Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, 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("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(39.8262892539\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.183945.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 12x^{2} + 3x + 18 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.39127\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53008 | −0.894520 | −0.447260 | − | 0.894404i | \(-0.647600\pi\) | ||||
−0.447260 | + | 0.894404i | \(0.647600\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.59867 | −0.199834 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −27.8841 | −1.50560 | −0.752801 | − | 0.658249i | \(-0.771298\pi\) | ||||
−0.752801 | + | 0.658249i | \(0.771298\pi\) | |||||||
\(8\) | 24.2855 | 1.07328 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −35.8155 | −0.981708 | −0.490854 | − | 0.871242i | \(-0.663315\pi\) | ||||
−0.490854 | + | 0.871242i | \(0.663315\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 27.3694 | 0.583917 | 0.291958 | − | 0.956431i | \(-0.405693\pi\) | ||||
0.291958 | + | 0.956431i | \(0.405693\pi\) | |||||||
\(14\) | 70.5492 | 1.34679 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −48.6549 | −0.760233 | ||||||||
\(17\) | 93.6094 | 1.33551 | 0.667753 | − | 0.744383i | \(-0.267256\pi\) | ||||
0.667753 | + | 0.744383i | \(0.267256\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 135.589 | 1.63717 | 0.818583 | − | 0.574388i | \(-0.194760\pi\) | ||||
0.818583 | + | 0.574388i | \(0.194760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 90.6163 | 0.878158 | ||||||||
\(23\) | −0.407389 | −0.00369332 | −0.00184666 | − | 0.999998i | \(-0.500588\pi\) | ||||
−0.00184666 | + | 0.999998i | \(0.500588\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −69.2470 | −0.522325 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 44.5775 | 0.300870 | ||||||||
\(29\) | −194.946 | −1.24829 | −0.624147 | − | 0.781307i | \(-0.714553\pi\) | ||||
−0.624147 | + | 0.781307i | \(0.714553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −96.7790 | −0.560710 | −0.280355 | − | 0.959896i | \(-0.590452\pi\) | ||||
−0.280355 | + | 0.959896i | \(0.590452\pi\) | |||||||
\(32\) | −71.1826 | −0.393232 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −236.840 | −1.19464 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 186.968 | 0.830737 | 0.415369 | − | 0.909653i | \(-0.363653\pi\) | ||||
0.415369 | + | 0.909653i | \(0.363653\pi\) | |||||||
\(38\) | −343.051 | −1.46448 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.6700 | 0.204435 | 0.102218 | − | 0.994762i | \(-0.467406\pi\) | ||||
0.102218 | + | 0.994762i | \(0.467406\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 519.172 | 1.84123 | 0.920616 | − | 0.390470i | \(-0.127687\pi\) | ||||
0.920616 | + | 0.390470i | \(0.127687\pi\) | |||||||
\(44\) | 57.2573 | 0.196179 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.03073 | 0.00330375 | ||||||||
\(47\) | 190.431 | 0.591006 | 0.295503 | − | 0.955342i | \(-0.404513\pi\) | ||||
0.295503 | + | 0.955342i | \(0.404513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 434.524 | 1.26683 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −43.7547 | −0.116686 | ||||||||
\(53\) | −533.255 | −1.38204 | −0.691021 | − | 0.722834i | \(-0.742839\pi\) | ||||
−0.691021 | + | 0.722834i | \(0.742839\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −677.178 | −1.61592 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 493.229 | 1.11662 | ||||||||
\(59\) | −472.800 | −1.04328 | −0.521639 | − | 0.853167i | \(-0.674679\pi\) | ||||
−0.521639 | + | 0.853167i | \(0.674679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −327.057 | −0.686480 | −0.343240 | − | 0.939248i | \(-0.611525\pi\) | ||||
−0.343240 | + | 0.939248i | \(0.611525\pi\) | |||||||
\(62\) | 244.859 | 0.501567 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 569.337 | 1.11199 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 78.0010 | 0.142229 | 0.0711145 | − | 0.997468i | \(-0.477344\pi\) | ||||
0.0711145 | + | 0.997468i | \(0.477344\pi\) | |||||||
\(68\) | −149.651 | −0.266879 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −707.467 | −1.18255 | −0.591274 | − | 0.806471i | \(-0.701375\pi\) | ||||
−0.591274 | + | 0.806471i | \(0.701375\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −344.812 | −0.552838 | −0.276419 | − | 0.961037i | \(-0.589148\pi\) | ||||
−0.276419 | + | 0.961037i | \(0.589148\pi\) | |||||||
\(74\) | −473.044 | −0.743111 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −216.761 | −0.327161 | ||||||||
\(77\) | 998.685 | 1.47806 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 98.3522 | 0.140069 | 0.0700347 | − | 0.997545i | \(-0.477689\pi\) | ||||
0.0700347 | + | 0.997545i | \(0.477689\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −135.790 | −0.182872 | ||||||||
\(83\) | 1248.37 | 1.65092 | 0.825460 | − | 0.564461i | \(-0.190916\pi\) | ||||
0.825460 | + | 0.564461i | \(0.190916\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1313.55 | −1.64702 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −869.796 | −1.05364 | ||||||||
\(89\) | 448.920 | 0.534668 | 0.267334 | − | 0.963604i | \(-0.413857\pi\) | ||||
0.267334 | + | 0.963604i | \(0.413857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −763.173 | −0.879145 | ||||||||
\(92\) | 0.651281 | 0.000738051 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −481.808 | −0.528667 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −472.081 | −0.494150 | −0.247075 | − | 0.968996i | \(-0.579469\pi\) | ||||
−0.247075 | + | 0.968996i | \(0.579469\pi\) | |||||||
\(98\) | −1099.38 | −1.13321 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1474.17 | −1.45233 | −0.726166 | − | 0.687519i | \(-0.758700\pi\) | ||||
−0.726166 | + | 0.687519i | \(0.758700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 967.934 | 0.925955 | 0.462977 | − | 0.886370i | \(-0.346781\pi\) | ||||
0.462977 | + | 0.886370i | \(0.346781\pi\) | |||||||
\(104\) | 664.679 | 0.626703 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1349.18 | 1.23626 | ||||||||
