Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(65,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.65");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.b (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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Root | \(0.707107 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.65 |
Dual form | 128.4.b.e.65.3 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 6.32456i | − 1.21716i | −0.793492 | − | 0.608581i | \(-0.791739\pi\) | ||||
0.793492 | − | 0.608581i | \(-0.208261\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 17.8885i | 1.60000i | 0.600000 | + | 0.800000i | \(0.295167\pi\) | ||||
−0.600000 | + | 0.800000i | \(0.704833\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.6274 | 1.22177 | 0.610883 | − | 0.791721i | \(-0.290815\pi\) | ||||
0.610883 | + | 0.791721i | \(0.290815\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −13.0000 | −0.481481 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44.2719i | 1.21350i | 0.794894 | + | 0.606749i | \(0.207527\pi\) | ||||
−0.794894 | + | 0.606749i | \(0.792473\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 17.8885i | − 0.381645i | −0.981625 | − | 0.190823i | \(-0.938884\pi\) | ||||
0.981625 | − | 0.190823i | \(-0.0611155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 113.137 | 1.94746 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 70.0000 | 0.998676 | 0.499338 | − | 0.866407i | \(-0.333577\pi\) | ||||
0.499338 | + | 0.866407i | \(0.333577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 82.2192i | − 0.992757i | −0.868106 | − | 0.496378i | \(-0.834663\pi\) | ||||
0.868106 | − | 0.496378i | \(-0.165337\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 143.108i | − 1.48709i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 158.392 | 1.43596 | 0.717978 | − | 0.696066i | \(-0.245068\pi\) | ||||
0.717978 | + | 0.696066i | \(0.245068\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −195.000 | −1.56000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 88.5438i | − 0.631121i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 125.220i | 0.801818i | 0.916118 | + | 0.400909i | \(0.131306\pi\) | ||||
−0.916118 | + | 0.400909i | \(0.868694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 280.000 | 1.47702 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 404.772i | 1.95483i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 375.659i | 1.66914i | 0.550905 | + | 0.834568i | \(0.314283\pi\) | ||||
−0.550905 | + | 0.834568i | \(0.685717\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −113.137 | −0.464524 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −182.000 | −0.693259 | −0.346630 | − | 0.938002i | \(-0.612674\pi\) | ||||
−0.346630 | + | 0.938002i | \(0.612674\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 132.816i | − 0.471028i | −0.971871 | − | 0.235514i | \(-0.924323\pi\) | ||||
0.971871 | − | 0.235514i | \(-0.0756773\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 232.551i | − 0.770370i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −316.784 | −0.983142 | −0.491571 | − | 0.870838i | \(-0.663577\pi\) | ||||
−0.491571 | + | 0.870838i | \(0.663577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 169.000 | 0.492711 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 442.719i | − 1.21555i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 125.220i | − 0.324533i | −0.986747 | − | 0.162267i | \(-0.948120\pi\) | ||||
0.986747 | − | 0.162267i | \(-0.0518805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −791.960 | −1.94160 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −520.000 | −1.20835 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 82.2192i | − 0.181424i | −0.995877 | − | 0.0907121i | \(-0.971086\pi\) | ||||
0.995877 | − | 0.0907121i | \(-0.0289143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 232.551i | − 0.488117i | −0.969761 | − | 0.244058i | \(-0.921521\pi\) | ||||
0.969761 | − | 0.244058i | \(-0.0784788\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −294.156 | −0.588258 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 320.000 | 0.610633 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 221.359i | 0.403632i | 0.979423 | + | 0.201816i | \(0.0646843\pi\) | ||||
−0.979423 | + | 0.201816i | \(0.935316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 1001.76i | − 1.74779i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 113.137 | 0.189111 | 0.0945556 | − | 0.995520i | \(-0.469857\pi\) | ||||
0.0945556 | + | 0.995520i | \(0.469857\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 910.000 | 1.45901 | 0.729503 | − | 0.683978i | \(-0.239751\pi\) | ||||
0.729503 | + | 0.683978i | \(0.239751\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1233.29i | 1.89877i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1001.76i | 1.48261i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −678.823 | −0.966753 | −0.483377 | − | 0.875413i | \(-0.660590\pi\) | ||||
−0.483377 | + | 0.875413i | \(0.660590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −911.000 | −1.24966 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 714.675i | − 0.945129i | −0.881296 | − | 0.472565i | \(-0.843328\pi\) | ||||
0.881296 | − | 0.472565i | \(-0.156672\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1252.20i | 1.59788i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 791.960 | 0.975942 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −546.000 | −0.650291 | −0.325145 | − | 0.945664i | \(-0.605413\pi\) | ||||
−0.325145 | + | 0.945664i | \(0.605413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 404.772i | − 0.466281i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1470.78 | 1.58841 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −490.000 | −0.512907 | −0.256453 | − | 0.966557i | \(-0.582554\pi\) | ||||
−0.256453 | + | 0.966557i | \(0.582554\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 575.535i | − 0.584277i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 232.551i | 0.229106i | 0.993417 | + | 0.114553i | \(0.0365436\pi\) | ||||
−0.993417 | + | 0.114553i | \(0.963456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −158.392 | −0.151523 | −0.0757613 | − | 0.997126i | \(-0.524139\pi\) | ||||
−0.0757613 | + | 0.997126i | \(0.524139\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2560.00 | 2.37934 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1726.60i | − 1.55997i | −0.625797 | − | 0.779986i | \(-0.715226\pi\) | ||||
