Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,4,Mod(1,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, 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("135.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.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: | \(7.96525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 135.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.00000 | −0.875000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.00000 | −0.323970 | −0.161985 | − | 0.986793i | \(-0.551790\pi\) | ||||
−0.161985 | + | 0.986793i | \(0.551790\pi\) | |||||||
\(8\) | 15.0000 | 0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.00000 | 0.158114 | ||||||||
\(11\) | 47.0000 | 1.28828 | 0.644138 | − | 0.764909i | \(-0.277216\pi\) | ||||
0.644138 | + | 0.764909i | \(0.277216\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | −0.106673 | −0.0533366 | − | 0.998577i | \(-0.516986\pi\) | ||||
−0.0533366 | + | 0.998577i | \(0.516986\pi\) | |||||||
\(14\) | 6.00000 | 0.114541 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | 131.000 | 1.86895 | 0.934475 | − | 0.356027i | \(-0.115869\pi\) | ||||
0.934475 | + | 0.356027i | \(0.115869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −56.0000 | −0.676173 | −0.338086 | − | 0.941115i | \(-0.609780\pi\) | ||||
−0.338086 | + | 0.941115i | \(0.609780\pi\) | |||||||
\(20\) | 35.0000 | 0.391312 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −47.0000 | −0.455474 | ||||||||
\(23\) | −3.00000 | −0.0271975 | −0.0135988 | − | 0.999908i | \(-0.504329\pi\) | ||||
−0.0135988 | + | 0.999908i | \(0.504329\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 5.00000 | 0.0377146 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 42.0000 | 0.283473 | ||||||||
\(29\) | 157.000 | 1.00532 | 0.502658 | − | 0.864485i | \(-0.332355\pi\) | ||||
0.502658 | + | 0.864485i | \(0.332355\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 225.000 | 1.30359 | 0.651793 | − | 0.758397i | \(-0.274017\pi\) | ||||
0.651793 | + | 0.758397i | \(0.274017\pi\) | |||||||
\(32\) | −161.000 | −0.889408 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −131.000 | −0.660774 | ||||||||
\(35\) | 30.0000 | 0.144884 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −70.0000 | −0.311025 | −0.155513 | − | 0.987834i | \(-0.549703\pi\) | ||||
−0.155513 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(38\) | 56.0000 | 0.239063 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −75.0000 | −0.296464 | ||||||||
\(41\) | −140.000 | −0.533276 | −0.266638 | − | 0.963797i | \(-0.585913\pi\) | ||||
−0.266638 | + | 0.963797i | \(0.585913\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 397.000 | 1.40795 | 0.703976 | − | 0.710224i | \(-0.251406\pi\) | ||||
0.703976 | + | 0.710224i | \(0.251406\pi\) | |||||||
\(44\) | −329.000 | −1.12724 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | 0.00961578 | ||||||||
\(47\) | 347.000 | 1.07692 | 0.538459 | − | 0.842652i | \(-0.319007\pi\) | ||||
0.538459 | + | 0.842652i | \(0.319007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −307.000 | −0.895044 | ||||||||
\(50\) | −25.0000 | −0.0707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 35.0000 | 0.0933390 | ||||||||
\(53\) | −4.00000 | −0.0103668 | −0.00518342 | − | 0.999987i | \(-0.501650\pi\) | ||||
−0.00518342 | + | 0.999987i | \(0.501650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −235.000 | −0.576134 | ||||||||
\(56\) | −90.0000 | −0.214763 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −157.000 | −0.355433 | ||||||||
\(59\) | −748.000 | −1.65053 | −0.825265 | − | 0.564745i | \(-0.808974\pi\) | ||||
−0.825265 | + | 0.564745i | \(0.808974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −338.000 | −0.709450 | −0.354725 | − | 0.934971i | \(-0.615426\pi\) | ||||
−0.354725 | + | 0.934971i | \(0.615426\pi\) | |||||||
\(62\) | −225.000 | −0.460888 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | 25.0000 | 0.0477057 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 492.000 | 0.897125 | 0.448562 | − | 0.893751i | \(-0.351936\pi\) | ||||
0.448562 | + | 0.893751i | \(0.351936\pi\) | |||||||
\(68\) | −917.000 | −1.63533 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −30.0000 | −0.0512241 | ||||||||
\(71\) | −32.0000 | −0.0534888 | −0.0267444 | − | 0.999642i | \(-0.508514\pi\) | ||||
