 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.6622 | −1.57069 | −0.785347 | − | 0.619056i | \(-0.787515\pi\) | ||||
−0.785347 | + | 0.619056i | \(0.787515\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.369182 | 0.0166950 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.3685 | −1.18999 | −0.594997 | − | 0.803728i | \(-0.702847\pi\) | ||||
−0.594997 | + | 0.803728i | \(0.702847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.28275 | −0.0577722 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.74965 | 0.438214 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −45.7520 | −2.05226 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.7512 | −1.42138 | −0.710689 | − | 0.703506i | \(-0.751617\pi\) | ||||
−0.710689 | + | 0.703506i | \(0.751617\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.10995 | −0.0495890 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.5992 | −1.05224 | −0.526118 | − | 0.850411i | \(-0.676353\pi\) | ||||
−0.526118 | + | 0.850411i | \(0.676353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.29284 | 0.0575305 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.90603 | 0.0846497 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.4949 | 1.48463 | 0.742317 | − | 0.670048i | \(-0.233727\pi\) | ||||
0.742317 | + | 0.670048i | \(0.233727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.01565 | −0.177642 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.43670 | −0.0634317 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.69720 | −0.206983 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.3966 | −0.941022 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.308635 | −0.0135476 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.2923 | −1.76524 | −0.882620 | − | 0.470087i | \(-0.844222\pi\) | ||||
−0.882620 | + | 0.470087i | \(0.844222\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.1087 | −1.79756 | −0.898778 | − | 0.438404i | \(-0.855544\pi\) | ||||
−0.898778 | + | 0.438404i | \(0.855544\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.212148 | 0.00925890 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.36562 | −0.103048 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9666 | −0.955070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.66500 | −0.159048 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.3375 | −0.707655 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.90373 | −0.125539 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.778030 | 0.0335745 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.0092 | 1.12030 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0005 | −0.644923 | −0.322461 | − | 0.946583i | \(-0.604510\pi\) | ||||
−0.322461 | + | 0.946583i | \(0.604510\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.12418 | −0.0482431 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.52516 | 0.151001 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.48196 | 0.362662 | 0.181331 | − | 0.983422i | \(-0.441959\pi\) | ||||
0.181331 | + | 0.983422i | \(0.441959\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.0853 | 1.15597 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.7675 | −0.629117 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.51465 | 0.234507 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0433650 | 0.00184074 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.8347 | −0.543823 | −0.271911 | − | 0.962322i | \(-0.587656\pi\) | ||||
−0.271911 | + | 0.962322i | \(0.587656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.67167 | −0.0707041 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0676969 | 0.00285816 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.1619 | −1.56619 | −0.783094 | − | 0.621903i | \(-0.786360\pi\) | ||||
−0.783094 | + | 0.621903i | \(0.786360\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.53383 | 0.190740 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 34.7466 | 1.45922 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.6682 | −0.447234 | −0.223617 | − | 0.974677i | \(-0.571786\pi\) | ||||
−0.223617 | + | 0.974677i | \(0.571786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.83451 | 0.118620 | 0.0593102 | − | 0.998240i | \(-0.481110\pi\) | ||||
0.0593102 | + | 0.998240i | \(0.481110\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.18227 | −0.0493898 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.01656 | 0.0423934 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.54980 | −0.355933 | −0.177966 | − | 0.984037i | \(-0.556952\pi\) | ||||
−0.177966 | + | 0.984037i | \(0.556952\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.745948 | 0.0310005 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.7613 | 1.60809 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.9933 | 1.28361 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20.7185 | −0.856606 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.2948 | −1.16785 | −0.583926 | − | 0.811807i | \(-0.698484\pi\) | ||||
−0.583926 | + | 0.811807i | \(0.698484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.2339 | −1.12216 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.942429 | −0.0387663 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.04491 | −0.0839743 | −0.0419872 | − | 0.999118i | \(-0.513369\pi\) | ||||
−0.0419872 | + | 0.999118i | \(0.513369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.47088 | −0.0603002 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.06669 | 0.0436567 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.317784 | −0.0129843 | −0.00649215 | − | 0.999979i | \(-0.502067\pi\) | ||||
−0.00649215 | + | 0.999979i | \(0.502067\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.97661 | 0.325373 | 0.162686 | − | 0.986678i | \(-0.447984\pi\) | ||||
0.162686 | + | 0.986678i | \(0.447984\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.2406 | 1.51655 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.417101 | 0.0169576 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.9256 | 1.57994 | 0.789971 | − | 0.613144i | \(-0.210096\pi\) | ||||
0.789971 | + | 0.613144i | \(0.210096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.716438 | −0.0290315 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 45.4690 | 1.83948 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.6279 | −1.47939 | −0.739694 | − | 0.672943i | \(-0.765030\pi\) | ||||
