Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,3,Mod(53,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(4.25069212402\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 15x^{6} + 10x^{5} + 97x^{4} + 252x^{3} + 700x^{2} + 1696x + 3792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 53.3 | ||
Root | \(1.12162 + 2.99753i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 156.53 |
Dual form | 156.3.d.a.53.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.121622 | − | 2.99753i | −0.0405406 | − | 0.999178i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.347906i | − | 0.0695812i | −0.999395 | − | 0.0347906i | \(-0.988924\pi\) | ||
0.999395 | − | 0.0347906i | \(-0.0110764\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.5746 | 1.51066 | 0.755330 | − | 0.655345i | \(-0.227477\pi\) | ||||
0.755330 | + | 0.655345i | \(0.227477\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.97042 | + | 0.729130i | −0.996713 | + | 0.0810145i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 16.7308i | − | 1.52098i | −0.649348 | − | 0.760491i | \(-0.724958\pi\) | ||
0.649348 | − | 0.760491i | \(-0.275042\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.60555 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.04286 | + | 0.0423129i | −0.0695239 | + | 0.00282086i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 27.6952i | − | 1.62913i | −0.580072 | − | 0.814565i | \(-0.696976\pi\) | ||
0.580072 | − | 0.814565i | \(-0.303024\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.1865 | −1.16771 | −0.583855 | − | 0.811858i | \(-0.698456\pi\) | ||||
−0.583855 | + | 0.811858i | \(0.698456\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.28610 | − | 31.6978i | −0.0612430 | − | 1.50942i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 32.7658i | 1.42460i | 0.701875 | + | 0.712300i | \(0.252347\pi\) | ||||
−0.701875 | + | 0.712300i | \(0.747653\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.8790 | 0.995158 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.27659 | + | 26.8004i | 0.121355 | + | 0.992609i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.31839i | 0.286841i | 0.989662 | + | 0.143421i | \(0.0458101\pi\) | ||||
−0.989662 | + | 0.143421i | \(0.954190\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 48.0555 | 1.55018 | 0.775089 | − | 0.631852i | \(-0.217705\pi\) | ||||
0.775089 | + | 0.631852i | \(0.217705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −50.1512 | + | 2.03483i | −1.51973 | + | 0.0616615i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.67897i | − | 0.105113i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.53736 | 0.0956043 | 0.0478022 | − | 0.998857i | \(-0.484778\pi\) | ||||
0.0478022 | + | 0.998857i | \(0.484778\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.438513 | + | 10.8078i | 0.0112439 | + | 0.277122i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 17.8480i | − | 0.435316i | −0.976025 | − | 0.217658i | \(-0.930158\pi\) | ||
0.976025 | − | 0.217658i | \(-0.0698418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 34.1327 | 0.793784 | 0.396892 | − | 0.917865i | \(-0.370089\pi\) | ||||
0.396892 | + | 0.917865i | \(0.370089\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.253669 | + | 3.12086i | 0.00563708 | + | 0.0693524i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 70.4757i | 1.49948i | 0.661730 | + | 0.749742i | \(0.269822\pi\) | ||||
−0.661730 | + | 0.749742i | \(0.730178\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 62.8225 | 1.28209 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −83.0173 | + | 3.36834i | −1.62779 | + | 0.0660459i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26.2604i | 0.495479i | 0.968827 | + | 0.247740i | \(0.0796877\pi\) | ||||
−0.968827 | + | 0.247740i | \(0.920312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.82075 | −0.105832 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.69836 | + | 66.5047i | 0.0473396 | + | 1.16675i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 54.7886i | 0.928621i | 0.885672 | + | 0.464311i | \(0.153698\pi\) | ||||
−0.885672 | + | 0.464311i | \(0.846302\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −68.2420 | −1.11872 | −0.559361 | − | 0.828924i | \(-0.688953\pi\) | ||||
−0.559361 | + | 0.828924i | \(0.688953\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −94.8587 | + | 7.71027i | −1.50569 | + | 0.122385i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.25439i | 0.0192983i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6589 | −0.188938 | −0.0944692 | − | 0.995528i | \(-0.530115\pi\) | ||||
−0.0944692 | + | 0.995528i | \(0.530115\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 98.2166 | − | 3.98503i | 1.42343 | − | 0.0577541i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.4891i | − | 0.147734i | −0.997268 | − | 0.0738668i | \(-0.976466\pi\) | ||
0.997268 | − | 0.0738668i | \(-0.0235340\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.4595 | −0.156979 | −0.0784895 | − | 0.996915i | \(-0.525010\pi\) | ||||
−0.0784895 | + | 0.996915i | \(0.525010\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.02582 | − | 74.5755i | −0.0403443 | − | 0.994340i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 176.922i | − | 2.29769i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 52.1738 | 0.660428 | 0.330214 | − | 0.943906i | \(-0.392879\pi\) | ||||
0.330214 | + | 0.943906i | \(0.392879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 79.9367 | − | 13.0812i | 0.986873 | − | 0.161496i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 70.6432i | 0.851123i | 0.904929 | + | 0.425562i | \(0.139923\pi\) | ||||
−0.904929 | + | 0.425562i | \(0.860077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.63532 | −0.113357 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.9347 | − | 1.01170i | 0.286605 | − | 0.0116287i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 101.408i | 1.13942i | 0.821847 | + | 0.569708i | \(0.192944\pi\) | ||||
−0.821847 | + | 0.569708i | \(0.807056\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −38.1273 | −0.418982 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.84459 | − | 144.048i | −0.0628451 | − | 1.54890i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.71881i | 0.0812506i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −72.1047 | −0.743347 | −0.371674 | − | 0.928363i | \(-0.621216\pi\) | ||||
−0.371674 | + | 0.928363i | \(0.621216\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.1989 | + | 150.082i | 0.123222 | + | 1.51598i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 69.9711i | − | 0.692783i | −0.938090 | − | 0.346392i | \(-0.887407\pi\) | ||
0.938090 | − | 0.346392i | \(-0.112593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 141.584 | 1.37460 | 0.687301 | − | 0.726373i | \(-0.258795\pi\) | ||||
0.687301 | + | 0.726373i | \(0.258795\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.0278 | + | 0.447442i | −0.105027 | + | 0.00426136i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 159.940i | − | 1.49477i | −0.664391 | − | 0.747385i | \(-0.731309\pi\) | ||
0.664391 | − | 0.747385i | \(-0.268691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 77.2962 | 0.709140 | 0.354570 | − | 0.935030i | \(-0.384627\pi\) | ||||
