Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 74x^{6} + 1469x^{4} - 8828x^{2} + 2500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(3.37406\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.95985 | 0.692912 | 0.346456 | − | 0.938066i | \(-0.387385\pi\) | ||||
0.346456 | + | 0.938066i | \(0.387385\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.15899 | −0.519874 | ||||||||
\(5\) | 11.8897 | 1.06344 | 0.531722 | − | 0.846919i | \(-0.321545\pi\) | ||||
0.531722 | + | 0.846919i | \(0.321545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −23.8298 | −1.05314 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 23.3019 | 0.736872 | ||||||||
\(11\) | 36.4130 | 0.998085 | 0.499043 | − | 0.866577i | \(-0.333685\pi\) | ||||
0.499043 | + | 0.866577i | \(0.333685\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.964525 | 0.0205778 | 0.0102889 | − | 0.999947i | \(-0.496725\pi\) | ||||
0.0102889 | + | 0.999947i | \(0.496725\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −13.4309 | −0.209858 | ||||||||
\(17\) | 98.2514 | 1.40173 | 0.700866 | − | 0.713293i | \(-0.252797\pi\) | ||||
0.700866 | + | 0.713293i | \(0.252797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −106.001 | −1.27991 | −0.639954 | − | 0.768413i | \(-0.721047\pi\) | ||||
−0.639954 | + | 0.768413i | \(0.721047\pi\) | |||||||
\(20\) | −49.4490 | −0.552856 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 71.3640 | 0.691585 | ||||||||
\(23\) | 54.3633 | 0.492849 | 0.246424 | − | 0.969162i | \(-0.420744\pi\) | ||||
0.246424 | + | 0.969162i | \(0.420744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 16.3640 | 0.130912 | ||||||||
\(26\) | 1.89032 | 0.0142586 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 229.725 | 1.47099 | 0.735497 | − | 0.677528i | \(-0.236949\pi\) | ||||
0.735497 | + | 0.677528i | \(0.236949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 127.729 | 0.740025 | 0.370013 | − | 0.929027i | \(-0.379353\pi\) | ||||
0.370013 | + | 0.929027i | \(0.379353\pi\) | |||||||
\(32\) | 164.316 | 0.907725 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 192.558 | 0.971277 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 311.816 | 1.38546 | 0.692732 | − | 0.721195i | \(-0.256407\pi\) | ||||
0.692732 | + | 0.721195i | \(0.256407\pi\) | |||||||
\(38\) | −207.746 | −0.886864 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −283.328 | −1.11995 | ||||||||
\(41\) | −419.919 | −1.59952 | −0.799760 | − | 0.600320i | \(-0.795040\pi\) | ||||
−0.799760 | + | 0.600320i | \(0.795040\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 523.180 | 1.85545 | 0.927723 | − | 0.373270i | \(-0.121763\pi\) | ||||
0.927723 | + | 0.373270i | \(0.121763\pi\) | |||||||
\(44\) | −151.441 | −0.518878 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 106.544 | 0.341501 | ||||||||
\(47\) | 270.328 | 0.838966 | 0.419483 | − | 0.907763i | \(-0.362211\pi\) | ||||
0.419483 | + | 0.907763i | \(0.362211\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 32.0711 | 0.0907107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.01145 | −0.0106978 | ||||||||
\(53\) | −251.082 | −0.650732 | −0.325366 | − | 0.945588i | \(-0.605487\pi\) | ||||
−0.325366 | + | 0.945588i | \(0.605487\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 432.938 | 1.06141 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 450.226 | 1.01927 | ||||||||
\(59\) | 408.029 | 0.900354 | 0.450177 | − | 0.892939i | \(-0.351361\pi\) | ||||
0.450177 | + | 0.892939i | \(0.351361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −860.546 | −1.80626 | −0.903128 | − | 0.429372i | \(-0.858735\pi\) | ||||
−0.903128 | + | 0.429372i | \(0.858735\pi\) | |||||||
\(62\) | 250.329 | 0.512772 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 429.481 | 0.838831 | ||||||||
\(65\) | 11.4679 | 0.0218833 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 506.360 | 0.923308 | 0.461654 | − | 0.887060i | \(-0.347256\pi\) | ||||
0.461654 | + | 0.887060i | \(0.347256\pi\) | |||||||
\(68\) | −408.626 | −0.728724 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −523.702 | −0.875380 | −0.437690 | − | 0.899126i | \(-0.644203\pi\) | ||||
−0.437690 | + | 0.899126i | \(0.644203\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 629.964 | 1.01002 | 0.505012 | − | 0.863113i | \(-0.331488\pi\) | ||||
0.505012 | + | 0.863113i | \(0.331488\pi\) | |||||||
\(74\) | 611.112 | 0.960004 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 440.856 | 0.665391 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 319.548 | 0.455089 | 0.227544 | − | 0.973768i | \(-0.426930\pi\) | ||||
0.227544 | + | 0.973768i | \(0.426930\pi\) | |||||||
\(80\) | −159.689 | −0.223172 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −822.978 | −1.10833 | ||||||||
\(83\) | 1309.16 | 1.73131 | 0.865654 | − | 0.500643i | \(-0.166903\pi\) | ||||
0.865654 | + | 0.500643i | \(0.166903\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1168.18 | 1.49066 | ||||||||
\(86\) | 1025.35 | 1.28566 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −867.715 | −1.05112 | ||||||||
\(89\) | −348.581 | −0.415163 | −0.207581 | − | 0.978218i | \(-0.566559\pi\) | ||||
−0.207581 | + | 0.978218i | \(0.566559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −226.096 | −0.256219 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 529.803 | 0.581329 | ||||||||
\(95\) | −1260.31 | −1.36111 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −161.996 | −0.169569 | −0.0847844 | − | 0.996399i | \(-0.527020\pi\) | ||||
−0.0847844 | + | 0.996399i | \(0.527020\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −68.0579 | −0.0680579 | ||||||||
\(101\) | −218.342 | −0.215108 | −0.107554 | − | 0.994199i | \(-0.534302\pi\) | ||||
−0.107554 | + | 0.994199i | \(0.534302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −231.090 | −0.221068 | −0.110534 | − | 0.993872i | \(-0.535256\pi\) | ||||
−0.110534 | + | 0.993872i | \(0.535256\pi\) | |||||||
\(104\) | −22.9844 | −0.0216712 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −492.083 | −0.450899 | ||||||||
\(107\) | −1865.12 | −1.68513 | −0.842563 | − | 0.538598i | \(-0.818954\pi\) | ||||
−0.842563 | + | 0.538598i | \(0.818954\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 601.004 | 0.528127 | 0.264063 | − | 0.964505i | \(-0.414937\pi\) | ||||