\(107\) | 1280.19 | 1.15664 | 0.578321 | − | 0.815809i | \(-0.303708\pi\) | ||||
0.578321 | + | 0.815809i | \(0.303708\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1445.89 | −1.27056 | −0.635281 | − | 0.772281i | \(-0.719116\pi\) | ||||
−0.635281 | + | 0.772281i | \(0.719116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1356.70 | 1.14461 | ||||||||
\(113\) | −2311.88 | −1.92463 | −0.962315 | − | 0.271938i | \(-0.912335\pi\) | ||||
−0.962315 | + | 0.271938i | \(0.912335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 311.654 | 0.249451 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1196.22 | 0.933232 | ||||||||
\(119\) | −2610.21 | −2.01074 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −48.2474 | −0.0362490 | ||||||||
\(122\) | 827.481 | 0.614071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 154.718 | 0.112049 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1483.99 | −1.03687 | −0.518435 | − | 0.855117i | \(-0.673485\pi\) | ||||
−0.518435 | + | 0.855117i | \(0.673485\pi\) | |||||||
\(128\) | −871.010 | −0.601462 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1950.53 | −1.30090 | −0.650452 | − | 0.759547i | \(-0.725421\pi\) | ||||
−0.650452 | + | 0.759547i | \(0.725421\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3780.77 | −2.46492 | ||||||||
\(134\) | −197.349 | −0.127227 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2273.35 | 1.43337 | ||||||||
\(137\) | −2318.92 | −1.44612 | −0.723060 | − | 0.690785i | \(-0.757265\pi\) | ||||
−0.723060 | + | 0.690785i | \(0.757265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1461.53 | 0.891836 | 0.445918 | − | 0.895074i | \(-0.352877\pi\) | ||||
0.445918 | + | 0.895074i | \(0.352877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1789.95 | 1.05781 | ||||||||
\(143\) | −980.251 | −0.573236 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 872.403 | 0.494524 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −298.900 | −0.166009 | ||||||||
\(149\) | −1404.10 | −0.772003 | −0.386002 | − | 0.922498i | \(-0.626144\pi\) | ||||
−0.386002 | + | 0.922498i | \(0.626144\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2722.74 | 1.46737 | 0.733687 | − | 0.679488i | \(-0.237798\pi\) | ||||
0.733687 | + | 0.679488i | \(0.237798\pi\) | |||||||
\(152\) | 3292.83 | 1.75713 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2526.76 | −1.32216 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2731.98 | −1.38876 | −0.694382 | − | 0.719607i | \(-0.744322\pi\) | ||||
−0.694382 | + | 0.719607i | \(0.744322\pi\) | |||||||
\(158\) | −248.839 | −0.125295 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3597 | 0.00556067 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2886.65 | −1.38712 | −0.693558 | − | 0.720401i | \(-0.743958\pi\) | ||||
−0.693558 | + | 0.720401i | \(0.743958\pi\) | |||||||
\(164\) | −85.8007 | −0.0408531 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3158.48 | −1.47678 | ||||||||
\(167\) | −636.737 | −0.295043 | −0.147522 | − | 0.989059i | \(-0.547130\pi\) | ||||
−0.147522 | + | 0.989059i | \(0.547130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1447.91 | −0.659041 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −829.985 | −0.367940 | ||||||||
\(173\) | −183.943 | −0.0808377 | −0.0404189 | − | 0.999183i | \(-0.512869\pi\) | ||||
−0.0404189 | + | 0.999183i | \(0.512869\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1742.60 | 0.746327 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1135.81 | −0.478271 | ||||||||
\(179\) | 4639.38 | 1.93723 | 0.968614 | − | 0.248570i | \(-0.0799607\pi\) | ||||
0.968614 | + | 0.248570i | \(0.0799607\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2196.49 | −0.902010 | −0.451005 | − | 0.892522i | \(-0.648934\pi\) | ||||
−0.451005 | + | 0.892522i | \(0.648934\pi\) | |||||||
\(182\) | 1930.89 | 0.786413 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.89362 | −0.00396395 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3352.67 | −1.31108 | ||||||||
\(188\) | −304.437 | −0.118103 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3135.80 | −1.18795 | −0.593975 | − | 0.804484i | \(-0.702442\pi\) | ||||
−0.593975 | + | 0.804484i | \(0.702442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3516.99 | 1.31170 | 0.655851 | − | 0.754890i | \(-0.272310\pi\) | ||||
0.655851 | + | 0.754890i | \(0.272310\pi\) | |||||||
\(194\) | 1194.41 | 0.442027 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −694.661 | −0.253156 | ||||||||
\(197\) | −3453.43 | −1.24897 | −0.624483 | − | 0.781038i | \(-0.714690\pi\) | ||||
−0.624483 | + | 0.781038i | \(0.714690\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2258.23 | 0.804429 | 0.402215 | − | 0.915545i | \(-0.368241\pi\) | ||||
0.402215 | + | 0.915545i | \(0.368241\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3729.78 | 1.29914 | ||||||||
\(203\) | 5435.89 | 1.87943 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2448.95 | −0.828285 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1331.66 | −0.443912 | ||||||||
\(209\) | −4856.18 | −1.60722 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 795.126 | 0.259425 | 0.129713 | − | 0.991552i | \(-0.458595\pi\) | ||||
0.129713 | + | 0.991552i | \(0.458595\pi\) | |||||||
\(212\) | 852.500 | 0.276179 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3238.99 | −1.03464 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2698.60 | 0.844206 | ||||||||
\(218\) | 3658.23 | 1.13654 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2562.04 | 0.779824 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2719.12 | −0.816529 | −0.408265 | − | 0.912864i | \(-0.633866\pi\) | ||||
−0.408265 | + | 0.912864i | \(0.633866\pi\) | |||||||
\(224\) | 1984.86 | 0.592051 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5849.25 | 1.72162 | ||||||||
\(227\) | −1935.94 | −0.566047 | −0.283024 | − | 0.959113i | \(-0.591337\pi\) | ||||
−0.283024 | + | 0.959113i | \(0.591337\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4781.62 | 1.37982 | 0.689909 | − | 0.723896i | \(-0.257651\pi\) | ||||