0.625797 | − | 0.779986i | \(-0.284774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1377.42i | − 1.21039i | −0.796077 | − | 0.605196i | \(-0.793095\pi\) | ||||
0.796077 | − | 0.605196i | \(-0.206905\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2375.88 | 2.03161 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −910.000 | −0.757572 | −0.378786 | − | 0.925484i | \(-0.623658\pi\) | ||||
−0.378786 | + | 0.925484i | \(0.623658\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2833.40i | 2.29753i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 232.551i | 0.183755i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1583.92 | 1.22015 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −629.000 | −0.472577 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1151.07i | 0.843808i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1252.20i | − 0.896000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1900.70 | −1.32803 | −0.664016 | − | 0.747718i | \(-0.731149\pi\) | ||||
−0.664016 | + | 0.747718i | \(0.731149\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −840.000 | −0.573317 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 170.763i | 0.113890i | 0.998377 | + | 0.0569452i | \(0.0181360\pi\) | ||||
−0.998377 | + | 0.0569452i | \(0.981864\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1860.41i | − 1.21292i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1583.92 | 1.00979 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1930.00 | 1.20358 | 0.601792 | − | 0.798653i | \(-0.294454\pi\) | ||||
0.601792 | + | 0.798653i | \(0.294454\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1144.74i | − 0.698532i | −0.937024 | − | 0.349266i | \(-0.886431\pi\) | ||||
0.937024 | − | 0.349266i | \(-0.113569\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2003.52i | 1.19664i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 791.960 | 0.463126 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2240.00 | −1.28291 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1068.85i | − 0.599709i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1627.86i | − 0.895029i | −0.894277 | − | 0.447514i | \(-0.852309\pi\) | ||||
0.894277 | − | 0.447514i | \(-0.147691\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2375.88 | −1.28044 | −0.640219 | − | 0.768192i | \(-0.721157\pi\) | ||||
−0.640219 | + | 0.768192i | \(0.721157\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −910.000 | −0.480844 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3488.27i | 1.77321i | 0.462528 | + | 0.886605i | \(0.346943\pi\) | ||||
−0.462528 | + | 0.886605i | \(0.653057\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −791.960 | −0.395009 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3584.00 | 1.75440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3497.48i | − 1.68064i | −0.542094 | − | 0.840318i | \(-0.682368\pi\) | ||||
0.542094 | − | 0.840318i | \(-0.317632\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5008.79i | 2.36324i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2059.09 | −0.954117 | −0.477059 | − | 0.878872i | \(-0.658297\pi\) | ||||
−0.477059 | + | 0.878872i | \(0.658297\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1877.00 | 0.854347 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1068.85i | 0.477994i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2021.41i | − 0.888350i | −0.895940 | − | 0.444175i | \(-0.853497\pi\) | ||||
0.895940 | − | 0.444175i | \(-0.146503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4412.35 | −1.90595 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −520.000 | −0.220823 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3586.02i | 1.49739i | 0.662917 | + | 0.748693i | \(0.269318\pi\) | ||||
−0.662917 | + | 0.748693i | \(0.730682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2486.51i | − 1.02111i | −0.859846 | − | 0.510554i | \(-0.829440\pi\) | ||||
0.859846 | − | 0.510554i | \(-0.170560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1470.78 | −0.594117 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6720.00 | −2.67062 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3099.03i | 1.21189i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2003.52i | − 0.771082i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2262.74 | 0.857205 | 0.428603 | − | 0.903493i | \(-0.359006\pi\) | ||||
0.428603 | + | 0.903493i | \(0.359006\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 630.000 | 0.234966 | 0.117483 | − | 0.993075i | \(-0.462517\pi\) | ||||
0.117483 | + | 0.993075i | \(0.462517\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 2023.86i | − 0.743238i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1878.30i | 0.679305i | 0.940551 | + | 0.339653i | \(0.110310\pi\) | ||||
−0.940551 | + | 0.339653i | \(0.889690\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3959.80 | −1.41057 | −0.705283 | − | 0.708926i | \(-0.749180\pi\) | ||||
−0.705283 | + | 0.708926i | \(0.749180\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1400.00 | 0.491286 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2833.40i | 0.979634i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 3255.71i | − 1.10921i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2059.09 | −0.691386 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3640.00 | 1.20471 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2789.13i | − 0.910007i | −0.890490 | − | 0.455004i | \(-0.849638\pi\) | ||||
0.890490 | − | 0.455004i | \(-0.150362\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 715.542i | − 0.230179i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2375.88 | 0.753645 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 5755.35i | − 1.77585i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1252.20i | − 0.381140i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2534.27 | −0.761019 | −0.380510 | − | 0.924777i | \(-0.624251\pi\) | ||||
−0.380510 | + | 0.924777i | \(0.624251\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2535.00 | 0.751111 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2219.92i | 0.649080i | 0.945872 | + | 0.324540i | \(0.105210\pi\) | ||||
−0.945872 | + | 0.324540i | \(0.894790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4275.36i | − 1.23373i | −0.787069 | − | 0.616864i | \(-0.788403\pi\) | ||||
0.787069 | − | 0.616864i | \(-0.211597\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6335.68 | 1.80458 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5010.00 | −1.40865 | −0.704326 | − | 0.709876i | \(-0.748751\pi\) | ||||