0.354570 | + | 0.935030i | \(0.384627\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.430220 | − | 10.6034i | −0.00387585 | − | 0.0955257i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 84.4027i | − | 0.746927i | −0.927645 | − | 0.373463i | \(-0.878170\pi\) | ||
0.927645 | − | 0.373463i | \(-0.121830\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.3994 | 0.0991253 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 32.3433 | − | 2.62892i | 0.276438 | − | 0.0224694i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 292.866i | − | 2.46106i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −158.920 | −1.31339 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −53.4999 | + | 2.17070i | −0.434958 | + | 0.0176480i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 17.3532i | − | 0.138825i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −40.9252 | −0.322246 | −0.161123 | − | 0.986934i | \(-0.551512\pi\) | ||||
−0.161123 | + | 0.986934i | \(0.551512\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.15128 | − | 102.314i | −0.0321805 | − | 0.793132i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 175.720i | 1.34138i | 0.741739 | + | 0.670688i | \(0.234001\pi\) | ||||
−0.741739 | + | 0.670688i | \(0.765999\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −234.614 | −1.76401 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.32403 | − | 1.13994i | 0.0690669 | − | 0.00844403i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 138.243i | 1.00907i | 0.863391 | + | 0.504535i | \(0.168336\pi\) | ||||
−0.863391 | + | 0.504535i | \(0.831664\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −27.4576 | −0.197537 | −0.0987685 | − | 0.995110i | \(-0.531490\pi\) | ||||
−0.0987685 | + | 0.995110i | \(0.531490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 211.253 | − | 8.57138i | 1.49825 | − | 0.0607899i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 60.3238i | 0.421845i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.89402 | 0.0199587 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.64058 | − | 188.313i | −0.0519767 | − | 1.28104i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 181.865i | 1.22057i | 0.792182 | + | 0.610285i | \(0.208945\pi\) | ||||
−0.792182 | + | 0.610285i | \(0.791055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −87.3314 | −0.578353 | −0.289177 | − | 0.957276i | \(-0.593382\pi\) | ||||
−0.289177 | + | 0.957276i | \(0.593382\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.1934 | + | 248.438i | 0.131983 | + | 1.62378i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 16.7188i | − | 0.107863i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −126.402 | −0.805107 | −0.402553 | − | 0.915397i | \(-0.631877\pi\) | ||||
−0.402553 | + | 0.915397i | \(0.631877\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 78.7164 | − | 3.19383i | 0.495072 | − | 0.0200870i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 346.486i | 2.15209i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 115.838 | 0.710662 | 0.355331 | − | 0.934741i | \(-0.384368\pi\) | ||||
0.355331 | + | 0.934741i | \(0.384368\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.707929 | + | 17.4479i | 0.00429048 | + | 0.105745i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 191.230i | − | 1.14509i | −0.819873 | − | 0.572546i | \(-0.805956\pi\) | ||
0.819873 | − | 0.572546i | \(-0.194044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 199.022 | − | 16.1768i | 1.16387 | − | 0.0946014i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 288.112i | − | 1.66539i | −0.553732 | − | 0.832695i | \(-0.686797\pi\) | ||
0.553732 | − | 0.832695i | \(-0.313203\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 263.085 | 1.50335 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 164.231 | − | 6.66349i | 0.927858 | − | 0.0376468i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 79.1969i | 0.442441i | 0.975224 | + | 0.221221i | \(0.0710041\pi\) | ||||
−0.975224 | + | 0.221221i | \(0.928996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −109.661 | −0.605861 | −0.302930 | − | 0.953013i | \(-0.597965\pi\) | ||||
−0.302930 | + | 0.953013i | \(0.597965\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.29971 | + | 204.558i | 0.0453536 | + | 1.11780i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.23067i | − | 0.00665226i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −463.363 | −2.47788 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 34.6487 | + | 283.404i | 0.183326 | + | 1.49949i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 231.869i | 1.21398i | 0.794711 | + | 0.606988i | \(0.207622\pi\) | ||||
−0.794711 | + | 0.606988i | \(0.792378\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −166.643 | −0.863438 | −0.431719 | − | 0.902008i | \(-0.642093\pi\) | ||||
−0.431719 | + | 0.902008i | \(0.642093\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.76008 | − | 0.152561i | 0.0192825 | − | 0.000782366i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 67.0787i | − | 0.340501i | −0.985401 | − | 0.170250i | \(-0.945542\pi\) | ||
0.985401 | − | 0.170250i | \(-0.0544577\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 94.2428 | 0.473582 | 0.236791 | − | 0.971561i | \(-0.423904\pi\) | ||||
0.236791 | + | 0.971561i | \(0.423904\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.53959 | + | 37.9454i | 0.00765967 | + | 0.188783i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 87.9638i | 0.433319i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.20941 | −0.0302898 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −23.8905 | − | 293.923i | −0.115413 | − | 1.41992i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 371.198i | 1.77607i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 295.363 | 1.39982 | 0.699912 | − | 0.714229i | \(-0.253222\pi\) | ||||
0.699912 | + | 0.714229i | \(0.253222\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −31.4414 | + | 1.27570i | −0.147612 | + | 0.00598921i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 11.8750i | − | 0.0552324i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 508.169 | 2.34179 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.39372 | + | 34.3501i | 0.00636401 | + | 0.156850i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 99.8565i | 0.451839i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −430.651 | −1.93117 | −0.965586 | − | 0.260084i | \(-0.916250\pi\) | ||||
−0.965586 | + | 0.260084i | \(0.916250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −223.175 | + | 18.1400i | −0.991887 | + | 0.0806222i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 254.188i | − | 1.11977i | −0.828570 | − | 0.559886i | \(-0.810845\pi\) | ||
0.828570 | − | 0.559886i | \(-0.189155\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −116.991 | −0.510880 | −0.255440 | − | 0.966825i | \(-0.582220\pi\) | ||||
−0.255440 | + | 0.966825i | \(0.582220\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −530.329 | + | 21.5175i | −2.29580 | + | 0.0931495i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 122.047i | − | 0.523805i | −0.965094 | − | 0.261903i | \(-0.915650\pi\) | ||
