Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,6,Mod(1,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.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: | \(32.0767639626\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{241}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 60 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-7.26209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −11.5242 | −0.739276 | −0.369638 | − | 0.929176i | \(-0.620518\pi\) | ||||
−0.369638 | + | 0.929176i | \(0.620518\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27.0483 | 0.208639 | 0.104320 | − | 0.994544i | \(-0.466734\pi\) | ||||
0.104320 | + | 0.994544i | \(0.466734\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −110.193 | −0.453471 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 226.008 | 0.563173 | 0.281586 | − | 0.959536i | \(-0.409139\pi\) | ||||
0.281586 | + | 0.959536i | \(0.409139\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 511.257 | 0.839037 | 0.419518 | − | 0.907747i | \(-0.362199\pi\) | ||||
0.419518 | + | 0.907747i | \(0.362199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 387.387 | 0.325104 | 0.162552 | − | 0.986700i | \(-0.448027\pi\) | ||||
0.162552 | + | 0.986700i | \(0.448027\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1335.93 | −0.848982 | −0.424491 | − | 0.905432i | \(-0.639547\pi\) | ||||
−0.424491 | + | 0.905432i | \(0.639547\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −311.710 | −0.154242 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 545.369 | 0.214967 | 0.107483 | − | 0.994207i | \(-0.465721\pi\) | ||||
0.107483 | + | 0.994207i | \(0.465721\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4070.26 | 1.07452 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4637.58 | −1.02399 | −0.511996 | − | 0.858988i | \(-0.671094\pi\) | ||||
−0.511996 | + | 0.858988i | \(0.671094\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2991.56 | 0.559105 | 0.279552 | − | 0.960130i | \(-0.409814\pi\) | ||||
0.279552 | + | 0.960130i | \(0.409814\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2604.55 | −0.416340 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1263.70 | −0.151754 | −0.0758770 | − | 0.997117i | \(-0.524176\pi\) | ||||
−0.0758770 | + | 0.997117i | \(0.524176\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5891.82 | −0.620280 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17197.6 | −1.59775 | −0.798875 | − | 0.601497i | \(-0.794571\pi\) | ||||
−0.798875 | + | 0.601497i | \(0.794571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16592.0 | −1.36845 | −0.684223 | − | 0.729272i | \(-0.739859\pi\) | ||||
−0.684223 | + | 0.729272i | \(0.739859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13036.0 | 0.860795 | 0.430397 | − | 0.902639i | \(-0.358373\pi\) | ||||
0.430397 | + | 0.902639i | \(0.358373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16075.4 | −0.956470 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4464.31 | −0.240342 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −28994.7 | −1.41785 | −0.708923 | − | 0.705286i | \(-0.750819\pi\) | ||||
−0.708923 | + | 0.705286i | \(0.750819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15395.4 | 0.627632 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −34429.9 | −1.28768 | −0.643838 | − | 0.765162i | \(-0.722659\pi\) | ||||
−0.643838 | + | 0.765162i | \(0.722659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24149.1 | −0.830952 | −0.415476 | − | 0.909604i | \(-0.636385\pi\) | ||||
−0.415476 | + | 0.909604i | \(0.636385\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2980.55 | −0.0946117 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 29389.7 | 0.799849 | 0.399925 | − | 0.916548i | \(-0.369036\pi\) | ||||
0.399925 | + | 0.916548i | \(0.369036\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6284.93 | −0.158920 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9064.32 | 0.213397 | 0.106699 | − | 0.994291i | \(-0.465972\pi\) | ||||
0.106699 | + | 0.994291i | \(0.465972\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55528.7 | −1.21958 | −0.609791 | − | 0.792563i | \(-0.708746\pi\) | ||||
−0.609791 | + | 0.792563i | \(0.708746\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6113.13 | 0.117500 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −101587. | −1.83135 | −0.915673 | − | 0.401924i | \(-0.868342\pi\) | ||||
−0.915673 | + | 0.401924i | \(0.868342\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −20129.4 | −0.340893 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 73240.4 | 1.16696 | 0.583479 | − | 0.812128i | \(-0.301691\pi\) | ||||
0.583479 | + | 0.812128i | \(0.301691\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 53444.3 | 0.757012 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −42498.5 | −0.568719 | −0.284360 | − | 0.958718i | \(-0.591781\pi\) | ||||
−0.284360 | + | 0.958718i | \(0.591781\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13828.7 | 0.175056 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −34475.2 | −0.413333 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10565.9 | 0.114019 | 0.0570093 | − | 0.998374i | \(-0.481844\pi\) | ||||
0.0570093 | + | 0.998374i | \(0.481844\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −24904.6 | −0.255382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 46486.0 | 0.453439 | 0.226719 | − | 0.973960i | \(-0.427200\pi\) | ||||
0.226719 | + | 0.973960i | \(0.427200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 119526. | 1.11012 | 0.555059 | − | 0.831811i | \(-0.312696\pi\) | ||||
0.555059 | + | 0.831811i | \(0.312696\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −22922.4 | −0.193553 | −0.0967765 | − | 0.995306i | \(-0.530853\pi\) | ||||