−0.704326 | + | 0.709876i | \(0.748751\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 5666.80i | − 1.57303i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4293.25i | 1.17669i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1583.92 | 0.428683 | 0.214341 | − | 0.976759i | \(-0.431239\pi\) | ||||
0.214341 | + | 0.976759i | \(0.431239\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1638.00 | 0.437813 | 0.218906 | − | 0.975746i | \(-0.429751\pi\) | ||||
0.218906 | + | 0.975746i | \(0.429751\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3370.99i | 0.889913i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3023.16i | 0.788338i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1470.78 | −0.378881 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4520.00 | −1.15037 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1233.29i | 0.310137i | 0.987904 | + | 0.155069i | \(0.0495599\pi\) | ||||
−0.987904 | + | 0.155069i | \(0.950440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7012.31i | 1.74253i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7919.60 | 1.94488 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1890.00 | 0.458735 | 0.229368 | − | 0.973340i | \(-0.426334\pi\) | ||||
0.229368 | + | 0.973340i | \(0.426334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8500.20i | 2.03929i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1627.86i | − 0.386061i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2647.41 | 0.620708 | 0.310354 | − | 0.950621i | \(-0.399552\pi\) | ||||
0.310354 | + | 0.950621i | \(0.399552\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2240.00 | 0.519253 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3453.21i | 0.791509i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3488.27i | 0.790644i | 0.918543 | + | 0.395322i | \(0.129367\pi\) | ||||
−0.918543 | + | 0.395322i | \(0.870633\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7919.60 | 1.77521 | 0.887604 | − | 0.460608i | \(-0.152369\pi\) | ||||
0.887604 | + | 0.460608i | \(0.152369\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2560.00 | −0.567539 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 8633.02i | − 1.89306i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4883.57i | 1.05930i | 0.848217 | + | 0.529649i | \(0.177676\pi\) | ||||
−0.848217 | + | 0.529649i | \(0.822324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1118.00 | 0.237346 | 0.118673 | − | 0.992933i | \(-0.462136\pi\) | ||||
0.118673 | + | 0.992933i | \(0.462136\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2118.73i | 0.445036i | 0.974929 | + | 0.222518i | \(0.0714276\pi\) | ||||
−0.974929 | + | 0.222518i | \(0.928572\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 9302.04i | − 1.93335i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4118.19 | −0.847000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.00264604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3099.03i | 0.624290i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 4275.36i | − 0.852455i | −0.904616 | − | 0.426227i | \(-0.859842\pi\) | ||||
0.904616 | − | 0.426227i | \(-0.140158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1470.78 | 0.290279 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3920.00 | 0.765864 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 2833.40i | − 0.548026i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3005.28i | − 0.575486i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1470.78 | 0.278859 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4160.00 | 0.780987 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7975.26i | − 1.48265i | −0.671148 | − | 0.741323i | \(-0.734199\pi\) | ||||
0.671148 | − | 0.741323i | \(-0.265801\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1001.76i | 0.184427i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10295.5 | 1.87718 | 0.938590 | − | 0.345035i | \(-0.112133\pi\) | ||||
0.938590 | + | 0.345035i | \(0.112133\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2170.00 | 0.391871 | 0.195936 | − | 0.980617i | \(-0.437226\pi\) | ||||
0.195936 | + | 0.980617i | \(0.437226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 5262.03i | − 0.941212i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 4883.57i | − 0.865264i | −0.901571 | − | 0.432632i | \(-0.857585\pi\) | ||||
0.901571 | − | 0.432632i | \(-0.142415\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5543.72 | −0.973005 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10920.0 | −1.89874 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5755.35i | − 0.991443i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3488.27i | 0.595367i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8711.56 | −1.47324 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7168.00 | −1.20117 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11732.1i | 1.94819i | 0.226133 | + | 0.974096i | \(0.427392\pi\) | ||||
−0.226133 | + | 0.974096i | \(0.572608\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 4883.57i | − 0.803658i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3959.80 | −0.645812 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10990.0 | −1.77645 | −0.888225 | − | 0.459409i | \(-0.848061\pi\) | ||||
−0.888225 | + | 0.459409i | \(0.848061\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5755.35i | 0.922087i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3937.17 | −0.619788 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17920.0 | 2.79646 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4117.29i | 0.636967i | 0.947928 | + | 0.318483i | \(0.103174\pi\) | ||||
−0.947928 | + | 0.318483i | \(0.896826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4275.36i | 0.655745i | 0.944722 | + | 0.327872i | \(0.106332\pi\) | ||||
−0.944722 | + | 0.327872i | \(0.893668\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1583.92 | −0.240864 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8610.00 | 1.29820 | 0.649099 | − | 0.760704i | \(-0.275146\pi\) | ||||
0.649099 | + | 0.760704i | \(0.275146\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2023.86i | 0.302578i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 10017.6i | − 1.48512i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10295.5 | −1.51358 | −0.756789 | − | 0.653659i | \(-0.773233\pi\) | ||||
−0.756789 | + | 0.653659i | \(0.773233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 99.0000 | 0.0144336 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3978.15i | 0.575202i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16278.6i | 2.33441i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2851.05 | −0.405515 | −0.202757 | − | 0.979229i | \(-0.564990\pi\) | ||||
