Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214 | 0.146447 | 0.0732233 | − | 0.997316i | \(-0.476671\pi\) | ||||
0.0732233 | + | 0.997316i | \(0.476671\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.82843 | −0.978553 | ||||||||
\(5\) | 0.100505 | 0.00898945 | 0.00449472 | − | 0.999990i | \(-0.498569\pi\) | ||||
0.00449472 | + | 0.999990i | \(0.498569\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −6.55635 | −0.289752 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.0416306 | 0.00131647 | ||||||||
\(11\) | 43.9411 | 1.20443 | 0.602216 | − | 0.798333i | \(-0.294285\pi\) | ||||
0.602216 | + | 0.798333i | \(0.294285\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.6447 | −0.355108 | −0.177554 | − | 0.984111i | \(-0.556818\pi\) | ||||
−0.177554 | + | 0.984111i | \(0.556818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 59.9117 | 0.936120 | ||||||||
\(17\) | 121.640 | 1.73541 | 0.867704 | − | 0.497081i | \(-0.165595\pi\) | ||||
0.867704 | + | 0.497081i | \(0.165595\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −127.113 | −1.53482 | −0.767412 | − | 0.641154i | \(-0.778456\pi\) | ||||
−0.767412 | + | 0.641154i | \(0.778456\pi\) | |||||||
\(20\) | −0.786797 | −0.00879665 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.2010 | 0.176385 | ||||||||
\(23\) | −53.5980 | −0.485911 | −0.242955 | − | 0.970037i | \(-0.578117\pi\) | ||||
−0.242955 | + | 0.970037i | \(0.578117\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.990 | −0.999919 | ||||||||
\(26\) | −6.89444 | −0.0520043 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −235.681 | −1.50913 | −0.754567 | − | 0.656223i | \(-0.772153\pi\) | ||||
−0.754567 | + | 0.656223i | \(0.772153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.7107 | −0.108404 | −0.0542022 | − | 0.998530i | \(-0.517262\pi\) | ||||
−0.0542022 | + | 0.998530i | \(0.517262\pi\) | |||||||
\(32\) | 77.2670 | 0.426844 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 50.3848 | 0.254145 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −191.882 | −0.852574 | −0.426287 | − | 0.904588i | \(-0.640179\pi\) | ||||
−0.426287 | + | 0.904588i | \(0.640179\pi\) | |||||||
\(38\) | −52.6518 | −0.224770 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.658946 | −0.00260471 | ||||||||
\(41\) | 319.713 | 1.21782 | 0.608912 | − | 0.793238i | \(-0.291606\pi\) | ||||
0.608912 | + | 0.793238i | \(0.291606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −218.579 | −0.775184 | −0.387592 | − | 0.921831i | \(-0.626693\pi\) | ||||
−0.387592 | + | 0.921831i | \(0.626693\pi\) | |||||||
\(44\) | −343.990 | −1.17860 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −22.2010 | −0.0711600 | ||||||||
\(47\) | −401.553 | −1.24623 | −0.623113 | − | 0.782132i | \(-0.714132\pi\) | ||||
−0.623113 | + | 0.782132i | \(0.714132\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −51.7725 | −0.146435 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 130.302 | 0.347492 | ||||||||
\(53\) | −643.117 | −1.66677 | −0.833386 | − | 0.552692i | \(-0.813601\pi\) | ||||
−0.833386 | + | 0.552692i | \(0.813601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.41631 | 0.0108272 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −97.6224 | −0.221008 | ||||||||
\(59\) | 11.6123 | 0.0256235 | 0.0128118 | − | 0.999918i | \(-0.495922\pi\) | ||||
0.0128118 | + | 0.999918i | \(0.495922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2426 | −0.0256969 | −0.0128484 | − | 0.999917i | \(-0.504090\pi\) | ||||
−0.0128484 | + | 0.999917i | \(0.504090\pi\) | |||||||
\(62\) | −7.75022 | −0.0158755 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −447.288 | −0.873610 | ||||||||
\(65\) | −1.67287 | −0.00319222 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 669.048 | 1.21996 | 0.609979 | − | 0.792417i | \(-0.291178\pi\) | ||||
0.609979 | + | 0.792417i | \(0.291178\pi\) | |||||||
\(68\) | −952.247 | −1.69819 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −822.098 | −1.37416 | −0.687078 | − | 0.726584i | \(-0.741107\pi\) | ||||
−0.687078 | + | 0.726584i | \(0.741107\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 515.100 | 0.825861 | 0.412930 | − | 0.910763i | \(-0.364505\pi\) | ||||
0.412930 | + | 0.910763i | \(0.364505\pi\) | |||||||
\(74\) | −79.4802 | −0.124857 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 995.092 | 1.50191 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −805.754 | −1.14752 | −0.573762 | − | 0.819022i | \(-0.694517\pi\) | ||||
−0.573762 | + | 0.819022i | \(0.694517\pi\) | |||||||
\(80\) | 6.02143 | 0.00841520 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 132.429 | 0.178346 | ||||||||
\(83\) | 394.863 | 0.522191 | 0.261095 | − | 0.965313i | \(-0.415916\pi\) | ||||
0.261095 | + | 0.965313i | \(0.415916\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.2254 | 0.0156004 | ||||||||
\(86\) | −90.5382 | −0.113523 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −288.093 | −0.348987 | ||||||||
\(89\) | −673.418 | −0.802047 | −0.401024 | − | 0.916068i | \(-0.631345\pi\) | ||||
−0.401024 | + | 0.916068i | \(0.631345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 419.588 | 0.475490 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −166.329 | −0.182505 | ||||||||
\(95\) | −12.7755 | −0.0137972 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1091.11 | −1.14212 | −0.571061 | − | 0.820908i | \(-0.693468\pi\) | ||||
−0.571061 | + | 0.820908i | \(0.693468\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 978.474 | 0.978474 | ||||||||
\(101\) | 1370.79 | 1.35048 | 0.675242 | − | 0.737597i | \(-0.264039\pi\) | ||||
0.675242 | + | 0.737597i | \(0.264039\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1413.96 | −1.35263 | −0.676316 | − | 0.736611i | \(-0.736425\pi\) | ||||
−0.676316 | + | 0.736611i | \(0.736425\pi\) | |||||||
\(104\) | 109.128 | 0.102893 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −266.388 | −0.244093 | ||||||||
\(107\) | 343.539 | 0.310385 | 0.155192 | − | 0.987884i | \(-0.450400\pi\) | ||||
0.155192 | + | 0.987884i | \(0.450400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −317.657 | −0.279138 | −0.139569 | − | 0.990212i | \(-0.544572\pi\) | ||||
−0.139569 | + | 0.990212i | \(0.544572\pi\) | |||||||
\(110\) | 1.82929 | 0.00158560 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −798.373 | −0.664643 | −0.332321 | − | 0.943166i | \(-0.607832\pi\) | ||||
