Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(1,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.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: | \(15.1044889615\) |
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: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 128) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.1 |
$q$-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 | ||||||||
\(3\) | 6.32456 | 1.21716 | 0.608581 | − | 0.793492i | \(-0.291739\pi\) | ||||
0.608581 | + | 0.793492i | \(0.291739\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −17.8885 | −1.60000 | −0.800000 | − | 0.600000i | \(-0.795167\pi\) | ||||
−0.800000 | + | 0.600000i | \(0.795167\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 44.2719 | 1.21350 | 0.606749 | − | 0.794894i | \(-0.292473\pi\) | ||||
0.606749 | + | 0.794894i | \(0.292473\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.8885 | −0.381645 | −0.190823 | − | 0.981625i | \(-0.561116\pi\) | ||||
−0.190823 | + | 0.981625i | \(0.561116\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 82.2192 | 0.992757 | 0.496378 | − | 0.868106i | \(-0.334663\pi\) | ||||
0.496378 | + | 0.868106i | \(0.334663\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 143.108 | 1.48709 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | −88.5438 | −0.631121 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 125.220 | 0.801818 | 0.400909 | − | 0.916118i | \(-0.368694\pi\) | ||||
0.400909 | + | 0.916118i | \(0.368694\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −404.772 | −1.95483 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −375.659 | −1.66914 | −0.834568 | − | 0.550905i | \(-0.814283\pi\) | ||||
−0.834568 | + | 0.550905i | \(0.814283\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −113.137 | −0.464524 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 182.000 | 0.693259 | 0.346630 | − | 0.938002i | \(-0.387326\pi\) | ||||
0.346630 | + | 0.938002i | \(0.387326\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −132.816 | −0.471028 | −0.235514 | − | 0.971871i | \(-0.575677\pi\) | ||||
−0.235514 | + | 0.971871i | \(0.575677\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −232.551 | −0.770370 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 316.784 | 0.983142 | 0.491571 | − | 0.870838i | \(-0.336423\pi\) | ||||
0.491571 | + | 0.870838i | \(0.336423\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 169.000 | 0.492711 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 442.719 | 1.21555 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 125.220 | 0.324533 | 0.162267 | − | 0.986747i | \(-0.448120\pi\) | ||||
0.162267 | + | 0.986747i | \(0.448120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −791.960 | −1.94160 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 520.000 | 1.20835 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −82.2192 | −0.181424 | −0.0907121 | − | 0.995877i | \(-0.528914\pi\) | ||||
−0.0907121 | + | 0.995877i | \(0.528914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −232.551 | −0.488117 | −0.244058 | − | 0.969761i | \(-0.578479\pi\) | ||||
−0.244058 | + | 0.969761i | \(0.578479\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 294.156 | 0.588258 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 320.000 | 0.610633 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −221.359 | −0.403632 | −0.201816 | − | 0.979423i | \(-0.564684\pi\) | ||||
−0.201816 | + | 0.979423i | \(0.564684\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1001.76 | 1.74779 | ||||||||
\(70\) | 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 | \(-0.760249\pi\) | ||||
−0.729503 | + | 0.683978i | \(0.760249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1233.29 | 1.89877 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1001.76 | 1.48261 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 678.823 | 0.966753 | 0.483377 | − | 0.875413i | \(-0.339410\pi\) | ||||
0.483377 | + | 0.875413i | \(0.339410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −911.000 | −1.24966 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 714.675 | 0.945129 | 0.472565 | − | 0.881296i | \(-0.343328\pi\) | ||||
0.472565 | + | 0.881296i | \(0.343328\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1252.20 | −1.59788 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 791.960 | 0.975942 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 546.000 | 0.650291 | 0.325145 | − | 0.945664i | \(-0.394587\pi\) | ||||
0.325145 | + | 0.945664i | \(0.394587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −404.772 | −0.466281 | ||||||||
\(92\) | 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 | ||||||||
\(99\) | 575.535 | 0.584277 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −232.551 | −0.229106 | −0.114553 | − | 0.993417i | \(-0.536544\pi\) | ||||
−0.114553 | + | 0.993417i | \(0.536544\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | −1726.60 | −1.55997 | −0.779986 | − | 0.625797i | \(-0.784774\pi\) | ||||
−0.779986 | + | 0.625797i | \(0.784774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1377.42 | −1.21039 | −0.605196 | − | 0.796077i | \(-0.706905\pi\) | ||||