−0.202757 | + | 0.979229i | \(0.564990\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2366.00 | 0.333791 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2833.40i | − 0.396504i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4883.57i | 0.677914i | 0.940802 | + | 0.338957i | \(0.110074\pi\) | ||||
−0.940802 | + | 0.338957i | \(0.889926\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7919.60 | −1.09058 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2240.00 | 0.306010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3674.57i | − 0.498021i | −0.968501 | − | 0.249010i | \(-0.919895\pi\) | ||||
0.968501 | − | 0.249010i | \(-0.0801053\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12021.1i | 1.61643i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2534.27 | −0.338108 | −0.169054 | − | 0.985607i | \(-0.554071\pi\) | ||||
−0.169054 | + | 0.985607i | \(0.554071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17920.0 | −2.37218 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1726.60i | 0.226791i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11395.0i | 1.48522i | 0.669726 | + | 0.742609i | \(0.266412\pi\) | ||||
−0.669726 | + | 0.742609i | \(0.733588\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11087.4 | 1.43406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1080.00 | 0.138623 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 12143.1i | − 1.54681i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 13255.4i | − 1.67574i | −0.545867 | − | 0.837872i | \(-0.683800\pi\) | ||||
0.545867 | − | 0.837872i | \(-0.316200\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11766.3 | −1.47631 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1722.00 | −0.214445 | −0.107223 | − | 0.994235i | \(-0.534196\pi\) | ||||
−0.107223 | + | 0.994235i | \(0.534196\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 16296.5i | − 1.99945i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16631.2 | −2.02549 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13594.0 | 1.64347 | 0.821736 | − | 0.569868i | \(-0.193006\pi\) | ||||
0.821736 | + | 0.569868i | \(0.193006\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 12206.4i | − 1.46496i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1860.41i | − 0.221658i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12784.5 | 1.51221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7240.00 | −0.850226 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4775.04i | 0.556744i | 0.960473 | + | 0.278372i | \(0.0897949\pi\) | ||||
−0.960473 | + | 0.278372i | \(0.910205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7888.85i | 0.913252i | 0.889659 | + | 0.456626i | \(0.150942\pi\) | ||||
−0.889659 | + | 0.456626i | \(0.849058\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4118.19 | 0.473365 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13650.0 | −1.55793 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5262.03i | − 0.596364i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 5008.79i | − 0.563699i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1583.92 | 0.177018 | 0.0885089 | − | 0.996075i | \(-0.471790\pi\) | ||||
0.0885089 | + | 0.996075i | \(0.471790\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14630.0 | 1.62373 | 0.811863 | − | 0.583849i | \(-0.198454\pi\) | ||||
0.811863 | + | 0.583849i | \(0.198454\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14167.0i | 1.56151i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 13022.9i | − 1.42556i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10295.5 | 1.11931 | 0.559654 | − | 0.828726i | \(-0.310934\pi\) | ||||
0.559654 | + | 0.828726i | \(0.310934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2197.00 | −0.237231 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17753.0i | 1.90400i | 0.306099 | + | 0.952000i | \(0.400976\pi\) | ||||
−0.306099 | + | 0.952000i | \(0.599024\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 9767.14i | − 1.04047i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10295.5 | −1.08939 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3894.00 | 0.409286 | 0.204643 | − | 0.978837i | \(-0.434397\pi\) | ||||
0.204643 | + | 0.978837i | \(0.434397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 8057.48i | − 0.841268i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15026.4i | 1.55850i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7240.77 | 0.746050 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2730.00 | 0.279440 | 0.139720 | − | 0.990191i | \(-0.455380\pi\) | ||||
0.139720 | + | 0.990191i | \(0.455380\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 6198.06i | − 0.630285i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 10250.1i | − 1.03557i | −0.855512 | − | 0.517784i | \(-0.826757\pi\) | ||||
0.855512 | − | 0.517784i | \(-0.173243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7648.07 | 0.767680 | 0.383840 | − | 0.923400i | \(-0.374601\pi\) | ||||
0.383840 | + | 0.923400i | \(0.374601\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13730.6i | 1.36055i | 0.732957 | + | 0.680275i | \(0.238140\pi\) | ||||
−0.732957 | + | 0.680275i | \(0.761860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5008.79i | 0.493144i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22061.7 | 2.15828 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5880.00 | 0.571591 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16032.7i | 1.54870i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1627.86i | 0.156257i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12671.4 | 1.20870 | 0.604352 | − | 0.796718i | \(-0.293432\pi\) | ||||
0.604352 | + | 0.796718i | \(0.293432\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6720.00 | 0.637018 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 22667.2i | − 2.13539i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 8765.39i | − 0.820651i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2059.09 | −0.191594 | −0.0957972 | − | 0.995401i | \(-0.530540\pi\) | ||||
−0.0957972 | + | 0.995401i | \(0.530540\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22120.0 | −2.04561 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5888.16i | 0.541200i | 0.962692 | + | 0.270600i | \(0.0872220\pi\) | ||||