−0.332321 | + | 0.943166i | \(0.607832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.38687 | −0.00436807 | ||||||||
\(116\) | 1845.01 | 1.47677 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.80996 | 0.00375248 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 599.823 | 0.450656 | ||||||||
\(122\) | −5.07107 | −0.00376322 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 146.475 | 0.106080 | ||||||||
\(125\) | −25.1253 | −0.0179782 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1071.40 | 0.748593 | 0.374297 | − | 0.927309i | \(-0.377884\pi\) | ||||
0.374297 | + | 0.927309i | \(0.377884\pi\) | |||||||
\(128\) | −803.409 | −0.554781 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.692927 | −0.000467490 0 | ||||||||
\(131\) | 2515.02 | 1.67739 | 0.838695 | − | 0.544601i | \(-0.183319\pi\) | ||||
0.838695 | + | 0.544601i | \(0.183319\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 277.129 | 0.178659 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −797.512 | −0.502839 | ||||||||
\(137\) | −251.064 | −0.156568 | −0.0782841 | − | 0.996931i | \(-0.524944\pi\) | ||||
−0.0782841 | + | 0.996931i | \(0.524944\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 886.067 | 0.540685 | 0.270343 | − | 0.962764i | \(-0.412863\pi\) | ||||
0.270343 | + | 0.962764i | \(0.412863\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −340.524 | −0.201240 | ||||||||
\(143\) | −731.385 | −0.427703 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.6872 | −0.0135663 | ||||||||
\(146\) | 213.361 | 0.120945 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1502.14 | 0.834289 | ||||||||
\(149\) | −582.626 | −0.320339 | −0.160170 | − | 0.987090i | \(-0.551204\pi\) | ||||
−0.160170 | + | 0.987090i | \(0.551204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2811.76 | −1.51535 | −0.757676 | − | 0.652631i | \(-0.773665\pi\) | ||||
−0.757676 | + | 0.652631i | \(0.773665\pi\) | |||||||
\(152\) | 833.395 | 0.444719 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.88052 | −0.000974496 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1691.34 | −0.859770 | −0.429885 | − | 0.902884i | \(-0.641446\pi\) | ||||
−0.429885 | + | 0.902884i | \(0.641446\pi\) | |||||||
\(158\) | −333.754 | −0.168051 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.76573 | 0.00383709 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −40.7232 | −0.0195686 | −0.00978432 | − | 0.999952i | \(-0.503114\pi\) | ||||
−0.00978432 | + | 0.999952i | \(0.503114\pi\) | |||||||
\(164\) | −2502.85 | −1.19170 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 163.558 | 0.0764731 | ||||||||
\(167\) | −2900.47 | −1.34398 | −0.671990 | − | 0.740560i | \(-0.734560\pi\) | ||||
−0.671990 | + | 0.740560i | \(0.734560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1919.96 | −0.873899 | ||||||||
\(170\) | 5.06393 | 0.00228462 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1711.13 | 0.758559 | ||||||||
\(173\) | 2146.15 | 0.943171 | 0.471585 | − | 0.881820i | \(-0.343682\pi\) | ||||
0.471585 | + | 0.881820i | \(0.343682\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2632.59 | 1.12749 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −278.939 | −0.117457 | ||||||||
\(179\) | −1203.54 | −0.502552 | −0.251276 | − | 0.967916i | \(-0.580850\pi\) | ||||
−0.251276 | + | 0.967916i | \(0.580850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2990.47 | −1.22807 | −0.614033 | − | 0.789280i | \(-0.710454\pi\) | ||||
−0.614033 | + | 0.789280i | \(0.710454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 351.407 | 0.140794 | ||||||||
\(185\) | −19.2851 | −0.00766417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5344.98 | 2.09018 | ||||||||
\(188\) | 3143.53 | 1.21950 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.29177 | −0.00202056 | ||||||||
\(191\) | 2807.41 | 1.06354 | 0.531772 | − | 0.846887i | \(-0.321526\pi\) | ||||
0.531772 | + | 0.846887i | \(0.321526\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3336.37 | 1.24434 | 0.622169 | − | 0.782883i | \(-0.286252\pi\) | ||||
0.622169 | + | 0.782883i | \(0.286252\pi\) | |||||||
\(194\) | −451.954 | −0.167260 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4226.65 | 1.52861 | 0.764305 | − | 0.644855i | \(-0.223082\pi\) | ||||
0.764305 | + | 0.644855i | \(0.223082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4385.69 | 1.56228 | 0.781140 | − | 0.624356i | \(-0.214639\pi\) | ||||
0.781140 | + | 0.624356i | \(0.214639\pi\) | |||||||
\(200\) | 819.477 | 0.289729 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 567.800 | 0.197774 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.1328 | 0.0109476 | ||||||||
\(206\) | −585.680 | −0.198088 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −997.210 | −0.332423 | ||||||||
\(209\) | −5585.48 | −1.84859 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2291.56 | 0.747665 | 0.373833 | − | 0.927496i | \(-0.378043\pi\) | ||||
0.373833 | + | 0.927496i | \(0.378043\pi\) | |||||||
\(212\) | 5034.59 | 1.63103 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 142.299 | 0.0454548 | ||||||||
\(215\) | −21.9683 | −0.00696848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −131.578 | −0.0408788 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −34.5727 | −0.0105950 | ||||||||
\(221\) | −2024.65 | −0.616257 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −217.970 | −0.0654544 | −0.0327272 | − | 0.999464i | \(-0.510419\pi\) | ||||
−0.0327272 | + | 0.999464i | \(0.510419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −330.697 | −0.0973347 | ||||||||
\(227\) | −1835.36 | −0.536639 | −0.268320 | − | 0.963330i | \(-0.586468\pi\) | ||||
−0.268320 | + | 0.963330i | \(0.586468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2774.01 | 0.800488 | 0.400244 | − | 0.916409i | \(-0.368925\pi\) | ||||
0.400244 | + | 0.916409i | \(0.368925\pi\) | |||||||
\(230\) | −2.23131 | −0.000639689 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1545.21 | 0.437275 | ||||||||
\(233\) | 988.712 | 0.277994 | 0.138997 | − | 0.990293i | \(-0.455612\pi\) | ||||
0.138997 | + | 0.990293i | \(0.455612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −40.3581 | −0.0112029 | ||||||||
\(236\) | −90.9058 | −0.0250740 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 837.928 | 0.226783 | 0.113391 | − | 0.993550i | \(-0.463829\pi\) | ||||