−0.0967765 | + | 0.995306i | \(0.530853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 210121. | 1.69396 | 0.846980 | − | 0.531624i | \(-0.178418\pi\) | ||||
0.846980 | + | 0.531624i | \(0.178418\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14563.1 | 0.112188 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −203886. | −1.50208 | −0.751039 | − | 0.660258i | \(-0.770447\pi\) | ||||
−0.751039 | + | 0.660258i | \(0.770447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −56337.2 | −0.380479 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10478.2 | 0.0678294 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −109972. | −0.682837 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 198188. | 1.18118 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −175022. | −0.962905 | −0.481453 | − | 0.876472i | \(-0.659891\pi\) | ||||
−0.481453 | + | 0.876472i | \(0.659891\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 191209. | 1.01166 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 149218. | 0.759701 | 0.379850 | − | 0.925048i | \(-0.375975\pi\) | ||||
0.379850 | + | 0.925048i | \(0.375975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −36134.6 | −0.177131 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −212180. | −0.965836 | −0.482918 | − | 0.875666i | \(-0.660423\pi\) | ||||
−0.482918 | + | 0.875666i | \(0.660423\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 77082.5 | 0.338391 | 0.169195 | − | 0.985583i | \(-0.445883\pi\) | ||||
0.169195 | + | 0.985583i | \(0.445883\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −150229. | −0.636365 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 115548. | 0.472522 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 185256. | 0.707095 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 470139. | 1.73485 | 0.867423 | − | 0.497571i | \(-0.165775\pi\) | ||||
0.867423 | + | 0.497571i | \(0.165775\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 311118. | 1.11041 | 0.555205 | − | 0.831714i | \(-0.312640\pi\) | ||||
0.555205 | + | 0.831714i | \(0.312640\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −42687.5 | −0.147425 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −543649. | −1.76023 | −0.880115 | − | 0.474760i | \(-0.842535\pi\) | ||||
−0.880115 | + | 0.474760i | \(0.842535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 334140. | 1.04818 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14751.3 | 0.0448504 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 298673. | 0.880495 | 0.440248 | − | 0.897876i | \(-0.354891\pi\) | ||||
0.440248 | + | 0.897876i | \(0.354891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −65486.6 | −0.181703 | −0.0908513 | − | 0.995864i | \(-0.528959\pi\) | ||||
−0.0908513 | + | 0.995864i | \(0.528959\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −109909. | −0.296017 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 147210. | 0.384989 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 355092. | 0.902040 | 0.451020 | − | 0.892514i | \(-0.351060\pi\) | ||||
0.451020 | + | 0.892514i | \(0.351060\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 396777. | 0.951947 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −39265.7 | −0.0915970 | −0.0457985 | − | 0.998951i | \(-0.514583\pi\) | ||||
−0.0457985 | + | 0.998951i | \(0.514583\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 99638.2 | 0.226063 | 0.113031 | − | 0.993591i | \(-0.463944\pi\) | ||||
0.113031 | + | 0.993591i | \(0.463944\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 278298. | 0.614303 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 87552.4 | 0.183090 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 110094. | 0.224186 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 380336. | 0.754369 | 0.377185 | − | 0.926138i | \(-0.376892\pi\) | ||||
0.377185 | + | 0.926138i | \(0.376892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 126401. | 0.244262 | 0.122131 | − | 0.992514i | \(-0.461027\pi\) | ||||
0.122131 | + | 0.992514i | \(0.461027\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −326136. | −0.598733 | −0.299366 | − | 0.954138i | \(-0.596775\pi\) | ||||
−0.299366 | + | 0.954138i | \(0.596775\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −498559. | −0.892451 | −0.446225 | − | 0.894921i | \(-0.647232\pi\) | ||||
−0.446225 | + | 0.894921i | \(0.647232\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −338692. | −0.591309 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −125439. | −0.213645 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −60096.1 | −0.0974811 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −301930. | −0.478123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −310763. | −0.480532 | −0.240266 | − | 0.970707i | \(-0.577235\pi\) | ||||
−0.240266 | + | 0.970707i | \(0.577235\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −104459. | −0.157760 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 80916.7 | 0.116651 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 639923. | 0.901607 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 198054. | 0.272774 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −627285. | −0.844700 | −0.422350 | − | 0.906433i | \(-0.638795\pi\) | ||||
−0.422350 | + | 0.906433i | \(0.638795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 450131. | 0.579794 | 0.289897 | − | 0.957058i | \(-0.406379\pi\) | ||||
0.289897 | + | 0.957058i | \(0.406379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −461485. | −0.581526 | −0.290763 | − | 0.956795i | \(-0.593909\pi\) | ||||