−0.605196 | + | 0.796077i | \(0.706905\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −2833.40 | −2.29753 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −232.551 | −0.183755 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1583.92 | 1.22015 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 629.000 | 0.472577 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1151.07 | 0.843808 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1252.20 | −0.896000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1900.70 | 1.32803 | 0.664016 | − | 0.747718i | \(-0.268851\pi\) | ||||
0.664016 | + | 0.747718i | \(0.268851\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −840.000 | −0.573317 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −170.763 | −0.113890 | −0.0569452 | − | 0.998377i | \(-0.518136\pi\) | ||||
−0.0569452 | + | 0.998377i | \(0.518136\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1860.41 | 1.21292 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1583.92 | 1.00979 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1930.00 | −1.20358 | −0.601792 | − | 0.798653i | \(-0.705546\pi\) | ||||
−0.601792 | + | 0.798653i | \(0.705546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1144.74 | −0.698532 | −0.349266 | − | 0.937024i | \(-0.613569\pi\) | ||||
−0.349266 | + | 0.937024i | \(0.613569\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2003.52 | 1.19664 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −791.960 | −0.463126 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2240.00 | −1.28291 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1068.85 | 0.599709 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1627.86 | 0.895029 | 0.447514 | − | 0.894277i | \(-0.352309\pi\) | ||||
0.447514 | + | 0.894277i | \(0.352309\pi\) | |||||||
\(150\) | 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 | ||||||||
\(157\) | 3488.27 | 1.77321 | 0.886605 | − | 0.462528i | \(-0.153057\pi\) | ||||
0.886605 | + | 0.462528i | \(0.153057\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 791.960 | 0.395009 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3584.00 | 1.75440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3497.48 | 1.68064 | 0.840318 | − | 0.542094i | \(-0.182368\pi\) | ||||
0.840318 | + | 0.542094i | \(0.182368\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5008.79 | −2.36324 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 1068.85 | 0.477994 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2021.41 | −0.888350 | −0.444175 | − | 0.895940i | \(-0.646503\pi\) | ||||
−0.444175 | + | 0.895940i | \(0.646503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4412.35 | 1.90595 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −520.000 | −0.220823 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3586.02 | −1.49739 | −0.748693 | − | 0.662917i | \(-0.769318\pi\) | ||||
−0.748693 | + | 0.662917i | \(0.769318\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2486.51 | 1.02111 | 0.510554 | − | 0.859846i | \(-0.329440\pi\) | ||||
0.510554 | + | 0.859846i | \(0.329440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1470.78 | −0.594117 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6720.00 | 2.67062 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3099.03 | 1.21189 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2003.52 | −0.771082 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2262.74 | −0.857205 | −0.428603 | − | 0.903493i | \(-0.640994\pi\) | ||||
−0.428603 | + | 0.903493i | \(0.640994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 630.000 | 0.234966 | 0.117483 | − | 0.993075i | \(-0.462517\pi\) | ||||
0.117483 | + | 0.993075i | \(0.462517\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2023.86 | 0.743238 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1878.30 | −0.679305 | −0.339653 | − | 0.940551i | \(-0.610310\pi\) | ||||
−0.339653 | + | 0.940551i | \(0.610310\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 2833.40 | 0.979634 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3255.71 | −1.10921 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2059.09 | 0.691386 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3640.00 | 1.20471 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2789.13 | 0.910007 | 0.455004 | − | 0.890490i | \(-0.349638\pi\) | ||||
0.455004 | + | 0.890490i | \(0.349638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 715.542 | 0.230179 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2375.88 | 0.753645 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5755.35 | −1.77585 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1252.20 | −0.381140 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2534.27 | 0.761019 | 0.380510 | − | 0.924777i | \(-0.375749\pi\) | ||||
0.380510 | + | 0.924777i | \(0.375749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2535.00 | 0.751111 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2219.92 | −0.649080 | −0.324540 | − | 0.945872i | \(-0.605210\pi\) | ||||
−0.324540 | + | 0.945872i | \(0.605210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4275.36 | 1.23373 | 0.616864 | − | 0.787069i | \(-0.288403\pi\) | ||||
0.616864 | + | 0.787069i | \(0.288403\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6335.68 | 1.80458 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5010.00 | 1.40865 | 0.704326 | − | 0.709876i | \(-0.251249\pi\) | ||||