0.264063 | + | 0.964505i | \(0.414937\pi\) | |||||||
\(110\) | 848.494 | 0.735461 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −475.349 | −0.395727 | −0.197863 | − | 0.980230i | \(-0.563400\pi\) | ||||
−0.197863 | + | 0.980230i | \(0.563400\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 646.361 | 0.524117 | ||||||||
\(116\) | −955.422 | −0.764731 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 799.676 | 0.623865 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.09213 | −0.00382580 | ||||||||
\(122\) | −1686.54 | −1.25158 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −531.223 | −0.384720 | ||||||||
\(125\) | −1291.64 | −0.924226 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −29.0876 | −0.0203237 | −0.0101619 | − | 0.999948i | \(-0.503235\pi\) | ||||
−0.0101619 | + | 0.999948i | \(0.503235\pi\) | |||||||
\(128\) | −472.807 | −0.326489 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 22.4753 | 0.0151632 | ||||||||
\(131\) | −2115.26 | −1.41077 | −0.705387 | − | 0.708822i | \(-0.749227\pi\) | ||||
−0.705387 | + | 0.708822i | \(0.749227\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 992.389 | 0.639771 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2341.31 | −1.47622 | ||||||||
\(137\) | 177.342 | 0.110594 | 0.0552968 | − | 0.998470i | \(-0.482390\pi\) | ||||
0.0552968 | + | 0.998470i | \(0.482390\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2369.18 | −1.44569 | −0.722846 | − | 0.691009i | \(-0.757166\pi\) | ||||
−0.722846 | + | 0.691009i | \(0.757166\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1026.38 | −0.606561 | ||||||||
\(143\) | 35.1213 | 0.0205384 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2731.35 | 1.56432 | ||||||||
\(146\) | 1234.63 | 0.699857 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1296.84 | −0.720266 | ||||||||
\(149\) | 1491.03 | 0.819801 | 0.409900 | − | 0.912130i | \(-0.365563\pi\) | ||||
0.409900 | + | 0.912130i | \(0.365563\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 410.461 | 0.221211 | 0.110605 | − | 0.993864i | \(-0.464721\pi\) | ||||
0.110605 | + | 0.993864i | \(0.464721\pi\) | |||||||
\(152\) | 2525.98 | 1.34792 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1518.65 | 0.786975 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −453.500 | −0.230530 | −0.115265 | − | 0.993335i | \(-0.536772\pi\) | ||||
−0.115265 | + | 0.993335i | \(0.536772\pi\) | |||||||
\(158\) | 626.267 | 0.315336 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1953.66 | 0.965314 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 748.166 | 0.359515 | 0.179757 | − | 0.983711i | \(-0.442469\pi\) | ||||
0.179757 | + | 0.983711i | \(0.442469\pi\) | |||||||
\(164\) | 1746.44 | 0.831548 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2565.75 | 1.19964 | ||||||||
\(167\) | −518.269 | −0.240149 | −0.120074 | − | 0.992765i | \(-0.538313\pi\) | ||||
−0.120074 | + | 0.992765i | \(0.538313\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2196.07 | −0.999577 | ||||||||
\(170\) | 2289.45 | 1.03290 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2175.90 | −0.964597 | ||||||||
\(173\) | −1313.48 | −0.577239 | −0.288620 | − | 0.957444i | \(-0.593196\pi\) | ||||
−0.288620 | + | 0.957444i | \(0.593196\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −489.060 | −0.209456 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −683.166 | −0.287671 | ||||||||
\(179\) | 4133.15 | 1.72584 | 0.862921 | − | 0.505339i | \(-0.168632\pi\) | ||||
0.862921 | + | 0.505339i | \(0.168632\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3714.04 | −1.52521 | −0.762603 | − | 0.646867i | \(-0.776079\pi\) | ||||
−0.762603 | + | 0.646867i | \(0.776079\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1295.47 | −0.519038 | ||||||||
\(185\) | 3707.38 | 1.47336 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3577.63 | 1.39905 | ||||||||
\(188\) | −1124.29 | −0.436156 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2470.03 | −0.943129 | ||||||||
\(191\) | −3068.37 | −1.16241 | −0.581203 | − | 0.813758i | \(-0.697418\pi\) | ||||
−0.581203 | + | 0.813758i | \(0.697418\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2089.53 | 0.779314 | 0.389657 | − | 0.920960i | \(-0.372593\pi\) | ||||
0.389657 | + | 0.920960i | \(0.372593\pi\) | |||||||
\(194\) | −317.487 | −0.117496 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3729.89 | −1.34895 | −0.674476 | − | 0.738297i | \(-0.735630\pi\) | ||||
−0.674476 | + | 0.738297i | \(0.735630\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2108.85 | −0.751217 | −0.375608 | − | 0.926778i | \(-0.622566\pi\) | ||||
−0.375608 | + | 0.926778i | \(0.622566\pi\) | |||||||
\(200\) | −389.952 | −0.137869 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −427.918 | −0.149051 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4992.69 | −1.70100 | ||||||||
\(206\) | −452.903 | −0.153181 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.9544 | −0.00431841 | ||||||||
\(209\) | −3859.81 | −1.27746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1546.53 | −0.504584 | −0.252292 | − | 0.967651i | \(-0.581184\pi\) | ||||
−0.252292 | + | 0.967651i | \(0.581184\pi\) | |||||||
\(212\) | 1044.25 | 0.338298 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3655.36 | −1.16764 | ||||||||
\(215\) | 6220.43 | 1.97316 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1177.88 | 0.365945 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1800.59 | −0.551798 | ||||||||
\(221\) | 94.7659 | 0.0288445 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4860.40 | −1.45954 | −0.729768 | − | 0.683695i | \(-0.760372\pi\) | ||||
−0.729768 | + | 0.683695i | \(0.760372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −931.614 | −0.274204 | ||||||||
\(227\) | −700.942 | −0.204948 | −0.102474 | − | 0.994736i | \(-0.532676\pi\) | ||||
−0.102474 | + | 0.994736i | \(0.532676\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3694.24 | 1.06604 | 0.533018 | − | 0.846104i | \(-0.321058\pi\) | ||||
0.533018 | + | 0.846104i | \(0.321058\pi\) | |||||||
\(230\) | 1266.77 | 0.363167 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5474.29 | −1.54916 | ||||||||
\(233\) | 344.322 | 0.0968124 | 0.0484062 | − | 0.998828i | \(-0.484586\pi\) | ||||
0.0484062 | + | 0.998828i | \(0.484586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3214.11 | 0.892193 | ||||||||