−0.290763 | + | 0.956795i | \(0.593909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −70448.8 | −0.0868648 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −675812. | −0.815523 | −0.407761 | − | 0.913089i | \(-0.633690\pi\) | ||||
−0.407761 | + | 0.913089i | \(0.633690\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.17071e6 | 1.35387 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.00730e6 | −1.14068 | −0.570338 | − | 0.821410i | \(-0.693188\pi\) | ||||
−0.570338 | + | 0.821410i | \(0.693188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −232091. | −0.257404 | −0.128702 | − | 0.991683i | \(-0.541081\pi\) | ||||
−0.128702 | + | 0.991683i | \(0.541081\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −757099. | −0.822502 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −683002. | −0.712327 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −844035. | −0.862704 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.77096e6 | −1.77429 | −0.887143 | − | 0.461494i | \(-0.847314\pi\) | ||||
−0.887143 | + | 0.461494i | \(0.847314\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 123258. | 0.121063 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 528458. | 0.499088 | 0.249544 | − | 0.968363i | \(-0.419719\pi\) | ||||
0.249544 | + | 0.968363i | \(0.419719\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34181.0 | −0.0316618 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 511030. | 0.464350 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.69907e6 | −1.51469 | −0.757344 | − | 0.653016i | \(-0.773503\pi\) | ||||
−0.757344 | + | 0.653016i | \(0.773503\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 489760. | 0.420441 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −648393. | −0.546333 | −0.273167 | − | 0.961967i | \(-0.588071\pi\) | ||||
−0.273167 | + | 0.961967i | \(0.588071\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.94947e6 | −1.61248 | −0.806239 | − | 0.591590i | \(-0.798500\pi\) | ||||
−0.806239 | + | 0.591590i | \(0.798500\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −159364. | −0.129415 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 313195. | 0.245254 | 0.122627 | − | 0.992453i | \(-0.460868\pi\) | ||||
0.122627 | + | 0.992453i | \(0.460868\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −329650. | −0.253538 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.72743e6 | 1.30507 | 0.652537 | − | 0.757757i | \(-0.273705\pi\) | ||||
0.652537 | + | 0.757757i | \(0.273705\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −205142. | −0.152261 | −0.0761306 | − | 0.997098i | \(-0.524257\pi\) | ||||
−0.0761306 | + | 0.997098i | \(0.524257\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −465167. | −0.333353 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.26979e6 | −0.894307 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −121763. | −0.0842912 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 390309. | 0.265607 | 0.132804 | − | 0.991142i | \(-0.457602\pi\) | ||||
0.132804 | + | 0.991142i | \(0.457602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 919911. | 0.605138 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 278824. | 0.180365 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −448787. | −0.285511 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −535713. | −0.335217 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.10708e6 | 0.670401 | 0.335201 | − | 0.942147i | \(-0.391196\pi\) | ||||
0.335201 | + | 0.942147i | \(0.391196\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.37744e6 | −0.820684 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.19106e6 | 1.28455 | 0.642277 | − | 0.766472i | \(-0.277990\pi\) | ||||
0.642277 | + | 0.766472i | \(0.277990\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.89050e6 | 1.66768 | 0.833840 | − | 0.552006i | \(-0.186138\pi\) | ||||
0.833840 | + | 0.552006i | \(0.186138\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.46652e6 | 0.819671 | 0.409835 | − | 0.912160i | \(-0.365586\pi\) | ||||
0.409835 | + | 0.912160i | \(0.365586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.04813e6 | −0.576684 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 264161. | 0.143089 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −517520. | −0.276008 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.42147e6 | −1.25230 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 352602. | 0.179595 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.23500e6 | −1.12126 | −0.560632 | − | 0.828065i | \(-0.689442\pi\) | ||||
−0.560632 | + | 0.828065i | \(0.689442\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 139251. | 0.0688160 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.48851e6 | −0.713966 | −0.356983 | − | 0.934111i | \(-0.616195\pi\) | ||||
−0.356983 | + | 0.934111i | \(0.616195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.34962e6 | 1.11045 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 676115. | 0.314872 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −889414. | −0.408196 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.34245e6 | 1.04435 | 0.522177 | − | 0.852837i | \(-0.325120\pi\) | ||||
0.522177 | + | 0.852837i | \(0.325120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −119901. | −0.0526940 | −0.0263470 | − | 0.999653i | \(-0.508387\pi\) | ||||
−0.0263470 | + | 0.999653i | \(0.508387\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.08095e6 | 0.901559 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.49528e6 | 1.06582 | 0.532909 | − | 0.846173i | \(-0.321099\pi\) | ||||