0.965094 | − | 0.261903i | \(-0.0843500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.5189 | 0.104336 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.34547 | − | 156.393i | −0.0267741 | − | 0.659886i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 110.327i | 0.461619i | 0.972999 | + | 0.230809i | \(0.0741374\pi\) | ||||
−0.972999 | + | 0.230809i | \(0.925863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −283.291 | −1.17548 | −0.587740 | − | 0.809050i | \(-0.699982\pi\) | ||||
−0.587740 | + | 0.809050i | \(0.699982\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −48.9334 | − | 238.022i | −0.201372 | − | 0.979515i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 21.8563i | − | 0.0892094i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 79.9945 | 0.323864 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 211.755 | − | 8.59175i | 0.850423 | − | 0.0345050i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 470.581i | − | 1.87483i | −0.348221 | − | 0.937413i | \(-0.613214\pi\) | ||
0.348221 | − | 0.937413i | \(-0.386786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 548.199 | 2.16679 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.17186 | + | 28.8822i | 0.00459555 | + | 0.113264i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 136.155i | − | 0.529787i | −0.964278 | − | 0.264894i | \(-0.914663\pi\) | ||
0.964278 | − | 0.264894i | \(-0.0853369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37.4062 | 0.144426 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.06519 | − | 74.6194i | −0.0232383 | − | 0.285898i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 273.452i | 1.03974i | 0.854245 | + | 0.519870i | \(0.174020\pi\) | ||||
−0.854245 | + | 0.519870i | \(0.825980\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.13614 | 0.0344760 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 303.974 | − | 12.3334i | 1.13848 | − | 0.0461926i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 240.819i | − | 0.895237i | −0.894225 | − | 0.447619i | \(-0.852272\pi\) | ||
0.894225 | − | 0.447619i | \(-0.147728\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 69.3747 | 0.255995 | 0.127998 | − | 0.991774i | \(-0.459145\pi\) | ||||
0.127998 | + | 0.991774i | \(0.459145\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.63711 | + | 114.288i | 0.0169857 | + | 0.418637i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 416.245i | − | 1.51362i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00717 | −0.00724609 | −0.00362304 | − | 0.999993i | \(-0.501153\pi\) | ||||
−0.00362304 | + | 0.999993i | \(0.501153\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −431.078 | + | 35.0387i | −1.54508 | + | 0.125587i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 216.383i | 0.770048i | 0.922907 | + | 0.385024i | \(0.125807\pi\) | ||||
−0.922907 | + | 0.385024i | \(0.874193\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 465.997 | 1.64663 | 0.823316 | − | 0.567584i | \(-0.192122\pi\) | ||||
0.823316 | + | 0.567584i | \(0.192122\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.1374 | − | 0.938774i | 0.0811838 | − | 0.00329394i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 188.735i | − | 0.657615i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −478.025 | −1.65407 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.76949 | + | 216.136i | 0.0301357 | + | 0.742736i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.5343i | 0.0666700i | 0.999444 | + | 0.0333350i | \(0.0106128\pi\) | ||||
−0.999444 | + | 0.0333350i | \(0.989387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.0613 | 0.0646145 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 448.393 | − | 54.8200i | 1.50974 | − | 0.184579i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 118.139i | − | 0.395113i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 360.940 | 1.19914 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −209.741 | + | 8.51001i | −0.692214 | + | 0.0280858i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.7418i | 0.0778419i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4743 | 0.0569197 | 0.0284598 | − | 0.999595i | \(-0.490940\pi\) | ||||
0.0284598 | + | 0.999595i | \(0.490940\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.2197 | − | 424.403i | −0.0557271 | − | 1.37347i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 517.444i | − | 1.66381i | −0.554920 | − | 0.831903i | \(-0.687251\pi\) | ||
0.554920 | − | 0.831903i | \(-0.312749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −221.491 | −0.707640 | −0.353820 | − | 0.935314i | \(-0.615117\pi\) | ||||
−0.353820 | + | 0.935314i | \(0.615117\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.68245 | + | 33.0019i | 0.00851571 | + | 0.104768i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 156.440i | − | 0.493501i | −0.969079 | − | 0.246750i | \(-0.920637\pi\) | ||
0.969079 | − | 0.246750i | \(-0.0793628\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 139.173 | 0.436280 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −479.427 | + | 19.4522i | −1.49354 | + | 0.0605988i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 614.460i | 1.90235i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −89.7024 | −0.276007 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.40090 | − | 231.698i | −0.0287489 | − | 0.708557i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 745.254i | 2.26521i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 324.729 | 0.981054 | 0.490527 | − | 0.871426i | \(-0.336804\pi\) | ||||
0.490527 | + | 0.871426i | \(0.336804\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −31.7316 | + | 2.57920i | −0.0952901 | + | 0.00774533i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.40410i | 0.0131466i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 263.236 | 0.781117 | 0.390558 | − | 0.920578i | \(-0.372282\pi\) | ||||
0.390558 | + | 0.920578i | \(0.372282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −253.000 | + | 10.2652i | −0.746313 | + | 0.0302808i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 804.008i | − | 2.35779i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 146.168 | 0.426145 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.38642 | − | 34.1701i | −0.00401860 | − | 0.0990438i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 266.003i | 0.766579i | 0.923628 | + | 0.383290i | \(0.125209\pi\) | ||||
−0.923628 | + | 0.383290i | \(0.874791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −236.747 | −0.678358 | −0.339179 | − | 0.940722i | \(-0.610149\pi\) | ||||
−0.339179 | + | 0.940722i | \(0.610149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.8139 | − | 96.6304i | −0.0336579 | − | 0.275300i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.87609i | 0.0138133i | 0.999976 | + | 0.00690665i | \(0.00219847\pi\) | ||||
−0.999976 | + | 0.00690665i | \(0.997802\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.64922 | −0.0102795 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −877.876 | + | 35.6189i | −2.45904 | + | 0.0997728i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 359.738i | 1.00205i | 0.865431 | + | 0.501027i | \(0.167044\pi\) | ||||