−0.962692 | + | 0.270600i | \(0.912778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8765.39i | 0.800757i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10295.5 | 0.934843 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2560.00 | 0.231050 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 10935.2i | − 0.981012i | −0.871438 | − | 0.490506i | \(-0.836812\pi\) | ||||
0.871438 | − | 0.490506i | \(-0.163188\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13022.9i | 1.16131i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14413.7 | −1.27768 | −0.638840 | − | 0.769339i | \(-0.720586\pi\) | ||||
−0.638840 | + | 0.769339i | \(0.720586\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4160.00 | −0.366569 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 11871.2i | − 1.03988i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12790.3i | 1.11379i | 0.830582 | + | 0.556896i | \(0.188008\pi\) | ||||
−0.830582 | + | 0.556896i | \(0.811992\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20590.9 | 1.78256 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7280.00 | −0.626549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2833.40i | − 0.242436i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 14024.6i | − 1.19304i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12784.5 | −1.08127 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16758.0 | −1.40918 | −0.704589 | − | 0.709616i | \(-0.748868\pi\) | ||||
−0.704589 | + | 0.709616i | \(0.748868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 16197.2i | − 1.35421i | −0.735885 | − | 0.677107i | \(-0.763234\pi\) | ||||
0.735885 | − | 0.677107i | \(-0.236766\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27906.1i | 2.31985i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12921.0 | 1.06197 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1068.85i | 0.0873524i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3255.71i | 0.264579i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30886.4 | 2.49596 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22680.0 | 1.82256 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7481.95i | 0.597904i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 375.659i | − 0.0298537i | −0.999889 | − | 0.0149269i | \(-0.995248\pi\) | ||||
0.999889 | − | 0.0149269i | \(-0.00475154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15726.1 | −1.24285 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24640.0 | 1.93663 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1638.06i | 0.128041i | 0.997949 | + | 0.0640205i | \(0.0203923\pi\) | ||||
−0.997949 | + | 0.0640205i | \(0.979608\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3023.16i | 0.235019i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10295.5 | 0.796011 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15360.0 | −1.18115 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42501.0i | 3.25057i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 19909.9i | − 1.51456i | −0.653089 | − | 0.757282i | \(-0.726527\pi\) | ||||
0.653089 | − | 0.757282i | \(-0.273473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2375.88 | −0.179766 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19600.0 | 1.47507 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 790.569i | − 0.0591803i | −0.999562 | − | 0.0295902i | \(-0.990580\pi\) | ||||
0.999562 | − | 0.0295902i | \(-0.00942022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 16278.6i | − 1.21211i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20613.6 | −1.52679 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20454.0 | −1.50699 | −0.753494 | − | 0.657455i | \(-0.771633\pi\) | ||||
−0.753494 | + | 0.657455i | \(0.771633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 5622.53i | − 0.412076i | −0.978544 | − | 0.206038i | \(-0.933943\pi\) | ||||
0.978544 | − | 0.206038i | \(-0.0660571\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 14310.8i | − 1.04336i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30886.4 | −2.24009 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22750.0 | −1.64141 | −0.820706 | − | 0.571351i | \(-0.806420\pi\) | ||||
−0.820706 | + | 0.571351i | \(0.806420\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 3984.47i | − 0.285991i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 16171.2i | − 1.15473i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5543.72 | 0.393820 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4160.00 | −0.294008 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 15843.0i | − 1.11399i | −0.830516 | − | 0.556994i | \(-0.811955\pi\) | ||||
0.830516 | − | 0.556994i | \(-0.188045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11879.4 | 0.826824 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12110.0 | −0.838614 | −0.419307 | − | 0.907845i | \(-0.637727\pi\) | ||||
−0.419307 | + | 0.907845i | \(0.637727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28334.0i | 1.95224i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25044.0i | 1.71689i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19120.2 | −1.30422 | −0.652111 | − | 0.758124i | \(-0.726116\pi\) | ||||
−0.652111 | + | 0.758124i | \(0.726116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4382.00 | 0.297413 | 0.148707 | − | 0.988881i | \(-0.452489\pi\) | ||||
0.148707 | + | 0.988881i | \(0.452489\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2877.67i | − 0.194341i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 11251.9i | − 0.756123i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8236.38 | −0.550749 | −0.275374 | − | 0.961337i | \(-0.588802\pi\) | ||||
−0.275374 | + | 0.961337i | \(0.588802\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17920.0 | 1.19237 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5666.80i | 0.375212i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2128.74i | − 0.140259i | −0.997538 | − | 0.0701296i | \(-0.977659\pi\) | ||||
0.997538 | − | 0.0701296i | \(-0.0223413\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20590.9 | −1.35009 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15470.0 | 1.00940 | 0.504699 | − | 0.863295i | \(-0.331603\pi\) | ||||
0.504699 | + | 0.863295i | \(0.331603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 19486.0i | − 1.26528i | −0.774447 | − | 0.632639i | \(-0.781972\pi\) | ||||
0.774447 | − | 0.632639i | \(-0.218028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 14024.6i | − 0.906262i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12354.6 | −0.794503 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1975.00 | −0.126400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 23021.4i | − 1.46632i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26296.2i | 1.66693i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6448.81 | −0.406851 | −0.203426 | − | 0.979090i | \(-0.565208\pi\) | ||||