0.532909 | + | 0.846173i | \(0.321099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −120752. | −0.0501447 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.43398e6 | 1.40625 | 0.703124 | − | 0.711068i | \(-0.251788\pi\) | ||||
0.703124 | + | 0.711068i | \(0.251788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −691400. | −0.279230 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.26733e6 | 0.504805 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.67310e6 | −1.81109 | −0.905545 | − | 0.424249i | \(-0.860538\pi\) | ||||
−0.905545 | + | 0.424249i | \(0.860538\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.89507e6 | 0.724533 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −784259. | −0.295818 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.03766e6 | 0.758333 | 0.379167 | − | 0.925328i | \(-0.376211\pi\) | ||||
0.379167 | + | 0.925328i | \(0.376211\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.37099e6 | −0.859166 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.78978e6 | 0.640032 | 0.320016 | − | 0.947412i | \(-0.396312\pi\) | ||||
0.320016 | + | 0.947412i | \(0.396312\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.01698e6 | 0.711853 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.04521e6 | −0.712429 | −0.356214 | − | 0.934404i | \(-0.615933\pi\) | ||||
−0.356214 | + | 0.934404i | \(0.615933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.82833e6 | 0.620551 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 234191. | 0.0784687 | 0.0392344 | − | 0.999230i | \(-0.487508\pi\) | ||||
0.0392344 | + | 0.999230i | \(0.487508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 211269. | 0.0698865 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.71961e6 | −0.561629 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.81706e6 | −0.897058 | −0.448529 | − | 0.893768i | \(-0.648052\pi\) | ||||
−0.448529 | + | 0.893768i | \(0.648052\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 416421. | 0.130949 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 735044. | 0.228272 | 0.114136 | − | 0.993465i | \(-0.463590\pi\) | ||||
0.114136 | + | 0.993465i | \(0.463590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.52946e6 | 0.469109 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −285606. | −0.0854636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.08894e6 | 1.79984 | 0.899918 | − | 0.436058i | \(-0.143626\pi\) | ||||
0.899918 | + | 0.436058i | \(0.143626\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.44520e6 | 0.714020 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −931273. | −0.268659 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −888312. | −0.250164 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.65964e6 | 1.57490 | 0.787452 | − | 0.616376i | \(-0.211400\pi\) | ||||
0.787452 | + | 0.616376i | \(0.211400\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.34902e6 | −1.74583 | −0.872914 | − | 0.487873i | \(-0.837773\pi\) | ||||
−0.872914 | + | 0.487873i | \(0.837773\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.43648e6 | −0.390345 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −653192. | −0.173369 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.33160e6 | −0.349325 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.03516e6 | 0.787024 | 0.393512 | − | 0.919320i | \(-0.371260\pi\) | ||||
0.393512 | + | 0.919320i | \(0.371260\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.50633e6 | 0.898739 | 0.449369 | − | 0.893346i | \(-0.351649\pi\) | ||||
0.449369 | + | 0.893346i | \(0.351649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −728573. | −0.182503 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.08849e6 | −1.50782 | −0.753908 | − | 0.656980i | \(-0.771834\pi\) | ||||
−0.753908 | + | 0.656980i | \(0.771834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.77140e6 | 0.433731 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.03357e6 | 1.46071 | 0.730357 | − | 0.683066i | \(-0.239354\pi\) | ||||
0.730357 | + | 0.683066i | \(0.239354\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.41797e6 | −1.28253 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.97943e6 | 0.931548 | 0.465774 | − | 0.884904i | \(-0.345776\pi\) | ||||
0.465774 | + | 0.884904i | \(0.345776\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.88680e6 | −0.899809 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.58538e6 | −0.820899 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 430533. | 0.0964308 | 0.0482154 | − | 0.998837i | \(-0.484647\pi\) | ||||
0.0482154 | + | 0.998837i | \(0.484647\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.57677e6 | 0.349330 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.80383e6 | 0.833622 | 0.416811 | − | 0.908993i | \(-0.363148\pi\) | ||||
0.416811 | + | 0.908993i | \(0.363148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.62853e6 | 1.65382 | 0.826911 | − | 0.562333i | \(-0.190096\pi\) | ||||
0.826911 | + | 0.562333i | \(0.190096\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.05102e6 | 1.92046 | 0.960230 | − | 0.279209i | \(-0.0900722\pi\) | ||||
0.960230 | + | 0.279209i | \(0.0900722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 794943. | 0.166880 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.26511e6 | 1.30130 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.74992e6 | −0.770672 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.19502e6 | 0.642952 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.51621e6 | −1.69593 | −0.847964 | − | 0.530054i | \(-0.822172\pi\) | ||||
−0.847964 | + | 0.530054i | \(0.822172\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −646076. | −0.127327 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −169997. | −0.0331569 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.65770e6 | −0.507789 | −0.253895 | − | 0.967232i | \(-0.581712\pi\) | ||||