−0.865431 | + | 0.501027i | \(0.832956\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 131.240 | 0.363546 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.3281 | + | 476.368i | 0.0532455 | + | 1.31231i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.98681i | 0.0109228i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.7979 | 0.0621196 | 0.0310598 | − | 0.999518i | \(-0.490112\pi\) | ||||
0.0310598 | + | 0.999518i | \(0.490112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.0135 | + | 160.104i | 0.0352669 | + | 0.433885i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 277.694i | 0.748500i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 101.862 | 0.273089 | 0.136544 | − | 0.990634i | \(-0.456400\pi\) | ||||
0.136544 | + | 0.990634i | \(0.456400\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −52.0167 | + | 2.11052i | −0.138711 | + | 0.00562806i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 29.9924i | − | 0.0795554i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −398.288 | −1.05089 | −0.525446 | − | 0.850827i | \(-0.676102\pi\) | ||||
−0.525446 | + | 0.850827i | \(0.676102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.97739 | + | 122.675i | 0.0130640 | + | 0.321981i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 441.572i | 1.15293i | 0.817122 | + | 0.576465i | \(0.195568\pi\) | ||||
−0.817122 | + | 0.576465i | \(0.804432\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −61.5521 | −0.159876 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −306.185 | + | 24.8872i | −0.791175 | + | 0.0643080i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 193.653i | 0.497822i | 0.968526 | + | 0.248911i | \(0.0800726\pi\) | ||||
−0.968526 | + | 0.248911i | \(0.919927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 907.456 | 2.32086 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 526.728 | − | 21.3714i | 1.34027 | − | 0.0543802i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 18.1516i | − | 0.0459534i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −146.313 | −0.368547 | −0.184274 | − | 0.982875i | \(-0.558993\pi\) | ||||
−0.184274 | + | 0.982875i | \(0.558993\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 28.5341 | + | 703.262i | 0.0715140 | + | 1.76256i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 384.050i | − | 0.957731i | −0.877888 | − | 0.478865i | \(-0.841048\pi\) | ||
0.877888 | − | 0.478865i | \(-0.158952\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −173.267 | −0.429942 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.55103 | − | 27.8105i | −0.0112371 | − | 0.0686678i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 59.1829i | − | 0.145413i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 148.770 | 0.363741 | 0.181870 | − | 0.983322i | \(-0.441785\pi\) | ||||
0.181870 | + | 0.983322i | \(0.441785\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 414.387 | − | 16.8133i | 1.00824 | − | 0.0409083i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 579.369i | 1.40283i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.5772 | 0.0592221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.33944 | + | 82.3052i | 0.00800826 | + | 0.197375i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 609.937i | 1.45570i | 0.685738 | + | 0.727848i | \(0.259480\pi\) | ||||
−0.685738 | + | 0.727848i | \(0.740520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 274.485 | 0.651984 | 0.325992 | − | 0.945372i | \(-0.394302\pi\) | ||||
0.325992 | + | 0.945372i | \(0.394302\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −51.3860 | − | 632.197i | −0.121480 | − | 1.49455i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 689.028i | − | 1.62124i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −721.633 | −1.69001 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 180.823 | − | 7.33668i | 0.421498 | − | 0.0171018i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 503.184i | 1.16748i | 0.811941 | + | 0.583740i | \(0.198411\pi\) | ||||
−0.811941 | + | 0.583740i | \(0.801589\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 657.164 | 1.51770 | 0.758850 | − | 0.651265i | \(-0.225761\pi\) | ||||
0.758850 | + | 0.651265i | \(0.225761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.351975 | − | 8.67491i | −0.000809138 | − | 0.0199423i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 726.958i | − | 1.66352i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 251.397 | 0.572659 | 0.286329 | − | 0.958131i | \(-0.407565\pi\) | ||||
0.286329 | + | 0.958131i | \(0.407565\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −563.544 | + | 45.8058i | −1.27788 | + | 0.103868i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 316.752i | − | 0.715016i | −0.933910 | − | 0.357508i | \(-0.883627\pi\) | ||
0.933910 | − | 0.357508i | \(-0.116373\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.2804 | 0.0792819 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 545.147 | − | 22.1187i | 1.21957 | − | 0.0494826i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 330.174i | 0.735355i | 0.929953 | + | 0.367678i | \(0.119847\pi\) | ||||
−0.929953 | + | 0.367678i | \(0.880153\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −298.611 | −0.662109 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.6214 | + | 261.779i | 0.0234468 | + | 0.577878i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.2647i | 0.0291532i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −726.602 | −1.58994 | −0.794970 | − | 0.606649i | \(-0.792513\pi\) | ||||
−0.794970 | + | 0.606649i | \(0.792513\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 742.244 | − | 90.7459i | 1.61709 | − | 0.197703i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 108.280i | 0.234881i | 0.993080 | + | 0.117441i | \(0.0374690\pi\) | ||||
−0.993080 | + | 0.117441i | \(0.962531\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −708.111 | −1.52940 | −0.764699 | − | 0.644388i | \(-0.777112\pi\) | ||||
−0.764699 | + | 0.644388i | \(0.777112\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −50.1151 | + | 2.03337i | −0.107774 | + | 0.00437283i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 700.234i | 1.49943i | 0.661761 | + | 0.749715i | \(0.269809\pi\) | ||||
−0.661761 | + | 0.749715i | \(0.730191\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −133.863 | −0.285422 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.3732 | + | 378.894i | 0.0326395 | + | 0.804445i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 571.068i | − | 1.20733i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −551.977 | −1.16206 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.1472 | − | 235.567i | −0.0401410 | − | 0.493850i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 519.311i | − | 1.08416i | −0.840328 | − | 0.542078i | \(-0.817638\pi\) | ||
0.840328 | − | 0.542078i | \(-0.182362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.7541 | −0.0265159 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1038.60 | − | 42.1402i | 2.15032 | − | 0.0872468i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.0856i | 0.0517229i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −114.400 | −0.234907 | −0.117454 | − | 0.993078i | \(-0.537473\pi\) | ||||