−0.203426 | + | 0.979090i | \(0.565208\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17640.0 | −1.10763 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 34000.8i | − 2.12485i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3023.16i | − 0.188041i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1470.78 | −0.0910536 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 182.000 | 0.0112146 | 0.00560731 | − | 0.999984i | \(-0.498215\pi\) | ||||
0.00560731 | + | 0.999984i | \(0.498215\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23293.3i | 1.42862i | 0.699832 | + | 0.714308i | \(0.253258\pi\) | ||||
−0.699832 | + | 0.714308i | \(0.746742\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 15026.4i | − 0.917307i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2059.09 | −0.125118 | −0.0625590 | − | 0.998041i | \(-0.519926\pi\) | ||||
−0.0625590 | + | 0.998041i | \(0.519926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3640.00 | 0.220158 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14650.7i | 0.877989i | 0.898490 | + | 0.438995i | \(0.144665\pi\) | ||||
−0.898490 | + | 0.438995i | \(0.855335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3054.70 | −0.182225 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11830.0 | −0.702484 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 10935.2i | − 0.646393i | −0.946332 | − | 0.323197i | \(-0.895242\pi\) | ||||
0.946332 | − | 0.323197i | \(-0.104758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3774.48i | − 0.222103i | −0.993815 | − | 0.111052i | \(-0.964578\pi\) | ||||
0.993815 | − | 0.111052i | \(-0.0354219\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7919.60 | −0.463909 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33280.0 | 1.94067 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19833.8i | 1.15138i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16028.1i | 0.926283i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10295.5 | 0.592328 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2410.00 | −0.138037 | −0.0690183 | − | 0.997615i | \(-0.521987\pi\) | ||||
−0.0690183 | + | 0.997615i | \(0.521987\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17266.0i | 0.984548i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27566.2i | 1.56493i | 0.622695 | + | 0.782464i | \(0.286038\pi\) | ||||
−0.622695 | + | 0.782464i | \(0.713962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11087.4 | −0.626652 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14040.0 | 0.790035 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2346.41i | 0.131454i | 0.997838 | + | 0.0657269i | \(0.0209366\pi\) | ||||
−0.997838 | + | 0.0657269i | \(0.979063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34524.9i | 1.92573i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27039.8 | −1.50165 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2240.00 | −0.123857 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 10277.4i | − 0.565804i | −0.959149 | − | 0.282902i | \(-0.908703\pi\) | ||||
0.959149 | − | 0.282902i | \(-0.0912972\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 13022.9i | − 0.713849i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20477.8 | 1.11765 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12740.0 | −0.692341 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31686.0i | 1.71456i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 626.099i | 0.0337339i | 0.999858 | + | 0.0168669i | \(0.00536916\pi\) | ||||
−0.999858 | + | 0.0168669i | \(0.994631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30886.4 | 1.65705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −35840.0 | −1.91463 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5262.03i | 0.279914i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 14650.7i | − 0.776050i | −0.921649 | − | 0.388025i | \(-0.873157\pi\) | ||||
0.921649 | − | 0.388025i | \(-0.126843\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8824.69 | 0.465474 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14167.0i | 0.741001i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 10017.6i | − 0.521776i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14255.3 | −0.739405 | −0.369702 | − | 0.929150i | \(-0.620540\pi\) | ||||
−0.369702 | + | 0.929150i | \(0.620540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3584.00 | −0.185125 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 10359.6i | − 0.532889i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 24417.9i | − 1.25084i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4276.58 | −0.218170 | −0.109085 | − | 0.994032i | \(-0.534792\pi\) | ||||
−0.109085 | + | 0.994032i | \(0.534792\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3277.00 | −0.166489 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 9297.10i | − 0.470404i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9284.15i | 0.467828i | 0.972257 | + | 0.233914i | \(0.0751534\pi\) | ||||
−0.972257 | + | 0.233914i | \(0.924847\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19120.2 | 0.959535 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9800.00 | −0.489807 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1726.60i | − 0.0859461i | −0.999076 | − | 0.0429730i | \(-0.986317\pi\) | ||||
0.999076 | − | 0.0429730i | \(-0.0136830\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9302.04i | 0.461159i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28352.2 | 1.39992 | 0.699959 | − | 0.714183i | \(-0.253201\pi\) | ||||
0.699959 | + | 0.714183i | \(0.253201\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29120.0 | 1.43205 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9290.77i | 0.455062i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 39068.6i | − 1.90592i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20590.9 | 1.00050 | 0.500249 | − | 0.865881i | \(-0.333242\pi\) | ||||
0.500249 | + | 0.865881i | \(0.333242\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7800.00 | 0.377487 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 42501.0i | − 2.04870i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 22664.8i | − 1.08820i | −0.839021 | − | 0.544099i | \(-0.816872\pi\) | ||||
0.839021 | − | 0.544099i | \(-0.183128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 44349.7 | 2.12094 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7098.00 | 0.338111 | 0.169055 | − | 0.985607i | \(-0.445928\pi\) | ||||