−0.253895 | + | 0.967232i | \(0.581712\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.44196e6 | −0.650929 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.05116e6 | −0.945557 | −0.472779 | − | 0.881181i | \(-0.656749\pi\) | ||||
−0.472779 | + | 0.881181i | \(0.656749\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.79654e6 | −0.332904 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 245175. | 0.0445230 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.15003e6 | −0.386538 | −0.193269 | − | 0.981146i | \(-0.561909\pi\) | ||||
−0.193269 | + | 0.981146i | \(0.561909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 754679. | 0.134328 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.79475e6 | −0.316289 | −0.158144 | − | 0.987416i | \(-0.550551\pi\) | ||||
−0.158144 | + | 0.987416i | \(0.550551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.26661e6 | 0.218839 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 697940. | 0.119405 | 0.0597027 | − | 0.998216i | \(-0.480985\pi\) | ||||
0.0597027 | + | 0.998216i | \(0.480985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.50196e6 | −0.254452 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.43757e6 | −0.912245 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.94624e6 | 0.484776 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.09214e6 | −0.666857 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.14928e6 | −0.185495 | −0.0927475 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927475 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.22071e6 | 1.15432 | 0.577159 | − | 0.816632i | \(-0.304161\pi\) | ||||
0.577159 | + | 0.816632i | \(0.304161\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.15889e6 | 0.181767 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.13892e6 | −0.953789 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.79395e6 | 0.583923 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.79241e6 | −1.34057 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 452505. | 0.0677155 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.63316e6 | −0.538657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.24720e7 | −1.83207 | −0.916035 | − | 0.401099i | \(-0.868628\pi\) | ||||
−0.916035 | + | 0.401099i | \(0.868628\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.14825e6 | −0.167123 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.58966e6 | 1.22746 | 0.613730 | − | 0.789516i | \(-0.289668\pi\) | ||||
0.613730 | + | 0.789516i | \(0.289668\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.66107e6 | 0.376812 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.19546e6 | 0.869350 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.74776e6 | −0.382090 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.38207e6 | −0.461896 | −0.230948 | − | 0.972966i | \(-0.574183\pi\) | ||||
−0.230948 | + | 0.972966i | \(0.574183\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.48278e6 | −1.14818 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.00897e6 | −0.135354 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.50247e6 | −0.199772 | −0.0998859 | − | 0.994999i | \(-0.531848\pi\) | ||||
−0.0998859 | + | 0.994999i | \(0.531848\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −544468. | −0.0711237 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.87838e6 | 0.243222 | 0.121611 | − | 0.992578i | \(-0.461194\pi\) | ||||
0.121611 | + | 0.992578i | \(0.461194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.49628e7 | −1.92053 | −0.960267 | − | 0.279082i | \(-0.909970\pi\) | ||||
−0.960267 | + | 0.279082i | \(0.909970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.38306e6 | −0.557687 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.03660e6 | −0.504750 | −0.252375 | − | 0.967630i | \(-0.581212\pi\) | ||||
−0.252375 | + | 0.967630i | \(0.581212\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.45666e6 | −0.180577 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.98103e6 | 0.243473 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.55303e6 | −0.798492 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.57983e7 | 1.89241 | 0.946203 | − | 0.323574i | \(-0.104885\pi\) | ||||
0.946203 | + | 0.323574i | \(0.104885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.99650e6 | −0.474670 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.75845e6 | 0.442629 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.37947e7 | −1.61092 | −0.805462 | − | 0.592647i | \(-0.798083\pi\) | ||||
−0.805462 | + | 0.592647i | \(0.798083\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.74549e6 | 0.659768 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −814106. | −0.0927073 | −0.0463537 | − | 0.998925i | \(-0.514760\pi\) | ||||
−0.0463537 | + | 0.998925i | \(0.514760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.55613e7 | −1.75736 | −0.878679 | − | 0.477413i | \(-0.841574\pi\) | ||||
−0.878679 | + | 0.477413i | \(0.841574\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.23855e6 | −0.362708 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.63191e7 | −1.79773 | −0.898865 | − | 0.438226i | \(-0.855607\pi\) | ||||
−0.898865 | + | 0.438226i | \(0.855607\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.44558e6 | 0.157942 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.66475e6 | 0.722239 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.38233e6 | 0.578520 | 0.289260 | − | 0.957250i | \(-0.406591\pi\) | ||||
0.289260 | + | 0.957250i | \(0.406591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.83565e6 | 0.617130 | 0.308565 | − | 0.951203i | \(-0.400151\pi\) | ||||