−0.117454 | + | 0.993078i | \(0.537473\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.0884 | − | 347.228i | −0.0288106 | − | 0.710077i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 41.6858i | − | 0.0848998i | −0.999099 | − | 0.0424499i | \(-0.986484\pi\) | ||
0.999099 | − | 0.0424499i | \(-0.0135163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 230.380 | 0.467301 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 52.2145 | − | 4.24408i | 0.105484 | − | 0.00857390i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 110.918i | − | 0.223175i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −148.957 | −0.298512 | −0.149256 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149256 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −573.219 | + | 23.2578i | −1.14415 | + | 0.0464227i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 41.2672i | − | 0.0820421i | −0.999158 | − | 0.0410210i | \(-0.986939\pi\) | ||
0.999158 | − | 0.0410210i | \(-0.0130611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.3434 | −0.0482047 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.58108 | − | 38.9679i | −0.00311850 | − | 0.0768598i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 815.589i | 1.60234i | 0.598440 | + | 0.801168i | \(0.295788\pi\) | ||||
−0.598440 | + | 0.801168i | \(0.704212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −121.179 | −0.237142 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −72.6960 | − | 594.608i | −0.141708 | − | 1.15908i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 49.2579i | − | 0.0956464i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1179.12 | 2.28069 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −863.627 | + | 35.0407i | −1.66402 | + | 0.0675158i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 424.001i | − | 0.813821i | −0.913468 | − | 0.406910i | \(-0.866606\pi\) | ||
0.913468 | − | 0.406910i | \(-0.133394\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −911.760 | −1.74333 | −0.871663 | − | 0.490105i | \(-0.836958\pi\) | ||||
−0.871663 | + | 0.490105i | \(0.836958\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −31.9969 | − | 788.608i | −0.0609465 | − | 1.50211i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1330.91i | − | 2.52544i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −544.598 | −1.02949 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.9481 | − | 491.477i | −0.0752317 | − | 0.925569i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 64.3518i | 0.120735i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −55.6442 | −0.104008 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 237.396 | − | 9.63207i | 0.442077 | − | 0.0179368i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1051.07i | − | 1.95004i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 471.354 | 0.871264 | 0.435632 | − | 0.900125i | \(-0.356525\pi\) | ||||
0.435632 | + | 0.900125i | \(0.356525\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.3371 | + | 328.712i | 0.0245619 | + | 0.605363i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 26.8918i | − | 0.0493428i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −891.112 | −1.62909 | −0.814545 | − | 0.580101i | \(-0.803013\pi\) | ||||
−0.814545 | + | 0.580101i | \(0.803013\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 612.159 | − | 49.7573i | 1.11504 | − | 0.0906326i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 184.556i | − | 0.334947i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 551.718 | 0.997682 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.68897 | + | 0.149676i | −0.00664679 | + | 0.000269686i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 56.0496i | 0.100628i | 0.998733 | + | 0.0503138i | \(0.0160221\pi\) | ||||
−0.998733 | + | 0.0503138i | \(0.983978\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −123.067 | −0.220156 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 56.3550 | + | 1388.95i | 0.100455 | + | 2.47584i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 156.015i | − | 0.277113i | −0.990355 | − | 0.138557i | \(-0.955754\pi\) | ||
0.990355 | − | 0.138557i | \(-0.0442463\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.3642 | −0.0519720 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 845.300 | − | 138.329i | 1.49083 | − | 0.243966i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 484.828i | − | 0.852071i | −0.904706 | − | 0.426035i | \(-0.859910\pi\) | ||
0.904706 | − | 0.426035i | \(-0.140090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 899.488 | 1.57529 | 0.787643 | − | 0.616133i | \(-0.211301\pi\) | ||||
0.787643 | + | 0.616133i | \(0.211301\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 695.036 | − | 28.2004i | 1.21298 | − | 0.0492153i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 815.179i | 1.41770i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 507.027 | 0.878730 | 0.439365 | − | 0.898309i | \(-0.355203\pi\) | ||||
0.439365 | + | 0.898309i | \(0.355203\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.2675 | + | 499.519i | 0.0350042 | + | 0.862728i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 747.025i | 1.28576i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 439.358 | 0.753615 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.914615 | − | 11.2524i | −0.00156344 | − | 0.0192349i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 693.001i | 1.18058i | 0.807191 | + | 0.590291i | \(0.200987\pi\) | ||||
−0.807191 | + | 0.590291i | \(0.799013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1066.18 | −1.81016 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −201.071 | + | 8.15822i | −0.340221 | + | 0.0138041i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 995.564i | − | 1.67886i | −0.543467 | − | 0.839430i | \(-0.682889\pi\) | ||
0.543467 | − | 0.839430i | \(-0.317111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −101.890 | −0.171243 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.4620 | − | 282.496i | −0.0191993 | − | 0.473193i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 83.0301i | − | 0.138615i | −0.997595 | − | 0.0693073i | \(-0.977921\pi\) | ||
0.997595 | − | 0.0693073i | \(-0.0220789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −717.072 | −1.19313 | −0.596566 | − | 0.802564i | \(-0.703469\pi\) | ||||
−0.596566 | + | 0.802564i | \(0.703469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 113.555 | − | 9.22997i | 0.188317 | − | 0.0153067i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 55.2892i | 0.0913871i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 553.785 | 0.912331 | 0.456166 | − | 0.889895i | \(-0.349222\pi\) | ||||
0.456166 | + | 0.889895i | \(0.349222\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 263.674 | − | 10.6983i | 0.432963 | − | 0.0175670i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 254.104i | − | 0.415882i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −945.189 | −1.54191 | −0.770954 | − | 0.636891i | \(-0.780220\pi\) | ||||
−0.770954 | + | 0.636891i | \(0.780220\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.755199 | + | 18.6129i | 0.00122797 | + | 0.0302649i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 44.3256i | − | 0.0718404i | −0.999355 | − | 0.0359202i | \(-0.988564\pi\) | ||