0.689909 | + | 0.723896i | \(0.257651\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4734.34 | −1.33976 | ||||||||
\(233\) | 794.207 | 0.223306 | 0.111653 | − | 0.993747i | \(-0.464386\pi\) | ||||
0.111653 | + | 0.993747i | \(0.464386\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 755.852 | 0.208482 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6604.07 | 1.79865 | ||||||||
\(239\) | 3253.17 | 0.880461 | 0.440230 | − | 0.897885i | \(-0.354897\pi\) | ||||
0.440230 | + | 0.897885i | \(0.354897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1428.53 | 0.381826 | 0.190913 | − | 0.981607i | \(-0.438855\pi\) | ||||
0.190913 | + | 0.981607i | \(0.438855\pi\) | |||||||
\(242\) | 122.070 | 0.0324254 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 522.856 | 0.137182 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3710.98 | 0.955968 | ||||||||
\(248\) | −2350.32 | −0.601797 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7809.50 | 1.96387 | 0.981935 | − | 0.189218i | \(-0.0605953\pi\) | ||||
0.981935 | + | 0.189218i | \(0.0605953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.5909 | 0.00362577 | ||||||||
\(254\) | 3754.61 | 0.927501 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2350.97 | −0.573967 | ||||||||
\(257\) | −2790.73 | −0.677359 | −0.338679 | − | 0.940902i | \(-0.609980\pi\) | ||||
−0.338679 | + | 0.940902i | \(0.609980\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5213.43 | −1.25076 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4935.00 | 1.16368 | ||||||||
\(263\) | 3146.75 | 0.737782 | 0.368891 | − | 0.929473i | \(-0.379737\pi\) | ||||
0.368891 | + | 0.929473i | \(0.379737\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9565.66 | 2.20492 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −124.698 | −0.0284222 | ||||||||
\(269\) | −8006.02 | −1.81463 | −0.907315 | − | 0.420452i | \(-0.861872\pi\) | ||||
−0.907315 | + | 0.420452i | \(0.861872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5598.74 | −1.25498 | −0.627489 | − | 0.778625i | \(-0.715917\pi\) | ||||
−0.627489 | + | 0.778625i | \(0.715917\pi\) | |||||||
\(272\) | −4554.55 | −1.01530 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5867.06 | 1.29358 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 759.525 | 0.164749 | 0.0823744 | − | 0.996601i | \(-0.473750\pi\) | ||||
0.0823744 | + | 0.996601i | \(0.473750\pi\) | |||||||
\(278\) | −3697.79 | −0.797765 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2516.27 | 0.534193 | 0.267097 | − | 0.963670i | \(-0.413936\pi\) | ||||
0.267097 | + | 0.963670i | \(0.413936\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7742.08 | 1.62622 | 0.813108 | − | 0.582113i | \(-0.197774\pi\) | ||||
0.813108 | + | 0.582113i | \(0.197774\pi\) | |||||||
\(284\) | 1131.01 | 0.236313 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2480.12 | 0.512771 | ||||||||
\(287\) | −1496.54 | −0.307798 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3849.71 | 0.783577 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 551.240 | 0.110476 | ||||||||
\(293\) | −577.798 | −0.115206 | −0.0576029 | − | 0.998340i | \(-0.518346\pi\) | ||||
−0.0576029 | + | 0.998340i | \(0.518346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4540.59 | 0.891610 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3552.50 | 0.690572 | ||||||||
\(299\) | −11.1500 | −0.00215659 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14476.7 | −2.77216 | ||||||||
\(302\) | −6888.76 | −1.31259 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6597.05 | −1.24463 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5530.03 | −1.02806 | −0.514031 | − | 0.857771i | \(-0.671849\pi\) | ||||
−0.514031 | + | 0.857771i | \(0.671849\pi\) | |||||||
\(308\) | −1596.57 | −0.295367 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7071.80 | −1.28941 | −0.644703 | − | 0.764433i | \(-0.723019\pi\) | ||||
−0.644703 | + | 0.764433i | \(0.723019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 54.0308 | 0.00975719 | 0.00487860 | − | 0.999988i | \(-0.498447\pi\) | ||||
0.00487860 | + | 0.999988i | \(0.498447\pi\) | |||||||
\(314\) | 6912.14 | 1.24228 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −157.233 | −0.0279906 | ||||||||
\(317\) | 158.754 | 0.0281279 | 0.0140639 | − | 0.999901i | \(-0.495523\pi\) | ||||
0.0140639 | + | 0.999901i | \(0.495523\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6982.09 | 1.22546 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −28.7410 | −0.00497413 | ||||||||
\(323\) | 12692.4 | 2.18645 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7303.47 | 1.24080 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1303.40 | 0.219416 | ||||||||
\(329\) | −5310.01 | −0.889819 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −914.263 | −0.151820 | −0.0759101 | − | 0.997115i | \(-0.524186\pi\) | ||||
−0.0759101 | + | 0.997115i | \(0.524186\pi\) | |||||||
\(332\) | −1995.73 | −0.329910 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1611.00 | 0.263922 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1258.22 | −0.203381 | −0.101691 | − | 0.994816i | \(-0.532425\pi\) | ||||
−0.101691 | + | 0.994816i | \(0.532425\pi\) | |||||||
\(338\) | 3663.35 | 0.589526 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3466.19 | 0.550454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2552.07 | −0.401746 | ||||||||
\(344\) | 12608.3 | 1.97615 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 465.392 | 0.0723110 | ||||||||
\(347\) | −591.507 | −0.0915094 | −0.0457547 | − | 0.998953i | \(-0.514569\pi\) | ||||
−0.0457547 | + | 0.998953i | \(0.514569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6362.97 | 0.975937 | 0.487969 | − | 0.872861i | \(-0.337738\pi\) | ||||
0.487969 | + | 0.872861i | \(0.337738\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2549.44 | 0.386039 | ||||||||
\(353\) | 2735.16 | 0.412402 | 0.206201 | − | 0.978510i | \(-0.433890\pi\) | ||||
0.206201 | + | 0.978510i | \(0.433890\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −717.676 | −0.106845 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11738.0 | −1.73289 | ||||||||