−0.0267444 | + | 0.999642i | \(0.508514\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 970.000 | 1.55520 | 0.777602 | − | 0.628757i | \(-0.216436\pi\) | ||||
0.777602 | + | 0.628757i | \(0.216436\pi\) | |||||||
\(74\) | 70.0000 | 0.109964 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 392.000 | 0.591651 | ||||||||
\(77\) | −282.000 | −0.417362 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1257.00 | −1.79017 | −0.895086 | − | 0.445894i | \(-0.852886\pi\) | ||||
−0.895086 | + | 0.445894i | \(0.852886\pi\) | |||||||
\(80\) | −205.000 | −0.286496 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 140.000 | 0.188542 | ||||||||
\(83\) | 102.000 | 0.134891 | 0.0674455 | − | 0.997723i | \(-0.478515\pi\) | ||||
0.0674455 | + | 0.997723i | \(0.478515\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −655.000 | −0.835820 | ||||||||
\(86\) | −397.000 | −0.497786 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 705.000 | 0.854014 | ||||||||
\(89\) | 1488.00 | 1.77222 | 0.886111 | − | 0.463474i | \(-0.153397\pi\) | ||||
0.886111 | + | 0.463474i | \(0.153397\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.0000 | 0.0345588 | ||||||||
\(92\) | 21.0000 | 0.0237978 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −347.000 | −0.380748 | ||||||||
\(95\) | 280.000 | 0.302394 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 974.000 | 1.01953 | 0.509767 | − | 0.860313i | \(-0.329732\pi\) | ||||
0.509767 | + | 0.860313i | \(0.329732\pi\) | |||||||
\(98\) | 307.000 | 0.316446 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −175.000 | −0.175000 | ||||||||
\(101\) | 1335.00 | 1.31522 | 0.657611 | − | 0.753357i | \(-0.271567\pi\) | ||||
0.657611 | + | 0.753357i | \(0.271567\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 686.000 | 0.656248 | 0.328124 | − | 0.944635i | \(-0.393584\pi\) | ||||
0.328124 | + | 0.944635i | \(0.393584\pi\) | |||||||
\(104\) | −75.0000 | −0.0707150 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00000 | 0.00366523 | ||||||||
\(107\) | 1098.00 | 0.992034 | 0.496017 | − | 0.868313i | \(-0.334795\pi\) | ||||
0.496017 | + | 0.868313i | \(0.334795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −700.000 | −0.615118 | −0.307559 | − | 0.951529i | \(-0.599512\pi\) | ||||
−0.307559 | + | 0.951529i | \(0.599512\pi\) | |||||||
\(110\) | 235.000 | 0.203694 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −246.000 | −0.207543 | ||||||||
\(113\) | 1055.00 | 0.878284 | 0.439142 | − | 0.898418i | \(-0.355283\pi\) | ||||
0.439142 | + | 0.898418i | \(0.355283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.0000 | 0.0121631 | ||||||||
\(116\) | −1099.00 | −0.879652 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 748.000 | 0.583551 | ||||||||
\(119\) | −786.000 | −0.605483 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 878.000 | 0.659654 | ||||||||
\(122\) | 338.000 | 0.250829 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1575.00 | −1.14064 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1646.00 | −1.15007 | −0.575035 | − | 0.818129i | \(-0.695012\pi\) | ||||
−0.575035 | + | 0.818129i | \(0.695012\pi\) | |||||||
\(128\) | 1455.00 | 1.00473 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −25.0000 | −0.0168665 | ||||||||
\(131\) | 1833.00 | 1.22252 | 0.611259 | − | 0.791430i | \(-0.290663\pi\) | ||||
0.611259 | + | 0.791430i | \(0.290663\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 336.000 | 0.219059 | ||||||||
\(134\) | −492.000 | −0.317182 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1965.00 | 1.23895 | ||||||||
\(137\) | −1098.00 | −0.684733 | −0.342367 | − | 0.939566i | \(-0.611229\pi\) | ||||
−0.342367 | + | 0.939566i | \(0.611229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1042.00 | −0.635837 | −0.317918 | − | 0.948118i | \(-0.602984\pi\) | ||||
−0.317918 | + | 0.948118i | \(0.602984\pi\) | |||||||
\(140\) | −210.000 | −0.126773 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 32.0000 | 0.0189111 | ||||||||
\(143\) | −235.000 | −0.137424 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −785.000 | −0.449591 | ||||||||
\(146\) | −970.000 | −0.549848 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 490.000 | 0.272147 | ||||||||
\(149\) | 2941.00 | 1.61702 | 0.808510 | − | 0.588482i | \(-0.200274\pi\) | ||||