0.113391 | + | 0.993550i | \(0.463829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3454.99 | −0.923466 | −0.461733 | − | 0.887019i | \(-0.652772\pi\) | ||||
−0.461733 | + | 0.887019i | \(0.652772\pi\) | |||||||
\(242\) | 248.455 | 0.0659970 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 95.8406 | 0.0251458 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2115.75 | 0.545028 | ||||||||
\(248\) | 122.674 | 0.0314104 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.4072 | −0.00263284 | ||||||||
\(251\) | −5635.01 | −1.41705 | −0.708523 | − | 0.705688i | \(-0.750638\pi\) | ||||
−0.708523 | + | 0.705688i | \(0.750638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2355.16 | −0.585246 | ||||||||
\(254\) | 443.788 | 0.109629 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3245.52 | 0.792364 | ||||||||
\(257\) | 2271.16 | 0.551248 | 0.275624 | − | 0.961265i | \(-0.411115\pi\) | ||||
0.275624 | + | 0.961265i | \(0.411115\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.0960 | 0.00312376 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1041.75 | 0.245648 | ||||||||
\(263\) | −163.867 | −0.0384201 | −0.0192101 | − | 0.999815i | \(-0.506115\pi\) | ||||
−0.0192101 | + | 0.999815i | \(0.506115\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −64.6365 | −0.0149834 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5237.59 | −1.19379 | ||||||||
\(269\) | 5167.10 | 1.17116 | 0.585582 | − | 0.810613i | \(-0.300866\pi\) | ||||
0.585582 | + | 0.810613i | \(0.300866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1622.27 | −0.363638 | −0.181819 | − | 0.983332i | \(-0.558199\pi\) | ||||
−0.181819 | + | 0.983332i | \(0.558199\pi\) | |||||||
\(272\) | 7287.63 | 1.62455 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −103.994 | −0.0229289 | ||||||||
\(275\) | −5492.20 | −1.20433 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4612.37 | −1.00047 | −0.500235 | − | 0.865890i | \(-0.666753\pi\) | ||||
−0.500235 | + | 0.865890i | \(0.666753\pi\) | |||||||
\(278\) | 367.021 | 0.0791815 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2125.22 | 0.451174 | 0.225587 | − | 0.974223i | \(-0.427570\pi\) | ||||
0.225587 | + | 0.974223i | \(0.427570\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2571.54 | 0.540149 | 0.270075 | − | 0.962839i | \(-0.412952\pi\) | ||||
0.270075 | + | 0.962839i | \(0.412952\pi\) | |||||||
\(284\) | 6435.73 | 1.34468 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −302.950 | −0.0626356 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9883.19 | 2.01164 | ||||||||
\(290\) | −9.81154 | −0.00198674 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4032.42 | −0.808149 | ||||||||
\(293\) | 3324.96 | 0.662957 | 0.331478 | − | 0.943463i | \(-0.392453\pi\) | ||||
0.331478 | + | 0.943463i | \(0.392453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.16709 | 0.000230341 0 | ||||||||
\(296\) | 1258.05 | 0.247035 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −241.331 | −0.0469126 | ||||||||
\(299\) | 892.120 | 0.172551 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1164.67 | −0.221918 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7615.54 | −1.43678 | ||||||||
\(305\) | −1.23045 | −0.000231001 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 887.096 | 0.164916 | 0.0824580 | − | 0.996595i | \(-0.473723\pi\) | ||||
0.0824580 | + | 0.996595i | \(0.473723\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.778936 | −0.000142712 0 | ||||||||
\(311\) | −4510.82 | −0.822460 | −0.411230 | − | 0.911532i | \(-0.634901\pi\) | ||||
−0.411230 | + | 0.911532i | \(0.634901\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3715.78 | −0.671018 | −0.335509 | − | 0.942037i | \(-0.608908\pi\) | ||||
−0.335509 | + | 0.942037i | \(0.608908\pi\) | |||||||
\(314\) | −700.577 | −0.125910 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6307.79 | 1.12291 | ||||||||
\(317\) | −6954.52 | −1.23219 | −0.616096 | − | 0.787671i | \(-0.711287\pi\) | ||||
−0.616096 | + | 0.787671i | \(0.711287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10356.1 | −1.81765 | ||||||||
\(320\) | −44.9548 | −0.00785327 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15461.9 | −2.66355 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2080.41 | 0.355079 | ||||||||
\(326\) | −16.8681 | −0.00286576 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2096.15 | −0.352867 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9863.18 | −1.63785 | −0.818926 | − | 0.573899i | \(-0.805430\pi\) | ||||
−0.818926 | + | 0.573899i | \(0.805430\pi\) | |||||||
\(332\) | −3091.16 | −0.510992 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1201.41 | −0.196821 | ||||||||
\(335\) | 67.2427 | 0.0109668 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5945.06 | −0.960974 | −0.480487 | − | 0.877002i | \(-0.659540\pi\) | ||||
−0.480487 | + | 0.877002i | \(0.659540\pi\) | |||||||
\(338\) | −795.272 | −0.127979 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −95.7056 | −0.0152658 | ||||||||
\(341\) | −822.168 | −0.130566 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1433.08 | 0.224612 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 888.963 | 0.138124 | ||||||||
\(347\) | −1169.57 | −0.180939 | −0.0904697 | − | 0.995899i | \(-0.528837\pi\) | ||||
−0.0904697 | + | 0.995899i | \(0.528837\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9176.66 | 1.40749 | 0.703747 | − | 0.710451i | \(-0.251509\pi\) | ||||
0.703747 | + | 0.710451i | \(0.251509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3395.20 | 0.514104 | ||||||||
\(353\) | 10587.2 | 1.59632 | 0.798158 | − | 0.602448i | \(-0.205808\pi\) | ||||
0.798158 | + | 0.602448i | \(0.205808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −82.6250 | −0.0123529 | ||||||||
\(356\) | 5271.81 | 0.784846 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −498.522 | −0.0735970 | ||||||||
\(359\) | −8615.21 | −1.26656 | −0.633278 | − | 0.773924i | \(-0.718291\pi\) | ||||
−0.633278 | + | 0.773924i | \(0.718291\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9298.64 | 1.35568 | ||||||||
\(362\) | −1238.69 | −0.179846 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 51.7701 | 0.00742403 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8297.79 | −1.18022 | −0.590110 | − | 0.807323i | \(-0.700916\pi\) | ||||