\(359\) | −2775.11 | −0.407980 | −0.203990 | − | 0.978973i | \(-0.565391\pi\) | ||||
−0.203990 | + | 0.978973i | \(0.565391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11525.3 | 1.68031 | ||||||||
\(362\) | 5557.30 | 0.806866 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1220.06 | 0.175683 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −716.105 | −0.101854 | −0.0509269 | − | 0.998702i | \(-0.516218\pi\) | ||||
−0.0509269 | + | 0.998702i | \(0.516218\pi\) | |||||||
\(368\) | 19.8215 | 0.00280779 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14869.4 | 2.08080 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11605.3 | 1.61099 | 0.805494 | − | 0.592603i | \(-0.201900\pi\) | ||||
0.805494 | + | 0.592603i | \(0.201900\pi\) | |||||||
\(374\) | 8482.54 | 1.17279 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4624.71 | 0.634312 | ||||||||
\(377\) | −5335.55 | −0.728899 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7893.11 | −1.06977 | −0.534884 | − | 0.844926i | \(-0.679645\pi\) | ||||
−0.534884 | + | 0.844926i | \(0.679645\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7933.84 | 1.06264 | ||||||||
\(383\) | 6965.23 | 0.929261 | 0.464630 | − | 0.885505i | \(-0.346187\pi\) | ||||
0.464630 | + | 0.885505i | \(0.346187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8898.29 | −1.17334 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 754.702 | 0.0987480 | ||||||||
\(389\) | 6906.36 | 0.900171 | 0.450085 | − | 0.892986i | \(-0.351394\pi\) | ||||
0.450085 | + | 0.892986i | \(0.351394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38.1354 | −0.00493246 | ||||||||
\(392\) | 10552.6 | 1.35966 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8737.46 | 1.11723 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8237.28 | −1.04135 | −0.520676 | − | 0.853754i | \(-0.674320\pi\) | ||||
−0.520676 | + | 0.853754i | \(0.674320\pi\) | |||||||
\(398\) | −5713.50 | −0.719578 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1460.02 | −0.181820 | −0.0909101 | − | 0.995859i | \(-0.528978\pi\) | ||||
−0.0909101 | + | 0.995859i | \(0.528978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2648.79 | −0.327408 | ||||||||
\(404\) | 2356.72 | 0.290225 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13753.3 | −1.68119 | ||||||||
\(407\) | −6696.34 | −0.815542 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9821.99 | −1.18745 | −0.593724 | − | 0.804669i | \(-0.702343\pi\) | ||||
−0.593724 | + | 0.804669i | \(0.702343\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1547.41 | −0.185037 | ||||||||
\(413\) | 13183.6 | 1.57076 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1948.23 | −0.229615 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12286.5 | 1.43769 | ||||||||
\(419\) | −14970.5 | −1.74549 | −0.872743 | − | 0.488181i | \(-0.837661\pi\) | ||||
−0.872743 | + | 0.488181i | \(0.837661\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12909.9 | 1.49452 | 0.747259 | − | 0.664533i | \(-0.231369\pi\) | ||||
0.747259 | + | 0.664533i | \(0.231369\pi\) | |||||||
\(422\) | −2011.74 | −0.232061 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12950.3 | −1.48331 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9119.69 | 1.03357 | ||||||||
\(428\) | −2046.60 | −0.231136 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5841.94 | −0.652892 | −0.326446 | − | 0.945216i | \(-0.605851\pi\) | ||||
−0.326446 | + | 0.945216i | \(0.605851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1317.13 | −0.146182 | −0.0730912 | − | 0.997325i | \(-0.523286\pi\) | ||||
−0.0730912 | + | 0.997325i | \(0.523286\pi\) | |||||||
\(434\) | −6827.68 | −0.755159 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2311.50 | 0.253901 | ||||||||
\(437\) | −55.2373 | −0.00604659 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10825.6 | −1.17694 | −0.588469 | − | 0.808520i | \(-0.700269\pi\) | ||||
−0.588469 | + | 0.808520i | \(0.700269\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6482.17 | −0.697568 | ||||||||
\(443\) | −7857.87 | −0.842751 | −0.421375 | − | 0.906886i | \(-0.638452\pi\) | ||||
−0.421375 | + | 0.906886i | \(0.638452\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6879.61 | 0.730402 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15875.5 | −1.67421 | ||||||||
\(449\) | −12512.7 | −1.31517 | −0.657587 | − | 0.753379i | \(-0.728423\pi\) | ||||
−0.657587 | + | 0.753379i | \(0.728423\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1922.22 | −0.200696 | ||||||||
\(452\) | 3695.93 | 0.384606 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4898.09 | 0.506341 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11041.9 | 1.13024 | 0.565118 | − | 0.825010i | \(-0.308830\pi\) | ||||
0.565118 | + | 0.825010i | \(0.308830\pi\) | |||||||
\(458\) | −12097.9 | −1.23427 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9204.91 | −0.929968 | −0.464984 | − | 0.885319i | \(-0.653940\pi\) | ||||
−0.464984 | + | 0.885319i | \(0.653940\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17536.1 | −1.76020 | −0.880101 | − | 0.474786i | \(-0.842525\pi\) | ||||
−0.880101 | + | 0.474786i | \(0.842525\pi\) | |||||||
\(464\) | 9485.06 | 0.948993 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2009.41 | −0.199752 | ||||||||
\(467\) | −13734.5 | −1.36093 | −0.680467 | − | 0.732779i | \(-0.738223\pi\) | ||||
−0.680467 | + | 0.732779i | \(0.738223\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2174.99 | −0.214140 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11482.2 | −1.11972 | ||||||||
\(473\) | −18594.4 | −1.80755 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4172.87 | 0.401814 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8230.80 | −0.787590 | ||||||||
\(479\) | 5272.93 | 0.502977 | 0.251489 | − | 0.967860i | \(-0.419080\pi\) | ||||
0.251489 | + | 0.967860i | \(0.419080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5117.20 | 0.485081 | ||||||||
\(482\) | −3614.31 | −0.341551 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 77.1317 | 0.00724377 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 918.490 | 0.0854636 | 0.0427318 | − | 0.999087i | \(-0.486394\pi\) | ||||