0.704326 | + | 0.709876i | \(0.251249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5666.80 | −1.57303 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4293.25 | 1.17669 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1583.92 | −0.428683 | −0.214341 | − | 0.976759i | \(-0.568761\pi\) | ||||
−0.214341 | + | 0.976759i | \(0.568761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1638.00 | 0.437813 | 0.218906 | − | 0.975746i | \(-0.429751\pi\) | ||||
0.218906 | + | 0.975746i | \(0.429751\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3370.99 | −0.889913 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3023.16 | −0.788338 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1470.78 | −0.378881 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4520.00 | 1.15037 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1233.29 | 0.310137 | 0.155069 | − | 0.987904i | \(-0.450440\pi\) | ||||
0.155069 | + | 0.987904i | \(0.450440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7012.31 | 1.74253 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | −8500.20 | −2.03929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1627.86 | 0.386061 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 3453.21 | 0.791509 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3488.27 | 0.790644 | 0.395322 | − | 0.918543i | \(-0.370633\pi\) | ||||
0.395322 | + | 0.918543i | \(0.370633\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7919.60 | −1.77521 | −0.887604 | − | 0.460608i | \(-0.847631\pi\) | ||||
−0.887604 | + | 0.460608i | \(0.847631\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2560.00 | −0.567539 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8633.02 | 1.89306 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4883.57 | −1.05930 | −0.529649 | − | 0.848217i | \(-0.677676\pi\) | ||||
−0.529649 | + | 0.848217i | \(0.677676\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1118.00 | −0.237346 | −0.118673 | − | 0.992933i | \(-0.537864\pi\) | ||||
−0.118673 | + | 0.992933i | \(0.537864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2118.73 | 0.445036 | 0.222518 | − | 0.974929i | \(-0.428572\pi\) | ||||
0.222518 | + | 0.974929i | \(0.428572\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9302.04 | −1.93335 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4118.19 | 0.847000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.00264604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3099.03 | −0.624290 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4275.36 | 0.852455 | 0.426227 | − | 0.904616i | \(-0.359842\pi\) | ||||
0.426227 | + | 0.904616i | \(0.359842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1470.78 | 0.290279 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3920.00 | −0.765864 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2833.40 | −0.548026 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3005.28 | −0.575486 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1470.78 | −0.278859 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4160.00 | 0.780987 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7975.26 | 1.48265 | 0.741323 | − | 0.671148i | \(-0.234199\pi\) | ||||
0.741323 | + | 0.671148i | \(0.234199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1001.76 | −0.184427 | ||||||||
\(310\) | 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 | \(-0.562774\pi\) | ||||
−0.195936 | + | 0.980617i | \(0.562774\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5262.03 | −0.941212 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4883.57 | −0.865264 | −0.432632 | − | 0.901571i | \(-0.642415\pi\) | ||||
−0.432632 | + | 0.901571i | \(0.642415\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5543.72 | 0.973005 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10920.0 | −1.89874 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5755.35 | 0.991443 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3488.27 | −0.595367 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8711.56 | −1.47324 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7168.00 | 1.20117 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11732.1 | 1.94819 | 0.974096 | − | 0.226133i | \(-0.0726085\pi\) | ||||
0.974096 | + | 0.226133i | \(0.0726085\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4883.57 | −0.803658 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −5755.35 | −0.922087 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3937.17 | −0.619788 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17920.0 | −2.79646 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4117.29 | 0.636967 | 0.318483 | − | 0.947928i | \(-0.396826\pi\) | ||||
0.318483 | + | 0.947928i | \(0.396826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4275.36 | 0.655745 | 0.327872 | − | 0.944722i | \(-0.393668\pi\) | ||||
0.327872 | + | 0.944722i | \(0.393668\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | −2023.86 | −0.302578 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10017.6 | 1.48512 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 3978.15 | 0.575202 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16278.6 | 2.33441 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2851.05 | 0.405515 | 0.202757 | − | 0.979229i | \(-0.435010\pi\) | ||||
0.202757 | + | 0.979229i | \(0.435010\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2366.00 | 0.333791 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2833.40 | 0.396504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4883.57 | −0.677914 | −0.338957 | − | 0.940802i | \(-0.610074\pi\) | ||||