0.808510 | + | 0.588482i | \(0.200274\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 511.000 | 0.275395 | 0.137697 | − | 0.990474i | \(-0.456030\pi\) | ||||
0.137697 | + | 0.990474i | \(0.456030\pi\) | |||||||
\(152\) | −840.000 | −0.448243 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 282.000 | 0.147560 | ||||||||
\(155\) | −1125.00 | −0.582982 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −571.000 | −0.290260 | −0.145130 | − | 0.989413i | \(-0.546360\pi\) | ||||
−0.145130 | + | 0.989413i | \(0.546360\pi\) | |||||||
\(158\) | 1257.00 | 0.632921 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 805.000 | 0.397755 | ||||||||
\(161\) | 18.0000 | 0.00881117 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 713.000 | 0.342616 | 0.171308 | − | 0.985217i | \(-0.445201\pi\) | ||||
0.171308 | + | 0.985217i | \(0.445201\pi\) | |||||||
\(164\) | 980.000 | 0.466617 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −102.000 | −0.0476912 | ||||||||
\(167\) | −1596.00 | −0.739534 | −0.369767 | − | 0.929125i | \(-0.620563\pi\) | ||||
−0.369767 | + | 0.929125i | \(0.620563\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2172.00 | −0.988621 | ||||||||
\(170\) | 655.000 | 0.295507 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2779.00 | −1.23196 | ||||||||
\(173\) | −4134.00 | −1.81678 | −0.908388 | − | 0.418129i | \(-0.862686\pi\) | ||||
−0.908388 | + | 0.418129i | \(0.862686\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −150.000 | −0.0647939 | ||||||||
\(176\) | 1927.00 | 0.825302 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1488.00 | −0.626575 | ||||||||
\(179\) | −1828.00 | −0.763302 | −0.381651 | − | 0.924306i | \(-0.624644\pi\) | ||||
−0.381651 | + | 0.924306i | \(0.624644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −520.000 | −0.213543 | −0.106772 | − | 0.994284i | \(-0.534051\pi\) | ||||
−0.106772 | + | 0.994284i | \(0.534051\pi\) | |||||||
\(182\) | −30.0000 | −0.0122184 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −45.0000 | −0.0180296 | ||||||||
\(185\) | 350.000 | 0.139095 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6157.00 | 2.40772 | ||||||||
\(188\) | −2429.00 | −0.942303 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −280.000 | −0.106912 | ||||||||
\(191\) | −4826.00 | −1.82826 | −0.914129 | − | 0.405424i | \(-0.867124\pi\) | ||||
−0.914129 | + | 0.405424i | \(0.867124\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1670.00 | 0.622846 | 0.311423 | − | 0.950271i | \(-0.399194\pi\) | ||||
0.311423 | + | 0.950271i | \(0.399194\pi\) | |||||||
\(194\) | −974.000 | −0.360459 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2149.00 | 0.783163 | ||||||||
\(197\) | 1380.00 | 0.499091 | 0.249546 | − | 0.968363i | \(-0.419719\pi\) | ||||
0.249546 | + | 0.968363i | \(0.419719\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4357.00 | 1.55206 | 0.776029 | − | 0.630697i | \(-0.217231\pi\) | ||||
0.776029 | + | 0.630697i | \(0.217231\pi\) | |||||||
\(200\) | 375.000 | 0.132583 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1335.00 | −0.465001 | ||||||||
\(203\) | −942.000 | −0.325692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 700.000 | 0.238488 | ||||||||
\(206\) | −686.000 | −0.232019 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −205.000 | −0.0683375 | ||||||||
\(209\) | −2632.00 | −0.871097 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4162.00 | −1.35793 | −0.678967 | − | 0.734169i | \(-0.737572\pi\) | ||||
−0.678967 | + | 0.734169i | \(0.737572\pi\) | |||||||
\(212\) | 28.0000 | 0.00907098 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1098.00 | −0.350737 | ||||||||
\(215\) | −1985.00 | −0.629655 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1350.00 | −0.422322 | ||||||||
\(218\) | 700.000 | 0.217477 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1645.00 | 0.504118 | ||||||||
\(221\) | −655.000 | −0.199367 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5956.00 | −1.78853 | −0.894267 | − | 0.447533i | \(-0.852303\pi\) | ||||
−0.894267 | + | 0.447533i | \(0.852303\pi\) | |||||||
\(224\) | 966.000 | 0.288141 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1055.00 | −0.310520 | ||||||||
\(227\) | −4940.00 | −1.44440 | −0.722201 | − | 0.691683i | \(-0.756870\pi\) | ||||