−0.739694 | + | 0.672943i | \(0.765030\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.129472 | −0.00522083 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.0675 | −0.928662 | −0.464331 | − | 0.885662i | \(-0.653705\pi\) | ||||
−0.464331 | + | 0.885662i | \(0.653705\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.1149 | 0.527131 | 0.263565 | − | 0.964642i | \(-0.415102\pi\) | ||||
0.263565 | + | 0.964642i | \(0.415102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.333987 | −0.0134024 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.995169 | −0.0398706 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.779352 | 0.0311243 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.300662 | −0.0119882 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.8199 | 0.908444 | 0.454222 | − | 0.890888i | \(-0.349917\pi\) | ||||
0.454222 | + | 0.890888i | \(0.349917\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.697976 | −0.0277420 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.8505 | 0.549638 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −55.2710 | −2.18992 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.4096 | 1.40078 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.76533 | −0.109224 | −0.0546121 | − | 0.998508i | \(-0.517392\pi\) | ||||
−0.0546121 | + | 0.998508i | \(0.517392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.3052 | 1.90497 | 0.952485 | − | 0.304585i | \(-0.0985179\pi\) | ||||
0.952485 | + | 0.304585i | \(0.0985179\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0132477 | −0.000521630 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.1138 | −0.908699 | −0.454349 | − | 0.890824i | \(-0.650128\pi\) | ||||
−0.454349 | + | 0.890824i | \(0.650128\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.97823 | 0.156159 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.32124 | −0.0517835 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.2971 | −1.53781 | −0.768907 | − | 0.639360i | \(-0.779199\pi\) | ||||
−0.768907 | + | 0.639360i | \(0.779199\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.4760 | 0.448405 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.10790 | 0.121251 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7465 | −0.808171 | −0.404085 | − | 0.914721i | \(-0.632410\pi\) | ||||
−0.404085 | + | 0.914721i | \(0.632410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.1256 | 1.05506 | 0.527531 | − | 0.849536i | \(-0.323118\pi\) | ||||
0.527531 | + | 0.849536i | \(0.323118\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.143860 | −0.00558704 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.9333 | −0.656646 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.43298 | −0.132926 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.141683 | −0.00547778 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.4001 | −1.13498 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.95240 | 0.190901 | 0.0954505 | − | 0.995434i | \(-0.469571\pi\) | ||||
0.0954505 | + | 0.995434i | \(0.469571\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.328547 | −0.0126458 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.1674 | 1.35159 | 0.675796 | − | 0.737089i | \(-0.263800\pi\) | ||||
0.675796 | + | 0.737089i | \(0.263800\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.6979 | 0.602431 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.870011 | 0.0333389 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.0119 | −1.26317 | −0.631584 | − | 0.775308i | \(-0.717595\pi\) | ||||
−0.631584 | + | 0.775308i | \(0.717595\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.2569 | 0.506521 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.243554 | −0.00929216 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −65.8624 | −2.50916 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.394264 | −0.0149985 | −0.00749926 | − | 0.999972i | \(-0.502387\pi\) | ||||
−0.00749926 | + | 0.999972i | \(0.502387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −37.7541 | −1.43416 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.87929 | 0.109218 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.897667 | 0.0340016 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.777131 | −0.0293938 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.2131 | 1.14113 | 0.570566 | − | 0.821252i | \(-0.306724\pi\) | ||||
0.570566 | + | 0.821252i | \(0.306724\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.46133 | −0.130546 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.360335 | 0.0135710 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.00633 | −0.188282 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.2139 | −0.496260 | −0.248130 | − | 0.968727i | \(-0.579816\pi\) | ||||
−0.248130 | + | 0.968727i | \(0.579816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.26805 | −0.160064 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.33104 | −0.237099 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.4892 | 0.841050 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.414308 | −0.0154726 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.77985 | 0.364727 | 0.182363 | − | 0.983231i | \(-0.441625\pi\) | ||||
0.182363 | + | 0.983231i | \(0.441625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.1892 | 0.677401 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.540979 | 0.0201192 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.37707 | −0.125421 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.0727 | 0.484839 | 0.242420 | − | 0.970172i | \(-0.422059\pi\) | ||||
0.242420 | + | 0.970172i | \(0.422059\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.8381 | −0.994002 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0918503 | 0.00339720 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.89623 | −0.0700389 | −0.0350194 | − | 0.999387i | \(-0.511149\pi\) | ||||
−0.0350194 | + | 0.999387i | \(0.511149\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.438015 | −0.0161564 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40.4233 | −1.48901 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.42230 | −0.273034 | −0.136517 | − | 0.990638i | \(-0.543591\pi\) | ||||
−0.136517 | + | 0.990638i | \(0.543591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.65617 | −0.0608408 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.4765 | −0.971328 | −0.485664 | − | 0.874146i | \(-0.661422\pi\) | ||||