−0.338957 | + | 0.940802i | \(0.610074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7919.60 | −1.09058 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2240.00 | −0.306010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3674.57 | −0.498021 | −0.249010 | − | 0.968501i | \(-0.580105\pi\) | ||||
−0.249010 | + | 0.968501i | \(0.580105\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12021.1 | 1.61643 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2534.27 | 0.338108 | 0.169054 | − | 0.985607i | \(-0.445929\pi\) | ||||
0.169054 | + | 0.985607i | \(0.445929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17920.0 | −2.37218 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1726.60 | −0.226791 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11395.0 | −1.48522 | −0.742609 | − | 0.669726i | \(-0.766412\pi\) | ||||
−0.742609 | + | 0.669726i | \(0.766412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11087.4 | 1.43406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1080.00 | −0.138623 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12143.1 | −1.54681 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13255.4 | −1.67574 | −0.837872 | − | 0.545867i | \(-0.816200\pi\) | ||||
−0.837872 | + | 0.545867i | \(0.816200\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 16296.5 | 1.99945 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16631.2 | −2.02549 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13594.0 | −1.64347 | −0.821736 | − | 0.569868i | \(-0.806994\pi\) | ||||
−0.821736 | + | 0.569868i | \(0.806994\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12206.4 | −1.46496 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1860.41 | −0.221658 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12784.5 | −1.51221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7240.00 | −0.850226 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4775.04 | −0.556744 | −0.278372 | − | 0.960473i | \(-0.589795\pi\) | ||||
−0.278372 | + | 0.960473i | \(0.589795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7888.85 | −0.913252 | −0.456626 | − | 0.889659i | \(-0.650942\pi\) | ||||
−0.456626 | + | 0.889659i | \(0.650942\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4118.19 | 0.473365 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13650.0 | 1.55793 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5262.03 | −0.596364 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5008.79 | −0.563699 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1583.92 | −0.177018 | −0.0885089 | − | 0.996075i | \(-0.528210\pi\) | ||||
−0.0885089 | + | 0.996075i | \(0.528210\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14630.0 | 1.62373 | 0.811863 | − | 0.583849i | \(-0.198454\pi\) | ||||
0.811863 | + | 0.583849i | \(0.198454\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14167.0 | −1.56151 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13022.9 | 1.42556 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | 17753.0 | 1.90400 | 0.952000 | − | 0.306099i | \(-0.0990238\pi\) | ||||
0.952000 | + | 0.306099i | \(0.0990238\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9767.14 | −1.04047 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | 8057.48 | 0.841268 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15026.4 | −1.55850 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7240.77 | 0.746050 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2730.00 | −0.279440 | −0.139720 | − | 0.990191i | \(-0.544620\pi\) | ||||
−0.139720 | + | 0.990191i | \(0.544620\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6198.06 | −0.630285 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10250.1 | −1.03557 | −0.517784 | − | 0.855512i | \(-0.673243\pi\) | ||||
−0.517784 | + | 0.855512i | \(0.673243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7648.07 | −0.767680 | −0.383840 | − | 0.923400i | \(-0.625399\pi\) | ||||
−0.383840 | + | 0.923400i | \(0.625399\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13730.6 | −1.36055 | −0.680275 | − | 0.732957i | \(-0.738140\pi\) | ||||
−0.680275 | + | 0.732957i | \(0.738140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5008.79 | −0.493144 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22061.7 | 2.15828 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5880.00 | −0.571591 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16032.7 | 1.54870 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1627.86 | 0.156257 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12671.4 | −1.20870 | −0.604352 | − | 0.796718i | \(-0.706568\pi\) | ||||
−0.604352 | + | 0.796718i | \(0.706568\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6720.00 | 0.637018 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22667.2 | 2.13539 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8765.39 | 0.820651 | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 5888.16 | 0.541200 | 0.270600 | − | 0.962692i | \(-0.412778\pi\) | ||||
0.270600 | + | 0.962692i | \(0.412778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8765.39 | 0.800757 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10295.5 | −0.934843 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2560.00 | 0.231050 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10935.2 | 0.981012 | 0.490506 | − | 0.871438i | \(-0.336812\pi\) | ||||
