Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(1101,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.7712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 89x^{12} + 3026x^{10} + 49092x^{8} + 390297x^{6} + 1440495x^{4} + 1994425x^{2} + 151875 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1101.4 | ||
Root | \(-2.93221i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1101 |
Dual form | 1900.3.e.g.1101.11 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.93221i | − | 0.977402i | −0.872451 | − | 0.488701i | \(-0.837471\pi\) | ||
0.872451 | − | 0.488701i | \(-0.162529\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.62705 | −0.803864 | −0.401932 | − | 0.915669i | \(-0.631661\pi\) | ||||
−0.401932 | + | 0.915669i | \(0.631661\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.402160 | 0.0446844 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.4504 | −1.58640 | −0.793198 | − | 0.608963i | \(-0.791586\pi\) | ||||
−0.793198 | + | 0.608963i | \(0.791586\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 7.35569i | − | 0.565823i | −0.959146 | − | 0.282911i | \(-0.908700\pi\) | ||
0.959146 | − | 0.282911i | \(-0.0913002\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.3144 | 1.48908 | 0.744541 | − | 0.667577i | \(-0.232668\pi\) | ||||
0.744541 | + | 0.667577i | \(0.232668\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.59985 | − | 18.8213i | −0.136834 | − | 0.990594i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.4997i | 0.785699i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19.3107 | −0.839598 | −0.419799 | − | 0.907617i | \(-0.637899\pi\) | ||||
−0.419799 | + | 0.907617i | \(0.637899\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.5691i | − | 1.02108i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.89731i | − | 0.168873i | −0.996429 | − | 0.0844363i | \(-0.973091\pi\) | ||
0.996429 | − | 0.0844363i | \(-0.0269089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 45.2147i | − | 1.45854i | −0.684226 | − | 0.729270i | \(-0.739860\pi\) | ||
0.684226 | − | 0.729270i | \(-0.260140\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 51.1681i | 1.55055i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.2986i | 0.683746i | 0.939746 | + | 0.341873i | \(0.111061\pi\) | ||||
−0.939746 | + | 0.341873i | \(0.888939\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21.5684 | −0.553036 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.2721i | 0.396881i | 0.980113 | + | 0.198440i | \(0.0635876\pi\) | ||||
−0.980113 | + | 0.198440i | \(0.936412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −28.0559 | −0.652462 | −0.326231 | − | 0.945290i | \(-0.605779\pi\) | ||||
−0.326231 | + | 0.945290i | \(0.605779\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 38.9299 | 0.828296 | 0.414148 | − | 0.910209i | \(-0.364080\pi\) | ||||
0.414148 | + | 0.910209i | \(0.364080\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.3363 | −0.353802 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 74.2270i | − | 1.45543i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 81.9687i | 1.54658i | 0.634053 | + | 0.773289i | \(0.281390\pi\) | ||||
−0.634053 | + | 0.773289i | \(0.718610\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −55.1879 | + | 7.62329i | −0.968209 | + | 0.133742i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 61.0035i | 1.03396i | 0.855998 | + | 0.516979i | \(0.172944\pi\) | ||||
−0.855998 | + | 0.516979i | \(0.827056\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −94.1024 | −1.54266 | −0.771331 | − | 0.636434i | \(-0.780409\pi\) | ||||
−0.771331 | + | 0.636434i | \(0.780409\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.26297 | −0.0359202 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 109.942i | 1.64092i | 0.571705 | + | 0.820459i | \(0.306282\pi\) | ||||
−0.571705 | + | 0.820459i | \(0.693718\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 56.6231i | 0.820625i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 57.6965i | − | 0.812627i | −0.913734 | − | 0.406313i | \(-0.866814\pi\) | ||
0.913734 | − | 0.406313i | \(-0.133186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −36.4469 | −0.499272 | −0.249636 | − | 0.968340i | \(-0.580311\pi\) | ||||
−0.249636 | + | 0.968340i | \(0.580311\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 98.1940 | 1.27525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 112.540i | 1.42455i | 0.701900 | + | 0.712276i | \(0.252335\pi\) | ||||
−0.701900 | + | 0.712276i | \(0.747665\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −77.2188 | −0.953319 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 42.1499 | 0.507830 | 0.253915 | − | 0.967227i | \(-0.418282\pi\) | ||||
0.253915 | + | 0.967227i | \(0.418282\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.3599 | −0.165057 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 101.024i | 1.13510i | 0.823339 | + | 0.567549i | \(0.192108\pi\) | ||||
−0.823339 | + | 0.567549i | \(0.807892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 41.3909i | 0.454845i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −132.579 | −1.42558 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 148.954i | 1.53560i | 0.640687 | + | 0.767802i | \(0.278650\pi\) | ||||
−0.640687 | + | 0.767802i | \(0.721350\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.01784 | −0.0708872 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 35.3143 | 0.349647 | 0.174823 | − | 0.984600i | \(-0.444065\pi\) | ||||
0.174823 | + | 0.984600i | \(0.444065\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 63.2704i | 0.614276i | 0.951665 | + | 0.307138i | \(0.0993712\pi\) | ||||
−0.951665 | + | 0.307138i | \(0.900629\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 197.887i | − | 1.84942i | −0.380677 | − | 0.924708i | \(-0.624309\pi\) | ||