\(236\) | −1696.99 | −0.468070 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6144.21 | 1.66291 | 0.831456 | − | 0.555590i | \(-0.187508\pi\) | ||||
0.831456 | + | 0.555590i | \(0.187508\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5626.11 | 1.50378 | 0.751888 | − | 0.659291i | \(-0.229144\pi\) | ||||
0.751888 | + | 0.659291i | \(0.229144\pi\) | |||||||
\(242\) | −9.97982 | −0.00265094 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3579.00 | 0.939025 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −102.240 | −0.0263377 | ||||||||
\(248\) | −3043.75 | −0.779349 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2531.43 | −0.640407 | ||||||||
\(251\) | 520.460 | 0.130881 | 0.0654405 | − | 0.997856i | \(-0.479155\pi\) | ||||
0.0654405 | + | 0.997856i | \(0.479155\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1979.53 | 0.491905 | ||||||||
\(254\) | −57.0074 | −0.0140825 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4362.48 | −1.06506 | ||||||||
\(257\) | −4009.50 | −0.973174 | −0.486587 | − | 0.873632i | \(-0.661758\pi\) | ||||
−0.486587 | + | 0.873632i | \(0.661758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −47.6948 | −0.0113766 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4145.60 | −0.977542 | ||||||||
\(263\) | −3585.19 | −0.840579 | −0.420290 | − | 0.907390i | \(-0.638072\pi\) | ||||
−0.420290 | + | 0.907390i | \(0.638072\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2985.28 | −0.692016 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2105.94 | −0.480004 | ||||||||
\(269\) | −5509.19 | −1.24870 | −0.624352 | − | 0.781143i | \(-0.714637\pi\) | ||||
−0.624352 | + | 0.781143i | \(0.714637\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5819.89 | 1.30455 | 0.652276 | − | 0.757982i | \(-0.273814\pi\) | ||||
0.652276 | + | 0.757982i | \(0.273814\pi\) | |||||||
\(272\) | −1319.60 | −0.294165 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 347.563 | 0.0766316 | ||||||||
\(275\) | 595.864 | 0.130662 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1150.45 | −0.249545 | −0.124772 | − | 0.992185i | \(-0.539820\pi\) | ||||
−0.124772 | + | 0.992185i | \(0.539820\pi\) | |||||||
\(278\) | −4643.24 | −1.00174 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −895.631 | −0.190138 | −0.0950692 | − | 0.995471i | \(-0.530307\pi\) | ||||
−0.0950692 | + | 0.995471i | \(0.530307\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −122.450 | −0.0257205 | −0.0128603 | − | 0.999917i | \(-0.504094\pi\) | ||||
−0.0128603 | + | 0.999917i | \(0.504094\pi\) | |||||||
\(284\) | 2178.07 | 0.455087 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 68.8324 | 0.0142313 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4740.33 | 0.964854 | ||||||||
\(290\) | 5353.03 | 1.08393 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2620.01 | −0.525084 | ||||||||
\(293\) | 7601.77 | 1.51570 | 0.757850 | − | 0.652429i | \(-0.226250\pi\) | ||||
0.757850 | + | 0.652429i | \(0.226250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4851.33 | 0.957475 | ||||||||
\(296\) | −7430.50 | −1.45909 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2922.20 | 0.568050 | ||||||||
\(299\) | 52.4347 | 0.0101417 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 804.441 | 0.153279 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1423.69 | 0.268599 | ||||||||
\(305\) | −10231.6 | −1.92085 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3539.05 | 0.657929 | 0.328964 | − | 0.944342i | \(-0.393300\pi\) | ||||
0.328964 | + | 0.944342i | \(0.393300\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2976.33 | 0.545304 | ||||||||
\(311\) | 3894.93 | 0.710165 | 0.355083 | − | 0.934835i | \(-0.384453\pi\) | ||||
0.355083 | + | 0.934835i | \(0.384453\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8682.58 | −1.56795 | −0.783975 | − | 0.620793i | \(-0.786811\pi\) | ||||
−0.783975 | + | 0.620793i | \(0.786811\pi\) | |||||||
\(314\) | −888.792 | −0.159737 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1329.00 | −0.236589 | ||||||||
\(317\) | 8495.52 | 1.50522 | 0.752612 | − | 0.658464i | \(-0.228794\pi\) | ||||
0.752612 | + | 0.658464i | \(0.228794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8364.97 | 1.46818 | ||||||||
\(320\) | 5106.39 | 0.892049 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10414.7 | −1.79409 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.7835 | 0.00269389 | ||||||||
\(326\) | 1466.29 | 0.249112 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10006.6 | 1.68451 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1270.71 | 0.211011 | 0.105505 | − | 0.994419i | \(-0.466354\pi\) | ||||
0.105505 | + | 0.994419i | \(0.466354\pi\) | |||||||
\(332\) | −5444.76 | −0.900061 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1015.73 | −0.166402 | ||||||||
\(335\) | 6020.44 | 0.981886 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4695.47 | 0.758986 | 0.379493 | − | 0.925195i | \(-0.376098\pi\) | ||||
0.379493 | + | 0.925195i | \(0.376098\pi\) | |||||||
\(338\) | −4303.97 | −0.692618 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4858.43 | −0.774957 | ||||||||
\(341\) | 4651.00 | 0.738609 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12467.3 | −1.95404 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2574.23 | −0.399976 | ||||||||
\(347\) | 6513.97 | 1.00775 | 0.503874 | − | 0.863777i | \(-0.331908\pi\) | ||||
0.503874 | + | 0.863777i | \(0.331908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7184.75 | −1.10198 | −0.550990 | − | 0.834512i | \(-0.685750\pi\) | ||||
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5983.23 | 0.905987 | ||||||||
\(353\) | −6068.55 | −0.915004 | −0.457502 | − | 0.889209i | \(-0.651256\pi\) | ||||
−0.457502 | + | 0.889209i | \(0.651256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6226.64 | −0.930918 | ||||||||
\(356\) | 1449.74 | 0.215832 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8100.34 | 1.19586 | ||||||||
\(359\) | 1743.71 | 0.256350 | 0.128175 | − | 0.991752i | \(-0.459088\pi\) | ||||
0.128175 | + | 0.991752i | \(0.459088\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4377.18 | 0.638167 | ||||||||