−0.485664 | + | 0.874146i | \(0.661422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.39273 | −0.197574 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.9992 | −1.09761 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.2443 | 0.410857 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3315 | 1.32576 | 0.662879 | − | 0.748727i | \(-0.269335\pi\) | ||||
0.662879 | + | 0.748727i | \(0.269335\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.20830 | −0.0440329 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.42119 | 0.0881160 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.6604 | 1.47783 | 0.738913 | − | 0.673801i | \(-0.235340\pi\) | ||||
0.738913 | + | 0.673801i | \(0.235340\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.181175 | 0.00657623 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.3976 | −0.993162 | −0.496581 | − | 0.867990i | \(-0.665411\pi\) | ||||
−0.496581 | + | 0.867990i | \(0.665411\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.6507 | −0.494187 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.13838 | 0.0411584 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.45396 | −0.305255 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.4027 | −0.952104 | −0.476052 | − | 0.879417i | \(-0.657933\pi\) | ||||
−0.476052 | + | 0.879417i | \(0.657933\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.951006 | 0.0342496 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.6528 | 1.64202 | 0.821008 | − | 0.570917i | \(-0.193412\pi\) | ||||
0.821008 | + | 0.570917i | \(0.193412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.22792 | −0.223714 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.167925 | −0.00602426 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.3343 | 0.370264 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.4359 | −1.37534 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.10953 | 0.0396513 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.904608 | −0.0322869 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.23031 | 0.150794 | 0.0753971 | − | 0.997154i | \(-0.475978\pi\) | ||||
0.0753971 | + | 0.997154i | \(0.475978\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.997694 | −0.0355188 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.5566 | −0.624241 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 62.4769 | 2.21862 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.521951 | −0.0185117 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.6939 | 0.803860 | 0.401930 | − | 0.915670i | \(-0.368340\pi\) | ||||
0.401930 | + | 0.915670i | \(0.368340\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.49830 | −0.0883836 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.770208 | 0.0272140 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.37352 | −0.119049 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.93647 | −0.138742 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.264957 | 0.00932694 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.9292 | −1.57963 | −0.789814 | − | 0.613347i | \(-0.789823\pi\) | ||||
−0.789814 | + | 0.613347i | \(0.789823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.6415 | −1.35689 | −0.678443 | − | 0.734653i | \(-0.737345\pi\) | ||||
−0.678443 | + | 0.734653i | \(0.737345\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.769257 | 0.0269790 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.73871 | −0.236047 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.05741 | 0.0369943 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 80.2295 | 2.80344 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.7155 | 0.408873 | 0.204437 | − | 0.978880i | \(-0.434464\pi\) | ||||
0.204437 | + | 0.978880i | \(0.434464\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.5615 | 1.10017 | 0.550083 | − | 0.835110i | \(-0.314596\pi\) | ||||
0.550083 | + | 0.835110i | \(0.314596\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.178224 | 0.00620497 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.7491 | 1.24312 | 0.621559 | − | 0.783368i | \(-0.286500\pi\) | ||||
0.621559 | + | 0.783368i | \(0.286500\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.0953 | 1.01052 | 0.505261 | − | 0.862967i | \(-0.331396\pi\) | ||||
0.505261 | + | 0.862967i | \(0.331396\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.925009 | −0.0320882 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.03688 | 0.105222 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.2600 | 0.701128 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.04617 | 0.0707259 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.2324 | −1.04374 | −0.521870 | − | 0.853025i | \(-0.674765\pi\) | ||||
−0.521870 | + | 0.853025i | \(0.674765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5954 | −0.606738 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.977311 | −0.0336604 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.7909 | −1.19684 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.61516 | −0.0554976 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.61123 | 0.0552973 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.804651 | −0.0275831 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.3299 | 1.17543 | 0.587716 | − | 0.809067i | \(-0.300027\pi\) | ||||
0.587716 | + | 0.809067i | \(0.300027\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.1055 | 0.448199 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.8787 | 1.80630 | 0.903152 | − | 0.429322i | \(-0.141247\pi\) | ||||
0.903152 | + | 0.429322i | \(0.141247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.06326 | 0.138637 | 0.0693183 | − | 0.997595i | \(-0.477918\pi\) | ||||
0.0693183 | + | 0.997595i | \(0.477918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.501363 | 0.0170864 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.0841 | 1.39852 | 0.699260 | − | 0.714867i | \(-0.253513\pi\) | ||||
0.699260 | + | 0.714867i | \(0.253513\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.63353 | 0.191546 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.923446 | −0.0313619 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.63282 | 0.157158 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 85.9018 | 2.91067 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.1494 | −0.411194 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.87235 | −0.130909 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.3791 | 1.43104 | 0.715521 | − | 0.698592i | \(-0.246190\pi\) | ||||