0.0427318 | + | 0.999087i | \(0.486394\pi\) | |||||||
\(488\) | −7942.72 | −0.736783 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1746.00 | −0.160480 | −0.0802400 | − | 0.996776i | \(-0.525569\pi\) | ||||
−0.0802400 | + | 0.996776i | \(0.525569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18248.7 | −1.66710 | ||||||||
\(494\) | −9389.10 | −0.855133 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4708.77 | 0.426270 | ||||||||
\(497\) | 19727.1 | 1.78044 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10841.2 | 0.972585 | 0.486292 | − | 0.873796i | \(-0.338349\pi\) | ||||
0.486292 | + | 0.873796i | \(0.338349\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19758.7 | −1.75672 | ||||||||
\(503\) | −6427.44 | −0.569752 | −0.284876 | − | 0.958564i | \(-0.591952\pi\) | ||||
−0.284876 | + | 0.958564i | \(0.591952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −36.9161 | −0.00324332 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2372.41 | 0.207202 | ||||||||
\(509\) | −5482.99 | −0.477464 | −0.238732 | − | 0.971085i | \(-0.576732\pi\) | ||||
−0.238732 | + | 0.971085i | \(0.576732\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9614.77 | 0.832353 | ||||||||
\(512\) | 12916.2 | 1.11489 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7060.79 | 0.605911 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6820.40 | −0.580195 | ||||||||
\(518\) | 13190.4 | 1.11883 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8507.07 | −0.715358 | −0.357679 | − | 0.933845i | \(-0.616432\pi\) | ||||
−0.357679 | + | 0.933845i | \(0.616432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5908.55 | 0.494002 | 0.247001 | − | 0.969015i | \(-0.420555\pi\) | ||||
0.247001 | + | 0.969015i | \(0.420555\pi\) | |||||||
\(524\) | 3118.25 | 0.259965 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7961.54 | −0.659961 | ||||||||
\(527\) | −9059.42 | −0.748832 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12166.8 | −0.999986 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6044.20 | 0.492574 | ||||||||
\(533\) | 1468.92 | 0.119373 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1894.29 | 0.152651 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20255.9 | 1.62322 | ||||||||
\(539\) | −15562.7 | −1.24366 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10557.4 | 0.838995 | 0.419497 | − | 0.907757i | \(-0.362206\pi\) | ||||
0.419497 | + | 0.907757i | \(0.362206\pi\) | |||||||
\(542\) | 14165.3 | 1.12260 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6663.36 | −0.525164 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6056.60 | 0.473421 | 0.236711 | − | 0.971580i | \(-0.423931\pi\) | ||||
0.236711 | + | 0.971580i | \(0.423931\pi\) | |||||||
\(548\) | 3707.18 | 0.288984 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26432.4 | −2.04366 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2742.46 | −0.210889 | ||||||||
\(554\) | −1921.66 | −0.147371 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2336.50 | −0.178219 | ||||||||
\(557\) | 816.783 | 0.0621332 | 0.0310666 | − | 0.999517i | \(-0.490110\pi\) | ||||
0.0310666 | + | 0.999517i | \(0.490110\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14209.4 | 1.07513 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6366.39 | −0.477847 | ||||||||
\(563\) | 6891.09 | 0.515852 | 0.257926 | − | 0.966165i | \(-0.416961\pi\) | ||||
0.257926 | + | 0.966165i | \(0.416961\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19588.1 | −1.45468 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17181.1 | −1.26920 | ||||||||
\(569\) | 9267.91 | 0.682831 | 0.341416 | − | 0.939912i | \(-0.389094\pi\) | ||||
0.341416 | + | 0.939912i | \(0.389094\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10142.9 | −0.743378 | −0.371689 | − | 0.928357i | \(-0.621221\pi\) | ||||
−0.371689 | + | 0.928357i | \(0.621221\pi\) | |||||||
\(572\) | 1567.10 | 0.114552 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3786.38 | 0.275332 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4905.22 | −0.353912 | −0.176956 | − | 0.984219i | \(-0.556625\pi\) | ||||
−0.176956 | + | 0.984219i | \(0.556625\pi\) | |||||||
\(578\) | −9740.10 | −0.700925 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34809.7 | −2.48563 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19098.8 | 1.35676 | ||||||||
\(584\) | −8373.91 | −0.593347 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1461.88 | 0.103054 | ||||||||
\(587\) | 2570.78 | 0.180762 | 0.0903810 | − | 0.995907i | \(-0.471192\pi\) | ||||
0.0903810 | + | 0.995907i | \(0.471192\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13122.1 | −0.917976 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9096.89 | −0.631554 | ||||||||
\(593\) | 4740.85 | 0.328303 | 0.164151 | − | 0.986435i | \(-0.447511\pi\) | ||||
0.164151 | + | 0.986435i | \(0.447511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2244.70 | 0.154272 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.2105 | 0.00192912 | ||||||||
\(599\) | −1784.53 | −0.121726 | −0.0608632 | − | 0.998146i | \(-0.519385\pi\) | ||||
−0.0608632 | + | 0.998146i | \(0.519385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11189.9 | −0.759479 | −0.379739 | − | 0.925094i | \(-0.623986\pi\) | ||||
−0.379739 | + | 0.925094i | \(0.623986\pi\) | |||||||
\(602\) | 36627.2 | 2.47975 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4352.76 | −0.293231 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21524.7 | 1.43931 | 0.719653 | − | 0.694334i | \(-0.244301\pi\) | ||||
0.719653 | + | 0.694334i | \(0.244301\pi\) | |||||||
\(608\) | −9651.55 | −0.643786 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5212.00 | 0.345098 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2787.57 | −0.183668 | −0.0918342 | − | 0.995774i | \(-0.529273\pi\) | ||||
−0.0918342 | + | 0.995774i | \(0.529273\pi\) | |||||||
\(614\) | 13991.4 | 0.919623 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24253.5 | 1.58637 | ||||||||