\(362\) | −7278.96 | −1.05683 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7490.06 | 1.07410 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9000.12 | 1.28012 | 0.640058 | − | 0.768327i | \(-0.278910\pi\) | ||||
0.640058 | + | 0.768327i | \(0.278910\pi\) | |||||||
\(368\) | −730.148 | −0.103428 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7265.91 | 1.02091 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5271.75 | 0.731799 | 0.365899 | − | 0.930654i | \(-0.380761\pi\) | ||||
0.365899 | + | 0.930654i | \(0.380761\pi\) | |||||||
\(374\) | 7011.61 | 0.969417 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6441.86 | −0.883547 | ||||||||
\(377\) | 221.575 | 0.0302698 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10480.0 | 1.42037 | 0.710185 | − | 0.704015i | \(-0.248611\pi\) | ||||
0.710185 | + | 0.704015i | \(0.248611\pi\) | |||||||
\(380\) | 5241.63 | 0.707606 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6013.55 | −0.805445 | ||||||||
\(383\) | −1374.03 | −0.183315 | −0.0916574 | − | 0.995791i | \(-0.529216\pi\) | ||||
−0.0916574 | + | 0.995791i | \(0.529216\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4095.17 | 0.539996 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 673.739 | 0.0881544 | ||||||||
\(389\) | 1898.27 | 0.247419 | 0.123710 | − | 0.992318i | \(-0.460521\pi\) | ||||
0.123710 | + | 0.992318i | \(0.460521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5341.26 | 0.690842 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7310.02 | −0.934704 | ||||||||
\(395\) | 3799.32 | 0.483961 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5572.30 | −0.704448 | −0.352224 | − | 0.935916i | \(-0.614574\pi\) | ||||
−0.352224 | + | 0.935916i | \(0.614574\pi\) | |||||||
\(398\) | −4133.02 | −0.520527 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −219.784 | −0.0274730 | ||||||||
\(401\) | −5716.38 | −0.711877 | −0.355938 | − | 0.934509i | \(-0.615839\pi\) | ||||
−0.355938 | + | 0.934509i | \(0.615839\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 123.198 | 0.0152281 | ||||||||
\(404\) | 908.083 | 0.111829 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11354.2 | 1.38281 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10348.5 | 1.25111 | 0.625553 | − | 0.780182i | \(-0.284874\pi\) | ||||
0.625553 | + | 0.780182i | \(0.284874\pi\) | |||||||
\(410\) | −9784.93 | −1.17864 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 961.103 | 0.114927 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15565.4 | 1.84115 | ||||||||
\(416\) | 158.487 | 0.0186790 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7564.65 | −0.885165 | ||||||||
\(419\) | −3251.80 | −0.379142 | −0.189571 | − | 0.981867i | \(-0.560710\pi\) | ||||
−0.189571 | + | 0.981867i | \(0.560710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3708.63 | 0.429329 | 0.214664 | − | 0.976688i | \(-0.431134\pi\) | ||||
0.214664 | + | 0.976688i | \(0.431134\pi\) | |||||||
\(422\) | −3030.96 | −0.349632 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5983.23 | 0.685310 | ||||||||
\(425\) | 1607.79 | 0.183504 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7757.03 | 0.876052 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12191.1 | 1.36723 | ||||||||
\(431\) | 4148.74 | 0.463661 | 0.231831 | − | 0.972756i | \(-0.425529\pi\) | ||||
0.231831 | + | 0.972756i | \(0.425529\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1985.64 | 0.220378 | 0.110189 | − | 0.993911i | \(-0.464854\pi\) | ||||
0.110189 | + | 0.993911i | \(0.464854\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2499.57 | −0.274559 | ||||||||
\(437\) | −5762.55 | −0.630802 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6914.42 | −0.751725 | −0.375863 | − | 0.926675i | \(-0.622654\pi\) | ||||
−0.375863 | + | 0.926675i | \(0.622654\pi\) | |||||||
\(440\) | −10316.8 | −1.11781 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 185.727 | 0.0199867 | ||||||||
\(443\) | 4237.47 | 0.454466 | 0.227233 | − | 0.973840i | \(-0.427032\pi\) | ||||
0.227233 | + | 0.973840i | \(0.427032\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4144.51 | −0.441502 | ||||||||
\(446\) | −9525.65 | −1.01133 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2097.02 | −0.220411 | −0.110206 | − | 0.993909i | \(-0.535151\pi\) | ||||
−0.110206 | + | 0.993909i | \(0.535151\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15290.5 | −1.59646 | ||||||||
\(452\) | 1976.97 | 0.205728 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1373.74 | −0.142011 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18676.3 | −1.91168 | −0.955842 | − | 0.293880i | \(-0.905053\pi\) | ||||
−0.955842 | + | 0.293880i | \(0.905053\pi\) | |||||||
\(458\) | 7240.15 | 0.738668 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2688.21 | −0.272475 | ||||||||
\(461\) | −13879.5 | −1.40224 | −0.701121 | − | 0.713043i | \(-0.747317\pi\) | ||||
−0.701121 | + | 0.713043i | \(0.747317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4780.89 | 0.479885 | 0.239942 | − | 0.970787i | \(-0.422871\pi\) | ||||
0.239942 | + | 0.970787i | \(0.422871\pi\) | |||||||
\(464\) | −3085.41 | −0.308699 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 674.819 | 0.0670824 | ||||||||
\(467\) | 8376.19 | 0.829986 | 0.414993 | − | 0.909824i | \(-0.363784\pi\) | ||||
0.414993 | + | 0.909824i | \(0.363784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6299.17 | 0.618211 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9723.25 | −0.948197 | ||||||||
\(473\) | 19050.6 | 1.85189 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1734.60 | −0.167556 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12041.7 | 1.15225 | ||||||||
\(479\) | −17011.4 | −1.62269 | −0.811346 | − | 0.584567i | \(-0.801265\pi\) | ||||
−0.811346 | + | 0.584567i | \(0.801265\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 300.754 | 0.0285098 | ||||||||
\(482\) | 11026.3 | 1.04198 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.1781 | 0.00198893 | ||||||||
\(485\) | −1926.07 | −0.180327 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6017.65 | 0.559930 | 0.279965 | − | 0.960010i | \(-0.409677\pi\) | ||||
0.279965 | + | 0.960010i | \(0.409677\pi\) | |||||||
\(488\) | 20506.6 | 1.90224 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12306.6 | −1.13113 | −0.565567 | − | 0.824702i | \(-0.691343\pi\) | ||||