0.380677 | − | 0.924708i | \(-0.375691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 179.503i | − | 1.64682i | −0.567450 | − | 0.823408i | \(-0.692070\pi\) | ||
0.567450 | − | 0.823408i | \(-0.307930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 74.1807 | 0.668295 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.3688i | 0.180255i | 0.995930 | + | 0.0901276i | \(0.0287275\pi\) | ||||
−0.995930 | + | 0.0901276i | \(0.971273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.95817i | − | 0.0252835i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −142.445 | −1.19702 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 183.515 | 1.51665 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 47.7132 | 0.387912 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 93.0448i | 0.732636i | 0.930490 | + | 0.366318i | \(0.119382\pi\) | ||||
−0.930490 | + | 0.366318i | \(0.880618\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 82.2656i | 0.637718i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −207.262 | −1.58215 | −0.791077 | − | 0.611717i | \(-0.790479\pi\) | ||||
−0.791077 | + | 0.611717i | \(0.790479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.6295 | + | 105.908i | 0.109996 | + | 0.796303i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −143.376 | −1.04654 | −0.523268 | − | 0.852168i | \(-0.675287\pi\) | ||||
−0.523268 | + | 0.852168i | \(0.675287\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −158.125 | −1.13759 | −0.568794 | − | 0.822480i | \(-0.692590\pi\) | ||||
−0.568794 | + | 0.822480i | \(0.692590\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 114.151i | − | 0.809579i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 128.360i | 0.897619i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 50.8337i | 0.345807i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 211.739 | 1.42107 | 0.710534 | − | 0.703663i | \(-0.248453\pi\) | ||||
0.710534 | + | 0.703663i | \(0.248453\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 242.067i | − | 1.60310i | −0.597930 | − | 0.801548i | \(-0.704010\pi\) | ||
0.597930 | − | 0.801548i | \(-0.295990\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.1804 | 0.0665388 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 137.436 | 0.875386 | 0.437693 | − | 0.899125i | \(-0.355796\pi\) | ||||
0.437693 | + | 0.899125i | \(0.355796\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 240.349 | 1.51163 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 108.663 | 0.674923 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 173.770 | 1.06607 | 0.533037 | − | 0.846092i | \(-0.321051\pi\) | ||||
0.533037 | + | 0.846092i | \(0.321051\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.88276i | 0.0352261i | 0.999845 | + | 0.0176131i | \(0.00560670\pi\) | ||||
−0.999845 | + | 0.0176131i | \(0.994393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 114.894 | 0.679845 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.04555 | − | 7.56917i | −0.00611435 | − | 0.0442641i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 254.130i | 1.46896i | 0.678630 | + | 0.734480i | \(0.262574\pi\) | ||||
−0.678630 | + | 0.734480i | \(0.737426\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 178.875 | 1.01059 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 144.808i | 0.808984i | 0.914541 | + | 0.404492i | \(0.132552\pi\) | ||||
−0.914541 | + | 0.404492i | \(0.867448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 98.4770i | − | 0.544072i | −0.962287 | − | 0.272036i | \(-0.912303\pi\) | ||
0.962287 | − | 0.272036i | \(-0.0876969\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 275.928i | 1.50780i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −441.745 | −2.36227 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 155.133i | 0.820807i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 326.880 | 1.71141 | 0.855706 | − | 0.517462i | \(-0.173123\pi\) | ||||
0.855706 | + | 0.517462i | \(0.173123\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 140.497i | 0.727965i | 0.931406 | + | 0.363982i | \(0.118583\pi\) | ||||
−0.931406 | + | 0.363982i | \(0.881417\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −344.527 | −1.74887 | −0.874433 | − | 0.485146i | \(-0.838767\pi\) | ||||
−0.874433 | + | 0.485146i | \(0.838767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −202.257 | −1.01637 | −0.508184 | − | 0.861249i | \(-0.669683\pi\) | ||||
−0.508184 | + | 0.861249i | \(0.669683\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 322.371 | 1.60384 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 27.5574i | 0.135751i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.76601 | −0.0375170 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 45.3683 | + | 328.438i | 0.217073 | + | 1.57147i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 126.032i | 0.597308i | 0.954361 | + | 0.298654i | \(0.0965377\pi\) | ||||
−0.954361 | + | 0.298654i | \(0.903462\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −169.178 | −0.794263 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 254.426i | 1.17247i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 106.870i | 0.487990i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 186.205i | − | 0.842556i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 359.998i | 1.61434i | 0.590320 | + | 0.807169i | \(0.299002\pi\) | ||||
−0.590320 | + | 0.807169i | \(0.700998\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 82.6104i | 0.363922i | 0.983306 | + | 0.181961i | \(0.0582445\pi\) | ||||
−0.983306 | + | 0.181961i | \(0.941755\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −42.1892 | −0.184232 | −0.0921161 | − | 0.995748i | \(-0.529363\pi\) | ||||