0.715521 | + | 0.698592i | \(0.246190\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.614717 | −0.0207339 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.82835 | 0.297435 | 0.148717 | − | 0.988880i | \(-0.452486\pi\) | ||||
0.148717 | + | 0.988880i | \(0.452486\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.06826 | 0.305171 | 0.152586 | − | 0.988290i | \(-0.451240\pi\) | ||||
0.152586 | + | 0.988290i | \(0.451240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0669965 | −0.00225206 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.34816 | 0.179574 | 0.0897869 | − | 0.995961i | \(-0.471381\pi\) | ||||
0.0897869 | + | 0.995961i | \(0.471381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53.6338 | −1.79882 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.1904 | 0.977915 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.7614 | −0.962463 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2014 | −0.474702 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.385007 | −0.0128550 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.0321 | 0.701461 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.61883 | 0.120561 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.0513000 | 0.00170716 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.5197 | 0.682098 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.5206 | −0.415740 | −0.207870 | − | 0.978156i | \(-0.566653\pi\) | ||||
−0.207870 | + | 0.978156i | \(0.566653\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.87463 | 0.128514 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.9114 | −0.659695 | −0.329847 | − | 0.944034i | \(-0.606997\pi\) | ||||
−0.329847 | + | 0.944034i | \(0.606997\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.5631 | 1.07768 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.495121 | 0.0163682 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.4392 | −1.46751 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.90519 | −0.260768 | −0.130384 | − | 0.991464i | \(-0.541621\pi\) | ||||
−0.130384 | + | 0.991464i | \(0.541621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.880477 | 0.0290127 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 81.6784 | 2.68848 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.791545 | −0.0260258 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.0775 | −0.462365 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.7571 | 0.746637 | 0.373319 | − | 0.927703i | \(-0.378220\pi\) | ||||
0.373319 | + | 0.927703i | \(0.378220\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.9617 | 1.14582 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.28934 | −0.0422112 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.23568 | −0.0404109 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.31048 | −0.206154 | −0.103077 | − | 0.994673i | \(-0.532869\pi\) | ||||
−0.103077 | + | 0.994673i | \(0.532869\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.134950 | −0.00440392 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.34624 | 0.304679 | 0.152339 | − | 0.988328i | \(-0.451319\pi\) | ||||
0.152339 | + | 0.988328i | \(0.451319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.40240 | 0.0782328 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.27225 | 0.0413863 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.05680 | 0.0993326 | 0.0496663 | − | 0.998766i | \(-0.484184\pi\) | ||||
0.0496663 | + | 0.998766i | \(0.484184\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.16890 | 0.232712 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.150212 | 0.00487097 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.6885 | −0.475808 | −0.237904 | − | 0.971289i | \(-0.576460\pi\) | ||||
−0.237904 | + | 0.971289i | \(0.576460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.5800 | 0.698312 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.601875 | −0.0194559 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −51.3355 | −1.65771 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.78703 | 0.251195 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.70248 | −0.280433 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.6158 | −0.438309 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.07041 | −0.0987377 | −0.0493689 | − | 0.998781i | \(-0.515721\pi\) | ||||
−0.0493689 | + | 0.998781i | \(0.515721\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0909984 | 0.00292329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.1214 | 0.838275 | 0.419137 | − | 0.907923i | \(-0.362333\pi\) | ||||
0.419137 | + | 0.907923i | \(0.362333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.1496 | −0.357440 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.378736 | −0.0121293 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.7437 | 0.727634 | 0.363817 | − | 0.931470i | \(-0.381473\pi\) | ||||
0.363817 | + | 0.931470i | \(0.381473\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.836034 | −0.0267198 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.5649 | 0.337311 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.1823 | 0.356660 | 0.178330 | − | 0.983971i | \(-0.442931\pi\) | ||||
0.178330 | + | 0.983971i | \(0.442931\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.2022 | 0.548108 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.39534 | −0.0444143 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.245816 | 0.00781649 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.2303 | −1.24619 | −0.623096 | − | 0.782145i | \(-0.714125\pi\) | ||||
−0.623096 | + | 0.782145i | \(0.714125\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.10622 | 0.0351048 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.4704 | −0.617253 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.3720 | 1.40527 | 0.702637 | − | 0.711549i | \(-0.252006\pi\) | ||||
0.702637 | + | 0.711549i | \(0.252006\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.260060 | 0.00822793 |
(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 | 8020.2.a.c.1.14 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.14 | ✓ | 28 | 1.1 | even | 1 | trivial |