0.308565 | + | 0.951203i | \(0.400151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.36289e6 | −0.352765 | −0.176383 | − | 0.984322i | \(-0.556440\pi\) | ||||
−0.176383 | + | 0.984322i | \(0.556440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.21980e6 | 0.230985 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.14951e6 | −0.118657 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.47949e6 | 0.353465 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −489541. | −0.0493358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.10425e6 | 0.810288 | 0.405144 | − | 0.914253i | \(-0.367221\pi\) | ||||
0.405144 | + | 0.914253i | \(0.367221\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.58128e6 | 0.355246 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.21866e6 | −0.802513 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −998828. | −0.0967695 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.08523e6 | 0.681097 | 0.340548 | − | 0.940227i | \(-0.389387\pi\) | ||||
0.340548 | + | 0.940227i | \(0.389387\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.72946e6 | 0.546495 | 0.273247 | − | 0.961944i | \(-0.411902\pi\) | ||||
0.273247 | + | 0.961944i | \(0.411902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.17751e6 | 0.204503 | 0.102251 | − | 0.994759i | \(-0.467395\pi\) | ||||
0.102251 | + | 0.994759i | \(0.467395\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.78143e6 | −0.725183 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −932498. | −0.0862374 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.42048e7 | 1.30363 | 0.651813 | − | 0.758379i | \(-0.274009\pi\) | ||||
0.651813 | + | 0.758379i | \(0.274009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.11890e6 | 0.553044 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.54033e7 | 1.38166 | 0.690829 | − | 0.723018i | \(-0.257246\pi\) | ||||
0.690829 | + | 0.723018i | \(0.257246\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −544048. | −0.0484322 | −0.0242161 | − | 0.999707i | \(-0.507709\pi\) | ||||
−0.0242161 | + | 0.999707i | \(0.507709\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.28241e6 | −0.201656 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.52919e6 | −0.220124 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.22894e6 | 0.624467 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.45787e6 | −0.467969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.37093e7 | 1.16675 | 0.583374 | − | 0.812203i | \(-0.301732\pi\) | ||||
0.583374 | + | 0.812203i | \(0.301732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.49910e7 | −1.25707 | −0.628536 | − | 0.777781i | \(-0.716345\pi\) | ||||
−0.628536 | + | 0.777781i | \(0.716345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 285789. | 0.0237887 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.18738e6 | −0.428628 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.47996e6 | 0.285445 | 0.142723 | − | 0.989763i | \(-0.454414\pi\) | ||||
0.142723 | + | 0.989763i | \(0.454414\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.31824e6 | 0.429908 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.48237e7 | −1.18962 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.09436e6 | 0.405877 | 0.202939 | − | 0.979191i | \(-0.434951\pi\) | ||||
0.202939 | + | 0.979191i | \(0.434951\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −673627. | −0.0532827 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.66213e6 | −0.519435 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.78817e6 | 0.602896 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.75839e7 | 1.35151 | 0.675755 | − | 0.737126i | \(-0.263818\pi\) | ||||
0.675755 | + | 0.737126i | \(0.263818\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.68821e6 | 0.128836 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.25737e6 | 0.0946051 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.35383e7 | 1.01146 | 0.505730 | − | 0.862692i | \(-0.331223\pi\) | ||||
0.505730 | + | 0.862692i | \(0.331223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.11942e7 | 0.830462 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.63150e6 | 0.120189 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.16083e7 | 0.843275 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.27911e7 | 0.922756 | 0.461378 | − | 0.887204i | \(-0.347355\pi\) | ||||
0.461378 | + | 0.887204i | \(0.347355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.23298e6 | 0.231614 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.67466e6 | 0.190293 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.11509e7 | −1.48420 | −0.742100 | − | 0.670289i | \(-0.766170\pi\) | ||||
−0.742100 | + | 0.670289i | \(0.766170\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.36164e7 | 0.948949 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.42753e6 | −0.444888 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.23015e7 | 0.845667 | 0.422833 | − | 0.906207i | \(-0.361036\pi\) | ||||
0.422833 | + | 0.906207i | \(0.361036\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.64230e6 | 0.450453 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.04425e7 | 0.703383 | 0.351691 | − | 0.936116i | \(-0.385607\pi\) | ||||
0.351691 | + | 0.936116i | \(0.385607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.87103e6 | 0.526606 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.63296e6 | −0.241429 | −0.120714 | − | 0.992687i | \(-0.538519\pi\) | ||||
−0.120714 | + | 0.992687i | \(0.538519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.07060e6 | −0.529181 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −620012. | −0.0403827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.77346e7 | −1.14741 | −0.573707 | − | 0.819060i | \(-0.694495\pi\) | ||||