−0.565567 | + | 0.824702i | \(0.691343\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22570.8 | 2.06194 | ||||||||
\(494\) | −200.376 | −0.0182497 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1715.51 | −0.155300 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8565.93 | 0.768464 | 0.384232 | − | 0.923237i | \(-0.374466\pi\) | ||||
0.384232 | + | 0.923237i | \(0.374466\pi\) | |||||||
\(500\) | 5371.94 | 0.480481 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1020.02 | 0.0906890 | ||||||||
\(503\) | −10520.4 | −0.932568 | −0.466284 | − | 0.884635i | \(-0.654408\pi\) | ||||
−0.466284 | + | 0.884635i | \(0.654408\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2596.02 | −0.228755 | ||||||||
\(506\) | 3879.58 | 0.340847 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 120.975 | 0.0105658 | ||||||||
\(509\) | 5445.41 | 0.474192 | 0.237096 | − | 0.971486i | \(-0.423804\pi\) | ||||
0.237096 | + | 0.971486i | \(0.423804\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4767.35 | −0.411502 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7858.02 | −0.674324 | ||||||||
\(515\) | −2747.59 | −0.235094 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9843.46 | 0.837360 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −273.277 | −0.0230461 | ||||||||
\(521\) | 22217.9 | 1.86830 | 0.934149 | − | 0.356883i | \(-0.116160\pi\) | ||||
0.934149 | + | 0.356883i | \(0.116160\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22109.9 | 1.84856 | 0.924281 | − | 0.381712i | \(-0.124665\pi\) | ||||
0.924281 | + | 0.381712i | \(0.124665\pi\) | |||||||
\(524\) | 8797.36 | 0.733425 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7026.44 | −0.582447 | ||||||||
\(527\) | 12549.5 | 1.03732 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9211.64 | −0.757100 | ||||||||
\(530\) | −5850.70 | −0.479506 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −405.022 | −0.0329146 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22175.7 | −1.79204 | ||||||||
\(536\) | −12066.4 | −0.972371 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10797.2 | −0.865241 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8631.34 | −0.685934 | −0.342967 | − | 0.939347i | \(-0.611432\pi\) | ||||
−0.342967 | + | 0.939347i | \(0.611432\pi\) | |||||||
\(542\) | 11406.1 | 0.903939 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16144.2 | 1.27239 | ||||||||
\(545\) | 7145.74 | 0.561633 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17846.7 | −1.39501 | −0.697505 | − | 0.716580i | \(-0.745707\pi\) | ||||
−0.697505 | + | 0.716580i | \(0.745707\pi\) | |||||||
\(548\) | −737.562 | −0.0574947 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1167.80 | 0.0905370 | ||||||||
\(551\) | −24351.0 | −1.88274 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2254.71 | −0.172913 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9853.39 | 0.751577 | ||||||||
\(557\) | 15703.3 | 1.19456 | 0.597279 | − | 0.802033i | \(-0.296248\pi\) | ||||
0.597279 | + | 0.802033i | \(0.296248\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 504.620 | 0.0381810 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1755.30 | −0.131749 | ||||||||
\(563\) | −673.679 | −0.0504302 | −0.0252151 | − | 0.999682i | \(-0.508027\pi\) | ||||
−0.0252151 | + | 0.999682i | \(0.508027\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5651.74 | −0.420833 | ||||||||
\(566\) | −239.984 | −0.0178221 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12479.7 | 0.921896 | ||||||||
\(569\) | −15186.2 | −1.11887 | −0.559436 | − | 0.828873i | \(-0.688982\pi\) | ||||
−0.559436 | + | 0.828873i | \(0.688982\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2526.66 | 0.185180 | 0.0925898 | − | 0.995704i | \(-0.470485\pi\) | ||||
0.0925898 | + | 0.995704i | \(0.470485\pi\) | |||||||
\(572\) | −146.069 | −0.0106774 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 889.603 | 0.0645200 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21680.4 | −1.56424 | −0.782119 | − | 0.623129i | \(-0.785861\pi\) | ||||
−0.782119 | + | 0.623129i | \(0.785861\pi\) | |||||||
\(578\) | 9290.33 | 0.668559 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11359.6 | −0.813248 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9142.66 | −0.649486 | ||||||||
\(584\) | −15011.9 | −1.06369 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14898.3 | 1.05025 | ||||||||
\(587\) | 17458.1 | 1.22755 | 0.613776 | − | 0.789481i | \(-0.289650\pi\) | ||||
0.613776 | + | 0.789481i | \(0.289650\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13539.4 | −0.947165 | ||||||||
\(590\) | 9507.87 | 0.663446 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4187.97 | −0.290751 | ||||||||
\(593\) | −5487.00 | −0.379973 | −0.189987 | − | 0.981787i | \(-0.560844\pi\) | ||||
−0.189987 | + | 0.981787i | \(0.560844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6201.20 | −0.426193 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 102.764 | 0.00702732 | ||||||||
\(599\) | −22997.3 | −1.56869 | −0.784343 | − | 0.620327i | \(-0.787000\pi\) | ||||
−0.784343 | + | 0.620327i | \(0.787000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18027.1 | −1.22353 | −0.611764 | − | 0.791040i | \(-0.709540\pi\) | ||||
−0.611764 | + | 0.791040i | \(0.709540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1707.10 | −0.115002 | ||||||||
\(605\) | −60.5437 | −0.00406852 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10285.1 | 0.687744 | 0.343872 | − | 0.939017i | \(-0.388261\pi\) | ||||
0.343872 | + | 0.939017i | \(0.388261\pi\) | |||||||
\(608\) | −17417.6 | −1.16181 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20052.4 | −1.33098 | ||||||||
\(611\) | 260.738 | 0.0172641 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1596.93 | −0.105219 | −0.0526096 | − | 0.998615i | \(-0.516754\pi\) | ||||
−0.0526096 | + | 0.998615i | \(0.516754\pi\) | |||||||
\(614\) | 6936.00 | 0.455886 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5850.74 | 0.381753 | 0.190877 | − | 0.981614i | \(-0.438867\pi\) | ||||
0.190877 | + | 0.981614i | \(0.438867\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1721.62 | 0.111789 | 0.0558947 | − | 0.998437i | \(-0.482199\pi\) | ||||
0.0558947 | + | 0.998437i | \(0.482199\pi\) | |||||||