−0.590110 | + | 0.807323i | \(0.700916\pi\) | |||||||
\(368\) | −3211.15 | −0.454871 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.98817 | −0.00112239 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5123.86 | −0.711269 | −0.355634 | − | 0.934625i | \(-0.615735\pi\) | ||||
−0.355634 | + | 0.934625i | \(0.615735\pi\) | |||||||
\(374\) | 2213.96 | 0.306100 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2632.72 | 0.361097 | ||||||||
\(377\) | 3922.83 | 0.535905 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1502.49 | −0.203635 | −0.101817 | − | 0.994803i | \(-0.532466\pi\) | ||||
−0.101817 | + | 0.994803i | \(0.532466\pi\) | |||||||
\(380\) | 100.012 | 0.0135013 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1162.87 | 0.155753 | ||||||||
\(383\) | −10872.9 | −1.45060 | −0.725301 | − | 0.688431i | \(-0.758300\pi\) | ||||
−0.725301 | + | 0.688431i | \(0.758300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1381.97 | 0.182229 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8541.71 | 1.11763 | ||||||||
\(389\) | −4618.99 | −0.602036 | −0.301018 | − | 0.953618i | \(-0.597326\pi\) | ||||
−0.301018 | + | 0.953618i | \(0.597326\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6519.64 | −0.843254 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1750.73 | 0.223860 | ||||||||
\(395\) | −80.9824 | −0.0103156 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9606.95 | −1.21451 | −0.607253 | − | 0.794508i | \(-0.707729\pi\) | ||||
−0.607253 | + | 0.794508i | \(0.707729\pi\) | |||||||
\(398\) | 1816.61 | 0.228791 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7488.36 | −0.936044 | ||||||||
\(401\) | 10501.0 | 1.30772 | 0.653862 | − | 0.756614i | \(-0.273148\pi\) | ||||
0.653862 | + | 0.756614i | \(0.273148\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 311.433 | 0.0384952 | ||||||||
\(404\) | −10731.1 | −1.32152 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8431.52 | −1.02687 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12066.9 | 1.45885 | 0.729427 | − | 0.684059i | \(-0.239787\pi\) | ||||
0.729427 | + | 0.684059i | \(0.239787\pi\) | |||||||
\(410\) | 13.3098 | 0.00160323 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11069.0 | 1.32362 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 39.6857 | 0.00469421 | ||||||||
\(416\) | −1286.08 | −0.151576 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2313.58 | −0.270720 | ||||||||
\(419\) | −6366.31 | −0.742278 | −0.371139 | − | 0.928577i | \(-0.621033\pi\) | ||||
−0.371139 | + | 0.928577i | \(0.621033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4731.84 | −0.547781 | −0.273890 | − | 0.961761i | \(-0.588311\pi\) | ||||
−0.273890 | + | 0.961761i | \(0.588311\pi\) | |||||||
\(422\) | 949.194 | 0.109493 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4216.50 | 0.482951 | ||||||||
\(425\) | −15203.7 | −1.73527 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2689.37 | −0.303728 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.09955 | −0.00102051 | ||||||||
\(431\) | −3752.78 | −0.419409 | −0.209704 | − | 0.977765i | \(-0.567250\pi\) | ||||
−0.209704 | + | 0.977765i | \(0.567250\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11709.2 | −1.29956 | −0.649780 | − | 0.760122i | \(-0.725139\pi\) | ||||
−0.649780 | + | 0.760122i | \(0.725139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2486.75 | 0.273151 | ||||||||
\(437\) | 6812.98 | 0.745788 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14924.7 | 1.62259 | 0.811296 | − | 0.584635i | \(-0.198762\pi\) | ||||
0.811296 | + | 0.584635i | \(0.198762\pi\) | |||||||
\(440\) | −28.9548 | −0.00313720 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −838.638 | −0.0902487 | ||||||||
\(443\) | 8517.66 | 0.913513 | 0.456756 | − | 0.889592i | \(-0.349011\pi\) | ||||
0.456756 | + | 0.889592i | \(0.349011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −67.6820 | −0.00720996 | ||||||||
\(446\) | −90.2860 | −0.00958557 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5965.73 | 0.627038 | 0.313519 | − | 0.949582i | \(-0.398492\pi\) | ||||
0.313519 | + | 0.949582i | \(0.398492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14048.5 | 1.46678 | ||||||||
\(452\) | 6250.01 | 0.650389 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −760.231 | −0.0785890 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13860.6 | −1.41875 | −0.709376 | − | 0.704830i | \(-0.751023\pi\) | ||||
−0.709376 | + | 0.704830i | \(0.751023\pi\) | |||||||
\(458\) | 1149.03 | 0.117229 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 42.1707 | 0.00427439 | ||||||||
\(461\) | −149.312 | −0.0150850 | −0.00754249 | − | 0.999972i | \(-0.502401\pi\) | ||||
−0.00754249 | + | 0.999972i | \(0.502401\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5403.95 | 0.542425 | 0.271213 | − | 0.962519i | \(-0.412575\pi\) | ||||
0.271213 | + | 0.962519i | \(0.412575\pi\) | |||||||
\(464\) | −14120.1 | −1.41273 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 409.538 | 0.0407113 | ||||||||
\(467\) | 3704.66 | 0.367090 | 0.183545 | − | 0.983011i | \(-0.441243\pi\) | ||||
0.183545 | + | 0.983011i | \(0.441243\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.7169 | −0.00164062 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −76.1341 | −0.00742448 | ||||||||
\(473\) | −9604.59 | −0.933657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15887.8 | 1.53470 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 347.081 | 0.0332115 | ||||||||
\(479\) | −10671.8 | −1.01796 | −0.508982 | − | 0.860777i | \(-0.669978\pi\) | ||||
−0.508982 | + | 0.860777i | \(0.669978\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3193.82 | 0.302756 | ||||||||
\(482\) | −1431.10 | −0.135238 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4695.67 | −0.440990 | ||||||||
\(485\) | −109.662 | −0.0102670 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5853.92 | 0.544695 | 0.272348 | − | 0.962199i | \(-0.412200\pi\) | ||||
0.272348 | + | 0.962199i | \(0.412200\pi\) | |||||||
\(488\) | 80.2670 | 0.00744573 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4065.31 | −0.373656 | −0.186828 | − | 0.982393i | \(-0.559821\pi\) | ||||
−0.186828 | + | 0.982393i | \(0.559821\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28668.2 | −2.61896 | ||||||||
