Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), degree \(2\), 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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{193})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-3.22311 - 5.58259i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.109 |
Dual form | 252.4.k.f.37.2 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.22311 | + | 10.7787i | 0.556612 | + | 0.964080i | 0.997776 | + | 0.0666538i | \(0.0212323\pi\) |
−0.441164 | + | 0.897426i | \(0.645434\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.3924 | − | 10.2992i | 0.831114 | − | 0.556102i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −25.5618 | + | 44.2743i | −0.700651 | + | 1.21356i | 0.267587 | + | 0.963534i | \(0.413774\pi\) |
−0.968238 | + | 0.250030i | \(0.919559\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.2311 | 0.794312 | 0.397156 | − | 0.917751i | \(-0.369997\pi\) | ||||
0.397156 | + | 0.917751i | \(0.369997\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.1076 | − | 19.2389i | 0.158469 | − | 0.274477i | −0.775848 | − | 0.630920i | \(-0.782677\pi\) |
0.934317 | + | 0.356444i | \(0.116011\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −27.1693 | − | 47.0587i | −0.328056 | − | 0.568210i | 0.654070 | − | 0.756434i | \(-0.273060\pi\) |
−0.982126 | + | 0.188224i | \(0.939727\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 88.4622 | + | 153.221i | 0.801985 | + | 1.38908i | 0.918308 | + | 0.395867i | \(0.129556\pi\) |
−0.116323 | + | 0.993211i | \(0.537111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.9542 | + | 25.9015i | −0.119634 | + | 0.207212i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −61.0916 | −0.391187 | −0.195593 | − | 0.980685i | \(-0.562663\pi\) | ||||
−0.195593 | + | 0.980685i | \(0.562663\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −159.962 | + | 277.063i | −0.926776 | + | 1.60522i | −0.138097 | + | 0.990419i | \(0.544099\pi\) |
−0.788679 | + | 0.614805i | \(0.789235\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 206.801 | + | 101.818i | 0.998735 | + | 0.491727i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 157.540 | + | 272.867i | 0.699984 | + | 1.21241i | 0.968471 | + | 0.249125i | \(0.0801430\pi\) |
−0.268487 | + | 0.963283i | \(0.586524\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 206.032 | 0.784800 | 0.392400 | − | 0.919795i | \(-0.371645\pi\) | ||||
0.392400 | + | 0.919795i | \(0.371645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 339.661 | 1.20460 | 0.602301 | − | 0.798269i | \(-0.294251\pi\) | ||||
0.602301 | + | 0.798269i | \(0.294251\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 71.0320 | + | 123.031i | 0.220449 | + | 0.381828i | 0.954944 | − | 0.296785i | \(-0.0959146\pi\) |
−0.734496 | + | 0.678613i | \(0.762581\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 130.855 | − | 317.058i | 0.381500 | − | 0.924369i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 155.008 | − | 268.482i | 0.401736 | − | 0.695826i | −0.592200 | − | 0.805791i | \(-0.701740\pi\) |
0.993936 | + | 0.109965i | \(0.0350738\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −636.295 | −1.55996 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −140.825 | + | 243.916i | −0.310743 | + | 0.538223i | −0.978523 | − | 0.206136i | \(-0.933911\pi\) |
0.667780 | + | 0.744358i | \(0.267245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 271.924 | + | 470.987i | 0.570760 | + | 0.988585i | 0.996488 | + | 0.0837341i | \(0.0266846\pi\) |
−0.425728 | + | 0.904851i | \(0.639982\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 231.693 | + | 401.305i | 0.442123 | + | 0.765780i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 239.680 | − | 415.137i | 0.437038 | − | 0.756971i | −0.560422 | − | 0.828207i | \(-0.689361\pi\) |
0.997459 | + | 0.0712360i | \(0.0226943\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1105.63 | −1.84809 | −0.924046 | − | 0.382280i | \(-0.875139\pi\) | ||||
−0.924046 | + | 0.382280i | \(0.875139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −119.675 | + | 207.283i | −0.191876 | + | 0.332338i | −0.945872 | − | 0.324541i | \(-0.894790\pi\) |
0.753996 | + | 0.656879i | \(0.228124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 62.5298 | + | 944.754i | 0.0925445 | + | 1.39824i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −580.333 | − | 1005.17i | −0.826488 | − | 1.43152i | −0.900777 | − | 0.434282i | \(-0.857002\pi\) |
0.0742888 | − | 0.997237i | \(-0.476331\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.93158 | 0.00387690 | 0.00193845 | − | 0.999998i | \(-0.499383\pi\) | ||||
0.00193845 | + | 0.999998i | \(0.499383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 276.494 | 0.352824 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −639.371 | − | 1107.42i | −0.761496 | − | 1.31895i | −0.942079 | − | 0.335390i | \(-0.891132\pi\) |
0.180583 | − | 0.983560i | \(-0.442202\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 573.078 | − | 383.449i | 0.660163 | − | 0.441719i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 338.156 | − | 585.703i | 0.365200 | − | 0.632545i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 79.0596 | 0.0827555 | 0.0413777 | − | 0.999144i | \(-0.486825\pi\) | ||||
0.0413777 | + | 0.999144i | \(0.486825\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 686.052 | − | 1188.28i | 0.675889 | − | 1.17067i | −0.300319 | − | 0.953839i | \(-0.597093\pi\) |
0.976208 | − | 0.216835i | \(-0.0695734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −129.265 | − | 223.894i | −0.123659 | − | 0.214184i | 0.797549 | − | 0.603254i | \(-0.206130\pi\) |
−0.921208 | + | 0.389070i | \(0.872796\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −631.184 | − | 1093.24i | −0.570270 | − | 0.987736i | −0.996538 | − | 0.0831393i | \(-0.973505\pi\) |
0.426268 | − | 0.904597i | \(-0.359828\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −138.416 | + | 239.744i | −0.121632 | + | 0.210673i | −0.920411 | − | 0.390951i | \(-0.872146\pi\) |