−0.0921161 | + | 0.995748i | \(0.529363\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 287.925i | − | 1.24643i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −125.229 | −0.537463 | −0.268731 | − | 0.963215i | \(-0.586604\pi\) | ||||
−0.268731 | + | 0.963215i | \(0.586604\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 329.989 | 1.39236 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −177.271 | −0.741720 | −0.370860 | − | 0.928689i | \(-0.620937\pi\) | ||||
−0.370860 | + | 0.928689i | \(0.620937\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 86.2189i | 0.357755i | 0.983871 | + | 0.178877i | \(0.0572465\pi\) | ||||
−0.983871 | + | 0.178877i | \(0.942753\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 21.7001i | − | 0.0893009i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −138.444 | + | 19.1237i | −0.560500 | + | 0.0774238i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 123.592i | − | 0.496354i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −300.306 | −1.19644 | −0.598219 | − | 0.801332i | \(-0.704125\pi\) | ||||
−0.598219 | + | 0.801332i | \(0.704125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 336.980 | 1.33194 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 232.749i | − | 0.905639i | −0.891602 | − | 0.452820i | \(-0.850418\pi\) | ||
0.891602 | − | 0.452820i | \(-0.149582\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 142.356i | − | 0.549639i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1.96950i | − | 0.00754598i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 280.549 | 1.06673 | 0.533363 | − | 0.845886i | \(-0.320928\pi\) | ||||
0.533363 | + | 0.845886i | \(0.320928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 296.223 | 1.10945 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 112.923i | − | 0.419787i | −0.977724 | − | 0.209893i | \(-0.932688\pi\) | ||
0.977724 | − | 0.209893i | \(-0.0673117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −95.7071 | −0.353163 | −0.176581 | − | 0.984286i | \(-0.556504\pi\) | ||||
−0.176581 | + | 0.984286i | \(0.556504\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 121.367 | 0.444566 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −53.9033 | −0.194597 | −0.0972983 | − | 0.995255i | \(-0.531020\pi\) | ||||
−0.0972983 | + | 0.995255i | \(0.531020\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 18.1836i | − | 0.0651740i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 68.4137i | − | 0.243465i | −0.992563 | − | 0.121732i | \(-0.961155\pi\) | ||
0.992563 | − | 0.121732i | \(-0.0388450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −378.615 | −1.33786 | −0.668932 | − | 0.743324i | \(-0.733248\pi\) | ||||
−0.668932 | + | 0.743324i | \(0.733248\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 91.5640i | − | 0.319038i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 351.818 | 1.21736 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 436.763 | 1.50090 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 20.3415i | − | 0.0694249i | −0.999397 | − | 0.0347125i | \(-0.988948\pi\) | ||
0.999397 | − | 0.0347125i | \(-0.0110515\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 481.090i | 1.61983i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 142.044i | 0.475063i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 157.872 | 0.524491 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 103.549i | − | 0.341746i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 315.163i | − | 1.02659i | −0.858212 | − | 0.513296i | \(-0.828424\pi\) | ||
0.858212 | − | 0.513296i | \(-0.171576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 185.522 | 0.600394 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 188.579 | 0.606363 | 0.303182 | − | 0.952933i | \(-0.401951\pi\) | ||||
0.303182 | + | 0.952933i | \(0.401951\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −154.013 | −0.492055 | −0.246028 | − | 0.969263i | \(-0.579125\pi\) | ||||
−0.246028 | + | 0.969263i | \(0.579125\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.01072i | 0.0126521i | 0.999980 | + | 0.00632606i | \(0.00201366\pi\) | ||||
−0.999980 | + | 0.00632606i | \(0.997986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 85.4598i | 0.267899i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −580.247 | −1.80762 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −65.8135 | − | 476.449i | −0.203757 | − | 1.47508i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −526.340 | −1.60960 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −219.061 | −0.665838 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 97.1158i | 0.293401i | 0.989181 | + | 0.146701i | \(0.0468654\pi\) | ||||
−0.989181 | + | 0.146701i | \(0.953135\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.1741i | 0.0305528i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 193.889i | − | 0.575337i | −0.957730 | − | 0.287669i | \(-0.907120\pi\) | ||
0.957730 | − | 0.287669i | \(-0.0928801\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 59.7257 | 0.176182 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 789.014i | 2.31382i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 373.278 | 1.08827 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 238.983 | 0.688712 | 0.344356 | − | 0.938839i | \(-0.388097\pi\) | ||||
0.344356 | + | 0.938839i | \(0.388097\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −46.7033 | −0.133820 | −0.0669102 | − | 0.997759i | \(-0.521314\pi\) | ||||
−0.0669102 | + | 0.997759i | \(0.521314\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −202.790 | −0.577749 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −323.922 | −0.917627 | −0.458813 | − | 0.888533i | \(-0.651725\pi\) | ||||
−0.458813 | + | 0.888533i | \(0.651725\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 417.679i | 1.16997i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −290.600 | −0.809472 | −0.404736 | − | 0.914434i | \(-0.632637\pi\) | ||||