−0.573707 | + | 0.819060i | \(0.694495\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.04088e7 | 1.31169 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.89094e6 | −0.500483 | −0.250241 | − | 0.968183i | \(-0.580510\pi\) | ||||
−0.250241 | + | 0.968183i | \(0.580510\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.42044e6 | −0.0894992 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.98455e7 | 1.24223 | 0.621114 | − | 0.783721i | \(-0.286681\pi\) | ||||
0.621114 | + | 0.783721i | \(0.286681\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.68343e6 | 0.353426 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.76026e7 | −1.08041 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.89976e6 | 0.237806 | 0.118903 | − | 0.992906i | \(-0.462062\pi\) | ||||
0.118903 | + | 0.992906i | \(0.462062\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.09004e6 | −0.368964 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.33736e6 | −0.140695 | −0.0703474 | − | 0.997523i | \(-0.522411\pi\) | ||||
−0.0703474 | + | 0.997523i | \(0.522411\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 393908. | 0.0234068 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.29748e7 | 1.35646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.04860e6 | 0.120180 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.88762e7 | −1.10030 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.52903e7 | −0.879993 | −0.439997 | − | 0.897999i | \(-0.645020\pi\) | ||||
−0.439997 | + | 0.897999i | \(0.645020\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.95804e7 | 1.11977 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.51479e6 | −0.313392 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.23464e7 | −0.697199 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.25972e7 | −0.702468 | −0.351234 | − | 0.936288i | \(-0.614238\pi\) | ||||
−0.351234 | + | 0.936288i | \(0.614238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.04997e6 | 0.279848 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.68305e6 | 0.257898 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.25499e7 | −0.686835 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.47219e6 | 0.403891 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.13476e7 | −0.609584 | −0.304792 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304792 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.91000e7 | −1.01972 | −0.509860 | − | 0.860257i | \(-0.670303\pi\) | ||||
−0.509860 | + | 0.860257i | \(0.670303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.24661e7 | 1.19207 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.21657e7 | 1.16179 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.52383e6 | −0.0793827 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.25668e6 | 0.0650678 | 0.0325339 | − | 0.999471i | \(-0.489642\pi\) | ||||
0.0325339 | + | 0.999471i | \(0.489642\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.95590e6 | −0.357976 | −0.178988 | − | 0.983851i | \(-0.557282\pi\) | ||||
−0.178988 | + | 0.983851i | \(0.557282\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.04638e6 | −0.459950 | −0.229975 | − | 0.973197i | \(-0.573864\pi\) | ||||
−0.229975 | + | 0.973197i | \(0.573864\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.54026e7 | −0.778407 | −0.389203 | − | 0.921152i | \(-0.627250\pi\) | ||||
−0.389203 | + | 0.921152i | \(0.627250\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.60932e6 | −0.181310 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.22739e6 | −0.310952 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.21764e7 | 0.600767 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.75941e7 | 0.862903 | 0.431451 | − | 0.902136i | \(-0.358002\pi\) | ||||
0.431451 | + | 0.902136i | \(0.358002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 995979. | 0.0485580 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.99072e7 | −0.964809 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.97455e6 | −0.142466 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.36410e6 | 0.112563 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −689183. | −0.0326220 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.06755e7 | 0.972934 | 0.486467 | − | 0.873699i | \(-0.338285\pi\) | ||||
0.486467 | + | 0.873699i | \(0.338285\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.16205e7 | −1.00557 | −0.502786 | − | 0.864411i | \(-0.667692\pi\) | ||||
−0.502786 | + | 0.864411i | \(0.667692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.70061e7 | −0.786362 | −0.393181 | − | 0.919461i | \(-0.628625\pi\) | ||||
−0.393181 | + | 0.919461i | \(0.628625\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.36067e6 | 0.246440 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.96043e7 | 1.35309 | 0.676547 | − | 0.736399i | \(-0.263475\pi\) | ||||
0.676547 | + | 0.736399i | \(0.263475\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.46333e7 | 0.661140 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.29594e7 | −1.03136 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.50257e7 | 0.671103 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.16429e6 | −0.0517041 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.77691e7 | 1.21917 | 0.609583 | − | 0.792722i | \(-0.291337\pi\) | ||||
0.609583 | + | 0.792722i | \(0.291337\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.49799e6 | −0.196357 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.16824e7 | 0.507099 | 0.253550 | − | 0.967322i | \(-0.418402\pi\) | ||||