0.798779 | + | 0.601624i | \(0.205479\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −52.9156 | −0.0440520 | −0.0220260 | − | 0.999757i | \(-0.507012\pi\) | ||||
−0.0220260 | + | 0.999757i | \(0.507012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1101.02 | + | 1907.02i | −0.892789 | + | 1.54636i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.1715 | − | 410.531i | −0.0209312 | − | 0.316247i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −641.309 | − | 1110.78i | −0.481825 | − | 0.834545i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1183.53 | 0.846866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 443.700 | 0.310016 | 0.155008 | − | 0.987913i | \(-0.450460\pi\) | ||||
0.155008 | + | 0.987913i | \(0.450460\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1076.74 | − | 1864.97i | −0.718133 | − | 1.24384i | −0.961739 | − | 0.273968i | \(-0.911664\pi\) |
0.243606 | − | 0.969874i | \(-0.421670\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −902.867 | − | 444.527i | −0.588635 | − | 0.289815i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 131.554 | − | 227.858i | 0.0820394 | − | 0.142096i | −0.822086 | − | 0.569363i | \(-0.807190\pi\) |
0.904126 | + | 0.427266i | \(0.140523\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1165.77 | 0.711360 | 0.355680 | − | 0.934608i | \(-0.384249\pi\) | ||||
0.355680 | + | 0.934608i | \(0.384249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −951.693 | + | 1648.38i | −0.556536 | + | 0.963948i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −380.180 | − | 658.490i | −0.217739 | − | 0.377135i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −882.597 | − | 1528.70i | −0.485270 | − | 0.840512i | 0.514587 | − | 0.857438i | \(-0.327945\pi\) |
−0.999857 | + | 0.0169263i | \(0.994612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1346.16 | + | 2331.61i | −0.725488 | + | 1.25658i | 0.233285 | + | 0.972408i | \(0.425052\pi\) |
−0.958773 | + | 0.284173i | \(0.908281\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3981.85 | −2.06342 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 970.691 | − | 1681.29i | 0.493437 | − | 0.854657i | −0.506535 | − | 0.862220i | \(-0.669074\pi\) |
0.999971 | + | 0.00756226i | \(0.00240716\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2939.70 | + | 1447.36i | 1.43901 | + | 0.708497i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1051.42 | − | 1821.11i | −0.505236 | − | 0.875094i | −0.999982 | − | 0.00605658i | \(-0.998072\pi\) |
0.494746 | − | 0.869038i | \(-0.335261\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2344.22 | 1.08623 | 0.543116 | − | 0.839658i | \(-0.317244\pi\) | ||||
0.543116 | + | 0.839658i | \(0.317244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −810.844 | −0.369069 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1735.32 | + | 3005.67i | 0.762626 | + | 1.32091i | 0.941493 | + | 0.337033i | \(0.109424\pi\) |
−0.178867 | + | 0.983873i | \(0.557243\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 36.5813 | + | 552.703i | 0.0158017 | + | 0.238745i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −477.885 | + | 827.722i | −0.199547 | + | 0.345625i | −0.948381 | − | 0.317132i | \(-0.897280\pi\) |
0.748835 | + | 0.662757i | \(0.230614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4220.26 | 1.73309 | 0.866546 | − | 0.499098i | \(-0.166335\pi\) | ||||
0.866546 | + | 0.499098i | \(0.166335\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1960.78 | + | 3396.17i | −0.779239 | + | 1.34968i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 567.858 | + | 983.558i | 0.222063 | + | 0.384625i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1759.02 | − | 3046.71i | −0.666377 | − | 1.15420i | −0.978910 | − | 0.204291i | \(-0.934511\pi\) |
0.312534 | − | 0.949907i | \(-0.398822\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2508.84 | − | 4345.43i | 0.935699 | − | 1.62068i | 0.162317 | − | 0.986739i | \(-0.448103\pi\) |
0.773382 | − | 0.633940i | \(-0.218563\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2838.14 | 1.02644 | 0.513221 | − | 0.858257i | \(-0.328452\pi\) | ||||
0.513221 | + | 0.858257i | \(0.328452\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −177.451 | + | 307.354i | −0.0632118 | + | 0.109486i | −0.895899 | − | 0.444257i | \(-0.853468\pi\) |
0.832688 | + | 0.553743i | \(0.186801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −940.348 | + | 629.192i | −0.325121 | + | 0.217540i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1282.16 | + | 2220.77i | 0.436829 | + | 0.756610i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2777.99 | 0.919413 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 752.672 | 0.245574 | 0.122787 | − | 0.992433i | \(-0.460817\pi\) | ||||
0.122787 | + | 0.992433i | \(0.460817\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2113.75 | + | 3661.12i | 0.670496 | + | 1.16133i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 391.303 | + | 5912.15i | 0.122412 | + | 1.84951i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 413.547 | − | 716.284i | 0.125874 | − | 0.218020i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3077.75 | −0.924221 | −0.462111 | − | 0.886822i | \(-0.652908\pi\) | ||||
−0.462111 | + | 0.886822i | \(0.652908\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3108.72 | + | 5384.46i | −0.908955 | + | 1.57436i | −0.0934368 | + | 0.995625i | \(0.529785\pi\) |
−0.815518 | + | 0.578731i | \(0.803548\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −251.627 | − | 435.831i | −0.0726113 | − | 0.125766i | 0.827434 | − | 0.561563i | \(-0.189800\pi\) |
−0.900045 | + | 0.435797i | \(0.856467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −134.170 | − | 232.389i | −0.0377243 | − | 0.0653404i | 0.846547 | − | 0.532314i | \(-0.178678\pi\) |