−0.722201 | + | 0.691683i | \(0.756870\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4344.00 | 1.25354 | 0.626768 | − | 0.779206i | \(-0.284378\pi\) | ||||
0.626768 | + | 0.779206i | \(0.284378\pi\) | |||||||
\(230\) | −15.0000 | −0.00430031 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2355.00 | 0.666437 | ||||||||
\(233\) | 5202.00 | 1.46264 | 0.731318 | − | 0.682036i | \(-0.238905\pi\) | ||||
0.731318 | + | 0.682036i | \(0.238905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1735.00 | −0.481612 | ||||||||
\(236\) | 5236.00 | 1.44421 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 786.000 | 0.214071 | ||||||||
\(239\) | −1546.00 | −0.418420 | −0.209210 | − | 0.977871i | \(-0.567089\pi\) | ||||
−0.209210 | + | 0.977871i | \(0.567089\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3659.00 | −0.977995 | −0.488998 | − | 0.872285i | \(-0.662637\pi\) | ||||
−0.488998 | + | 0.872285i | \(0.662637\pi\) | |||||||
\(242\) | −878.000 | −0.233223 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2366.00 | 0.620769 | ||||||||
\(245\) | 1535.00 | 0.400276 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 280.000 | 0.0721294 | ||||||||
\(248\) | 3375.00 | 0.864164 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 125.000 | 0.0316228 | ||||||||
\(251\) | −1221.00 | −0.307047 | −0.153524 | − | 0.988145i | \(-0.549062\pi\) | ||||
−0.153524 | + | 0.988145i | \(0.549062\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −141.000 | −0.0350379 | ||||||||
\(254\) | 1646.00 | 0.406611 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | 6255.00 | 1.51820 | 0.759098 | − | 0.650977i | \(-0.225640\pi\) | ||||
0.759098 | + | 0.650977i | \(0.225640\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 420.000 | 0.100763 | ||||||||
\(260\) | −175.000 | −0.0417425 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1833.00 | −0.432226 | ||||||||
\(263\) | −836.000 | −0.196007 | −0.0980037 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980037 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.0000 | 0.00463619 | ||||||||
\(266\) | −336.000 | −0.0774492 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3444.00 | −0.784984 | ||||||||
\(269\) | 2231.00 | 0.505675 | 0.252837 | − | 0.967509i | \(-0.418636\pi\) | ||||
0.252837 | + | 0.967509i | \(0.418636\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4832.00 | −1.08311 | −0.541556 | − | 0.840665i | \(-0.682164\pi\) | ||||
−0.541556 | + | 0.840665i | \(0.682164\pi\) | |||||||
\(272\) | 5371.00 | 1.19730 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1098.00 | 0.242090 | ||||||||
\(275\) | 1175.00 | 0.257655 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6450.00 | 1.39907 | 0.699536 | − | 0.714597i | \(-0.253390\pi\) | ||||
0.699536 | + | 0.714597i | \(0.253390\pi\) | |||||||
\(278\) | 1042.00 | 0.224802 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 450.000 | 0.0960452 | ||||||||
\(281\) | 1050.00 | 0.222910 | 0.111455 | − | 0.993769i | \(-0.464449\pi\) | ||||
0.111455 | + | 0.993769i | \(0.464449\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1584.00 | −0.332717 | −0.166359 | − | 0.986065i | \(-0.553201\pi\) | ||||
−0.166359 | + | 0.986065i | \(0.553201\pi\) | |||||||
\(284\) | 224.000 | 0.0468027 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 235.000 | 0.0485869 | ||||||||
\(287\) | 840.000 | 0.172765 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12248.0 | 2.49298 | ||||||||
\(290\) | 785.000 | 0.158954 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6790.00 | −1.36080 | ||||||||
\(293\) | −6594.00 | −1.31476 | −0.657382 | − | 0.753558i | \(-0.728336\pi\) | ||||
−0.657382 | + | 0.753558i | \(0.728336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3740.00 | 0.738140 | ||||||||
\(296\) | −1050.00 | −0.206182 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2941.00 | −0.571703 | ||||||||
\(299\) | 15.0000 | 0.00290125 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2382.00 | −0.456134 | ||||||||
\(302\) | −511.000 | −0.0973667 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2296.00 | −0.433173 | ||||||||
\(305\) | 1690.00 | 0.317276 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4343.00 | −0.807388 | −0.403694 | − | 0.914894i | \(-0.632274\pi\) | ||||
−0.403694 | + | 0.914894i | \(0.632274\pi\) | |||||||