0.253550 | + | 0.967322i | \(0.418402\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.66919e7 | −1.15207 | −0.576034 | − | 0.817426i | \(-0.695400\pi\) | ||||
−0.576034 | + | 0.817426i | \(0.695400\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.95714e7 | 1.68878 | 0.844388 | − | 0.535733i | \(-0.179964\pi\) | ||||
0.844388 | + | 0.535733i | \(0.179964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.73406e6 | −0.200900 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.54940e6 | −0.191982 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.74151e7 | −0.730799 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.21321e6 | −0.133339 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.38736e7 | −0.572518 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.12322e7 | −0.460948 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.17189e6 | 0.211072 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.79635e7 | −1.12869 | −0.564343 | − | 0.825541i | \(-0.690870\pi\) | ||||
−0.564343 | + | 0.825541i | \(0.690870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.12245e6 | −0.205621 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.87296e7 | −0.747710 | −0.373855 | − | 0.927487i | \(-0.621964\pi\) | ||||
−0.373855 | + | 0.927487i | \(0.621964\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.65529e7 | 0.657199 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.03610e6 | 0.158503 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.77613e6 | −0.303721 | −0.151861 | − | 0.988402i | \(-0.548526\pi\) | ||||
−0.151861 | + | 0.988402i | \(0.548526\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.27582e7 | −0.495612 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.63420e6 | 0.179048 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.31710e7 | −0.503406 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.88269e7 | −1.47602 | −0.738011 | − | 0.674788i | \(-0.764235\pi\) | ||||
−0.738011 | + | 0.674788i | \(0.764235\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.14755e7 | 0.812026 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.52501e7 | −0.949640 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.75302e7 | 0.652288 | 0.326144 | − | 0.945320i | \(-0.394251\pi\) | ||||
0.326144 | + | 0.945320i | \(0.394251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.33107e7 | −1.23288 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.29638e6 | −0.158172 | −0.0790859 | − | 0.996868i | \(-0.525200\pi\) | ||||
−0.0790859 | + | 0.996868i | \(0.525200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.37905e6 | −0.343463 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.43637e7 | 1.60751 | 0.803754 | − | 0.594962i | \(-0.202833\pi\) | ||||
0.803754 | + | 0.594962i | \(0.202833\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.83895e7 | −1.02327 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.69004e7 | −0.605963 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.71990e6 | −0.204012 | −0.102006 | − | 0.994784i | \(-0.532526\pi\) | ||||
−0.102006 | + | 0.994784i | \(0.532526\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.20788e7 | 0.426329 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.73912e6 | −0.201511 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96797e7 | −0.687402 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.52589e6 | 0.0877706 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.00548e7 | 1.03359 | 0.516794 | − | 0.856110i | \(-0.327125\pi\) | ||||
0.516794 | + | 0.856110i | \(0.327125\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.96399e6 | 0.204046 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.89662e7 | 0.645552 | 0.322776 | − | 0.946475i | \(-0.395384\pi\) | ||||
0.322776 | + | 0.946475i | \(0.395384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.08495e6 | 0.0706015 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.45541e7 | −0.822975 | −0.411488 | − | 0.911415i | \(-0.634991\pi\) | ||||
−0.411488 | + | 0.911415i | \(0.634991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.60498e6 | −0.320287 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.31540e7 | −0.768162 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.35539e7 | −1.10754 | −0.553769 | − | 0.832670i | \(-0.686811\pi\) | ||||
−0.553769 | + | 0.832670i | \(0.686811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.06345e6 | −0.132771 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.04877e6 | −0.294170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.05230e7 | 0.663830 | 0.331915 | − | 0.943309i | \(-0.392305\pi\) | ||||
0.331915 | + | 0.943309i | \(0.392305\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.57565e7 | 0.828924 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.25729e7 | −0.400589 | −0.200294 | − | 0.979736i | \(-0.564190\pi\) | ||||
−0.200294 | + | 0.979736i | \(0.564190\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.14359e6 | −0.163062 |
(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 | 200.6.a.f.1.1 | yes | 2 | |
4.3 | odd | 2 | 400.6.a.r.1.2 | 2 | |||
5.2 | odd | 4 | 200.6.c.f.49.3 | 4 | |||
5.3 | odd | 4 | 200.6.c.f.49.2 | 4 | |||
5.4 | even | 2 | 200.6.a.e.1.2 | ✓ | 2 | ||
20.3 | even | 4 | 400.6.c.o.49.3 | 4 | |||
20.7 | even | 4 | 400.6.c.o.49.2 | 4 | |||
20.19 | odd | 2 | 400.6.a.u.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.6.a.e.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
200.6.a.f.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
200.6.c.f.49.2 | 4 | 5.3 | odd | 4 | |||
200.6.c.f.49.3 | 4 | 5.2 | odd | 4 | |||
400.6.a.r.1.2 | 2 | 4.3 | odd | 2 | |||
400.6.a.u.1.1 | 2 | 20.19 | odd | 2 | |||
400.6.c.o.49.2 | 4 | 20.7 | even | 4 | |||
400.6.c.o.49.3 | 4 | 20.3 | even | 4 |