\(494\) | 876.371 | 0.0798174 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1120.99 | −0.101480 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4811.19 | 0.431620 | 0.215810 | − | 0.976435i | \(-0.430761\pi\) | ||||
0.215810 | + | 0.976435i | \(0.430761\pi\) | |||||||
\(500\) | 196.691 | 0.0175926 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2334.10 | −0.207522 | ||||||||
\(503\) | 17001.2 | 1.50705 | 0.753526 | − | 0.657418i | \(-0.228351\pi\) | ||||
0.753526 | + | 0.657418i | \(0.228351\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 137.771 | 0.0121401 | ||||||||
\(506\) | −975.537 | −0.0857074 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8387.37 | −0.732538 | ||||||||
\(509\) | 13797.2 | 1.20148 | 0.600738 | − | 0.799446i | \(-0.294874\pi\) | ||||
0.600738 | + | 0.799446i | \(0.294874\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7771.61 | 0.670820 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 940.744 | 0.0807284 | ||||||||
\(515\) | −142.110 | −0.0121594 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17644.7 | −1.50099 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.9679 | 0.000924954 0 | ||||||||
\(521\) | 3936.61 | 0.331029 | 0.165515 | − | 0.986207i | \(-0.447072\pi\) | ||||
0.165515 | + | 0.986207i | \(0.447072\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17459.3 | −1.45973 | −0.729866 | − | 0.683590i | \(-0.760418\pi\) | ||||
−0.729866 | + | 0.683590i | \(0.760418\pi\) | |||||||
\(524\) | −19688.6 | −1.64142 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −67.8760 | −0.00562649 | ||||||||
\(527\) | −2275.96 | −0.188126 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9294.26 | −0.763891 | ||||||||
\(530\) | −26.7733 | −0.00219426 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5321.51 | −0.432458 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.5274 | 0.00279019 | ||||||||
\(536\) | −4386.51 | −0.353486 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2140.28 | 0.171513 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19101.3 | 1.51798 | 0.758992 | − | 0.651100i | \(-0.225692\pi\) | ||||
0.758992 | + | 0.651100i | \(0.225692\pi\) | |||||||
\(542\) | −671.967 | −0.0532536 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9398.73 | 0.740749 | ||||||||
\(545\) | −31.9261 | −0.00250929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15413.5 | 1.20481 | 0.602407 | − | 0.798189i | \(-0.294208\pi\) | ||||
0.602407 | + | 0.798189i | \(0.294208\pi\) | |||||||
\(548\) | 1965.44 | 0.153210 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2274.94 | −0.176371 | ||||||||
\(551\) | 29958.1 | 2.31626 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1910.51 | −0.146516 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6936.51 | −0.529089 | ||||||||
\(557\) | 20492.9 | 1.55891 | 0.779453 | − | 0.626460i | \(-0.215497\pi\) | ||||
0.779453 | + | 0.626460i | \(0.215497\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3638.17 | 0.275274 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 880.294 | 0.0660729 | ||||||||
\(563\) | −7142.49 | −0.534671 | −0.267336 | − | 0.963603i | \(-0.586143\pi\) | ||||
−0.267336 | + | 0.963603i | \(0.586143\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −80.2406 | −0.00597477 | ||||||||
\(566\) | 1065.17 | 0.0791030 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5389.96 | 0.398165 | ||||||||
\(569\) | −4097.91 | −0.301922 | −0.150961 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150961 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2838.48 | −0.208033 | −0.104016 | − | 0.994576i | \(-0.533169\pi\) | ||||
−0.104016 | + | 0.994576i | \(0.533169\pi\) | |||||||
\(572\) | 5725.60 | 0.418530 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6699.21 | 0.485872 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15464.5 | 1.11576 | 0.557881 | − | 0.829921i | \(-0.311615\pi\) | ||||
0.557881 | + | 0.829921i | \(0.311615\pi\) | |||||||
\(578\) | 4093.75 | 0.294598 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 185.433 | 0.0132753 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28259.3 | −2.00751 | ||||||||
\(584\) | −3377.17 | −0.239295 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1377.24 | 0.0970878 | ||||||||
\(587\) | 14003.6 | 0.984652 | 0.492326 | − | 0.870411i | \(-0.336147\pi\) | ||||
0.492326 | + | 0.870411i | \(0.336147\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2378.36 | 0.166382 | ||||||||
\(590\) | 0.483425 | 3.37327e−5 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11496.0 | −0.798112 | ||||||||
\(593\) | 6504.50 | 0.450435 | 0.225217 | − | 0.974309i | \(-0.427691\pi\) | ||||
0.225217 | + | 0.974309i | \(0.427691\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4561.04 | 0.313469 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 369.528 | 0.0252695 | ||||||||
\(599\) | 12616.1 | 0.860567 | 0.430284 | − | 0.902694i | \(-0.358414\pi\) | ||||
0.430284 | + | 0.902694i | \(0.358414\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8270.87 | −0.561358 | −0.280679 | − | 0.959802i | \(-0.590560\pi\) | ||||
−0.280679 | + | 0.959802i | \(0.590560\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22011.7 | 1.48285 | ||||||||
\(605\) | 60.2852 | 0.00405114 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3811.84 | −0.254889 | −0.127445 | − | 0.991846i | \(-0.540677\pi\) | ||||
−0.127445 | + | 0.991846i | \(0.540677\pi\) | |||||||
\(608\) | −9821.62 | −0.655130 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.509668 | −3.38293e−5 0 | ||||||||
\(611\) | 6683.72 | 0.442544 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11359.3 | 0.748445 | 0.374222 | − | 0.927339i | \(-0.377910\pi\) | ||||
0.374222 | + | 0.927339i | \(0.377910\pi\) | |||||||
\(614\) | 367.447 | 0.0241514 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18272.2 | 1.19224 | 0.596118 | − | 0.802896i | \(-0.296709\pi\) | ||||
0.596118 | + | 0.802896i | \(0.296709\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29600.2 | −1.92203 | −0.961013 | − | 0.276503i | \(-0.910824\pi\) | ||||
−0.961013 | + | 0.276503i | \(0.910824\pi\) | |||||||
\(620\) | 14.7215 | 0.000953596 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1868.44 | −0.120447 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15621.2 | 0.999758 | ||||||||