−0.884271 | + | 0.466974i | \(0.845344\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −884.080 | + | 1531.27i | −0.245409 | + | 0.425060i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5189.77 | 1.40459 | 0.702297 | − | 0.711884i | \(-0.252158\pi\) | ||||
0.702297 | + | 0.711884i | \(0.252158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3085.47 | + | 5344.19i | −0.824699 | + | 1.42842i | 0.0774495 | + | 0.996996i | \(0.475322\pi\) |
−0.902149 | + | 0.431425i | \(0.858011\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4231.82 | − | 562.641i | 1.10351 | − | 0.146718i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1011.54 | − | 1752.05i | −0.260579 | − | 0.451336i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1891.91 | −0.475763 | −0.237882 | − | 0.971294i | \(-0.576453\pi\) | ||||
−0.237882 | + | 0.971294i | \(0.576453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9045.01 | −2.24765 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3269.97 | − | 5663.75i | −0.793676 | − | 1.37469i | −0.923676 | − | 0.383174i | \(-0.874831\pi\) |
0.130000 | − | 0.991514i | \(-0.458502\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5235.23 | + | 2577.56i | 1.25599 | + | 0.618386i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2687.95 | − | 4655.67i | 0.630214 | − | 1.09156i | −0.357294 | − | 0.933992i | \(-0.616301\pi\) |
0.987508 | − | 0.157570i | \(-0.0503661\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3858.53 | 0.894443 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1619.44 | + | 2804.95i | −0.367060 | + | 0.635766i | −0.989104 | − | 0.147216i | \(-0.952969\pi\) |
0.622045 | + | 0.782982i | \(0.286302\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −678.729 | − | 1175.59i | −0.152140 | − | 0.263514i | 0.779874 | − | 0.625936i | \(-0.215283\pi\) |
−0.932014 | + | 0.362423i | \(0.881950\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −764.513 | − | 1324.18i | −0.167643 | − | 0.290366i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1280.82 | − | 2218.44i | 0.277823 | − | 0.481203i | −0.693021 | − | 0.720918i | \(-0.743721\pi\) |
0.970843 | + | 0.239715i | \(0.0770539\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1786.17 | −0.379196 | −0.189598 | − | 0.981862i | \(-0.560718\pi\) | ||||
−0.189598 | + | 0.981862i | \(0.560718\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3694.14 | − | 6398.44i | 0.775950 | − | 1.34398i | −0.158309 | − | 0.987390i | \(-0.550604\pi\) |
0.934259 | − | 0.356595i | \(-0.116063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3171.34 | − | 2121.96i | 0.652258 | − | 0.436429i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2209.74 | + | 3827.39i | 0.449775 | + | 0.779033i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −492.981 | −0.0982945 | −0.0491472 | − | 0.998792i | \(-0.515650\pi\) | ||||
−0.0491472 | + | 0.998792i | \(0.515650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3505.48 | −0.691853 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3293.55 | + | 5704.59i | 0.637026 | + | 1.10336i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5228.22 | − | 3498.23i | 1.00116 | − | 0.669882i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3384.43 | + | 5862.01i | −0.635384 | + | 1.10052i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −988.810 | −0.183825 | −0.0919126 | − | 0.995767i | \(-0.529298\pi\) | ||||
−0.0919126 | + | 0.995767i | \(0.529298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4798.28 | + | 8310.87i | −0.874874 | + | 1.51533i | −0.0179763 | + | 0.999838i | \(0.505722\pi\) |
−0.856897 | + | 0.515487i | \(0.827611\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −482.856 | − | 836.332i | −0.0871970 | − | 0.151030i | 0.819128 | − | 0.573610i | \(-0.194458\pi\) |
−0.906325 | + | 0.422581i | \(0.861124\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4492.99 | − | 7782.08i | −0.796061 | − | 1.37882i | −0.922163 | − | 0.386801i | \(-0.873580\pi\) |
0.126103 | − | 0.992017i | \(-0.459753\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1561.61 | − | 2704.79i | 0.274086 | − | 0.474730i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1207.14 | −0.207947 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −556.762 | + | 964.340i | −0.0950265 | + | 0.164591i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2360.47 | + | 1162.18i | 0.395553 | + | 0.194751i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1903.65 | + | 3297.22i | 0.316115 | + | 0.547527i | 0.979674 | − | 0.200597i | \(-0.0642882\pi\) |
−0.663559 | + | 0.748124i | \(0.730955\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5966.21 | 0.973041 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1649.82 | −0.266681 | −0.133340 | − | 0.991070i | \(-0.542570\pi\) | ||||
−0.133340 | + | 0.991070i | \(0.542570\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8177.84 | − | 14164.4i | −1.29869 | − | 2.24940i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1251.26 | − | 6228.00i | −0.196973 | − | 0.980409i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2855.00 | − | 4945.00i | 0.441684 | − | 0.765019i | −0.556131 | − | 0.831095i | \(-0.687715\pi\) |
0.997815 | + | 0.0660760i | \(0.0210480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −447.244 | −0.0685973 | −0.0342986 | − | 0.999412i | \(-0.510920\pi\) | ||||
−0.0342986 | + | 0.999412i | \(0.510920\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5322.85 | + | 9219.45i | −0.802569 | + | 1.39009i | 0.115352 | + | 0.993325i | \(0.463201\pi\) |
−0.917920 | + | 0.396765i | \(0.870133\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6880.48 | − | 11917.3i | −1.02867 | − | 1.78171i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4548.73 | − | 7878.64i | −0.668727 | − | 1.15827i | −0.978260 | − | 0.207381i | \(-0.933506\pi\) |
0.309533 | − | 0.950889i | \(-0.399827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1953.15 | − | 3382.96i | 0.284758 | − | 0.493215i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2979.01 | −0.427201 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2643.91 | + | 4579.39i | −0.376052 | + | 0.651341i | −0.990484 | − | 0.137629i | \(-0.956052\pi\) |