0.999355 | − | 0.0359202i | \(-0.0114362\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1049.94 | −1.69619 | −0.848094 | − | 0.529846i | \(-0.822250\pi\) | ||||
−0.848094 | + | 0.529846i | \(0.822250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −878.138 | + | 107.360i | −1.41407 | + | 0.172883i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1072.35i | 1.72127i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 615.937 | 0.985499 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1112.68 | − | 45.1457i | 1.77461 | − | 0.0720027i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 97.9680i | − | 0.155752i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 613.583 | 0.972398 | 0.486199 | − | 0.873848i | \(-0.338383\pi\) | ||||
0.486199 | + | 0.873848i | \(0.338383\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35.9225 | − | 885.361i | −0.0567497 | − | 1.39867i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.2381i | 0.0224222i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −226.510 | −0.355588 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.64791 | + | 94.0915i | 0.0119686 | + | 0.147248i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1125.37i | 1.75565i | 0.478979 | + | 0.877826i | \(0.341007\pi\) | ||||
−0.478979 | + | 0.877826i | \(0.658993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −560.059 | −0.871009 | −0.435505 | − | 0.900187i | \(-0.643430\pi\) | ||||
−0.435505 | + | 0.900187i | \(0.643430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −35.5956 | + | 1.44425i | −0.0551870 | + | 0.00223915i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 675.328i | − | 1.04378i | −0.853012 | − | 0.521892i | \(-0.825226\pi\) | ||
0.853012 | − | 0.521892i | \(-0.174774\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 916.658 | 1.41242 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −61.8043 | − | 1523.25i | −0.0949375 | − | 2.33987i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 563.974i | 0.863666i | 0.901954 | + | 0.431833i | \(0.142133\pi\) | ||||
−0.901954 | + | 0.431833i | \(0.857867\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 61.1341 | 0.0933345 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 102.796 | − | 8.35544i | 0.156463 | − | 0.0127176i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 564.784i | 0.857031i | 0.903534 | + | 0.428516i | \(0.140963\pi\) | ||||
−0.903534 | + | 0.428516i | \(0.859037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −607.478 | −0.919028 | −0.459514 | − | 0.888171i | \(-0.651976\pi\) | ||||
−0.459514 | + | 0.888171i | \(0.651976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 299.323 | − | 12.1447i | 0.451468 | − | 0.0183178i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 81.6234i | 0.122742i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −272.559 | −0.408634 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 52.3765 | + | 1290.89i | 0.0782908 | + | 1.92958i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1141.74i | 1.70156i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −798.788 | −1.18691 | −0.593454 | − | 0.804868i | \(-0.702236\pi\) | ||||
−0.593454 | + | 0.804868i | \(0.702236\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 81.5181 | + | 666.767i | 0.120768 | + | 0.987803i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 391.116i | − | 0.577719i | −0.957371 | − | 0.288860i | \(-0.906724\pi\) | ||
0.957371 | − | 0.288860i | \(-0.0932761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −762.479 | −1.12294 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −761.938 | + | 30.9148i | −1.11885 | + | 0.0453962i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1130.48i | − | 1.65518i | −0.561337 | − | 0.827588i | \(-0.689713\pi\) | ||
0.561337 | − | 0.827588i | \(-0.310287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.0954 | 0.0702123 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.2287 | + | 350.686i | 0.0207113 | + | 0.510460i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 94.6832i | − | 0.137421i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 350.909 | 0.507828 | 0.253914 | − | 0.967227i | \(-0.418282\pi\) | ||||
0.253914 | + | 0.967227i | \(0.418282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 128.999 | + | 1587.06i | 0.186146 | + | 2.29013i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.55267i | 0.0137448i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −494.303 | −0.709187 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −365.839 | + | 14.8435i | −0.523375 | + | 0.0212354i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1005.60i | 1.43452i | 0.696808 | + | 0.717258i | \(0.254603\pi\) | ||||
−0.696808 | + | 0.717258i | \(0.745397\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −78.4816 | −0.111638 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.98203 | − | 73.4963i | −0.00422983 | − | 0.104250i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 739.918i | − | 1.04656i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 895.241 | 1.26268 | 0.631341 | − | 0.775506i | \(-0.282505\pi\) | ||||
0.631341 | + | 0.775506i | \(0.282505\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −468.021 | + | 38.0415i | −0.658258 | + | 0.0535043i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1574.58i | 2.20838i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.9870 | 0.0293524 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 330.709 | − | 13.4181i | 0.461239 | − | 0.0187143i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 456.136i | 0.634404i | 0.948358 | + | 0.317202i | \(0.102743\pi\) | ||||
−0.948358 | + | 0.317202i | \(0.897257\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1497.20 | 2.07656 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.4543 | + | 849.174i | 0.0476546 | + | 1.17451i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 206.953i | 0.285452i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −426.245 | −0.586307 | −0.293153 | − | 0.956065i | \(-0.594705\pi\) | ||||
−0.293153 | + | 0.956065i | \(0.594705\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −707.528 | + | 175.628i | −0.970546 | + | 0.240916i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 945.313i | − | 1.29318i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −923.521 | −1.25992 | −0.629960 | − | 0.776628i | \(-0.716929\pi\) | ||||
−0.629960 | + | 0.776628i | \(0.716929\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −65.5150 | + | 2.65820i | −0.0891361 | + | 0.00361660i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 211.793i | 0.287372i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1128.09 | 1.52651 | 0.763254 | − | 0.646099i | \(-0.223601\pi\) | ||||
0.763254 | + | 0.646099i | \(0.223601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.72907 | − | 239.786i | −0.0131296 | − | 0.323598i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 506.769i | − | 0.682058i | −0.940053 | − | 0.341029i | \(-0.889225\pi\) | ||