\(308\) | 1974.00 | 0.365192 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1125.00 | 0.206115 | ||||||||
\(311\) | 2124.00 | 0.387270 | 0.193635 | − | 0.981074i | \(-0.437972\pi\) | ||||
0.193635 | + | 0.981074i | \(0.437972\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7516.00 | −1.35728 | −0.678641 | − | 0.734470i | \(-0.737431\pi\) | ||||
−0.678641 | + | 0.734470i | \(0.737431\pi\) | |||||||
\(314\) | 571.000 | 0.102622 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8799.00 | 1.56640 | ||||||||
\(317\) | 6880.00 | 1.21899 | 0.609494 | − | 0.792791i | \(-0.291373\pi\) | ||||
0.609494 | + | 0.792791i | \(0.291373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7379.00 | 1.29512 | ||||||||
\(320\) | 835.000 | 0.145868 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −18.0000 | −0.00311522 | ||||||||
\(323\) | −7336.00 | −1.26373 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −125.000 | −0.0213346 | ||||||||
\(326\) | −713.000 | −0.121133 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2100.00 | −0.353516 | ||||||||
\(329\) | −2082.00 | −0.348889 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4986.00 | −0.827962 | −0.413981 | − | 0.910286i | \(-0.635862\pi\) | ||||
−0.413981 | + | 0.910286i | \(0.635862\pi\) | |||||||
\(332\) | −714.000 | −0.118030 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1596.00 | 0.261465 | ||||||||
\(335\) | −2460.00 | −0.401206 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 904.000 | 0.146125 | 0.0730623 | − | 0.997327i | \(-0.476723\pi\) | ||||
0.0730623 | + | 0.997327i | \(0.476723\pi\) | |||||||
\(338\) | 2172.00 | 0.349530 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4585.00 | 0.731343 | ||||||||
\(341\) | 10575.0 | 1.67938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3900.00 | 0.613936 | ||||||||
\(344\) | 5955.00 | 0.933349 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4134.00 | 0.642327 | ||||||||
\(347\) | −8860.00 | −1.37069 | −0.685345 | − | 0.728218i | \(-0.740349\pi\) | ||||
−0.685345 | + | 0.728218i | \(0.740349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4454.00 | −0.683144 | −0.341572 | − | 0.939856i | \(-0.610959\pi\) | ||||
−0.341572 | + | 0.939856i | \(0.610959\pi\) | |||||||
\(350\) | 150.000 | 0.0229081 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7567.00 | −1.14580 | ||||||||
\(353\) | 8781.00 | 1.32398 | 0.661991 | − | 0.749512i | \(-0.269712\pi\) | ||||
0.661991 | + | 0.749512i | \(0.269712\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 160.000 | 0.0239209 | ||||||||
\(356\) | −10416.0 | −1.55069 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1828.00 | 0.269868 | ||||||||
\(359\) | −2928.00 | −0.430457 | −0.215228 | − | 0.976564i | \(-0.569050\pi\) | ||||
−0.215228 | + | 0.976564i | \(0.569050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3723.00 | −0.542790 | ||||||||
\(362\) | 520.000 | 0.0754989 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −210.000 | −0.0302390 | ||||||||
\(365\) | −4850.00 | −0.695508 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9102.00 | 1.29461 | 0.647303 | − | 0.762233i | \(-0.275897\pi\) | ||||
0.647303 | + | 0.762233i | \(0.275897\pi\) | |||||||
\(368\) | −123.000 | −0.0174234 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −350.000 | −0.0491774 | ||||||||
\(371\) | 24.0000 | 0.00335854 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8183.00 | −1.13592 | −0.567962 | − | 0.823055i | \(-0.692268\pi\) | ||||
−0.567962 | + | 0.823055i | \(0.692268\pi\) | |||||||
\(374\) | −6157.00 | −0.851259 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5205.00 | 0.713903 | ||||||||
\(377\) | −785.000 | −0.107240 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6136.00 | 0.831623 | 0.415812 | − | 0.909451i | \(-0.363498\pi\) | ||||
0.415812 | + | 0.909451i | \(0.363498\pi\) | |||||||
\(380\) | −1960.00 | −0.264594 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4826.00 | 0.646386 | ||||||||
\(383\) | −5643.00 | −0.752856 | −0.376428 | − | 0.926446i | \(-0.622848\pi\) | ||||
−0.376428 | + | 0.926446i | \(0.622848\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1410.00 | 0.186650 | ||||||||
\(386\) | −1670.00 | −0.220209 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6818.00 | −0.892092 | ||||||||