0.614432 | + | 0.788970i | \(0.289385\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −379.184 | − | 5729.04i | −0.0530627 | − | 0.801717i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2947.51 | − | 5105.23i | −0.409159 | − | 0.708683i | 0.585637 | − | 0.810573i | \(-0.300844\pi\) |
−0.994796 | + | 0.101890i | \(0.967511\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2274.51 | −0.310724 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3842.41 | 0.520769 | 0.260384 | − | 0.965505i | \(-0.416151\pi\) | ||||
0.260384 | + | 0.965505i | \(0.416151\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2506.87 | + | 4342.02i | 0.334452 | + | 0.579287i | 0.983379 | − | 0.181563i | \(-0.0581156\pi\) |
−0.648928 | + | 0.760850i | \(0.724782\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9794.14 | + | 6553.30i | −1.29651 | + | 0.867499i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5591.24 | − | 9684.31i | 0.728758 | − | 1.26225i | −0.228650 | − | 0.973509i | \(-0.573431\pi\) |
0.957408 | − | 0.288738i | \(-0.0932355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3930.40 | 0.508360 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7222.95 | − | 12510.5i | 0.920066 | − | 1.59360i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1703.40 | + | 2950.37i | 0.215343 | + | 0.372985i | 0.953379 | − | 0.301777i | \(-0.0975798\pi\) |
−0.738036 | + | 0.674762i | \(0.764246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 41.5201 | + | 71.9149i | 0.00517061 | + | 0.00895575i | 0.868599 | − | 0.495515i | \(-0.165021\pi\) |
−0.863429 | + | 0.504471i | \(0.831687\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5955.57 | + | 10315.4i | −0.736149 | + | 1.27505i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16108.0 | −1.96178 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1228.10 | + | 2127.13i | −0.148473 | + | 0.257164i | −0.930663 | − | 0.365876i | \(-0.880769\pi\) |
0.782190 | + | 0.623040i | \(0.214103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 344.489 | + | 5204.84i | 0.0410440 | + | 0.620129i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.2435 | + | 31.5987i | 0.00215793 | + | 0.00373764i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3437.96 | 0.400848 | 0.200424 | − | 0.979709i | \(-0.435768\pi\) | ||||
0.200424 | + | 0.979709i | \(0.435768\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5347.62 | −0.619067 | −0.309533 | − | 0.950889i | \(-0.600173\pi\) | ||||
−0.309533 | + | 0.950889i | \(0.600173\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 332.210 | + | 575.404i | 0.0379166 | + | 0.0656734i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9036.35 | + | 4449.05i | 1.02412 | + | 0.504226i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 425.821 | − | 737.544i | 0.0475895 | − | 0.0824275i | −0.841249 | − | 0.540647i | \(-0.818179\pi\) |
0.888839 | + | 0.458220i | \(0.151513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3433.42 | −0.381061 | −0.190531 | − | 0.981681i | \(-0.561021\pi\) | ||||
−0.190531 | + | 0.981681i | \(0.561021\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4806.92 | − | 8325.83i | 0.526192 | − | 0.911392i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4869.20 | + | 8433.70i | 0.529371 | + | 0.916898i | 0.999413 | + | 0.0342540i | \(0.0109055\pi\) |
−0.470042 | + | 0.882644i | \(0.655761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4967.48 | + | 8603.93i | 0.532759 | + | 0.922765i | 0.999268 | + | 0.0382491i | \(0.0121780\pi\) |
−0.466509 | + | 0.884516i | \(0.654489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7957.75 | − | 13783.2i | 0.847716 | − | 1.46829i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7557.33 | 0.794327 | 0.397163 | − | 0.917748i | \(-0.369995\pi\) | ||||
0.397163 | + | 0.917748i | \(0.369995\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5266.54 | + | 9121.92i | −0.549871 | + | 0.952405i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7699.43 | + | 3790.81i | 0.793307 | + | 0.390585i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7005.92 | − | 12134.6i | −0.717118 | − | 1.24209i | −0.962137 | − | 0.272567i | \(-0.912127\pi\) |
0.245018 | − | 0.969518i | \(-0.421206\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1669.61 | 0.168680 | 0.0843399 | − | 0.996437i | \(-0.473122\pi\) | ||||
0.0843399 | + | 0.996437i | \(0.473122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14785.4 | 1.48409 | 0.742046 | − | 0.670349i | \(-0.233856\pi\) | ||||
0.742046 | + | 0.670349i | \(0.233856\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2301.58 | + | 3986.46i | 0.228061 | + | 0.395014i | 0.957233 | − | 0.289317i | \(-0.0934280\pi\) |
−0.729172 | + | 0.684330i | \(0.760095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −586.309 | − | 8858.47i | −0.0577255 | − | 0.872167i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8682.35 | + | 15038.3i | −0.844006 | + | 1.46186i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1625.18 | 0.156987 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1738.68 | − | 3011.47i | 0.165850 | − | 0.287261i | −0.771107 | − | 0.636706i | \(-0.780297\pi\) |
0.936957 | + | 0.349445i | \(0.113630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5865.39 | + | 10159.2i | 0.556006 | + | 0.963030i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 491.996 | + | 852.163i | 0.0460627 | + | 0.0797829i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2172.08 | + | 3762.16i | −0.202108 | + | 0.350061i | −0.949207 | − | 0.314651i | \(-0.898112\pi\) |
0.747100 | + | 0.664712i | \(0.231446\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4982.89 | −0.457993 | −0.228997 | − | 0.973427i | \(-0.573544\pi\) | ||||