0.490506 | + | 0.871438i | \(0.336812\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13022.9 | −1.16131 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | −11871.2 | −1.03988 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12790.3 | 1.11379 | 0.556896 | − | 0.830582i | \(-0.311992\pi\) | ||||
0.556896 | + | 0.830582i | \(0.311992\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20590.9 | −1.78256 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7280.00 | −0.626549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2833.40 | 0.242436 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14024.6 | 1.19304 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12784.5 | −1.08127 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16758.0 | 1.40918 | 0.704589 | − | 0.709616i | \(-0.251132\pi\) | ||||
0.704589 | + | 0.709616i | \(0.251132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16197.2 | −1.35421 | −0.677107 | − | 0.735885i | \(-0.736766\pi\) | ||||
−0.677107 | + | 0.735885i | \(0.736766\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27906.1 | 2.31985 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12921.0 | 1.06197 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1068.85 | −0.0873524 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3255.71 | −0.264579 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30886.4 | 2.49596 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22680.0 | −1.82256 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7481.95 | 0.597904 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −375.659 | −0.0298537 | −0.0149269 | − | 0.999889i | \(-0.504752\pi\) | ||||
−0.0149269 | + | 0.999889i | \(0.504752\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15726.1 | 1.24285 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24640.0 | 1.93663 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1638.06 | −0.128041 | −0.0640205 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640205 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3023.16 | −0.235019 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10295.5 | 0.796011 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15360.0 | 1.18115 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42501.0 | 3.25057 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19909.9 | −1.51456 | −0.757282 | − | 0.653089i | \(-0.773473\pi\) | ||||
−0.757282 | + | 0.653089i | \(0.773473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2375.88 | 0.179766 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19600.0 | 1.47507 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 790.569 | 0.0591803 | 0.0295902 | − | 0.999562i | \(-0.490580\pi\) | ||||
0.0295902 | + | 0.999562i | \(0.490580\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16278.6 | 1.21211 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20613.6 | −1.52679 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20454.0 | 1.50699 | 0.753494 | − | 0.657455i | \(-0.228367\pi\) | ||||
0.753494 | + | 0.657455i | \(0.228367\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5622.53 | −0.412076 | −0.206038 | − | 0.978544i | \(-0.566057\pi\) | ||||
−0.206038 | + | 0.978544i | \(0.566057\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14310.8 | −1.04336 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 3984.47 | 0.285991 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16171.2 | 1.15473 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5543.72 | 0.393820 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4160.00 | 0.294008 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15843.0 | −1.11399 | −0.556994 | − | 0.830516i | \(-0.688045\pi\) | ||||
−0.556994 | + | 0.830516i | \(0.688045\pi\) | |||||||
\(588\) | 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 | ||||||||
\(595\) | −28334.0 | −1.95224 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25044.0 | −1.71689 | ||||||||
\(598\) | 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 | \(-0.547511\pi\) | ||||
−0.148707 | + | 0.988881i | \(0.547511\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2877.67 | −0.194341 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11251.9 | −0.756123 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8236.38 | 0.550749 | 0.275374 | − | 0.961337i | \(-0.411198\pi\) | ||||
0.275374 | + | 0.961337i | \(0.411198\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17920.0 | 1.19237 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5666.80 | −0.375212 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2128.74 | 0.140259 | 0.0701296 | − | 0.997538i | \(-0.477659\pi\) | ||||
0.0701296 | + | 0.997538i | \(0.477659\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20590.9 | −1.35009 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15470.0 | −1.00940 | −0.504699 | − | 0.863295i | \(-0.668397\pi\) | ||||
−0.504699 | + | 0.863295i | \(0.668397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19486.0 | −1.26528 | −0.632639 | − | 0.774447i | \(-0.718028\pi\) | ||||