\(617\) | 8076.49 | 0.526981 | 0.263490 | − | 0.964662i | \(-0.415126\pi\) | ||||
0.263490 | + | 0.964662i | \(0.415126\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28161.9 | −1.82863 | −0.914315 | − | 0.405005i | \(-0.867270\pi\) | ||||
−0.914315 | + | 0.405005i | \(0.867270\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17892.3 | 1.15340 | ||||||||
\(623\) | −12517.8 | −0.804997 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −136.703 | −0.00872801 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4367.54 | 0.277522 | ||||||||
\(629\) | 17501.9 | 1.10945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3519.36 | 0.222034 | 0.111017 | − | 0.993818i | \(-0.464589\pi\) | ||||
0.111017 | + | 0.993818i | \(0.464589\pi\) | |||||||
\(632\) | 2388.53 | 0.150333 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −401.662 | −0.0251609 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11892.7 | 0.739726 | ||||||||
\(638\) | −17665.3 | −1.09620 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17397.1 | −1.07199 | −0.535995 | − | 0.844221i | \(-0.680063\pi\) | ||||
−0.535995 | + | 0.844221i | \(0.680063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5773.23 | −0.354081 | −0.177040 | − | 0.984204i | \(-0.556652\pi\) | ||||
−0.177040 | + | 0.984204i | \(0.556652\pi\) | |||||||
\(644\) | −18.1604 | −0.00111121 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −32112.7 | −1.95582 | ||||||||
\(647\) | −27954.2 | −1.69860 | −0.849299 | − | 0.527913i | \(-0.822975\pi\) | ||||
−0.849299 | + | 0.527913i | \(0.822975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16933.6 | 1.02419 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4614.80 | 0.277193 | ||||||||
\(653\) | −3933.82 | −0.235746 | −0.117873 | − | 0.993029i | \(-0.537608\pi\) | ||||
−0.117873 | + | 0.993029i | \(0.537608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2611.31 | −0.155418 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13434.8 | 0.795961 | ||||||||
\(659\) | −24920.9 | −1.47311 | −0.736555 | − | 0.676377i | \(-0.763549\pi\) | ||||
−0.736555 | + | 0.676377i | \(0.763549\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4021.88 | 0.236661 | 0.118331 | − | 0.992974i | \(-0.462246\pi\) | ||||
0.118331 | + | 0.992974i | \(0.462246\pi\) | |||||||
\(662\) | 2313.16 | 0.135806 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 30317.2 | 1.77189 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 79.4187 | 0.00461035 | ||||||||
\(668\) | 1017.93 | 0.0589596 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11713.7 | 0.673924 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20002.2 | 1.14566 | 0.572828 | − | 0.819675i | \(-0.305846\pi\) | ||||
0.572828 | + | 0.819675i | \(0.305846\pi\) | |||||||
\(674\) | 3183.40 | 0.181929 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2314.74 | 0.131699 | ||||||||
\(677\) | 1955.82 | 0.111031 | 0.0555156 | − | 0.998458i | \(-0.482320\pi\) | ||||
0.0555156 | + | 0.998458i | \(0.482320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13163.6 | 0.743993 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8769.76 | −0.492392 | ||||||||
\(683\) | 7805.42 | 0.437285 | 0.218643 | − | 0.975805i | \(-0.429837\pi\) | ||||
0.218643 | + | 0.975805i | \(0.429837\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6456.96 | 0.359370 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25260.2 | −1.39976 | ||||||||
\(689\) | −14594.9 | −0.806998 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4435.06 | −0.244165 | −0.122082 | − | 0.992520i | \(-0.538957\pi\) | ||||
−0.122082 | + | 0.992520i | \(0.538957\pi\) | |||||||
\(692\) | 294.064 | 0.0161541 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1496.56 | 0.0818570 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5024.02 | 0.273025 | ||||||||
\(698\) | −16098.9 | −0.872996 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12579.2 | −0.677762 | −0.338881 | − | 0.940829i | \(-0.610048\pi\) | ||||
−0.338881 | + | 0.940829i | \(0.610048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25350.7 | 1.36005 | ||||||||
\(704\) | −20391.1 | −1.09165 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6920.19 | −0.368902 | ||||||||
\(707\) | 41106.0 | 2.18663 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18736.3 | 0.992461 | 0.496231 | − | 0.868191i | \(-0.334717\pi\) | ||||
0.496231 | + | 0.868191i | \(0.334717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10902.2 | 0.573846 | ||||||||
\(713\) | 39.4267 | 0.00207089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7416.85 | −0.387124 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7021.27 | 0.364946 | ||||||||
\(719\) | 6632.57 | 0.344024 | 0.172012 | − | 0.985095i | \(-0.444973\pi\) | ||||
0.172012 | + | 0.985095i | \(0.444973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26990.0 | −1.39412 | ||||||||
\(722\) | −29159.9 | −1.50307 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3511.46 | 0.180252 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5599.91 | 0.285680 | 0.142840 | − | 0.989746i | \(-0.454377\pi\) | ||||
0.142840 | + | 0.989746i | \(0.454377\pi\) | |||||||
\(728\) | −18534.0 | −0.943565 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48599.3 | 2.45898 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25381.4 | 1.27897 | 0.639483 | − | 0.768805i | \(-0.279148\pi\) | ||||
0.639483 | + | 0.768805i | \(0.279148\pi\) | |||||||
\(734\) | 1811.81 | 0.0911103 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.9990 | 0.00145233 | ||||||||
\(737\) | −2793.65 | −0.139627 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3153.26 | 0.156962 | 0.0784808 | − | 0.996916i | \(-0.474993\pi\) | ||||
0.0784808 | + | 0.996916i | \(0.474993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −37620.7 | −1.86132 | ||||||||
\(743\) | −23892.5 | −1.17972 | −0.589859 | − | 0.807506i | \(-0.700817\pi\) | ||||
−0.589859 | + | 0.807506i | \(0.700817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −29362.4 | −1.44106 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5359.81 | 0.261998 | ||||||||