−0.228997 | + | 0.973427i | \(0.573544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −678.578 | + | 1175.33i | −0.0619911 | + | 0.107372i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17018.4 | + | 11387.1i | −1.53598 | + | 1.02773i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7663.08 | − | 13272.8i | −0.687468 | − | 1.19073i | −0.972654 | − | 0.232257i | \(-0.925389\pi\) |
0.285187 | − | 0.958472i | \(-0.407944\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1516.04 | 0.134387 | 0.0671936 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671936 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17077.5 | 1.50483 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1326.82 | + | 2298.12i | 0.115541 | + | 0.200122i | 0.917996 | − | 0.396590i | \(-0.129807\pi\) |
−0.802455 | + | 0.596713i | \(0.796473\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 292.752 | + | 4423.15i | 0.0253436 | + | 0.382913i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1608.86 | − | 2786.64i | 0.137660 | − | 0.238435i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7262.82 | −0.617830 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6566.06 | + | 11372.8i | −0.552139 | + | 0.956333i | 0.445981 | + | 0.895042i | \(0.352855\pi\) |
−0.998120 | + | 0.0612905i | \(0.980478\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1543.17 | + | 2672.85i | 0.129021 | + | 0.223471i | 0.923298 | − | 0.384085i | \(-0.125483\pi\) |
−0.794276 | + | 0.607557i | \(0.792150\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3553.58 | + | 6154.98i | 0.293731 | + | 0.508757i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9567.63 | + | 16571.6i | −0.786359 | + | 1.36201i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7670.80 | 0.623376 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7855.86 | − | 13606.7i | 0.634838 | − | 1.09957i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10692.7 | + | 13898.1i | 0.854482 | + | 1.11064i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −463.047 | − | 802.022i | −0.0367985 | − | 0.0637368i | 0.847040 | − | 0.531530i | \(-0.178383\pi\) |
−0.883838 | + | 0.467793i | \(0.845049\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3445.52 | −0.270807 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 592.871 | 0.0463425 | 0.0231712 | − | 0.999732i | \(-0.492624\pi\) | ||||
0.0231712 | + | 0.999732i | \(0.492624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1659.82 | + | 2874.89i | 0.128331 | + | 0.222276i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19285.1 | − | 9495.02i | −1.48298 | − | 0.730144i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6122.67 | + | 10604.8i | −0.465756 | + | 0.806713i | −0.999235 | − | 0.0391003i | \(-0.987551\pi\) |
0.533480 | + | 0.845813i | \(0.320884\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12646.0 | 0.956829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7297.31 | − | 12639.3i | 0.546261 | − | 0.946152i | −0.452266 | − | 0.891883i | \(-0.649384\pi\) |
0.998526 | − | 0.0542682i | \(-0.0172826\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −329.300 | − | 570.364i | −0.0245199 | − | 0.0424697i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11455.6 | + | 19841.7i | 0.844015 | + | 1.46188i | 0.886474 | + | 0.462779i | \(0.153147\pi\) |
−0.0424590 | + | 0.999098i | \(0.513519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2952.32 | + | 5113.57i | −0.216376 | + | 0.374774i | −0.953697 | − | 0.300768i | \(-0.902757\pi\) |
0.737321 | + | 0.675542i | \(0.236090\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5291.53 | −0.383778 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4756.61 | + | 8238.68i | −0.343189 | + | 0.594421i | −0.985023 | − | 0.172423i | \(-0.944840\pi\) |
0.641834 | + | 0.766844i | \(0.278174\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.1242 | − | 30.1928i | 0.00322214 | − | 0.00215595i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7924.56 | + | 13725.7i | 0.562953 | + | 0.975064i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22790.6 | 1.60250 | 0.801252 | − | 0.598327i | \(-0.204167\pi\) | ||||
0.801252 | + | 0.598327i | \(0.204167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17384.3 | 1.21614 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9131.39 | − | 15816.0i | −0.632346 | − | 1.09526i | −0.987071 | − | 0.160285i | \(-0.948759\pi\) |
0.354724 | − | 0.934971i | \(-0.384575\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4255.92 | − | 2847.66i | 0.293237 | − | 0.196206i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3479.05 | − | 6025.88i | 0.237312 | − | 0.411037i | −0.722630 | − | 0.691235i | \(-0.757067\pi\) |
0.959942 | + | 0.280198i | \(0.0904003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2305.39 | 0.156471 | 0.0782353 | − | 0.996935i | \(-0.475071\pi\) | ||||
0.0782353 | + | 0.996935i | \(0.475071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7981.87 | − | 13825.0i | 0.536379 | − | 0.929036i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8089.62 | + | 14011.6i | 0.540935 | + | 0.936927i | 0.998851 | + | 0.0479312i | \(0.0152628\pi\) |
−0.457916 | + | 0.888996i | \(0.651404\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2644.60 | + | 4580.58i | 0.175105 | + | 0.303291i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10270.4 | + | 17788.8i | −0.676699 | + | 1.17208i | 0.299271 | + | 0.954168i | \(0.403257\pi\) |
−0.975969 | + | 0.217908i | \(0.930077\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6918.19 | −0.451403 | −0.225702 | − | 0.974196i | \(-0.572467\pi\) | ||||
−0.225702 | + | 0.974196i | \(0.572467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4040.81 | − | 6998.89i | 0.262381 | − | 0.454457i | −0.704493 | − | 0.709711i | \(-0.748826\pi\) |
0.966874 | + | 0.255254i | \(0.0821589\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21247.0 | − | 10461.0i | −1.36636 | − | 0.672728i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9234.52 | + | 15994.7i | 0.591009 | + | 1.02366i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6999.54 | 0.443704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27293.3 | −1.72191 | −0.860957 | − | 0.508677i | \(-0.830135\pi\) | ||||