\(389\) | −8991.00 | −1.17188 | −0.585941 | − | 0.810354i | \(-0.699275\pi\) | ||||
−0.585941 | + | 0.810354i | \(0.699275\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −393.000 | −0.0508309 | ||||||||
\(392\) | −4605.00 | −0.593336 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1380.00 | −0.176455 | ||||||||
\(395\) | 6285.00 | 0.800589 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12449.0 | −1.57380 | −0.786898 | − | 0.617082i | \(-0.788314\pi\) | ||||
−0.786898 | + | 0.617082i | \(0.788314\pi\) | |||||||
\(398\) | −4357.00 | −0.548735 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1025.00 | 0.128125 | ||||||||
\(401\) | −8076.00 | −1.00573 | −0.502863 | − | 0.864366i | \(-0.667720\pi\) | ||||
−0.502863 | + | 0.864366i | \(0.667720\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1125.00 | −0.139058 | ||||||||
\(404\) | −9345.00 | −1.15082 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 942.000 | 0.115149 | ||||||||
\(407\) | −3290.00 | −0.400686 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2833.00 | −0.342501 | −0.171250 | − | 0.985228i | \(-0.554781\pi\) | ||||
−0.171250 | + | 0.985228i | \(0.554781\pi\) | |||||||
\(410\) | −700.000 | −0.0843184 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4802.00 | −0.574217 | ||||||||
\(413\) | 4488.00 | 0.534722 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −510.000 | −0.0603251 | ||||||||
\(416\) | 805.000 | 0.0948759 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2632.00 | 0.307979 | ||||||||
\(419\) | 4777.00 | 0.556973 | 0.278487 | − | 0.960440i | \(-0.410167\pi\) | ||||
0.278487 | + | 0.960440i | \(0.410167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6464.00 | −0.748304 | −0.374152 | − | 0.927367i | \(-0.622066\pi\) | ||||
−0.374152 | + | 0.927367i | \(0.622066\pi\) | |||||||
\(422\) | 4162.00 | 0.480102 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −60.0000 | −0.00687231 | ||||||||
\(425\) | 3275.00 | 0.373790 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2028.00 | 0.229840 | ||||||||
\(428\) | −7686.00 | −0.868030 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1985.00 | 0.222617 | ||||||||
\(431\) | −10680.0 | −1.19359 | −0.596795 | − | 0.802394i | \(-0.703560\pi\) | ||||
−0.596795 | + | 0.802394i | \(0.703560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11566.0 | 1.28366 | 0.641832 | − | 0.766845i | \(-0.278175\pi\) | ||||
0.641832 | + | 0.766845i | \(0.278175\pi\) | |||||||
\(434\) | 1350.00 | 0.149314 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4900.00 | 0.538228 | ||||||||
\(437\) | 168.000 | 0.0183902 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1448.00 | −0.157424 | −0.0787122 | − | 0.996897i | \(-0.525081\pi\) | ||||
−0.0787122 | + | 0.996897i | \(0.525081\pi\) | |||||||
\(440\) | −3525.00 | −0.381927 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 655.000 | 0.0704868 | ||||||||
\(443\) | 2376.00 | 0.254824 | 0.127412 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127412 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7440.00 | −0.792561 | ||||||||
\(446\) | 5956.00 | 0.632343 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1002.00 | 0.105670 | ||||||||
\(449\) | 14894.0 | 1.56546 | 0.782730 | − | 0.622362i | \(-0.213827\pi\) | ||||
0.782730 | + | 0.622362i | \(0.213827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6580.00 | −0.687007 | ||||||||
\(452\) | −7385.00 | −0.768498 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4940.00 | 0.510673 | ||||||||
\(455\) | −150.000 | −0.0154552 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16204.0 | 1.65862 | 0.829312 | − | 0.558786i | \(-0.188733\pi\) | ||||
0.829312 | + | 0.558786i | \(0.188733\pi\) | |||||||
\(458\) | −4344.00 | −0.443192 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −105.000 | −0.0106427 | ||||||||
\(461\) | 5082.00 | 0.513432 | 0.256716 | − | 0.966487i | \(-0.417359\pi\) | ||||
0.256716 | + | 0.966487i | \(0.417359\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10326.0 | −1.03648 | −0.518240 | − | 0.855235i | \(-0.673412\pi\) | ||||
−0.518240 | + | 0.855235i | \(0.673412\pi\) | |||||||
\(464\) | 6437.00 | 0.644031 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5202.00 | −0.517120 | ||||||||
\(467\) | −4184.00 | −0.414588 | −0.207294 | − | 0.978279i | \(-0.566466\pi\) | ||||