−0.404736 | + | 0.914434i | \(0.632637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −347.482 | + | 97.8649i | −0.962553 | + | 0.271094i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 538.104i | − | 1.48238i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 218.143 | 0.594396 | 0.297198 | − | 0.954816i | \(-0.403948\pi\) | ||||
0.297198 | + | 0.954816i | \(0.403948\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.54399i | 0.0177344i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 461.242i | − | 1.24324i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 244.913i | − | 0.656603i | −0.944573 | − | 0.328302i | \(-0.893524\pi\) | ||
0.944573 | − | 0.328302i | \(-0.106476\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36.0231 | −0.0955519 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 550.720i | 1.45309i | 0.687120 | + | 0.726543i | \(0.258874\pi\) | ||||
−0.687120 | + | 0.726543i | \(0.741126\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 272.827 | 0.716080 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 349.640i | 0.912897i | 0.889750 | + | 0.456449i | \(0.150879\pi\) | ||||
−0.889750 | + | 0.456449i | \(0.849121\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.2829 | −0.0291549 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −348.489 | −0.895858 | −0.447929 | − | 0.894069i | \(-0.647838\pi\) | ||||
−0.447929 | + | 0.894069i | \(0.647838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −488.840 | −1.25023 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 607.736i | 1.54640i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.4266 | −0.0640468 | −0.0320234 | − | 0.999487i | \(-0.510195\pi\) | ||||
−0.0320234 | + | 0.999487i | \(0.510195\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 310.545 | − | 42.8966i | 0.778309 | − | 0.107510i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 638.917i | − | 1.59331i | −0.604435 | − | 0.796654i | \(-0.706601\pi\) | ||
0.604435 | − | 0.796654i | \(-0.293399\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −332.586 | −0.825275 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 441.469i | − | 1.08469i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 522.383i | − | 1.27722i | −0.769531 | − | 0.638610i | \(-0.779510\pi\) | ||
0.769531 | − | 0.638610i | \(-0.220490\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 420.407i | 1.02289i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 343.270i | − | 0.831162i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 463.655i | 1.11188i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −621.068 | −1.48226 | −0.741132 | − | 0.671360i | \(-0.765711\pi\) | ||||
−0.741132 | + | 0.671360i | \(0.765711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 303.897i | 0.721845i | 0.932596 | + | 0.360922i | \(0.117538\pi\) | ||||
−0.932596 | + | 0.360922i | \(0.882462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.6561 | 0.0370120 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 529.519 | 1.24009 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 376.377 | 0.877335 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 86.3824i | 0.200423i | 0.994966 | + | 0.100212i | \(0.0319520\pi\) | ||||
−0.994966 | + | 0.100212i | \(0.968048\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 51.3805i | 0.118662i | 0.998238 | + | 0.0593308i | \(0.0188967\pi\) | ||||
−0.998238 | + | 0.0593308i | \(0.981103\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 50.2050 | + | 363.453i | 0.114886 | + | 0.831701i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 736.743i | 1.67823i | 0.543954 | + | 0.839115i | \(0.316926\pi\) | ||||
−0.543954 | + | 0.839115i | \(0.683074\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.97197 | −0.0158095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 50.2064 | 0.113333 | 0.0566664 | − | 0.998393i | \(-0.481953\pi\) | ||||
0.0566664 | + | 0.998393i | \(0.481953\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 620.863i | − | 1.38896i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 211.982i | − | 0.472121i | −0.971738 | − | 0.236060i | \(-0.924144\pi\) | ||
0.971738 | − | 0.236060i | \(-0.0758563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 283.954i | − | 0.629610i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −709.792 | −1.56687 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 438.611 | 0.959761 | 0.479880 | − | 0.877334i | \(-0.340680\pi\) | ||||
0.479880 | + | 0.877334i | \(0.340680\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 697.895i | − | 1.52047i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −206.072 | −0.447011 | −0.223506 | − | 0.974703i | \(-0.571750\pi\) | ||||
−0.223506 | + | 0.974703i | \(0.571750\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 164.050 | 0.354319 | 0.177159 | − | 0.984182i | \(-0.443309\pi\) | ||||
0.177159 | + | 0.984182i | \(0.443309\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 296.903 | 0.635766 | 0.317883 | − | 0.948130i | \(-0.397028\pi\) | ||||
0.317883 | + | 0.948130i | \(0.397028\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 618.646i | − | 1.31908i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 402.990i | − | 0.855604i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 489.585 | 1.03506 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.9645i | 0.0691080i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 319.593 | 0.667208 | 0.333604 | − | 0.942713i | \(-0.391735\pi\) | ||||
0.333604 | + | 0.942713i | \(0.391735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 186.089 | 0.386879 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 318.621i | − | 0.659671i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 257.490i | − | 0.528727i | −0.964423 | − | 0.264364i | \(-0.914838\pi\) | ||