\(620\) | −6316.06 | −0.409128 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7633.48 | 0.492082 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17402.7 | −1.11377 | ||||||||
\(626\) | −17016.5 | −1.08645 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1886.10 | 0.119847 | ||||||||
\(629\) | 30636.3 | 1.94205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19533.5 | −1.23235 | −0.616177 | − | 0.787608i | \(-0.711319\pi\) | ||||
−0.616177 | + | 0.787608i | \(0.711319\pi\) | |||||||
\(632\) | −7614.77 | −0.479271 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16649.9 | 1.04299 | ||||||||
\(635\) | −345.842 | −0.0216131 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16394.1 | 1.01732 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5621.52 | −0.347203 | ||||||||
\(641\) | −23496.2 | −1.44781 | −0.723903 | − | 0.689902i | \(-0.757654\pi\) | ||||
−0.723903 | + | 0.689902i | \(0.757654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1537.40 | 0.0942913 | 0.0471456 | − | 0.998888i | \(-0.484988\pi\) | ||||
0.0471456 | + | 0.998888i | \(0.484988\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20411.3 | −1.24315 | ||||||||
\(647\) | −28273.0 | −1.71797 | −0.858985 | − | 0.512000i | \(-0.828905\pi\) | ||||
−0.858985 | + | 0.512000i | \(0.828905\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14857.6 | 0.898630 | ||||||||
\(650\) | 30.9333 | 0.00186662 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3111.62 | −0.186902 | ||||||||
\(653\) | −2668.97 | −0.159946 | −0.0799730 | − | 0.996797i | \(-0.525483\pi\) | ||||
−0.0799730 | + | 0.996797i | \(0.525483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25149.8 | −1.50028 | ||||||||
\(656\) | 5639.89 | 0.335672 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6343.74 | −0.374988 | −0.187494 | − | 0.982266i | \(-0.560036\pi\) | ||||
−0.187494 | + | 0.982266i | \(0.560036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8409.15 | 0.494823 | 0.247412 | − | 0.968910i | \(-0.420420\pi\) | ||||
0.247412 | + | 0.968910i | \(0.420420\pi\) | |||||||
\(662\) | 2490.40 | 0.146212 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31196.9 | −1.82331 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12488.6 | 0.724977 | ||||||||
\(668\) | 2155.48 | 0.124847 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11799.2 | 0.680360 | ||||||||
\(671\) | −31335.1 | −1.80280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15326.7 | −0.877862 | −0.438931 | − | 0.898521i | \(-0.644643\pi\) | ||||
−0.438931 | + | 0.898521i | \(0.644643\pi\) | |||||||
\(674\) | 9202.41 | 0.525910 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9133.43 | 0.519653 | ||||||||
\(677\) | 13011.6 | 0.738666 | 0.369333 | − | 0.929297i | \(-0.379586\pi\) | ||||
0.369333 | + | 0.929297i | \(0.379586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −27837.4 | −1.56987 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9115.25 | 0.511790 | ||||||||
\(683\) | −17472.0 | −0.978840 | −0.489420 | − | 0.872048i | \(-0.662791\pi\) | ||||
−0.489420 | + | 0.872048i | \(0.662791\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2108.53 | 0.117610 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7026.78 | −0.389380 | ||||||||
\(689\) | −242.175 | −0.0133906 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7317.10 | 0.402830 | 0.201415 | − | 0.979506i | \(-0.435446\pi\) | ||||
0.201415 | + | 0.979506i | \(0.435446\pi\) | |||||||
\(692\) | 5462.77 | 0.300091 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12766.4 | 0.698280 | ||||||||
\(695\) | −28168.7 | −1.53741 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41257.6 | −2.24210 | ||||||||
\(698\) | −14081.0 | −0.763575 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7874.65 | 0.424282 | 0.212141 | − | 0.977239i | \(-0.431956\pi\) | ||||
0.212141 | + | 0.977239i | \(0.431956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33052.7 | −1.77327 | ||||||||
\(704\) | 15638.7 | 0.837225 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11893.4 | −0.634017 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25236.8 | −1.33680 | −0.668398 | − | 0.743804i | \(-0.733020\pi\) | ||||
−0.668398 | + | 0.743804i | \(0.733020\pi\) | |||||||
\(710\) | −12203.3 | −0.645044 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8306.61 | 0.437224 | ||||||||
\(713\) | 6943.76 | 0.364721 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 417.580 | 0.0218414 | ||||||||
\(716\) | −17189.7 | −0.897220 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3417.42 | 0.177628 | ||||||||
\(719\) | −19673.0 | −1.02041 | −0.510207 | − | 0.860052i | \(-0.670431\pi\) | ||||
−0.510207 | + | 0.860052i | \(0.670431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8578.62 | 0.442193 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15446.6 | 0.792914 | ||||||||
\(725\) | 3759.22 | 0.192571 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31921.7 | 1.62849 | 0.814243 | − | 0.580525i | \(-0.197152\pi\) | ||||
0.814243 | + | 0.580525i | \(0.197152\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14679.4 | 0.744258 | ||||||||
\(731\) | 51403.1 | 2.60084 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13545.3 | −0.682547 | −0.341274 | − | 0.939964i | \(-0.610858\pi\) | ||||
−0.341274 | + | 0.939964i | \(0.610858\pi\) | |||||||
\(734\) | 17638.9 | 0.887007 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8932.74 | 0.447371 | ||||||||
\(737\) | 18438.1 | 0.921541 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25497.6 | 1.26921 | 0.634604 | − | 0.772837i | \(-0.281163\pi\) | ||||
0.634604 | + | 0.772837i | \(0.281163\pi\) | |||||||
\(740\) | −15419.0 | −0.765963 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11146.9 | −0.550390 | −0.275195 | − | 0.961388i | \(-0.588742\pi\) | ||||
−0.275195 | + | 0.961388i | \(0.588742\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17727.9 | 0.871812 | ||||||||
\(746\) | 10331.8 | 0.507072 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14879.3 | −0.727328 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21412.5 | 1.04042 | 0.520208 | − | 0.854040i | \(-0.325854\pi\) | ||||
0.520208 | + | 0.854040i | \(0.325854\pi\) | |||||||
\(752\) | −3630.75 | −0.176064 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 434.254 | 0.0209743 | ||||||||