0.940053 | − | 0.341029i | \(-0.110775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 63.2719 | 0.0849287 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −51.5081 | − | 633.699i | −0.0689533 | − | 0.848325i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1691.31i | − | 2.25809i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1167.71 | 1.55488 | 0.777438 | − | 0.628960i | \(-0.216519\pi\) | ||||
0.777438 | + | 0.628960i | \(0.216519\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1410.58 | + | 57.2329i | −1.87328 | + | 0.0760065i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.3831i | 0.0402425i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 670.756 | 0.886071 | 0.443036 | − | 0.896504i | \(-0.353901\pi\) | ||||
0.443036 | + | 0.896504i | \(0.353901\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −66.6728 | − | 1643.24i | −0.0878430 | − | 2.16501i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 92.8836i | 0.122055i | 0.998136 | + | 0.0610273i | \(0.0194377\pi\) | ||||
−0.998136 | + | 0.0610273i | \(0.980562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 817.378 | 1.07127 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 86.4329 | − | 7.02541i | 0.112984 | − | 0.00918354i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 197.543i | − | 0.257553i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 865.644 | 1.12567 | 0.562837 | − | 0.826568i | \(-0.309710\pi\) | ||||
0.562837 | + | 0.826568i | \(0.309710\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −408.130 | + | 16.5594i | −0.529352 | + | 0.0214779i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 900.561i | 1.16502i | 0.812823 | + | 0.582510i | \(0.197929\pi\) | ||||
−0.812823 | + | 0.582510i | \(0.802071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1195.57 | 1.54267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.54941 | − | 112.126i | −0.00585509 | − | 0.144307i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 395.984i | 0.508323i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −175.491 | −0.224700 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −222.937 | + | 27.2560i | −0.284721 | + | 0.0348096i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43.9759i | 0.0560203i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1280.16 | −1.62663 | −0.813315 | − | 0.581823i | \(-0.802340\pi\) | ||||
−0.813315 | + | 0.581823i | \(0.802340\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 819.680 | − | 33.2576i | 1.03889 | − | 0.0421516i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 892.526i | − | 1.12835i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 246.050 | 0.310277 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.11115 | − | 27.3859i | −0.00139768 | − | 0.0344477i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 697.579i | 0.875256i | 0.899156 | + | 0.437628i | \(0.144181\pi\) | ||||
−0.899156 | + | 0.437628i | \(0.855819\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1951.84 | 2.44285 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −73.9396 | − | 909.672i | −0.0923092 | − | 1.13567i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 191.726i | 0.238762i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 120.544 | 0.149745 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −721.862 | + | 29.2888i | −0.894501 | + | 0.0362934i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 156.783i | 0.193799i | 0.995294 | + | 0.0968993i | \(0.0308925\pi\) | ||||
−0.995294 | + | 0.0968993i | \(0.969108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −708.896 | −0.874101 | −0.437050 | − | 0.899437i | \(-0.643977\pi\) | ||||
−0.437050 | + | 0.899437i | \(0.643977\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.43746 | − | 207.953i | −0.0103782 | − | 0.255785i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 40.3007i | − | 0.0494487i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −757.285 | −0.926910 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 342.018 | − | 27.7998i | 0.417604 | − | 0.0339436i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 904.304i | 1.10147i | 0.834681 | + | 0.550733i | \(0.185652\pi\) | ||||
−0.834681 | + | 0.550733i | \(0.814348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −917.496 | −1.11482 | −0.557409 | − | 0.830238i | \(-0.688205\pi\) | ||||
−0.557409 | + | 0.830238i | \(0.688205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1247.71 | + | 50.6244i | −1.51237 | + | 0.0613630i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 373.879i | 0.452091i | 0.974117 | + | 0.226045i | \(0.0725798\pi\) | ||||
−0.974117 | + | 0.226045i | \(0.927420\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −473.628 | −0.571325 | −0.285662 | − | 0.958330i | \(-0.592214\pi\) | ||||
−0.285662 | + | 0.958330i | \(0.592214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.244115 | + | 6.01655i | 0.000293761 | + | 0.00724013i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1739.88i | − | 2.08869i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −66.5301 | −0.0796768 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 157.458 | + | 1287.91i | 0.188122 | + | 1.53872i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 447.115i | − | 0.532915i | −0.963847 | − | 0.266457i | \(-0.914147\pi\) | ||
0.963847 | − | 0.266457i | \(-0.0858531\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 771.804 | 0.917722 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 648.616 | − | 26.3169i | 0.769415 | − | 0.0312182i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 4.52277i | − | 0.00535240i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1680.52 | −1.98408 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −56.6753 | − | 1396.84i | −0.0667554 | − | 1.64528i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 115.904i | 0.136198i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 407.791 | 0.478067 | 0.239033 | − | 0.971011i | \(-0.423169\pi\) | ||||
0.239033 | + | 0.971011i | \(0.423169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.62801 | − | 69.2409i | −0.00658247 | − | 0.0809835i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 969.943i | − | 1.13179i | −0.824478 | − | 0.565894i | \(-0.808531\pi\) | ||
0.824478 | − | 0.565894i | \(-0.191469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 501.577 | 0.583908 | 0.291954 | − | 0.956432i | \(-0.405695\pi\) | ||||
0.291954 | + | 0.956432i | \(0.405695\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −565.741 | + | 22.9543i | −0.657074 | + | 0.0266601i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 809.427i | − | 0.937922i | −0.883219 | − | 0.468961i | \(-0.844629\pi\) | ||
0.883219 | − | 0.468961i | \(-0.155371\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −100.236 | −0.115880 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 58.1382 | + | 1432.90i | 0.0670568 | + | 1.65271i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 872.911i | − | 1.00450i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.6422 | 0.0524021 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 646.809 | − | 52.5737i | 0.740904 | − | 0.0602219i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 183.503i | − | 0.209718i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 554.476 | 0.632242 | 0.316121 | − | 0.948719i | \(-0.397619\pi\) | ||||