0.964423 | − | 0.264364i | \(-0.0851619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 509.530i | − | 1.04198i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −897.982 | −1.82888 | −0.914442 | − | 0.404716i | \(-0.867370\pi\) | ||||
−0.914442 | + | 0.404716i | \(0.867370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 123.972i | − | 0.251465i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 324.661i | 0.653241i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −786.631 | −1.57641 | −0.788207 | − | 0.615410i | \(-0.788990\pi\) | ||||
−0.788207 | + | 0.615410i | \(0.788990\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.2495 | 0.0344301 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −48.2524 | −0.0959292 | −0.0479646 | − | 0.998849i | \(-0.515273\pi\) | ||||
−0.0479646 | + | 0.998849i | \(0.515273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 336.892i | − | 0.664482i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 974.111i | − | 1.91377i | −0.290460 | − | 0.956887i | \(-0.593808\pi\) | ||
0.290460 | − | 0.956887i | \(-0.406192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 205.088 | 0.401347 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −518.886 | + | 71.6754i | −1.01147 | + | 0.139718i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −679.341 | −1.31401 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 745.162 | 1.43576 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 442.872i | 0.850043i | 0.905183 | + | 0.425021i | \(0.139733\pi\) | ||||
−0.905183 | + | 0.425021i | \(0.860267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 104.045i | 0.198940i | 0.995041 | + | 0.0994699i | \(0.0317147\pi\) | ||||
−0.995041 | + | 0.0994699i | \(0.968285\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1144.58i | − | 2.17189i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −156.095 | −0.295076 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.5332i | 0.0462018i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 119.693 | 0.224564 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 424.608 | 0.790703 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 302.525 | 0.561271 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −463.659 | −0.857042 | −0.428521 | − | 0.903532i | \(-0.640965\pi\) | ||||
−0.428521 | + | 0.903532i | \(0.640965\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −288.755 | −0.531777 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 456.359i | − | 0.834294i | −0.908839 | − | 0.417147i | \(-0.863030\pi\) | ||
0.908839 | − | 0.417147i | \(-0.136970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −37.8442 | −0.0689330 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −92.1736 | + | 12.7322i | −0.167284 | + | 0.0231075i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 633.266i | − | 1.14515i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 188.836 | 0.339024 | 0.169512 | − | 0.985528i | \(-0.445781\pi\) | ||||
0.169512 | + | 0.985528i | \(0.445781\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 206.370i | 0.369178i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1295.29i | 2.30889i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 561.830i | − | 0.997923i | −0.866624 | − | 0.498961i | \(-0.833715\pi\) | ||
0.866624 | − | 0.498961i | \(-0.166285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 434.514 | 0.766339 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 34.7296i | − | 0.0610362i | −0.999534 | − | 0.0305181i | \(-0.990284\pi\) | ||
0.999534 | − | 0.0305181i | \(-0.00971573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −215.723 | −0.377798 | −0.188899 | − | 0.981997i | \(-0.560492\pi\) | ||||
−0.188899 | + | 0.981997i | \(0.560492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 958.479i | − | 1.67274i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −698.445 | −1.21048 | −0.605239 | − | 0.796044i | \(-0.706922\pi\) | ||||
−0.605239 | + | 0.796044i | \(0.706922\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 411.967 | 0.711515 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −237.180 | −0.408226 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1430.38i | − | 2.45349i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −312.489 | −0.532349 | −0.266175 | − | 0.963925i | \(-0.585760\pi\) | ||||
−0.266175 | + | 0.963925i | \(0.585760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −851.000 | + | 117.551i | −1.44482 | + | 0.199578i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1010.22i | 1.70935i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1086.81 | 1.83273 | 0.916367 | − | 0.400339i | \(-0.131108\pi\) | ||||
0.916367 | + | 0.400339i | \(0.131108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 593.060i | 0.993400i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 791.665i | − | 1.32164i | −0.750543 | − | 0.660822i | \(-0.770208\pi\) | ||
0.750543 | − | 0.660822i | \(-0.229792\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 113.205i | 0.188362i | 0.995555 | + | 0.0941808i | \(0.0300232\pi\) | ||||
−0.995555 | + | 0.0941808i | \(0.969977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 44.2141i | 0.0733235i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 193.212i | − | 0.318306i | −0.987254 | − | 0.159153i | \(-0.949124\pi\) | ||
0.987254 | − | 0.159153i | \(-0.0508764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 80.8040 | 0.132683 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 286.357i | − | 0.468669i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 133.846 | 0.218346 | 0.109173 | − | 0.994023i | \(-0.465180\pi\) | ||||
0.109173 | + | 0.994023i | \(0.465180\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −602.743 | −0.976893 | −0.488447 | − | 0.872594i | \(-0.662436\pi\) | ||||