−0.632639 | + | 0.774447i | \(0.718028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14024.6 | −0.906262 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12354.6 | 0.794503 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1975.00 | −0.126400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23021.4 | 1.46632 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26296.2 | −1.66693 | ||||||||
\(630\) | 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 | ||||||||
\(635\) | −34000.8 | −2.12485 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3023.16 | −0.188041 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | −23293.3 | −1.42862 | −0.714308 | − | 0.699832i | \(-0.753258\pi\) | ||||
−0.714308 | + | 0.699832i | \(0.753258\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15026.4 | 0.917307 | ||||||||
\(646\) | 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 | ||||||||
\(653\) | 14650.7 | 0.877989 | 0.438995 | − | 0.898490i | \(-0.355335\pi\) | ||||
0.438995 | + | 0.898490i | \(0.355335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3054.70 | 0.182225 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11830.0 | −0.702484 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10935.2 | 0.646393 | 0.323197 | − | 0.946332i | \(-0.395242\pi\) | ||||
0.323197 | + | 0.946332i | \(0.395242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3774.48 | 0.222103 | 0.111052 | − | 0.993815i | \(-0.464578\pi\) | ||||
0.111052 | + | 0.993815i | \(0.464578\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7919.60 | −0.463909 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −33280.0 | −1.94067 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19833.8 | 1.15138 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16028.1 | 0.926283 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | −17266.0 | −0.984548 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27566.2 | −1.56493 | −0.782464 | − | 0.622695i | \(-0.786038\pi\) | ||||
−0.782464 | + | 0.622695i | \(0.786038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11087.4 | −0.626652 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14040.0 | −0.790035 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2346.41 | 0.131454 | 0.0657269 | − | 0.997838i | \(-0.479063\pi\) | ||||
0.0657269 | + | 0.997838i | \(0.479063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34524.9 | 1.92573 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27039.8 | 1.50165 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2240.00 | −0.123857 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10277.4 | 0.565804 | 0.282902 | − | 0.959149i | \(-0.408703\pi\) | ||||
0.282902 | + | 0.959149i | \(0.408703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13022.9 | 0.713849 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20477.8 | 1.11765 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12740.0 | 0.692341 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31686.0 | 1.71456 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 626.099 | 0.0337339 | 0.0168669 | − | 0.999858i | \(-0.494631\pi\) | ||||
0.0168669 | + | 0.999858i | \(0.494631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30886.4 | −1.65705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −35840.0 | −1.91463 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5262.03 | −0.279914 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14650.7 | 0.776050 | 0.388025 | − | 0.921649i | \(-0.373157\pi\) | ||||
0.388025 | + | 0.921649i | \(0.373157\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8824.69 | 0.465474 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14167.0 | 0.741001 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10017.6 | −0.521776 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14255.3 | 0.739405 | 0.369702 | − | 0.929150i | \(-0.379460\pi\) | ||||
0.369702 | + | 0.929150i | \(0.379460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3584.00 | −0.185125 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10359.6 | 0.532889 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24417.9 | 1.25084 | ||||||||
\(726\) | 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 | ||||||||
\(731\) | −9297.10 | −0.470404 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9284.15 | 0.467828 | 0.233914 | − | 0.972257i | \(-0.424847\pi\) | ||||
0.233914 | + | 0.972257i | \(0.424847\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19120.2 | −0.959535 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9800.00 | −0.489807 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1726.60 | 0.0859461 | 0.0429730 | − | 0.999076i | \(-0.486317\pi\) | ||||
0.0429730 | + | 0.999076i | \(0.486317\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9302.04 | −0.461159 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 9290.77 | 0.455062 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −39068.6 | −1.90592 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20590.9 | −1.00050 | −0.500249 | − | 0.865881i | \(-0.666758\pi\) | ||||
−0.500249 | + | 0.865881i | \(0.666758\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7800.00 | 0.377487 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42501.0 | 2.04870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22664.8 | 1.08820 | 0.544099 | − | 0.839021i | \(-0.316872\pi\) | ||||
0.544099 | + | 0.839021i | \(0.316872\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 44349.7 | 2.12094 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7098.00 | −0.338111 | −0.169055 | − | 0.985607i | \(-0.554072\pi\) | ||||