0.316121 | + | 0.948719i | \(0.397619\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 58.5548 | − | 2.37580i | 0.0666152 | − | 0.00270284i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1167.11i | − | 1.32476i | −0.749168 | − | 0.662380i | \(-0.769546\pi\) | ||
0.749168 | − | 0.662380i | \(-0.230454\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −502.216 | −0.568761 | −0.284381 | − | 0.958711i | \(-0.591788\pi\) | ||||
−0.284381 | + | 0.958711i | \(0.591788\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.31827 | − | 57.1368i | −0.00261951 | − | 0.0645614i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 251.594i | − | 0.283646i | −0.989892 | − | 0.141823i | \(-0.954704\pi\) | ||
0.989892 | − | 0.141823i | \(-0.0452964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −432.768 | −0.486803 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −218.859 | − | 1337.41i | −0.245633 | − | 1.50102i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1563.61i | − | 1.75096i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.5531 | 0.0307856 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −354.125 | + | 14.3682i | −0.394788 | + | 0.0160181i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 399.745i | 0.444655i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 727.287 | 0.807200 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −43.8982 | − | 1081.93i | −0.0486137 | − | 1.19815i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38.1516i | 0.0421565i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.05962 | 0.00557842 | 0.00278921 | − | 0.999996i | \(-0.499112\pi\) | ||||
0.00278921 | + | 0.999996i | \(0.499112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 51.0181 | + | 627.670i | 0.0561255 | + | 0.690506i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 52.1811i | − | 0.0572789i | −0.999590 | − | 0.0286395i | \(-0.990883\pi\) | ||
0.999590 | − | 0.0286395i | \(-0.00911747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1181.92 | 1.29454 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 71.1668 | − | 2.88752i | 0.0777779 | − | 0.00315575i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1858.18i | 2.02636i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −417.586 | −0.454392 | −0.227196 | − | 0.973849i | \(-0.572956\pi\) | ||||
−0.227196 | + | 0.973849i | \(0.572956\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.12526 | − | 52.3799i | −0.00230756 | − | 0.0568729i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.8190i | 0.0409740i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 88.0059 | 0.0951415 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1270.07 | + | 103.233i | −1.37008 | + | 0.111363i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 591.593i | − | 0.636807i | −0.947955 | − | 0.318403i | \(-0.896853\pi\) | ||
0.947955 | − | 0.318403i | \(-0.103147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1393.81 | −1.49711 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1551.06 | + | 62.9324i | −1.66244 | + | 0.0674517i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 161.207i | 0.172414i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 415.023 | 0.442927 | 0.221464 | − | 0.975169i | \(-0.428917\pi\) | ||||
0.221464 | + | 0.975169i | \(0.428917\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.9382 | + | 663.928i | 0.0286881 | + | 0.707058i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 192.556i | 0.204629i | 0.994752 | + | 0.102314i | \(0.0326248\pi\) | ||||
−0.994752 | + | 0.102314i | \(0.967375\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 584.803 | 0.620152 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 98.5980 | − | 12.0545i | 0.104337 | − | 0.0127561i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 149.806i | − | 0.158190i | −0.996867 | − | 0.0790951i | \(-0.974797\pi\) | ||
0.996867 | − | 0.0790951i | \(-0.0252031\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.3177 | 0.0435381 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −468.933 | + | 19.0265i | −0.493095 | + | 0.0200068i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 231.170i | − | 0.242571i | −0.992618 | − | 0.121286i | \(-0.961298\pi\) | ||
0.992618 | − | 0.121286i | \(-0.0387017\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 80.6687 | 0.0844699 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.9265 | − | 417.177i | −0.0176870 | − | 0.435922i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1461.86i | 1.52436i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1348.33 | 1.40305 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 116.617 | + | 1434.73i | 0.121098 | + | 1.48986i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57.9762i | 0.0600790i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 403.483 | 0.417252 | 0.208626 | − | 0.977995i | \(-0.433101\pi\) | ||||
0.208626 | + | 0.977995i | \(0.433101\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1841.86 | − | 74.7316i | 1.90079 | − | 0.0771224i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 121.687i | 0.125321i | 0.998035 | + | 0.0626605i | \(0.0199585\pi\) | ||||
−0.998035 | + | 0.0626605i | \(0.980041\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −290.354 | −0.298411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.9098 | + | 268.886i | 0.0111895 | + | 0.275780i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1825.82i | 1.86880i | 0.356223 | + | 0.934401i | \(0.384064\pi\) | ||||
−0.356223 | + | 0.934401i | \(0.615936\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1696.64 | 1.73303 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −693.379 | + | 56.3590i | −0.706809 | + | 0.0574506i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 71.7807i | 0.0730220i | 0.999333 | + | 0.0365110i | \(0.0116244\pi\) | ||||
−0.999333 | + | 0.0365110i | \(0.988376\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.3371 | −0.0236924 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2233.92 | − | 90.6390i | 2.26335 | − | 0.0918329i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1118.39i | 1.13083i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1104.62 | −1.11465 | −0.557324 | − | 0.830295i | \(-0.688172\pi\) | ||||
−0.557324 | + | 0.830295i | \(0.688172\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −39.4941 | − | 973.385i | −0.0397725 | − | 0.980247i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 32.7876i | − | 0.0329524i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 204.813 | 0.205429 | 0.102714 | − | 0.994711i | \(-0.467247\pi\) | ||||
0.102714 | + | 0.994711i | \(0.467247\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.5905 | + | 94.8028i | 0.0116021 | + | 0.0948977i |
(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 | 156.3.d.a.53.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 156.3.d.a.53.4 | yes | 8 | |
4.3 | odd | 2 | 624.3.f.a.209.6 | 8 | |||
12.11 | even | 2 | 624.3.f.a.209.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.3.d.a.53.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
156.3.d.a.53.4 | yes | 8 | 3.2 | odd | 2 | inner | |
624.3.f.a.209.5 | 8 | 12.11 | even | 2 | |||
624.3.f.a.209.6 | 8 | 4.3 | odd | 2 |