−0.860957 | + | 0.508677i | \(0.830135\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2761.20 | + | 4782.53i | 0.172559 | + | 0.298880i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4871.86 | − | 11804.4i | 0.303030 | − | 0.734237i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9627.82 | − | 16675.9i | 0.593254 | − | 1.02755i | −0.400536 | − | 0.916281i | \(-0.631176\pi\) |
0.993791 | − | 0.111266i | \(-0.0354905\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19996.4 | −1.22641 | −0.613204 | − | 0.789925i | \(-0.710120\pi\) | ||||
−0.613204 | + | 0.789925i | \(0.710120\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3532.10 | − | 6117.77i | 0.214623 | − | 0.371738i | −0.738533 | − | 0.674218i | \(-0.764481\pi\) |
0.953156 | + | 0.302479i | \(0.0978144\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7199.47 | − | 12469.8i | −0.435445 | − | 0.754213i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6910.53 | − | 11969.4i | −0.414134 | − | 0.717302i | 0.581203 | − | 0.813759i | \(-0.302582\pi\) |
−0.995337 | + | 0.0964570i | \(0.969249\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13401.4 | − | 23211.9i | 0.799443 | − | 1.38468i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7802.80 | 0.461235 | 0.230617 | − | 0.973044i | \(-0.425925\pi\) | ||||
0.230617 | + | 0.973044i | \(0.425925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7908.65 | + | 13698.2i | −0.465372 | + | 0.806048i | −0.999218 | − | 0.0395338i | \(-0.987413\pi\) |
0.533846 | + | 0.845581i | \(0.320746\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −827.204 | − | 12498.1i | −0.0482370 | − | 0.728806i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5404.29 | − | 9360.51i | −0.313726 | − | 0.543389i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27803.5 | −1.59962 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2943.30 | 0.168582 | 0.0842911 | − | 0.996441i | \(-0.473137\pi\) | ||||
0.0842911 | + | 0.996441i | \(0.473137\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1585.74 | − | 2746.58i | −0.0900220 | − | 0.155923i | 0.817498 | − | 0.575931i | \(-0.195360\pi\) |
−0.907520 | + | 0.420009i | \(0.862027\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1216.92 | − | 814.247i | 0.0687792 | − | 0.0460205i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12226.6 | + | 21177.1i | −0.684975 | + | 1.18641i | 0.288470 | + | 0.957489i | \(0.406854\pi\) |
−0.973445 | + | 0.228923i | \(0.926480\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3274.70 | 0.182656 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5771.12 | − | 9995.87i | 0.319103 | − | 0.552703i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4297.95 | − | 7444.26i | −0.236616 | − | 0.409831i | 0.723125 | − | 0.690717i | \(-0.242705\pi\) |
−0.959741 | + | 0.280886i | \(0.909372\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7254.69 | + | 12565.5i | 0.395951 | + | 0.685808i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2288.51 | − | 3963.82i | 0.124367 | − | 0.215409i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21476.1 | 1.15712 | 0.578561 | − | 0.815639i | \(-0.303615\pi\) | ||||
0.578561 | + | 0.815639i | \(0.303615\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8560.51 | − | 14827.2i | 0.459269 | − | 0.795477i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1678.24 | − | 25356.3i | −0.0892738 | − | 1.34883i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6769.46 | + | 11725.0i | 0.358579 | + | 0.621077i | 0.987724 | − | 0.156211i | \(-0.0499281\pi\) |
−0.629145 | + | 0.777288i | \(0.716595\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −56602.5 | −2.97304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23690.0 | −1.23910 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6941.84 | + | 12023.6i | 0.360065 | + | 0.623652i | 0.987971 | − | 0.154638i | \(-0.0494210\pi\) |
−0.627906 | + | 0.778289i | \(0.716088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4295.63 | − | 2114.95i | −0.221883 | − | 0.109244i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 913.577 | − | 1582.36i | 0.0467992 | − | 0.0810585i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18292.9 | −0.933215 | −0.466607 | − | 0.884465i | \(-0.654524\pi\) | ||||
−0.466607 | + | 0.884465i | \(0.654524\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3772.81 | − | 6534.69i | 0.190892 | − | 0.330635i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7122.92 | − | 12337.3i | −0.358924 | − | 0.621674i | 0.628857 | − | 0.777521i | \(-0.283523\pi\) |
−0.987781 | + | 0.155846i | \(0.950190\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12253.3 | + | 21223.3i | 0.612422 | + | 1.06075i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 681.947 | − | 1181.17i | 0.0339456 | − | 0.0587956i | −0.848553 | − | 0.529110i | \(-0.822526\pi\) |
0.882499 | + | 0.470314i | \(0.155859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21789.4 | −1.07588 | −0.537938 | − | 0.842984i | \(-0.680797\pi\) | ||||
−0.537938 | + | 0.842984i | \(0.680797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10985.0 | − | 19026.6i | 0.540214 | − | 0.935678i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20974.9 | − | 10327.0i | −1.02324 | − | 0.503793i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1059.78 | + | 1835.59i | 0.0514937 | + | 0.0891898i | 0.890623 | − | 0.454742i | \(-0.150268\pi\) |
−0.839130 | + | 0.543932i | \(0.816935\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33509.1 | −1.61526 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28202.4 | 1.35408 | 0.677038 | − | 0.735948i | \(-0.263263\pi\) | ||||
0.677038 | + | 0.735948i | \(0.263263\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5573.52 | + | 9653.62i | 0.265493 | + | 0.459847i | 0.967693 | − | 0.252133i | \(-0.0811321\pi\) |