−0.169055 | + | 0.985607i | \(0.554072\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31167.4 | −1.47882 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16278.6 | −0.769350 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 11953.4 | 0.558355 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6529.32 | −0.303808 | −0.151904 | − | 0.988395i | \(-0.548540\pi\) | ||||
−0.151904 | + | 0.988395i | \(0.548540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −53760.0 | −2.48215 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14963.9 | 0.688238 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5008.79 | 0.229486 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11087.4 | −0.506044 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62400.0 | −2.83714 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2384.36 | 0.107996 | 0.0539982 | − | 0.998541i | \(-0.482803\pi\) | ||||
0.0539982 | + | 0.998541i | \(0.482803\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16743.7 | 0.755502 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20590.9 | −0.925575 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4160.00 | 0.186287 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14167.0 | −0.632015 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29534.0 | 1.31261 | 0.656303 | − | 0.754497i | \(-0.272119\pi\) | ||||
0.656303 | + | 0.754497i | \(0.272119\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22174.9 | 0.981840 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7098.00 | 0.313103 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40287.4 | −1.77050 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −64112.5 | −2.80704 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22061.7 | 0.962342 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10934.0 | 0.475178 | 0.237589 | − | 0.971366i | \(-0.423643\pi\) | ||||
0.237589 | + | 0.971366i | \(0.423643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17348.3 | 0.751146 | 0.375573 | − | 0.926793i | \(-0.377446\pi\) | ||||
0.375573 | + | 0.926793i | \(0.377446\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −50087.9 | −2.16071 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −62564.8 | −2.68902 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10920.0 | −0.467616 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5262.03 | −0.224506 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14901.2 | −0.633440 | −0.316720 | − | 0.948519i | \(-0.602581\pi\) | ||||
−0.316720 | + | 0.948519i | \(0.602581\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | 25899.1 | 1.08899 | 0.544497 | − | 0.838763i | \(-0.316721\pi\) | ||||
0.544497 | + | 0.838763i | \(0.316721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25276.5 | −1.05897 | −0.529487 | − | 0.848318i | \(-0.677616\pi\) | ||||
−0.529487 | + | 0.848318i | \(0.677616\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30886.4 | −1.28934 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11830.0 | 0.492059 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36834.2 | 1.52659 | ||||||||
\(836\) | 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 | ||||||||
\(843\) | −7070.85 | −0.288889 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33576.8 | 1.36695 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14232.6 | 0.577378 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13400.0 | 0.541681 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −59501.4 | −2.39681 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21770.4 | −0.873860 | −0.436930 | − | 0.899495i | \(-0.643934\pi\) | ||||
−0.436930 | + | 0.899495i | \(0.643934\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19120.2 | −0.764791 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24570.0 | −0.979341 | −0.489670 | − | 0.871908i | \(-0.662883\pi\) | ||||
−0.489670 | + | 0.871908i | \(0.662883\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5837.56 | 0.231869 | 0.115934 | − | 0.993257i | \(-0.463014\pi\) | ||||
0.115934 | + | 0.993257i | \(0.463014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26045.7 | 1.03094 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23713.5 | 0.935363 | 0.467681 | − | 0.883897i | \(-0.345089\pi\) | ||||
0.467681 | + | 0.883897i | \(0.345089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36160.0 | 1.42136 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −82.2192 | −0.00322066 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30052.8 | 1.17315 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3959.80 | 0.154044 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6370.00 | −0.246955 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28334.0 | −1.09470 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43701.7 | 1.68267 | 0.841335 | − | 0.540514i | \(-0.181770\pi\) | ||||
0.841335 | + | 0.540514i | \(0.181770\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −27492.8 | −1.04780 | −0.523900 | − | 0.851780i | \(-0.675524\pi\) | ||||