\(749\) | −35697.0 | −1.74144 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7232.32 | 0.351413 | 0.175707 | − | 0.984443i | \(-0.443779\pi\) | ||||
0.175707 | + | 0.984443i | \(0.443779\pi\) | |||||||
\(752\) | −9265.42 | −0.449302 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13499.4 | 0.652015 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9385.12 | −0.450605 | −0.225302 | − | 0.974289i | \(-0.572337\pi\) | ||||
−0.225302 | + | 0.974289i | \(0.572337\pi\) | |||||||
\(758\) | 19970.2 | 0.956929 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13138.3 | −0.625840 | −0.312920 | − | 0.949779i | \(-0.601307\pi\) | ||||
−0.312920 | + | 0.949779i | \(0.601307\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40317.4 | 1.91296 | ||||||||
\(764\) | 5013.11 | 0.237393 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17622.6 | −0.831242 | ||||||||
\(767\) | −12940.3 | −0.609187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34393.8 | −1.61284 | −0.806419 | − | 0.591344i | \(-0.798597\pi\) | ||||
−0.806419 | + | 0.591344i | \(0.798597\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5622.51 | −0.262123 | ||||||||
\(773\) | −5527.75 | −0.257205 | −0.128602 | − | 0.991696i | \(-0.541049\pi\) | ||||
−0.128602 | + | 0.991696i | \(0.541049\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11464.7 | −0.530359 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17473.7 | −0.805221 | ||||||||
\(779\) | 7277.05 | 0.334695 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25338.3 | 1.16092 | ||||||||
\(782\) | 96.4858 | 0.00441218 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21141.7 | −0.963089 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39668.3 | −1.79673 | −0.898363 | − | 0.439254i | \(-0.855243\pi\) | ||||
−0.898363 | + | 0.439254i | \(0.855243\pi\) | |||||||
\(788\) | 5520.89 | 0.249586 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 64464.7 | 2.89772 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8951.35 | −0.400847 | ||||||||
\(794\) | 20841.0 | 0.931511 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3610.16 | −0.160752 | ||||||||
\(797\) | 11474.1 | 0.509956 | 0.254978 | − | 0.966947i | \(-0.417932\pi\) | ||||
0.254978 | + | 0.966947i | \(0.417932\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17826.2 | 0.789292 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3693.97 | 0.162642 | ||||||||
\(803\) | 12349.6 | 0.542725 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6701.65 | 0.292873 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −35800.9 | −1.55875 | ||||||||
\(809\) | 38806.9 | 1.68650 | 0.843249 | − | 0.537524i | \(-0.180640\pi\) | ||||
0.843249 | + | 0.537524i | \(0.180640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1873.12 | 0.0811027 | 0.0405513 | − | 0.999177i | \(-0.487089\pi\) | ||||
0.0405513 | + | 0.999177i | \(0.487089\pi\) | |||||||
\(812\) | −8690.20 | −0.375574 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16942.3 | 0.729518 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 70393.8 | 3.01440 | ||||||||
\(818\) | 24850.5 | 1.06220 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39300.8 | −1.67066 | −0.835328 | − | 0.549752i | \(-0.814722\pi\) | ||||
−0.835328 | + | 0.549752i | \(0.814722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44666.5 | −1.89183 | −0.945916 | − | 0.324413i | \(-0.894833\pi\) | ||||
−0.945916 | + | 0.324413i | \(0.894833\pi\) | |||||||
\(824\) | 23506.7 | 0.993805 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −33355.7 | −1.40508 | ||||||||
\(827\) | 39263.8 | 1.65095 | 0.825475 | − | 0.564438i | \(-0.190907\pi\) | ||||
0.825475 | + | 0.564438i | \(0.190907\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1566.69 | 0.0656372 | 0.0328186 | − | 0.999461i | \(-0.489552\pi\) | ||||
0.0328186 | + | 0.999461i | \(0.489552\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15582.4 | 0.649307 | ||||||||
\(833\) | 40675.5 | 1.69187 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7763.43 | 0.321177 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37876.7 | 1.56137 | ||||||||
\(839\) | 15525.9 | 0.638870 | 0.319435 | − | 0.947608i | \(-0.396507\pi\) | ||||
0.319435 | + | 0.947608i | \(0.396507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13614.8 | 0.558237 | ||||||||
\(842\) | −32663.2 | −1.33688 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1271.14 | −0.0518420 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1345.34 | 0.0545765 | ||||||||
\(848\) | 25945.5 | 1.05067 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −76.1685 | −0.00306818 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9716.17 | 0.390006 | 0.195003 | − | 0.980803i | \(-0.437528\pi\) | ||||
0.195003 | + | 0.980803i | \(0.437528\pi\) | |||||||
\(854\) | −23073.6 | −0.924545 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31090.0 | 1.24140 | ||||||||
\(857\) | −12663.6 | −0.504762 | −0.252381 | − | 0.967628i | \(-0.581214\pi\) | ||||
−0.252381 | + | 0.967628i | \(0.581214\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22605.5 | −0.897892 | −0.448946 | − | 0.893559i | \(-0.648200\pi\) | ||||
−0.448946 | + | 0.893559i | \(0.648200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14780.6 | 0.584025 | ||||||||
\(863\) | 1672.68 | 0.0659778 | 0.0329889 | − | 0.999456i | \(-0.489497\pi\) | ||||
0.0329889 | + | 0.999456i | \(0.489497\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3332.44 | 0.130763 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4314.17 | −0.168701 | ||||||||
\(869\) | −3522.54 | −0.137507 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2134.84 | 0.0830499 | ||||||||
\(872\) | −35114.1 | −1.36366 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 139.755 | 0.00540879 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3237.58 | 0.124658 | 0.0623291 | − | 0.998056i | \(-0.480147\pi\) | ||||
0.0623291 | + | 0.998056i | \(0.480147\pi\) | |||||||
\(878\) | 27389.6 | 1.05279 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8650.65 | 0.330815 | 0.165407 | − | 0.986225i | \(-0.447106\pi\) | ||||