\(755\) | 4880.24 | 0.235245 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33963.9 | −1.63070 | −0.815350 | − | 0.578968i | \(-0.803456\pi\) | ||||
−0.815350 | + | 0.578968i | \(0.803456\pi\) | |||||||
\(758\) | 20539.2 | 0.984191 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 30033.0 | 1.43344 | ||||||||
\(761\) | 19920.0 | 0.948880 | 0.474440 | − | 0.880288i | \(-0.342651\pi\) | ||||
0.474440 | + | 0.880288i | \(0.342651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12761.3 | 0.604305 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2692.89 | −0.127021 | ||||||||
\(767\) | 393.554 | 0.0185273 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10039.2 | −0.470769 | −0.235385 | − | 0.971902i | \(-0.575635\pi\) | ||||
−0.235385 | + | 0.971902i | \(0.575635\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8690.33 | −0.405145 | ||||||||
\(773\) | 21385.3 | 0.995054 | 0.497527 | − | 0.867449i | \(-0.334242\pi\) | ||||
0.497527 | + | 0.867449i | \(0.334242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2090.16 | 0.0968785 | ||||||||
\(776\) | 3860.33 | 0.178579 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3720.32 | 0.171440 | ||||||||
\(779\) | 44511.8 | 2.04724 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19069.6 | −0.873704 | ||||||||
\(782\) | 10468.1 | 0.478693 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5391.96 | −0.245156 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37421.3 | −1.69495 | −0.847475 | − | 0.530835i | \(-0.821878\pi\) | ||||
−0.847475 | + | 0.530835i | \(0.821878\pi\) | |||||||
\(788\) | 15512.6 | 0.701284 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7446.10 | 0.335342 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −830.018 | −0.0371687 | ||||||||
\(794\) | −10920.9 | −0.488120 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8770.67 | 0.390538 | ||||||||
\(797\) | −30888.7 | −1.37281 | −0.686407 | − | 0.727217i | \(-0.740813\pi\) | ||||
−0.686407 | + | 0.727217i | \(0.740813\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26560.1 | 1.17601 | ||||||||
\(800\) | 2688.87 | 0.118832 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11203.3 | −0.493268 | ||||||||
\(803\) | 22938.9 | 1.00809 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 241.449 | 0.0105517 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5203.05 | 0.226538 | ||||||||
\(809\) | 7238.50 | 0.314576 | 0.157288 | − | 0.987553i | \(-0.449725\pi\) | ||||
0.157288 | + | 0.987553i | \(0.449725\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35466.4 | 1.53563 | 0.767814 | − | 0.640673i | \(-0.221344\pi\) | ||||
0.767814 | + | 0.640673i | \(0.221344\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22252.4 | 0.958166 | ||||||||
\(815\) | 8895.44 | 0.382324 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −55457.5 | −2.37480 | ||||||||
\(818\) | 20281.6 | 0.866905 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20764.6 | 0.884304 | ||||||||
\(821\) | −37947.3 | −1.61312 | −0.806558 | − | 0.591154i | \(-0.798672\pi\) | ||||
−0.806558 | + | 0.591154i | \(0.798672\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26932.2 | 1.14070 | 0.570351 | − | 0.821401i | \(-0.306807\pi\) | ||||
0.570351 | + | 0.821401i | \(0.306807\pi\) | |||||||
\(824\) | 5506.84 | 0.232815 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1913.98 | −0.0804783 | −0.0402391 | − | 0.999190i | \(-0.512812\pi\) | ||||
−0.0402391 | + | 0.999190i | \(0.512812\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15281.9 | 0.640245 | 0.320122 | − | 0.947376i | \(-0.396276\pi\) | ||||
0.320122 | + | 0.947376i | \(0.396276\pi\) | |||||||
\(830\) | 30505.9 | 1.27575 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 414.246 | 0.0172613 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6162.04 | −0.255385 | ||||||||
\(836\) | 16052.9 | 0.664117 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6373.03 | −0.262712 | ||||||||
\(839\) | −25779.5 | −1.06079 | −0.530397 | − | 0.847749i | \(-0.677957\pi\) | ||||
−0.530397 | + | 0.847749i | \(0.677957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28384.4 | 1.16382 | ||||||||
\(842\) | 7268.35 | 0.297487 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6431.98 | 0.262320 | ||||||||
\(845\) | −26110.5 | −1.06299 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3372.26 | 0.136561 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3151.03 | 0.127152 | ||||||||
\(851\) | 16951.3 | 0.682825 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6452.21 | 0.258991 | 0.129496 | − | 0.991580i | \(-0.458664\pi\) | ||||
0.129496 | + | 0.991580i | \(0.458664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44445.5 | 1.77467 | ||||||||
\(857\) | −32061.8 | −1.27796 | −0.638980 | − | 0.769224i | \(-0.720643\pi\) | ||||
−0.638980 | + | 0.769224i | \(0.720643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3934.64 | 0.156284 | 0.0781421 | − | 0.996942i | \(-0.475101\pi\) | ||||
0.0781421 | + | 0.996942i | \(0.475101\pi\) | |||||||
\(860\) | −25870.7 | −1.02579 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8130.91 | 0.321276 | ||||||||
\(863\) | −14043.1 | −0.553921 | −0.276961 | − | 0.960881i | \(-0.589327\pi\) | ||||
−0.276961 | + | 0.960881i | \(0.589327\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15616.9 | −0.613861 | ||||||||
\(866\) | 3891.56 | 0.152703 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11635.7 | 0.454217 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 488.396 | 0.0189996 | ||||||||
\(872\) | −14321.8 | −0.556190 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11293.7 | −0.437090 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2091.31 | 0.0805228 | 0.0402614 | − | 0.999189i | \(-0.487181\pi\) | ||||
0.0402614 | + | 0.999189i | \(0.487181\pi\) | |||||||
\(878\) | −13551.2 | −0.520879 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5814.75 | −0.222745 | ||||||||
\(881\) | −11548.6 | −0.441639 | −0.220819 | − | 0.975315i | \(-0.570873\pi\) | ||||
−0.220819 | + | 0.975315i | \(0.570873\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7531.24 | 0.287029 | 0.143514 | − | 0.989648i | \(-0.454160\pi\) | ||||
0.143514 | + | 0.989648i | \(0.454160\pi\) | |||||||
\(884\) | −394.130 | −0.0149955 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8304.80 | 0.314904 | ||||||||