\(626\) | −1539.13 | −0.0982682 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13240.6 | 0.841331 | ||||||||
\(629\) | −23340.5 | −1.47956 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7185.41 | 0.453322 | 0.226661 | − | 0.973974i | \(-0.427219\pi\) | ||||
0.226661 | + | 0.973974i | \(0.427219\pi\) | |||||||
\(632\) | 5282.81 | 0.332498 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2880.66 | −0.180450 | ||||||||
\(635\) | 107.681 | 0.00672944 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4289.64 | −0.266189 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −80.7467 | −0.00498718 | ||||||||
\(641\) | 232.982 | 0.0143561 | 0.00717803 | − | 0.999974i | \(-0.497715\pi\) | ||||
0.00717803 | + | 0.999974i | \(0.497715\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1837.96 | 0.112725 | 0.0563624 | − | 0.998410i | \(-0.482050\pi\) | ||||
0.0563624 | + | 0.998410i | \(0.482050\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6404.54 | −0.390067 | ||||||||
\(647\) | −18594.7 | −1.12988 | −0.564941 | − | 0.825131i | \(-0.691101\pi\) | ||||
−0.564941 | + | 0.825131i | \(0.691101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 510.256 | 0.0308618 | ||||||||
\(650\) | 861.736 | 0.0520001 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 318.799 | 0.0191490 | ||||||||
\(653\) | 28864.7 | 1.72980 | 0.864902 | − | 0.501940i | \(-0.167380\pi\) | ||||
0.864902 | + | 0.501940i | \(0.167380\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 252.772 | 0.0150788 | ||||||||
\(656\) | 19154.5 | 1.14003 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29066.3 | 1.71815 | 0.859076 | − | 0.511847i | \(-0.171039\pi\) | ||||
0.859076 | + | 0.511847i | \(0.171039\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3979.51 | 0.234168 | 0.117084 | − | 0.993122i | \(-0.462645\pi\) | ||||
0.117084 | + | 0.993122i | \(0.462645\pi\) | |||||||
\(662\) | −4085.46 | −0.239858 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2588.86 | −0.151306 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12632.0 | 0.733305 | ||||||||
\(668\) | 22706.1 | 1.31516 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.8528 | 0.00160604 | ||||||||
\(671\) | −537.955 | −0.0309501 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −184.229 | −0.0105520 | −0.00527601 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527601 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(674\) | −2462.52 | −0.140731 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15030.2 | 0.855156 | ||||||||
\(677\) | −16683.5 | −0.947116 | −0.473558 | − | 0.880763i | \(-0.657031\pi\) | ||||
−0.473558 | + | 0.880763i | \(0.657031\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −80.1540 | −0.00452024 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −340.553 | −0.0191209 | ||||||||
\(683\) | −17808.2 | −0.997676 | −0.498838 | − | 0.866695i | \(-0.666240\pi\) | ||||
−0.498838 | + | 0.866695i | \(0.666240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.2332 | −0.00140746 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13095.4 | −0.725666 | ||||||||
\(689\) | 10704.5 | 0.591883 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20145.7 | 1.10908 | 0.554542 | − | 0.832156i | \(-0.312894\pi\) | ||||
0.554542 | + | 0.832156i | \(0.312894\pi\) | |||||||
\(692\) | −16801.0 | −0.922943 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −484.453 | −0.0264980 | ||||||||
\(695\) | 89.0542 | 0.00486046 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38889.7 | 2.11342 | ||||||||
\(698\) | 3801.10 | 0.206123 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2719.67 | 0.146534 | 0.0732672 | − | 0.997312i | \(-0.476657\pi\) | ||||
0.0732672 | + | 0.997312i | \(0.476657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24390.7 | 1.30855 | ||||||||
\(704\) | −19654.4 | −1.05220 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4385.36 | 0.233775 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −625.708 | −0.0331438 | −0.0165719 | − | 0.999863i | \(-0.505275\pi\) | ||||
−0.0165719 | + | 0.999863i | \(0.505275\pi\) | |||||||
\(710\) | −34.2244 | −0.00180904 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4415.17 | 0.232395 | ||||||||
\(713\) | 1002.85 | 0.0526749 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −73.5079 | −0.00384481 | ||||||||
\(716\) | 9421.82 | 0.491774 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3568.54 | −0.185483 | ||||||||
\(719\) | −9577.54 | −0.496776 | −0.248388 | − | 0.968661i | \(-0.579901\pi\) | ||||
−0.248388 | + | 0.968661i | \(0.579901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3851.62 | 0.198535 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23410.7 | 1.20173 | ||||||||
\(725\) | 29457.8 | 1.50901 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16741.2 | 0.854053 | 0.427027 | − | 0.904239i | \(-0.359561\pi\) | ||||
0.427027 | + | 0.904239i | \(0.359561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.4439 | 0.00108722 | ||||||||
\(731\) | −26587.8 | −1.34526 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6496.04 | 0.327335 | 0.163668 | − | 0.986516i | \(-0.447668\pi\) | ||||
0.163668 | + | 0.986516i | \(0.447668\pi\) | |||||||
\(734\) | −3437.06 | −0.172839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4141.36 | −0.207408 | ||||||||
\(737\) | 29398.7 | 1.46936 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 499.280 | 0.0248529 | 0.0124265 | − | 0.999923i | \(-0.496044\pi\) | ||||
0.0124265 | + | 0.999923i | \(0.496044\pi\) | |||||||
\(740\) | 150.972 | 0.00749980 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6367.30 | 0.314393 | 0.157196 | − | 0.987567i | \(-0.449754\pi\) | ||||
0.157196 | + | 0.987567i | \(0.449754\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −58.5568 | −0.00287967 | ||||||||
\(746\) | −2122.37 | −0.104163 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −41842.8 | −2.04535 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 496.098 | 0.0241050 | 0.0120525 | − | 0.999927i | \(-0.496163\pi\) | ||||
0.0120525 | + | 0.999927i | \(0.496163\pi\) | |||||||
\(752\) | −24057.7 | −1.16662 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1624.89 | 0.0784815 | ||||||||
\(755\) | −282.597 | −0.0136222 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13025.9 | 0.625408 | 0.312704 | − | 0.949851i | \(-0.398765\pi\) | ||||