−0.488447 | + | 0.872594i | \(0.662436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 136.718 | 0.220869 | 0.110434 | − | 0.993883i | \(-0.464776\pi\) | ||||
0.110434 | + | 0.993883i | \(0.464776\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 532.380i | 0.857294i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 568.466i | − | 0.912465i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 963.049 | − | 133.029i | 1.53596 | − | 0.212168i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 640.418i | 1.01815i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1197.46 | 1.89772 | 0.948862 | − | 0.315691i | \(-0.102236\pi\) | ||||
0.948862 | + | 0.315691i | \(0.102236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 369.552 | 0.583811 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 127.521i | 0.200189i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 23.2032i | − | 0.0363118i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 144.826i | − | 0.225938i | −0.993599 | − | 0.112969i | \(-0.963964\pi\) | ||
0.993599 | − | 0.112969i | \(-0.0360360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 423.852 | 0.659179 | 0.329589 | − | 0.944124i | \(-0.393090\pi\) | ||||
0.329589 | + | 0.944124i | \(0.393090\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −767.957 | −1.18695 | −0.593475 | − | 0.804852i | \(-0.702245\pi\) | ||||
−0.593475 | + | 0.804852i | \(0.702245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1064.53i | − | 1.64027i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 746.029 | 1.14597 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 148.725 | 0.227756 | 0.113878 | − | 0.993495i | \(-0.463673\pi\) | ||||
0.113878 | + | 0.993495i | \(0.463673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.6575 | −0.0223097 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1058.23i | 1.60581i | 0.596109 | + | 0.802904i | \(0.296713\pi\) | ||||
−0.596109 | + | 0.802904i | \(0.703287\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 714.976i | 1.08166i | 0.841132 | + | 0.540829i | \(0.181889\pi\) | ||||
−0.841132 | + | 0.540829i | \(0.818111\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −545.991 | −0.823516 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 94.5706i | 0.141785i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1055.59 | 1.57786 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1642.12 | 2.44727 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 624.276i | − | 0.927602i | −0.885939 | − | 0.463801i | \(-0.846485\pi\) | ||
0.885939 | − | 0.463801i | \(-0.153515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 79.4837i | − | 0.117406i | −0.998275 | − | 0.0587029i | \(-0.981304\pi\) | ||
0.998275 | − | 0.0587029i | \(-0.0186965\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 838.170i | − | 1.23442i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 242.231 | 0.355699 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 918.987i | − | 1.34552i | −0.739863 | − | 0.672758i | \(-0.765110\pi\) | ||
0.739863 | − | 0.672758i | \(-0.234890\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 123.707i | 0.180069i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 602.936 | 0.875089 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −555.126 | −0.803366 | −0.401683 | − | 0.915779i | \(-0.631575\pi\) | ||||
−0.401683 | + | 0.915779i | \(0.631575\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 39.4897 | 0.0569837 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 411.919i | 0.590988i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 367.197i | 0.525318i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 73.5776 | 0.104961 | 0.0524805 | − | 0.998622i | \(-0.483287\pi\) | ||||
0.0524805 | + | 0.998622i | \(0.483287\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 476.152 | − | 65.7724i | 0.677314 | − | 0.0935596i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −198.715 | −0.281069 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −578.030 | −0.815275 | −0.407638 | − | 0.913144i | \(-0.633647\pi\) | ||||
−0.407638 | + | 0.913144i | \(0.633647\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 45.2589i | 0.0636553i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 873.131i | 1.22459i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 519.795i | 0.724959i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −870.924 | −1.21130 | −0.605649 | − | 0.795732i | \(-0.707087\pi\) | ||||
−0.605649 | + | 0.795732i | \(0.707087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 356.026i | − | 0.493794i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 252.812 | 0.349670 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −651.673 | −0.896386 | −0.448193 | − | 0.893937i | \(-0.647932\pi\) | ||||
−0.448193 | + | 0.893937i | \(0.647932\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −758.599 | −1.04060 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −710.217 | −0.971569 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2720 | 0.0221992 | 0.0110996 | − | 0.999938i | \(-0.496467\pi\) | ||||
0.0110996 | + | 0.999938i | \(0.496467\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1918.52i | − | 2.60315i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 970.120 | 1.31275 | 0.656373 | − | 0.754436i | \(-0.272090\pi\) | ||||
0.656373 | + | 0.754436i | \(0.272090\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 56.0746 | + | 405.945i | 0.0756742 | + | 0.547835i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 669.599i | − | 0.901211i | −0.892723 | − | 0.450605i | \(-0.851208\pi\) | ||
0.892723 | − | 0.450605i | \(-0.148792\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.9510 | 0.0226921 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1113.52i | 1.48668i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 798.869i | − | 1.06374i | −0.846826 | − | 0.531870i | \(-0.821489\pi\) | ||