0.169055 | + | 0.985607i | \(0.445928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 31167.4i | − 1.47882i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 16278.6i | − 0.769350i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1470.78 | −0.0692397 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17654.0 | 0.827854 | 0.413927 | − | 0.910310i | \(-0.364157\pi\) | ||||
0.413927 | + | 0.910310i | \(0.364157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 11953.4i | − 0.558355i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6529.32i | 0.303808i | 0.988395 | + | 0.151904i | \(0.0485404\pi\) | ||||
−0.988395 | + | 0.151904i | \(0.951460\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 53760.0 | 2.48215 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14963.9i | 0.688238i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5008.79i | 0.229486i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11087.4 | 0.506044 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62400.0 | −2.83714 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2384.36i | − 0.107996i | −0.998541 | − | 0.0539982i | \(-0.982803\pi\) | ||||
0.998541 | − | 0.0539982i | \(-0.0171965\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 16743.7i | − 0.755502i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20590.9 | −0.925575 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4160.00 | −0.186287 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 14167.0i | − 0.632015i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29534.0i | 1.31261i | 0.754497 | + | 0.656303i | \(0.227881\pi\) | ||||
−0.754497 | + | 0.656303i | \(0.772119\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22174.9 | −0.981840 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7098.00 | 0.313103 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 40287.4i | 1.77050i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 64112.5i | 2.80704i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22061.7 | 0.962342 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10934.0 | −0.475178 | −0.237589 | − | 0.971366i | \(-0.576357\pi\) | ||||
−0.237589 | + | 0.971366i | \(0.576357\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17348.3i | 0.751146i | 0.926793 | + | 0.375573i | \(0.122554\pi\) | ||||
−0.926793 | + | 0.375573i | \(0.877446\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 50087.9i | − 2.16071i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 62564.8 | 2.68902 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10920.0 | −0.467616 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5262.03i | 0.224506i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14901.2i | 0.633440i | 0.948519 | + | 0.316720i | \(0.102581\pi\) | ||||
−0.948519 | + | 0.316720i | \(0.897419\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17943.5 | −0.759991 | −0.379995 | − | 0.924988i | \(-0.624074\pi\) | ||||
−0.379995 | + | 0.924988i | \(0.624074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −54600.0 | −2.30416 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25899.1i | 1.08899i | 0.838763 | + | 0.544497i | \(0.183279\pi\) | ||||
−0.838763 | + | 0.544497i | \(0.816721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 25276.5i | − 1.05897i | −0.848318 | − | 0.529487i | \(-0.822384\pi\) | ||||
0.848318 | − | 0.529487i | \(-0.177616\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30886.4 | 1.28934 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11830.0 | 0.492059 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 36834.2i | − 1.52659i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10295.5 | −0.423646 | −0.211823 | − | 0.977308i | \(-0.567940\pi\) | ||||
−0.211823 | + | 0.977308i | \(0.567940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8709.00 | 0.357087 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 7070.85i | − 0.288889i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33576.8i | 1.36695i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14232.6 | −0.577378 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13400.0 | 0.541681 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 59501.4i | 2.39681i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21770.4i | 0.873860i | 0.899495 | + | 0.436930i | \(0.143934\pi\) | ||||
−0.899495 | + | 0.436930i | \(0.856066\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19120.2 | −0.764791 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24570.0 | 0.979341 | 0.489670 | − | 0.871908i | \(-0.337117\pi\) | ||||
0.489670 | + | 0.871908i | \(0.337117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5837.56i | 0.231869i | 0.993257 | + | 0.115934i | \(0.0369862\pi\) | ||||
−0.993257 | + | 0.115934i | \(0.963014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26045.7i | 1.03094i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23713.5 | −0.935363 | −0.467681 | − | 0.883897i | \(-0.654911\pi\) | ||||
−0.467681 | + | 0.883897i | \(0.654911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36160.0 | 1.42136 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 82.2192i | 0.00322066i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 30052.8i | − 1.17315i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3959.80 | 0.154044 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6370.00 | 0.246955 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 28334.0i | − 1.09470i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43701.7i | 1.68267i | 0.540514 | + | 0.841335i | \(0.318230\pi\) | ||||
−0.540514 | + | 0.841335i | \(0.681770\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27039.8 | −1.03758 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17038.0 | −0.651561 | −0.325780 | − | 0.945446i | \(-0.605627\pi\) | ||||
−0.325780 | + | 0.945446i | \(0.605627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27492.8i | 1.04780i | 0.851780 | + | 0.523900i | \(0.175524\pi\) | ||||
−0.851780 | + | 0.523900i | \(0.824476\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 9302.04i | − 0.353316i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43241.0 | 1.63686 | 0.818428 | − | 0.574610i | \(-0.194846\pi\) | ||||