\(887\) | 38502.7 | 1.45749 | 0.728745 | − | 0.684785i | \(-0.240104\pi\) | ||||
0.728745 | + | 0.684785i | \(0.240104\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8122.61 | −0.305922 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20214.3 | 0.758774 | ||||||||
\(893\) | −28655.0 | −1.07380 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 49141.7 | 1.83534 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4109.85 | −0.152725 | ||||||||
\(899\) | 29342.5 | 1.08857 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24669.2 | −0.912152 | ||||||||
\(902\) | −29967.1 | −1.10620 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11327.5 | 0.416755 | ||||||||
\(905\) | −44158.7 | −1.62197 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31306.7 | −1.14611 | −0.573054 | − | 0.819517i | \(-0.694242\pi\) | ||||
−0.573054 | + | 0.819517i | \(0.694242\pi\) | |||||||
\(908\) | 2915.21 | 0.106547 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34154.3 | 1.24213 | 0.621067 | − | 0.783758i | \(-0.286700\pi\) | ||||
0.621067 | + | 0.783758i | \(0.286700\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47670.3 | 1.72799 | ||||||||
\(914\) | −36602.7 | −1.32463 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15364.3 | −0.554204 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35988.9 | 1.29180 | 0.645899 | − | 0.763423i | \(-0.276483\pi\) | ||||
0.645899 | + | 0.763423i | \(0.276483\pi\) | |||||||
\(920\) | −15402.6 | −0.551967 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27201.8 | −0.971629 | ||||||||
\(923\) | −505.124 | −0.0180134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5102.57 | 0.181374 | ||||||||
\(926\) | 9369.82 | 0.332518 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 37747.4 | 1.33526 | ||||||||
\(929\) | −13906.0 | −0.491109 | −0.245554 | − | 0.969383i | \(-0.578970\pi\) | ||||
−0.245554 | + | 0.969383i | \(0.578970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1432.03 | −0.0503302 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16416.1 | 0.575107 | ||||||||
\(935\) | 42536.8 | 1.48781 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40905.3 | 1.42617 | 0.713083 | − | 0.701079i | \(-0.247298\pi\) | ||||
0.713083 | + | 0.701079i | \(0.247298\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13367.4 | −0.463828 | ||||||||
\(941\) | 8067.50 | 0.279482 | 0.139741 | − | 0.990188i | \(-0.455373\pi\) | ||||
0.139741 | + | 0.990188i | \(0.455373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22828.2 | −0.788321 | ||||||||
\(944\) | −5480.20 | −0.188946 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 37336.2 | 1.28320 | ||||||||
\(947\) | 39781.2 | 1.36506 | 0.682531 | − | 0.730856i | \(-0.260879\pi\) | ||||
0.682531 | + | 0.730856i | \(0.260879\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 607.616 | 0.0207840 | ||||||||
\(950\) | −3399.56 | −0.116101 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32354.0 | 1.09974 | 0.549868 | − | 0.835252i | \(-0.314678\pi\) | ||||
0.549868 | + | 0.835252i | \(0.314678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36481.9 | −1.23615 | ||||||||
\(956\) | −25553.7 | −0.864504 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −33339.7 | −1.12438 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13476.3 | −0.452362 | ||||||||
\(962\) | 589.433 | 0.0197548 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23398.9 | −0.781773 | ||||||||
\(965\) | 24843.8 | 0.828757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17389.2 | 0.578282 | 0.289141 | − | 0.957287i | \(-0.406630\pi\) | ||||
0.289141 | + | 0.957287i | \(0.406630\pi\) | |||||||
\(968\) | 121.344 | 0.00402909 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3774.82 | −0.124951 | ||||||||
\(971\) | −52406.2 | −1.73202 | −0.866012 | − | 0.500023i | \(-0.833325\pi\) | ||||
−0.866012 | + | 0.500023i | \(0.833325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11793.7 | 0.387982 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11557.9 | 0.379057 | ||||||||
\(977\) | 6846.70 | 0.224202 | 0.112101 | − | 0.993697i | \(-0.464242\pi\) | ||||
0.112101 | + | 0.993697i | \(0.464242\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12692.9 | −0.414368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24119.0 | −0.783776 | ||||||||
\(983\) | −37647.9 | −1.22155 | −0.610774 | − | 0.791805i | \(-0.709142\pi\) | ||||
−0.610774 | + | 0.791805i | \(0.709142\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44347.1 | −1.43453 | ||||||||
\(986\) | 44235.3 | 1.42874 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 425.217 | 0.0136923 | ||||||||
\(989\) | 28441.8 | 0.914454 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2036.17 | 0.0652686 | 0.0326343 | − | 0.999467i | \(-0.489610\pi\) | ||||
0.0326343 | + | 0.999467i | \(0.489610\pi\) | |||||||
\(992\) | 20987.9 | 0.671740 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25073.5 | −0.798877 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13540.6 | 0.430127 | 0.215064 | − | 0.976600i | \(-0.431004\pi\) | ||||
0.215064 | + | 0.976600i | \(0.431004\pi\) | |||||||
\(998\) | 16787.9 | 0.532478 | ||||||||
\(999\) | 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 | 441.4.a.x.1.6 | yes | 8 | |
3.2 | odd | 2 | inner | 441.4.a.x.1.3 | ✓ | 8 | |
7.2 | even | 3 | 441.4.e.z.361.3 | 16 | |||
7.3 | odd | 6 | 441.4.e.z.226.4 | 16 | |||
7.4 | even | 3 | 441.4.e.z.226.3 | 16 | |||
7.5 | odd | 6 | 441.4.e.z.361.4 | 16 | |||
7.6 | odd | 2 | inner | 441.4.a.x.1.5 | yes | 8 | |
21.2 | odd | 6 | 441.4.e.z.361.6 | 16 | |||
21.5 | even | 6 | 441.4.e.z.361.5 | 16 | |||
21.11 | odd | 6 | 441.4.e.z.226.6 | 16 | |||
21.17 | even | 6 | 441.4.e.z.226.5 | 16 | |||
21.20 | even | 2 | inner | 441.4.a.x.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.a.x.1.3 | ✓ | 8 | 3.2 | odd | 2 | inner | |
441.4.a.x.1.4 | yes | 8 | 21.20 | even | 2 | inner | |
441.4.a.x.1.5 | yes | 8 | 7.6 | odd | 2 | inner | |
441.4.a.x.1.6 | yes | 8 | 1.1 | even | 1 | trivial | |
441.4.e.z.226.3 | 16 | 7.4 | even | 3 | |||
441.4.e.z.226.4 | 16 | 7.3 | odd | 6 | |||
441.4.e.z.226.5 | 16 | 21.17 | even | 6 | |||
441.4.e.z.226.6 | 16 | 21.11 | odd | 6 | |||
441.4.e.z.361.3 | 16 | 7.2 | even | 3 | |||
441.4.e.z.361.4 | 16 | 7.5 | odd | 6 | |||
441.4.e.z.361.5 | 16 | 21.5 | even | 6 | |||
441.4.e.z.361.6 | 16 | 21.2 | odd | 6 |