−0.207294 | + | 0.978279i | \(0.566466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2952.00 | −0.290641 | ||||||||
\(470\) | 1735.00 | 0.170276 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11220.0 | −1.09416 | ||||||||
\(473\) | 18659.0 | 1.81383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1400.00 | −0.135235 | ||||||||
\(476\) | 5502.00 | 0.529798 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1546.00 | 0.147934 | ||||||||
\(479\) | 15576.0 | 1.48577 | 0.742887 | − | 0.669417i | \(-0.233456\pi\) | ||||
0.742887 | + | 0.669417i | \(0.233456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 350.000 | 0.0331780 | ||||||||
\(482\) | 3659.00 | 0.345774 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6146.00 | −0.577198 | ||||||||
\(485\) | −4870.00 | −0.455949 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10220.0 | 0.950949 | 0.475475 | − | 0.879729i | \(-0.342276\pi\) | ||||
0.475475 | + | 0.879729i | \(0.342276\pi\) | |||||||
\(488\) | −5070.00 | −0.470304 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1535.00 | −0.141519 | ||||||||
\(491\) | 2692.00 | 0.247430 | 0.123715 | − | 0.992318i | \(-0.460519\pi\) | ||||
0.123715 | + | 0.992318i | \(0.460519\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20567.0 | 1.87889 | ||||||||
\(494\) | −280.000 | −0.0255016 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9225.00 | 0.835110 | ||||||||
\(497\) | 192.000 | 0.0173287 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5764.00 | 0.517098 | 0.258549 | − | 0.965998i | \(-0.416756\pi\) | ||||
0.258549 | + | 0.965998i | \(0.416756\pi\) | |||||||
\(500\) | 875.000 | 0.0782624 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1221.00 | 0.108558 | ||||||||
\(503\) | 2437.00 | 0.216025 | 0.108012 | − | 0.994150i | \(-0.465551\pi\) | ||||
0.108012 | + | 0.994150i | \(0.465551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6675.00 | −0.588185 | ||||||||
\(506\) | 141.000 | 0.0123878 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11522.0 | 1.00631 | ||||||||
\(509\) | 5849.00 | 0.509337 | 0.254668 | − | 0.967028i | \(-0.418034\pi\) | ||||
0.254668 | + | 0.967028i | \(0.418034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5820.00 | −0.503839 | ||||||||
\(512\) | −11521.0 | −0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6255.00 | −0.536763 | ||||||||
\(515\) | −3430.00 | −0.293483 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16309.0 | 1.38737 | ||||||||
\(518\) | −420.000 | −0.0356250 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 375.000 | 0.0316247 | ||||||||
\(521\) | 17032.0 | 1.43222 | 0.716109 | − | 0.697989i | \(-0.245921\pi\) | ||||
0.716109 | + | 0.697989i | \(0.245921\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4147.00 | 0.346722 | 0.173361 | − | 0.984858i | \(-0.444537\pi\) | ||||
0.173361 | + | 0.984858i | \(0.444537\pi\) | |||||||
\(524\) | −12831.0 | −1.06970 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 836.000 | 0.0692991 | ||||||||
\(527\) | 29475.0 | 2.43634 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12158.0 | −0.999260 | ||||||||
\(530\) | −20.0000 | −0.00163914 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2352.00 | −0.191677 | ||||||||
\(533\) | 700.000 | 0.0568862 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5490.00 | −0.443651 | ||||||||
\(536\) | 7380.00 | 0.594715 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2231.00 | −0.178783 | ||||||||
\(539\) | −14429.0 | −1.15306 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3942.00 | −0.313271 | −0.156636 | − | 0.987656i | \(-0.550065\pi\) | ||||
−0.156636 | + | 0.987656i | \(0.550065\pi\) | |||||||
\(542\) | 4832.00 | 0.382938 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −21091.0 | −1.66226 | ||||||||
\(545\) | 3500.00 | 0.275089 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13751.0 | −1.07486 | −0.537432 | − | 0.843307i | \(-0.680605\pi\) | ||||
−0.537432 | + | 0.843307i | \(0.680605\pi\) | |||||||
\(548\) | 7686.00 | 0.599142 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1175.00 | −0.0910949 | ||||||||
\(551\) | −8792.00 | −0.679767 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7542.00 | 0.579961 | ||||||||
\(554\) | −6450.00 | −0.494647 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7294.00 | 0.556357 | ||||||||