0.846826 | − | 0.531870i | \(-0.178511\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 880.560i | 1.16940i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 843.963 | 1.11488 | 0.557439 | − | 0.830218i | \(-0.311784\pi\) | ||||
0.557439 | + | 0.830218i | \(0.311784\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 988.094i | − | 1.30184i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 174.165 | 0.228863 | 0.114431 | − | 0.993431i | \(-0.463495\pi\) | ||||
0.114431 | + | 0.993431i | \(0.463495\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1010.07i | 1.32382i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 448.723 | 0.585037 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 215.531 | 0.280274 | 0.140137 | − | 0.990132i | \(-0.455246\pi\) | ||||
0.140137 | + | 0.990132i | \(0.455246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −682.469 | −0.885174 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 589.413i | − | 0.762501i | −0.924472 | − | 0.381251i | \(-0.875493\pi\) | ||
0.924472 | − | 0.381251i | \(-0.124507\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −417.418 | −0.537218 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 306.262 | − | 42.3050i | 0.393148 | − | 0.0543068i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1006.82i | 1.28915i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −135.014 | −0.172432 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1145.89i | 1.45602i | 0.685568 | + | 0.728009i | \(0.259554\pi\) | ||||
−0.685568 | + | 0.728009i | \(0.740446\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 822.628i | − | 1.04262i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 114.616i | − | 0.144901i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 692.188i | 0.872873i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1240.74i | − | 1.55677i | −0.627789 | − | 0.778384i | \(-0.716040\pi\) | ||
0.627789 | − | 0.778384i | \(-0.283960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 985.488 | 1.23340 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.6277i | 0.0507212i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 636.011 | 0.792044 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −331.113 | −0.410301 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 214.567 | 0.265225 | 0.132612 | − | 0.991168i | \(-0.457663\pi\) | ||||
0.132612 | + | 0.991168i | \(0.457663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 443.871i | − | 0.547313i | −0.961827 | − | 0.273657i | \(-0.911767\pi\) | ||
0.961827 | − | 0.273657i | \(-0.0882332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 280.633i | 0.345182i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 72.9409 | + | 528.047i | 0.0892790 | + | 0.646325i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.6457i | 0.0203245i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 239.094 | 0.291223 | 0.145611 | − | 0.989342i | \(-0.453485\pi\) | ||||
0.145611 | + | 0.989342i | \(0.453485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 367.550 | 0.446598 | 0.223299 | − | 0.974750i | \(-0.428317\pi\) | ||||
0.223299 | + | 0.974750i | \(0.428317\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 432.940i | − | 0.523507i | −0.965135 | − | 0.261753i | \(-0.915699\pi\) | ||
0.965135 | − | 0.261753i | \(-0.0843007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 424.324i | − | 0.511851i | −0.966697 | − | 0.255925i | \(-0.917620\pi\) | ||
0.966697 | − | 0.255925i | \(-0.0823801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 158.056i | 0.190199i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −438.858 | −0.526841 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1246.53 | −1.48928 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1198.38i | 1.42834i | 0.699974 | + | 0.714169i | \(0.253195\pi\) | ||||
−0.699974 | + | 0.714169i | \(0.746805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 817.016 | 0.971482 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −200.603 | −0.237963 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1032.65 | −1.21918 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1110.18i | 1.30763i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 488.535i | − | 0.574071i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1631.88 | 1.91311 | 0.956555 | − | 0.291553i | \(-0.0941721\pi\) | ||||
0.956555 | + | 0.291553i | \(0.0941721\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1704.86i | 1.98933i | 0.103147 | + | 0.994666i | \(0.467109\pi\) | ||||
−0.103147 | + | 0.994666i | \(0.532891\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1190.68 | −1.38612 | −0.693061 | − | 0.720879i | \(-0.743738\pi\) | ||||
−0.693061 | + | 0.720879i | \(0.743738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −268.485 | −0.311829 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1219.71i | − | 1.41334i | −0.707543 | − | 0.706670i | \(-0.750197\pi\) | ||
0.707543 | − | 0.706670i | \(-0.249803\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1031.60i | − | 1.18986i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1963.86i | − | 2.25990i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 808.696 | 0.928468 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 59.9032i | 0.0686176i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1096.08i | − | 1.24981i | −0.780702 | − | 0.624904i | \(-0.785138\pi\) | ||
0.780702 | − | 0.624904i | \(-0.214862\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −59.6455 | −0.0678561 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −175.525 | −0.199234 | −0.0996170 | − | 0.995026i | \(-0.531762\pi\) | ||||
−0.0996170 | + | 0.995026i | \(0.531762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1733.12 | −1.96277 | −0.981384 | − | 0.192055i | \(-0.938485\pi\) | ||||