−0.702200 | + | 0.711980i | \(0.747799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 338.597 | + | 5115.82i | 0.0160656 | + | 0.242733i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5243.07 | + | 9081.26i | −0.246827 | + | 0.427517i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4109.29 | −0.192698 | −0.0963491 | − | 0.995348i | \(-0.530717\pi\) | ||||
−0.0963491 | + | 0.995348i | \(0.530717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6945.68 | − | 12030.3i | 0.323181 | − | 0.559766i | −0.657962 | − | 0.753052i | \(-0.728581\pi\) |
0.981143 | + | 0.193286i | \(0.0619144\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4784.22 | − | 8286.51i | −0.221747 | − | 0.384078i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5597.75 | − | 9695.59i | −0.257459 | − | 0.445931i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28262.0 | − | 48951.2i | 1.29487 | − | 2.24278i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24162.9 | 1.09861 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4671.18 | − | 8090.71i | 0.211575 | − | 0.366458i | −0.740633 | − | 0.671910i | \(-0.765474\pi\) |
0.952208 | + | 0.305452i | \(0.0988074\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −814.500 | + | 544.986i | −0.0366123 | + | 0.0244974i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10124.0 | + | 17535.4i | 0.453361 | + | 0.785245i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24324.3 | 1.08107 | 0.540534 | − | 0.841322i | \(-0.318222\pi\) | ||||
0.540534 | + | 0.841322i | \(0.318222\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3155.97 | 0.139737 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6118.22 | − | 10597.1i | −0.268876 | − | 0.465706i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2693.34 | + | 40693.3i | 0.117923 | + | 1.78168i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17227.5 | − | 29838.8i | 0.748684 | − | 1.29676i | −0.199770 | − | 0.979843i | \(-0.564020\pi\) |
0.948454 | − | 0.316915i | \(-0.102647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8350.13 | −0.361545 | −0.180772 | − | 0.983525i | \(-0.557860\pi\) | ||||
−0.180772 | + | 0.983525i | \(0.557860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13086.2 | − | 22665.9i | 0.562441 | − | 0.974176i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9228.37 | − | 15984.0i | −0.395177 | − | 0.684467i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9417.38 | − | 16311.4i | −0.400327 | − | 0.693387i | 0.593438 | − | 0.804880i | \(-0.297770\pi\) |
−0.993765 | + | 0.111492i | \(0.964437\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4828.38 | + | 8363.00i | −0.204504 | + | 0.354211i | −0.949975 | − | 0.312327i | \(-0.898891\pi\) |
0.745471 | + | 0.666538i | \(0.232225\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20759.6 | 0.872892 | 0.436446 | − | 0.899731i | \(-0.356237\pi\) | ||||
0.436446 | + | 0.899731i | \(0.356237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7808.05 | − | 13523.9i | 0.327123 | − | 0.566593i | −0.654817 | − | 0.755787i | \(-0.727254\pi\) |
0.981940 | + | 0.189194i | \(0.0605876\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4646.36 | − | 6039.24i | −0.193262 | − | 0.251197i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14588.3 | + | 25267.7i | 0.604610 | + | 1.04722i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 417.027 | 0.0171601 | 0.00858007 | − | 0.999963i | \(-0.497269\pi\) | ||||
0.00858007 | + | 0.999963i | \(0.497269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20656.8 | −0.846973 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5045.98 | − | 8739.89i | −0.205428 | − | 0.355812i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21311.4 | − | 10492.7i | −0.864544 | − | 0.425658i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27872.7 | + | 48276.9i | −1.12275 | + | 1.94467i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24917.4 | −1.00018 | −0.500092 | − | 0.865972i | \(-0.666700\pi\) | ||||
−0.500092 | + | 0.865972i | \(0.666700\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22261.9 | + | 38558.7i | −0.887342 | + | 1.53692i | −0.0443361 | + | 0.999017i | \(0.514117\pi\) |
−0.843006 | + | 0.537904i | \(0.819216\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12073.2 | + | 20911.4i | 0.479548 | + | 0.830602i | 0.999725 | − | 0.0234566i | \(-0.00746716\pi\) |
−0.520176 | + | 0.854059i | \(0.674134\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13221.3 | − | 22900.0i | −0.521505 | − | 0.903273i | −0.999687 | − | 0.0250123i | \(-0.992037\pi\) |
0.478182 | − | 0.878261i | \(-0.341296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21598.2 | + | 37409.2i | −0.848973 | + | 1.47046i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 59337.4 | 2.31632 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8923.54 | − | 15456.0i | 0.347144 | − | 0.601271i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18217.4 | − | 12189.4i | 0.703842 | − | 0.470944i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11258.1 | + | 19499.5i | 0.433475 | + | 0.750801i | 0.997170 | − | 0.0751826i | \(-0.0239540\pi\) |
−0.563695 | + | 0.825983i | \(0.690621\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10120.6 | −0.387027 | −0.193514 | − | 0.981098i | \(-0.561988\pi\) | ||||
−0.193514 | + | 0.981098i | \(0.561988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20748.5 | −0.790761 | −0.395380 | − | 0.918517i | \(-0.629387\pi\) | ||||
−0.395380 | + | 0.918517i | \(0.629387\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12749.7 | + | 22083.1i | 0.482630 | + | 0.835939i | 0.999801 | − | 0.0199428i | \(-0.00634841\pi\) |