0.312704 | + | 0.949851i | \(0.398765\pi\) | |||||||
\(758\) | −622.350 | −0.0298216 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 83.7604 | 0.00399778 | ||||||||
\(761\) | −25474.6 | −1.21347 | −0.606736 | − | 0.794904i | \(-0.707521\pi\) | ||||
−0.606736 | + | 0.794904i | \(0.707521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −21977.6 | −1.04074 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4503.72 | −0.212436 | ||||||||
\(767\) | −193.282 | −0.00909911 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29054.0 | 1.36244 | 0.681218 | − | 0.732080i | \(-0.261450\pi\) | ||||
0.681218 | + | 0.732080i | \(0.261450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26118.5 | −1.21765 | ||||||||
\(773\) | 1897.35 | 0.0882834 | 0.0441417 | − | 0.999025i | \(-0.485945\pi\) | ||||
0.0441417 | + | 0.999025i | \(0.485945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2338.65 | 0.108396 | ||||||||
\(776\) | 7153.72 | 0.330933 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1913.25 | −0.0881662 | ||||||||
\(779\) | −40639.6 | −1.86914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36123.9 | −1.65508 | ||||||||
\(782\) | −2700.52 | −0.123492 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −169.989 | −0.00772886 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42650.3 | −1.93179 | −0.965895 | − | 0.258936i | \(-0.916628\pi\) | ||||
−0.965895 | + | 0.258936i | \(0.916628\pi\) | |||||||
\(788\) | −33088.0 | −1.49583 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −33.5440 | −0.00151069 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 203.775 | 0.00912516 | ||||||||
\(794\) | −3979.33 | −0.177860 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34333.1 | −1.52877 | ||||||||
\(797\) | 36822.8 | 1.63655 | 0.818275 | − | 0.574828i | \(-0.194931\pi\) | ||||
0.818275 | + | 0.574828i | \(0.194931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48844.8 | −2.16271 | ||||||||
\(800\) | −9657.60 | −0.426810 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4349.68 | 0.191512 | ||||||||
\(803\) | 22634.1 | 0.994693 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 129.000 | 0.00563750 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8987.38 | −0.391306 | ||||||||
\(809\) | −5081.94 | −0.220855 | −0.110427 | − | 0.993884i | \(-0.535222\pi\) | ||||
−0.110427 | + | 0.993884i | \(0.535222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11873.4 | −0.514097 | −0.257048 | − | 0.966399i | \(-0.582750\pi\) | ||||
−0.257048 | + | 0.966399i | \(0.582750\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3492.45 | −0.150381 | ||||||||
\(815\) | −4.09289 | −0.000175911 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27784.1 | 1.18977 | ||||||||
\(818\) | 4998.29 | 0.213644 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −251.549 | −0.0107128 | ||||||||
\(821\) | −16969.4 | −0.721361 | −0.360681 | − | 0.932689i | \(-0.617456\pi\) | ||||
−0.360681 | + | 0.932689i | \(0.617456\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3995.94 | 0.169246 | 0.0846231 | − | 0.996413i | \(-0.473031\pi\) | ||||
0.0846231 | + | 0.996413i | \(0.473031\pi\) | |||||||
\(824\) | 9270.39 | 0.391929 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13589.7 | 0.571417 | 0.285708 | − | 0.958317i | \(-0.407771\pi\) | ||||
0.285708 | + | 0.958317i | \(0.407771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30646.0 | 1.28393 | 0.641966 | − | 0.766733i | \(-0.278119\pi\) | ||||
0.641966 | + | 0.766733i | \(0.278119\pi\) | |||||||
\(830\) | 16.4384 | 0.000687451 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7444.96 | 0.310226 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −291.511 | −0.0120816 | ||||||||
\(836\) | 43725.5 | 1.80894 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2637.01 | −0.108704 | ||||||||
\(839\) | −7497.57 | −0.308516 | −0.154258 | − | 0.988031i | \(-0.549299\pi\) | ||||
−0.154258 | + | 0.988031i | \(0.549299\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31156.6 | 1.27749 | ||||||||
\(842\) | −1959.99 | −0.0802207 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17939.3 | −0.731630 | ||||||||
\(845\) | −192.965 | −0.00785586 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −38530.2 | −1.56030 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6297.59 | −0.254124 | ||||||||
\(851\) | 10284.5 | 0.414275 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10347.6 | 0.415352 | 0.207676 | − | 0.978198i | \(-0.433410\pi\) | ||||
0.207676 | + | 0.978198i | \(0.433410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2252.36 | −0.0899348 | ||||||||
\(857\) | 1550.00 | 0.0617817 | 0.0308909 | − | 0.999523i | \(-0.490166\pi\) | ||||
0.0308909 | + | 0.999523i | \(0.490166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15187.5 | −0.603250 | −0.301625 | − | 0.953427i | \(-0.597529\pi\) | ||||
−0.301625 | + | 0.953427i | \(0.597529\pi\) | |||||||
\(860\) | 171.977 | 0.00681903 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1554.45 | −0.0614210 | ||||||||
\(863\) | −41550.2 | −1.63892 | −0.819459 | − | 0.573138i | \(-0.805726\pi\) | ||||
−0.819459 | + | 0.573138i | \(0.805726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 215.699 | 0.00847858 | ||||||||
\(866\) | −4850.12 | −0.190316 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35405.8 | −1.38212 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11136.1 | −0.433216 | ||||||||
\(872\) | 2082.67 | 0.0808808 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2822.03 | 0.109218 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27837.4 | 1.07184 | 0.535919 | − | 0.844269i | \(-0.319965\pi\) | ||||
0.535919 | + | 0.844269i | \(0.319965\pi\) | |||||||
\(878\) | 6182.02 | 0.237623 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 264.588 | 0.0101355 | ||||||||
\(881\) | −2587.85 | −0.0989635 | −0.0494817 | − | 0.998775i | \(-0.515757\pi\) | ||||
−0.0494817 | + | 0.998775i | \(0.515757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16382.0 | −0.624346 | −0.312173 | − | 0.950025i | \(-0.601057\pi\) | ||||
−0.312173 | + | 0.950025i | \(0.601057\pi\) | |||||||
\(884\) | 15849.8 | 0.603040 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3528.13 | 0.133781 | ||||||||
\(887\) | −22980.2 | −0.869896 | −0.434948 | − | 0.900456i | \(-0.643233\pi\) | ||||