0.818428 | + | 0.574610i | \(0.194846\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43008.0 | −1.62254 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 40331.7i | − 1.51646i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26045.7i | 0.976021i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −64148.7 | −2.39582 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17920.0 | −0.667036 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 8765.39i | − 0.324104i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19007.0 | −0.700459 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 44480.0 | 1.63377 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 40154.6i | − 1.47002i | −0.678054 | − | 0.735012i | \(-0.737177\pi\) | ||||
0.678054 | − | 0.735012i | \(-0.262823\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 3023.16i | − 0.110310i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11087.4 | −0.403231 | −0.201615 | − | 0.979465i | \(-0.564619\pi\) | ||||
−0.201615 | + | 0.979465i | \(0.564619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31640.0 | 1.14691 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 26310.2i | − 0.950587i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3863.93i | 0.139147i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1470.78 | −0.0527928 | −0.0263964 | − | 0.999652i | \(-0.508403\pi\) | ||||
−0.0263964 | + | 0.999652i | \(0.508403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −50440.0 | −1.80462 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2023.86i | − 0.0721734i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 73253.6i | − 2.60385i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2059.09 | 0.0729553 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32214.0 | 1.13768 | 0.568841 | − | 0.822447i | \(-0.307392\pi\) | ||||
0.568841 | + | 0.822447i | \(0.307392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 13895.0i | − 0.489143i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 65114.3i | − 2.28483i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −55437.2 | −1.93903 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13650.0 | −0.475908 | −0.237954 | − | 0.971276i | \(-0.576477\pi\) | ||||
−0.237954 | + | 0.971276i | \(0.576477\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 13724.3i | − 0.476970i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 6529.32i | − 0.226195i | −0.993584 | − | 0.113098i | \(-0.963923\pi\) | ||||
0.993584 | − | 0.113098i | \(-0.0360773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28827.3 | −0.995490 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 35840.0 | 1.23373 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11555.0i | 0.396500i | 0.980151 | + | 0.198250i | \(0.0635258\pi\) | ||||
−0.980151 | + | 0.198250i | \(0.936474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 16278.6i | − 0.556823i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30886.4 | −1.05317 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10470.0 | −0.355883 | −0.177942 | − | 0.984041i | \(-0.556944\pi\) | ||||
−0.177942 | + | 0.984041i | \(0.556944\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40477.2i | 1.37153i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35061.5i | 1.18430i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43670.9 | 1.47050 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29791.0 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22445.8i | 0.751098i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11269.8i | 0.375945i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40706.7 | −1.35371 | −0.676856 | − | 0.736115i | \(-0.736658\pi\) | ||||
−0.676856 | + | 0.736115i | \(0.736658\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36400.0 | −1.20675 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49502.3i | 1.63605i | 0.575183 | + | 0.818025i | \(0.304931\pi\) | ||||
−0.575183 | + | 0.818025i | \(0.695069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 25902.6i | − 0.853443i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 22061.7 | 0.724657 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51770.0 | −1.69526 | −0.847630 | − | 0.530588i | \(-0.821971\pi\) | ||||
−0.847630 | + | 0.530588i | \(0.821971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 24172.5i | − 0.789127i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17906.4i | 0.582781i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22333.3 | 0.724639 | 0.362320 | − | 0.932054i | \(-0.381985\pi\) | ||||
0.362320 | + | 0.932054i | \(0.381985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33600.0 | −1.08689 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 45334.4i | 1.46202i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 21036.9i | − 0.676376i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52948.2 | −1.69723 | −0.848614 | − | 0.529012i | \(-0.822563\pi\) | ||||
−0.848614 | + | 0.529012i | \(0.822563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 74200.0 | 2.37126 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 70835.0i | − 2.25691i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17548.7i | 0.557444i | 0.960372 | + | 0.278722i | \(0.0899108\pi\) | ||||
−0.960372 | + | 0.278722i | \(0.910089\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33262.3 | 1.05343 |
(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 | 128.4.b.e.65.2 | yes | 4 | |
3.2 | odd | 2 | 1152.4.d.j.577.2 | 4 | |||
4.3 | odd | 2 | inner | 128.4.b.e.65.4 | yes | 4 | |
8.3 | odd | 2 | inner | 128.4.b.e.65.1 | ✓ | 4 | |
8.5 | even | 2 | inner | 128.4.b.e.65.3 | yes | 4 | |
12.11 | even | 2 | 1152.4.d.j.577.1 | 4 | |||
16.3 | odd | 4 | 256.4.a.n.1.2 | 4 | |||
16.5 | even | 4 | 256.4.a.n.1.1 | 4 | |||
16.11 | odd | 4 | 256.4.a.n.1.3 | 4 | |||
16.13 | even | 4 | 256.4.a.n.1.4 | 4 | |||
24.5 | odd | 2 | 1152.4.d.j.577.4 | 4 | |||
24.11 | even | 2 | 1152.4.d.j.577.3 | 4 | |||
48.5 | odd | 4 | 2304.4.a.bz.1.3 | 4 | |||
48.11 | even | 4 | 2304.4.a.bz.1.4 | 4 | |||
48.29 | odd | 4 | 2304.4.a.bz.1.1 | 4 | |||
48.35 | even | 4 | 2304.4.a.bz.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.4.b.e.65.1 | ✓ | 4 | 8.3 | odd | 2 | inner | |
128.4.b.e.65.2 | yes | 4 | 1.1 | even | 1 | trivial | |
128.4.b.e.65.3 | yes | 4 | 8.5 | even | 2 | inner | |
128.4.b.e.65.4 | yes | 4 | 4.3 | odd | 2 | inner | |
256.4.a.n.1.1 | 4 | 16.5 | even | 4 | |||
256.4.a.n.1.2 | 4 | 16.3 | odd | 4 | |||
256.4.a.n.1.3 | 4 | 16.11 | odd | 4 | |||
256.4.a.n.1.4 | 4 | 16.13 | even | 4 | |||
1152.4.d.j.577.1 | 4 | 12.11 | even | 2 | |||
1152.4.d.j.577.2 | 4 | 3.2 | odd | 2 | |||
1152.4.d.j.577.3 | 4 | 24.11 | even | 2 | |||
1152.4.d.j.577.4 | 4 | 24.5 | odd | 2 | |||
2304.4.a.bz.1.1 | 4 | 48.29 | odd | 4 | |||
2304.4.a.bz.1.2 | 4 | 48.35 | even | 4 | |||
2304.4.a.bz.1.3 | 4 | 48.5 | odd | 4 | |||
2304.4.a.bz.1.4 | 4 | 48.11 | even | 4 |