0.165407 | + | 0.986225i | \(0.447106\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16846.2 | −0.642037 | −0.321018 | − | 0.947073i | \(-0.604025\pi\) | ||||
−0.321018 | + | 0.947073i | \(0.604025\pi\) | |||||||
\(884\) | −4095.85 | −0.155835 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19881.1 | 0.753857 | ||||||||
\(887\) | −47809.6 | −1.80980 | −0.904899 | − | 0.425627i | \(-0.860053\pi\) | ||||
−0.904899 | + | 0.425627i | \(0.860053\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41379.7 | 1.56111 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4346.98 | 0.163170 | ||||||||
\(893\) | 25820.3 | 0.967575 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24287.4 | 0.905562 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31658.3 | 1.17645 | ||||||||
\(899\) | 18866.7 | 0.699931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49917.7 | −1.84573 | ||||||||
\(902\) | 4863.38 | 0.179527 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −56145.0 | −2.06566 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1628.39 | −0.0596140 | −0.0298070 | − | 0.999556i | \(-0.509489\pi\) | ||||
−0.0298070 | + | 0.999556i | \(0.509489\pi\) | |||||||
\(908\) | 3094.93 | 0.113115 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17753.9 | 0.645677 | 0.322839 | − | 0.946454i | \(-0.395363\pi\) | ||||
0.322839 | + | 0.946454i | \(0.395363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44711.0 | −1.62072 | ||||||||
\(914\) | −27936.9 | −1.01102 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7644.24 | −0.275734 | ||||||||
\(917\) | 54388.8 | 1.95864 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42025.9 | −1.50849 | −0.754247 | − | 0.656591i | \(-0.771998\pi\) | ||||
−0.754247 | + | 0.656591i | \(0.771998\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23289.2 | 0.831875 | ||||||||
\(923\) | −19363.0 | −0.690509 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 44367.9 | 1.57454 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13876.7 | 0.490869 | ||||||||
\(929\) | −24361.1 | −0.860348 | −0.430174 | − | 0.902746i | \(-0.641548\pi\) | ||||
−0.430174 | + | 0.902746i | \(0.641548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 58916.5 | 2.07402 | ||||||||
\(932\) | −1269.68 | −0.0446241 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34749.4 | 1.21738 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51718.7 | −1.80318 | −0.901589 | − | 0.432595i | \(-0.857598\pi\) | ||||
−0.901589 | + | 0.432595i | \(0.857598\pi\) | |||||||
\(938\) | 5502.91 | 0.191553 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24630.2 | 0.853266 | 0.426633 | − | 0.904425i | \(-0.359700\pi\) | ||||
0.426633 | + | 0.904425i | \(0.359700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.8646 | −0.000755046 0 | ||||||||
\(944\) | 23004.0 | 0.793133 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 47045.5 | 1.61689 | ||||||||
\(947\) | −19674.2 | −0.675105 | −0.337552 | − | 0.941307i | \(-0.609599\pi\) | ||||
−0.337552 | + | 0.941307i | \(0.609599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9437.30 | −0.322811 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −63390.2 | −2.15808 | ||||||||
\(953\) | −40472.3 | −1.37568 | −0.687841 | − | 0.725861i | \(-0.741442\pi\) | ||||
−0.687841 | + | 0.725861i | \(0.741442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5200.75 | −0.175946 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13341.0 | −0.449923 | ||||||||
\(959\) | 64661.0 | 2.17728 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20424.8 | −0.685604 | ||||||||
\(962\) | −12946.9 | −0.433915 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2283.76 | −0.0763017 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29381.6 | −0.977093 | −0.488547 | − | 0.872538i | \(-0.662473\pi\) | ||||
−0.488547 | + | 0.872538i | \(0.662473\pi\) | |||||||
\(968\) | −1171.71 | −0.0389051 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22752.2 | 0.751961 | 0.375981 | − | 0.926628i | \(-0.377306\pi\) | ||||
0.375981 | + | 0.926628i | \(0.377306\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40753.4 | −1.34275 | ||||||||
\(974\) | −2323.86 | −0.0764489 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15912.9 | 0.521885 | ||||||||
\(977\) | 10823.1 | 0.354413 | 0.177206 | − | 0.984174i | \(-0.443294\pi\) | ||||
0.177206 | + | 0.984174i | \(0.443294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16078.3 | −0.524888 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4417.52 | 0.143553 | ||||||||
\(983\) | 17495.4 | 0.567666 | 0.283833 | − | 0.958874i | \(-0.408394\pi\) | ||||
0.283833 | + | 0.958874i | \(0.408394\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 46170.9 | 1.49126 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5932.64 | −0.191035 | ||||||||
\(989\) | −211.505 | −0.00680027 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 300.294 | 0.00962578 | 0.00481289 | − | 0.999988i | \(-0.498468\pi\) | ||||
0.00481289 | + | 0.999988i | \(0.498468\pi\) | |||||||
\(992\) | 6888.98 | 0.220489 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −49911.2 | −1.59264 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6360.83 | 0.202056 | 0.101028 | − | 0.994884i | \(-0.467787\pi\) | ||||
0.101028 | + | 0.994884i | \(0.467787\pi\) | |||||||
\(998\) | −27429.2 | −0.869997 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 675.4.a.u.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 675.4.a.y.1.3 | yes | 4 | ||
5.2 | odd | 4 | 675.4.b.p.649.3 | 8 | |||
5.3 | odd | 4 | 675.4.b.p.649.6 | 8 | |||
5.4 | even | 2 | 675.4.a.z.1.3 | yes | 4 | ||
15.2 | even | 4 | 675.4.b.q.649.6 | 8 | |||
15.8 | even | 4 | 675.4.b.q.649.3 | 8 | |||
15.14 | odd | 2 | 675.4.a.v.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
675.4.a.u.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
675.4.a.v.1.2 | yes | 4 | 15.14 | odd | 2 | ||
675.4.a.y.1.3 | yes | 4 | 3.2 | odd | 2 | ||
675.4.a.z.1.3 | yes | 4 | 5.4 | even | 2 | ||
675.4.b.p.649.3 | 8 | 5.2 | odd | 4 | |||
675.4.b.p.649.6 | 8 | 5.3 | odd | 4 | |||
675.4.b.q.649.3 | 8 | 15.8 | even | 4 | |||
675.4.b.q.649.6 | 8 | 15.2 | even | 4 |