−0.434948 | + | 0.900456i | \(0.643233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −28.0348 | −0.00105587 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1706.36 | 0.0640506 | ||||||||
\(893\) | 51042.5 | 1.91274 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −120.962 | −0.00451766 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2471.09 | 0.0918276 | ||||||||
\(899\) | 4409.76 | 0.163597 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −78228.5 | −2.89253 | ||||||||
\(902\) | 5819.10 | 0.214806 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5234.42 | 0.192582 | ||||||||
\(905\) | −300.557 | −0.0110396 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22715.4 | −0.831590 | −0.415795 | − | 0.909458i | \(-0.636497\pi\) | ||||
−0.415795 | + | 0.909458i | \(0.636497\pi\) | |||||||
\(908\) | 14368.0 | 0.525130 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34922.3 | −1.27006 | −0.635031 | − | 0.772487i | \(-0.719013\pi\) | ||||
−0.635031 | + | 0.772487i | \(0.719013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17350.7 | 0.628943 | ||||||||
\(914\) | −5741.24 | −0.207772 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21716.1 | −0.783320 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11702.6 | 0.420059 | 0.210030 | − | 0.977695i | \(-0.432644\pi\) | ||||
0.210030 | + | 0.977695i | \(0.432644\pi\) | |||||||
\(920\) | 35.3182 | 0.00126566 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −61.8473 | −0.00220914 | ||||||||
\(923\) | 13683.5 | 0.487973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23983.3 | 0.852505 | ||||||||
\(926\) | 2238.39 | 0.0794364 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18210.4 | −0.644165 | ||||||||
\(929\) | −53096.5 | −1.87518 | −0.937588 | − | 0.347747i | \(-0.886947\pi\) | ||||
−0.937588 | + | 0.347747i | \(0.886947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7740.06 | −0.272032 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1534.52 | 0.0537591 | ||||||||
\(935\) | 537.198 | 0.0187896 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39020.6 | 1.36046 | 0.680229 | − | 0.733000i | \(-0.261880\pi\) | ||||
0.680229 | + | 0.733000i | \(0.261880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 315.941 | 0.0109626 | ||||||||
\(941\) | 30743.8 | 1.06506 | 0.532528 | − | 0.846412i | \(-0.321242\pi\) | ||||
0.532528 | + | 0.846412i | \(0.321242\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17136.0 | −0.591754 | ||||||||
\(944\) | 695.710 | 0.0239867 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3978.35 | −0.136731 | ||||||||
\(947\) | −16300.3 | −0.559332 | −0.279666 | − | 0.960097i | \(-0.590224\pi\) | ||||
−0.279666 | + | 0.960097i | \(0.590224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8573.66 | −0.293269 | ||||||||
\(950\) | 6580.94 | 0.224752 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11512.7 | 0.391325 | 0.195663 | − | 0.980671i | \(-0.437314\pi\) | ||||
0.195663 | + | 0.980671i | \(0.437314\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 282.159 | 0.00956068 | ||||||||
\(956\) | −6559.65 | −0.221919 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4420.39 | −0.149078 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29440.9 | −0.988248 | ||||||||
\(962\) | 1322.92 | 0.0443375 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27047.1 | 0.903661 | ||||||||
\(965\) | 335.322 | 0.0111859 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18178.4 | −0.604528 | −0.302264 | − | 0.953224i | \(-0.597742\pi\) | ||||
−0.302264 | + | 0.953224i | \(0.597742\pi\) | |||||||
\(968\) | −3932.65 | −0.130579 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −45.4237 | −0.00150357 | ||||||||
\(971\) | −28276.7 | −0.934543 | −0.467271 | − | 0.884114i | \(-0.654763\pi\) | ||||
−0.467271 | + | 0.884114i | \(0.654763\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2424.77 | 0.0797688 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −733.477 | −0.0240554 | ||||||||
\(977\) | 13947.1 | 0.456710 | 0.228355 | − | 0.973578i | \(-0.426665\pi\) | ||||
0.228355 | + | 0.973578i | \(0.426665\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29590.8 | −0.966011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1683.91 | −0.0547206 | ||||||||
\(983\) | 26576.8 | 0.862327 | 0.431164 | − | 0.902274i | \(-0.358103\pi\) | ||||
0.431164 | + | 0.902274i | \(0.358103\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 424.799 | 0.0137414 | ||||||||
\(986\) | −11874.7 | −0.383539 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16563.0 | −0.533339 | ||||||||
\(989\) | 11715.4 | 0.376671 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16249.9 | 0.520884 | 0.260442 | − | 0.965490i | \(-0.416132\pi\) | ||||
0.260442 | + | 0.965490i | \(0.416132\pi\) | |||||||
\(992\) | −1445.72 | −0.0462718 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 440.784 | 0.0140440 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18814.1 | 0.597642 | 0.298821 | − | 0.954309i | \(-0.403407\pi\) | ||||
0.298821 | + | 0.954309i | \(0.403407\pi\) | |||||||
\(998\) | 1992.86 | 0.0632092 | ||||||||
\(999\) | 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 | 441.4.a.o.1.2 | 2 | ||
3.2 | odd | 2 | 147.4.a.k.1.1 | yes | 2 | ||
7.2 | even | 3 | 441.4.e.u.361.1 | 4 | |||
7.3 | odd | 6 | 441.4.e.v.226.1 | 4 | |||
7.4 | even | 3 | 441.4.e.u.226.1 | 4 | |||
7.5 | odd | 6 | 441.4.e.v.361.1 | 4 | |||
7.6 | odd | 2 | 441.4.a.n.1.2 | 2 | |||
12.11 | even | 2 | 2352.4.a.bl.1.2 | 2 | |||
21.2 | odd | 6 | 147.4.e.j.67.2 | 4 | |||
21.5 | even | 6 | 147.4.e.k.67.2 | 4 | |||
21.11 | odd | 6 | 147.4.e.j.79.2 | 4 | |||
21.17 | even | 6 | 147.4.e.k.79.2 | 4 | |||
21.20 | even | 2 | 147.4.a.j.1.1 | ✓ | 2 | ||
84.83 | odd | 2 | 2352.4.a.cf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.a.j.1.1 | ✓ | 2 | 21.20 | even | 2 | ||
147.4.a.k.1.1 | yes | 2 | 3.2 | odd | 2 | ||
147.4.e.j.67.2 | 4 | 21.2 | odd | 6 | |||
147.4.e.j.79.2 | 4 | 21.11 | odd | 6 | |||
147.4.e.k.67.2 | 4 | 21.5 | even | 6 | |||
147.4.e.k.79.2 | 4 | 21.17 | even | 6 | |||
441.4.a.n.1.2 | 2 | 7.6 | odd | 2 | |||
441.4.a.o.1.2 | 2 | 1.1 | even | 1 | trivial | ||
441.4.e.u.226.1 | 4 | 7.4 | even | 3 | |||
441.4.e.u.361.1 | 4 | 7.2 | even | 3 | |||
441.4.e.v.226.1 | 4 | 7.3 | odd | 6 | |||
441.4.e.v.361.1 | 4 | 7.5 | odd | 6 | |||
2352.4.a.bl.1.2 | 2 | 12.11 | even | 2 | |||
2352.4.a.cf.1.1 | 2 | 84.83 | odd | 2 |