−0.517172 | + | 0.855882i | \(0.673015\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6829.63 | − | 4569.74i | 0.257659 | − | 0.172401i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3859.78 | − | 6685.34i | 0.144639 | − | 0.250522i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11895.7 | −0.444280 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9772.34 | − | 16926.2i | 0.362543 | − | 0.627942i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3443.52 | − | 5964.35i | −0.127326 | − | 0.220534i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26263.1 | + | 45489.1i | 0.964659 | + | 1.67084i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18903.5 | + | 32741.8i | −0.692040 | + | 1.19865i | 0.279128 | + | 0.960254i | \(0.409954\pi\) |
−0.971168 | + | 0.238395i | \(0.923379\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3230.08 | 0.117472 | 0.0587362 | − | 0.998274i | \(-0.481293\pi\) | ||||
0.0587362 | + | 0.998274i | \(0.481293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −74.9364 | + | 129.794i | −0.00271635 | + | 0.00470486i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35781.3 | − | 17616.9i | −1.28855 | − | 0.634419i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17671.6 | + | 30608.0i | 0.634310 | + | 1.09866i | 0.986661 | + | 0.162789i | \(0.0520490\pi\) |
−0.352351 | + | 0.935868i | \(0.614618\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41164.0 | −1.46796 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9423.55 | −0.334967 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16515.1 | + | 28605.0i | 0.583254 | + | 1.01023i | 0.995091 | + | 0.0989684i | \(0.0315543\pi\) |
−0.411836 | + | 0.911258i | \(0.635112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18475.6 | + | 2456.42i | −0.650390 | + | 0.0864725i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7067.68 | + | 12241.6i | −0.247206 | + | 0.428174i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54695.9 | 1.90698 | 0.953488 | − | 0.301430i | \(-0.0974640\pi\) | ||||
0.953488 | + | 0.301430i | \(0.0974640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9127.64 | + | 15809.5i | −0.316209 | + | 0.547690i | −0.979694 | − | 0.200500i | \(-0.935743\pi\) |
0.663485 | + | 0.748190i | \(0.269077\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18226.0 | + | 31568.4i | 0.629397 | + | 1.09015i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3107.88 | + | 5383.00i | 0.106645 | + | 0.184714i | 0.914409 | − | 0.404792i | \(-0.132656\pi\) |
−0.807764 | + | 0.589506i | \(0.799323\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4455.64 | + | 7717.39i | −0.152409 | + | 0.263980i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8594.53 | −0.292135 | −0.146067 | − | 0.989275i | \(-0.546662\pi\) | ||||
−0.146067 | + | 0.989275i | \(0.546662\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21893.1 | − | 37920.0i | 0.741826 | − | 1.28488i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −321.810 | − | 4862.18i | −0.0108361 | − | 0.163721i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36280.3 | − | 62839.4i | −1.21783 | − | 2.10934i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 62451.1 | 2.08329 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17168.1 | −0.570929 | −0.285464 | − | 0.958389i | \(-0.592148\pi\) | ||||
−0.285464 | + | 0.958389i | \(0.592148\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5963.11 | + | 10328.4i | 0.197081 | + | 0.341354i | 0.947581 | − | 0.319517i | \(-0.103521\pi\) |
−0.750500 | + | 0.660871i | \(0.770187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17944.0 | − | 12006.4i | 0.591221 | − | 0.395589i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7019.12 | − | 12157.5i | 0.229848 | − | 0.398108i | −0.727915 | − | 0.685667i | \(-0.759510\pi\) |
0.957763 | + | 0.287559i | \(0.0928438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 65373.8 | 2.13417 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10175.7 | − | 17624.8i | 0.330167 | − | 0.571866i | −0.652378 | − | 0.757894i | \(-0.726228\pi\) |
0.982544 | + | 0.186028i | \(0.0595617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17662.0 | + | 30591.6i | 0.571329 | + | 0.989571i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30047.2 | + | 52043.3i | 0.966072 | + | 1.67329i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16252.9 | − | 28150.8i | 0.520978 | − | 0.902360i | −0.478724 | − | 0.877965i | \(-0.658901\pi\) |
0.999702 | − | 0.0243951i | \(-0.00776598\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4417.18 | −0.140738 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12423.5 | − | 21518.2i | 0.394641 | − | 0.683539i | −0.598414 | − | 0.801187i | \(-0.704202\pi\) |
0.993055 | + | 0.117648i | \(0.0375356\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.4.k.f.109.2 | 4 | ||
3.2 | odd | 2 | 84.4.i.a.25.1 | ✓ | 4 | ||
7.2 | even | 3 | inner | 252.4.k.f.37.2 | 4 | ||
7.3 | odd | 6 | 1764.4.a.y.1.2 | 2 | |||
7.4 | even | 3 | 1764.4.a.o.1.1 | 2 | |||
7.5 | odd | 6 | 1764.4.k.q.1549.1 | 4 | |||
7.6 | odd | 2 | 1764.4.k.q.361.1 | 4 | |||
12.11 | even | 2 | 336.4.q.i.193.1 | 4 | |||
21.2 | odd | 6 | 84.4.i.a.37.1 | yes | 4 | ||
21.5 | even | 6 | 588.4.i.j.373.2 | 4 | |||
21.11 | odd | 6 | 588.4.a.i.1.2 | 2 | |||
21.17 | even | 6 | 588.4.a.f.1.1 | 2 | |||
21.20 | even | 2 | 588.4.i.j.361.2 | 4 | |||
84.11 | even | 6 | 2352.4.a.bt.1.2 | 2 | |||
84.23 | even | 6 | 336.4.q.i.289.1 | 4 | |||
84.59 | odd | 6 | 2352.4.a.bx.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.a.25.1 | ✓ | 4 | 3.2 | odd | 2 | ||
84.4.i.a.37.1 | yes | 4 | 21.2 | odd | 6 | ||
252.4.k.f.37.2 | 4 | 7.2 | even | 3 | inner | ||
252.4.k.f.109.2 | 4 | 1.1 | even | 1 | trivial | ||
336.4.q.i.193.1 | 4 | 12.11 | even | 2 | |||
336.4.q.i.289.1 | 4 | 84.23 | even | 6 | |||
588.4.a.f.1.1 | 2 | 21.17 | even | 6 | |||
588.4.a.i.1.2 | 2 | 21.11 | odd | 6 | |||
588.4.i.j.361.2 | 4 | 21.20 | even | 2 | |||
588.4.i.j.373.2 | 4 | 21.5 | even | 6 | |||
1764.4.a.o.1.1 | 2 | 7.4 | even | 3 | |||
1764.4.a.y.1.2 | 2 | 7.3 | odd | 6 | |||
1764.4.k.q.361.1 | 4 | 7.6 | odd | 2 | |||
1764.4.k.q.1549.1 | 4 | 7.5 | odd | 6 | |||
2352.4.a.bt.1.2 | 2 | 84.11 | even | 6 | |||
2352.4.a.bx.1.1 | 2 | 84.59 | odd | 6 |