−0.523900 | + | 0.851780i | \(0.675524\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9302.04 | 0.353316 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | −40331.7 | −1.51646 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26045.7 | 0.976021 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64148.7 | 2.39582 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17920.0 | −0.667036 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8765.39 | 0.324104 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19007.0 | −0.700459 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44480.0 | −1.63377 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40154.6 | −1.47002 | −0.735012 | − | 0.678054i | \(-0.762823\pi\) | ||||
−0.735012 | + | 0.678054i | \(0.762823\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3023.16 | −0.110310 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11087.4 | 0.403231 | 0.201615 | − | 0.979465i | \(-0.435381\pi\) | ||||
0.201615 | + | 0.979465i | \(0.435381\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31640.0 | 1.14691 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26310.2 | 0.950587 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3863.93 | −0.139147 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | −2023.86 | −0.0721734 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −73253.6 | −2.60385 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 13895.0 | 0.489143 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 65114.3 | 2.28483 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −55437.2 | −1.93903 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13650.0 | 0.475908 | 0.237954 | − | 0.971276i | \(-0.423523\pi\) | ||||
0.237954 | + | 0.971276i | \(0.423523\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13724.3 | −0.476970 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6529.32 | −0.226195 | −0.113098 | − | 0.993584i | \(-0.536077\pi\) | ||||
−0.113098 | + | 0.993584i | \(0.536077\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28827.3 | 0.995490 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 35840.0 | 1.23373 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11555.0 | −0.396500 | −0.198250 | − | 0.980151i | \(-0.563526\pi\) | ||||
−0.198250 | + | 0.980151i | \(0.563526\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16278.6 | 0.556823 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30886.4 | −1.05317 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10470.0 | 0.355883 | 0.177942 | − | 0.984041i | \(-0.443056\pi\) | ||||
0.177942 | + | 0.984041i | \(0.443056\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40477.2 | 1.37153 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35061.5 | 1.18430 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43670.9 | −1.47050 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29791.0 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22445.8 | −0.751098 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11269.8 | −0.375945 | ||||||||
\(966\) | 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 | ||||||||
\(971\) | 49502.3 | 1.63605 | 0.818025 | − | 0.575183i | \(-0.195069\pi\) | ||||
0.818025 | + | 0.575183i | \(0.195069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25902.6 | −0.853443 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 24172.5 | 0.789127 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17906.4 | −0.582781 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 45334.4 | 1.46202 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21036.9 | −0.676376 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52948.2 | 1.69723 | 0.848614 | − | 0.529012i | \(-0.177437\pi\) | ||||
0.848614 | + | 0.529012i | \(0.177437\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 74200.0 | 2.37126 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 70835.0 | 2.25691 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17548.7 | −0.557444 | −0.278722 | − | 0.960372i | \(-0.589911\pi\) | ||||
−0.278722 | + | 0.960372i | \(0.589911\pi\) | |||||||
\(998\) | 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 | 256.4.a.n.1.3 | 4 | ||
3.2 | odd | 2 | 2304.4.a.bz.1.4 | 4 | |||
4.3 | odd | 2 | inner | 256.4.a.n.1.1 | 4 | ||
8.3 | odd | 2 | inner | 256.4.a.n.1.4 | 4 | ||
8.5 | even | 2 | inner | 256.4.a.n.1.2 | 4 | ||
12.11 | even | 2 | 2304.4.a.bz.1.3 | 4 | |||
16.3 | odd | 4 | 128.4.b.e.65.2 | yes | 4 | ||
16.5 | even | 4 | 128.4.b.e.65.1 | ✓ | 4 | ||
16.11 | odd | 4 | 128.4.b.e.65.3 | yes | 4 | ||
16.13 | even | 4 | 128.4.b.e.65.4 | yes | 4 | ||
24.5 | odd | 2 | 2304.4.a.bz.1.2 | 4 | |||
24.11 | even | 2 | 2304.4.a.bz.1.1 | 4 | |||
48.5 | odd | 4 | 1152.4.d.j.577.3 | 4 | |||
48.11 | even | 4 | 1152.4.d.j.577.4 | 4 | |||
48.29 | odd | 4 | 1152.4.d.j.577.1 | 4 | |||
48.35 | even | 4 | 1152.4.d.j.577.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.4.b.e.65.1 | ✓ | 4 | 16.5 | even | 4 | ||
128.4.b.e.65.2 | yes | 4 | 16.3 | odd | 4 | ||
128.4.b.e.65.3 | yes | 4 | 16.11 | odd | 4 | ||
128.4.b.e.65.4 | yes | 4 | 16.13 | even | 4 | ||
256.4.a.n.1.1 | 4 | 4.3 | odd | 2 | inner | ||
256.4.a.n.1.2 | 4 | 8.5 | even | 2 | inner | ||
256.4.a.n.1.3 | 4 | 1.1 | even | 1 | trivial | ||
256.4.a.n.1.4 | 4 | 8.3 | odd | 2 | inner | ||
1152.4.d.j.577.1 | 4 | 48.29 | odd | 4 | |||
1152.4.d.j.577.2 | 4 | 48.35 | even | 4 | |||
1152.4.d.j.577.3 | 4 | 48.5 | odd | 4 | |||
1152.4.d.j.577.4 | 4 | 48.11 | even | 4 | |||
2304.4.a.bz.1.1 | 4 | 24.11 | even | 2 | |||
2304.4.a.bz.1.2 | 4 | 24.5 | odd | 2 | |||
2304.4.a.bz.1.3 | 4 | 12.11 | even | 2 | |||
2304.4.a.bz.1.4 | 4 | 3.2 | odd | 2 |