−0.981384 | + | 0.192055i | \(0.938485\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 134.522i | − | 0.151660i | −0.997121 | − | 0.0758298i | \(-0.975839\pi\) | ||
0.997121 | − | 0.0758298i | \(-0.0241606\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 523.568i | − | 0.588940i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1347.50 | 1.51234 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −101.212 | − | 732.711i | −0.113339 | − | 0.820505i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 416.502 | 0.464328 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −221.430 | −0.246307 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2074.99i | 2.30298i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 462.913i | − | 0.512638i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 293.274i | 0.323345i | 0.986844 | + | 0.161672i | \(0.0516888\pi\) | ||||
−0.986844 | + | 0.161672i | \(0.948311\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.2020 | 0.0156238 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 303.681i | − | 0.333349i | −0.986012 | − | 0.166674i | \(-0.946697\pi\) | ||
0.986012 | − | 0.166674i | \(-0.0533029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −735.531 | −0.805620 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1166.27 | 1.27184 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1466.07 | 1.59529 | 0.797644 | − | 0.603128i | \(-0.206079\pi\) | ||||
0.797644 | + | 0.603128i | \(0.206079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −924.125 | −1.00339 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −424.398 | −0.459803 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.4448i | 0.0274486i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1278.74 | −1.37647 | −0.688234 | − | 0.725489i | \(-0.741614\pi\) | ||||
−0.688234 | + | 0.725489i | \(0.741614\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.0718 | + | 326.292i | 0.0484122 | + | 0.350475i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 552.953i | − | 0.592661i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −746.023 | −0.796182 | −0.398091 | − | 0.917346i | \(-0.630327\pi\) | ||||
−0.398091 | + | 0.917346i | \(0.630327\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 451.599i | 0.480936i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1753.70i | − | 1.86365i | −0.362905 | − | 0.931826i | \(-0.618215\pi\) | ||
0.362905 | − | 0.931826i | \(-0.381785\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 314.227i | − | 0.333220i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1195.95 | 1.26288 | 0.631440 | − | 0.775425i | \(-0.282464\pi\) | ||||
0.631440 | + | 0.775425i | \(0.282464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 268.092i | 0.282500i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.7603 | 0.0123662 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 667.620i | 0.700546i | 0.936648 | + | 0.350273i | \(0.113911\pi\) | ||||
−0.936648 | + | 0.350273i | \(0.886089\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 250.586 | 0.261845 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 806.781 | 0.841273 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1083.37 | −1.12734 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 79.5824i | − | 0.0826401i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1708.02 | 1.76630 | 0.883152 | − | 0.469086i | \(-0.155417\pi\) | ||||
0.883152 | + | 0.469086i | \(0.155417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1397.05 | + | 192.979i | −1.44174 | + | 0.199153i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 216.028i | − | 0.222480i | −0.993794 | − | 0.111240i | \(-0.964518\pi\) | ||
0.993794 | − | 0.111240i | \(-0.0354822\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 889.776 | 0.914466 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 57.4013i | − | 0.0587526i | −0.999568 | − | 0.0293763i | \(-0.990648\pi\) | ||
0.999568 | − | 0.0293763i | \(-0.00935211\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1762.90i | − | 1.80072i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 72.1889i | − | 0.0735870i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 207.431i | 0.211019i | 0.994418 | + | 0.105509i | \(0.0336473\pi\) | ||||
−0.994418 | + | 0.105509i | \(0.966353\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 642.331i | 0.650792i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 541.780 | 0.547805 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 828.905i | 0.836432i | 0.908348 | + | 0.418216i | \(0.137345\pi\) | ||||
−0.908348 | + | 0.418216i | \(0.862655\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 284.764 | 0.286771 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1735.54 | −1.74076 | −0.870380 | − | 0.492381i | \(-0.836127\pi\) | ||||
−0.870380 | + | 0.492381i | \(0.836127\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 697.459 | 0.698157 |
(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 | 1900.3.e.g.1101.4 | ✓ | 14 | |
5.2 | odd | 4 | 1900.3.g.d.949.7 | 28 | |||
5.3 | odd | 4 | 1900.3.g.d.949.22 | 28 | |||
5.4 | even | 2 | 1900.3.e.h.1101.11 | yes | 14 | ||
19.18 | odd | 2 | inner | 1900.3.e.g.1101.11 | yes | 14 | |
95.18 | even | 4 | 1900.3.g.d.949.8 | 28 | |||
95.37 | even | 4 | 1900.3.g.d.949.21 | 28 | |||
95.94 | odd | 2 | 1900.3.e.h.1101.4 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.3.e.g.1101.4 | ✓ | 14 | 1.1 | even | 1 | trivial | |
1900.3.e.g.1101.11 | yes | 14 | 19.18 | odd | 2 | inner | |
1900.3.e.h.1101.4 | yes | 14 | 95.94 | odd | 2 | ||
1900.3.e.h.1101.11 | yes | 14 | 5.4 | even | 2 | ||
1900.3.g.d.949.7 | 28 | 5.2 | odd | 4 | |||
1900.3.g.d.949.8 | 28 | 95.18 | even | 4 | |||
1900.3.g.d.949.21 | 28 | 95.37 | even | 4 | |||
1900.3.g.d.949.22 | 28 | 5.3 | odd | 4 |