\(557\) | −7944.00 | −0.604305 | −0.302153 | − | 0.953260i | \(-0.597705\pi\) | ||||
−0.302153 | + | 0.953260i | \(0.597705\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1985.00 | −0.150191 | ||||||||
\(560\) | 1230.00 | 0.0928160 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1050.00 | −0.0788106 | ||||||||
\(563\) | 6702.00 | 0.501697 | 0.250849 | − | 0.968026i | \(-0.419290\pi\) | ||||
0.250849 | + | 0.968026i | \(0.419290\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5275.00 | −0.392780 | ||||||||
\(566\) | 1584.00 | 0.117633 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −480.000 | −0.0354584 | ||||||||
\(569\) | 2760.00 | 0.203348 | 0.101674 | − | 0.994818i | \(-0.467580\pi\) | ||||
0.101674 | + | 0.994818i | \(0.467580\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8930.00 | 0.654481 | 0.327241 | − | 0.944941i | \(-0.393881\pi\) | ||||
0.327241 | + | 0.944941i | \(0.393881\pi\) | |||||||
\(572\) | 1645.00 | 0.120246 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −840.000 | −0.0610817 | ||||||||
\(575\) | −75.0000 | −0.00543951 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6944.00 | 0.501010 | 0.250505 | − | 0.968115i | \(-0.419403\pi\) | ||||
0.250505 | + | 0.968115i | \(0.419403\pi\) | |||||||
\(578\) | −12248.0 | −0.881401 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5495.00 | 0.393392 | ||||||||
\(581\) | −612.000 | −0.0437006 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −188.000 | −0.0133553 | ||||||||
\(584\) | 14550.0 | 1.03096 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6594.00 | 0.464839 | ||||||||
\(587\) | 4206.00 | 0.295741 | 0.147871 | − | 0.989007i | \(-0.452758\pi\) | ||||
0.147871 | + | 0.989007i | \(0.452758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12600.0 | −0.881450 | ||||||||
\(590\) | −3740.00 | −0.260972 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2870.00 | −0.199250 | ||||||||
\(593\) | 6571.00 | 0.455040 | 0.227520 | − | 0.973773i | \(-0.426938\pi\) | ||||
0.227520 | + | 0.973773i | \(0.426938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3930.00 | 0.270780 | ||||||||
\(596\) | −20587.0 | −1.41489 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.0000 | −0.00102575 | ||||||||
\(599\) | 9490.00 | 0.647330 | 0.323665 | − | 0.946172i | \(-0.395085\pi\) | ||||
0.323665 | + | 0.946172i | \(0.395085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11861.0 | 0.805025 | 0.402513 | − | 0.915414i | \(-0.368137\pi\) | ||||
0.402513 | + | 0.915414i | \(0.368137\pi\) | |||||||
\(602\) | 2382.00 | 0.161268 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3577.00 | −0.240970 | ||||||||
\(605\) | −4390.00 | −0.295006 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −518.000 | −0.0346375 | −0.0173188 | − | 0.999850i | \(-0.505513\pi\) | ||||
−0.0173188 | + | 0.999850i | \(0.505513\pi\) | |||||||
\(608\) | 9016.00 | 0.601393 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1690.00 | −0.112174 | ||||||||
\(611\) | −1735.00 | −0.114878 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15163.0 | 0.999067 | 0.499533 | − | 0.866295i | \(-0.333505\pi\) | ||||
0.499533 | + | 0.866295i | \(0.333505\pi\) | |||||||
\(614\) | 4343.00 | 0.285455 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4230.00 | −0.276675 | ||||||||
\(617\) | −19011.0 | −1.24044 | −0.620222 | − | 0.784426i | \(-0.712958\pi\) | ||||
−0.620222 | + | 0.784426i | \(0.712958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7906.00 | −0.513359 | −0.256679 | − | 0.966497i | \(-0.582628\pi\) | ||||
−0.256679 | + | 0.966497i | \(0.582628\pi\) | |||||||
\(620\) | 7875.00 | 0.510109 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2124.00 | −0.136921 | ||||||||
\(623\) | −8928.00 | −0.574146 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 7516.00 | 0.479872 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3997.00 | 0.253977 | ||||||||
\(629\) | −9170.00 | −0.581291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3416.00 | −0.215513 | −0.107757 | − | 0.994177i | \(-0.534367\pi\) | ||||
−0.107757 | + | 0.994177i | \(0.534367\pi\) | |||||||
\(632\) | −18855.0 | −1.18673 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6880.00 | −0.430977 | ||||||||
\(635\) | 8230.00 | 0.514327 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1535.00 | 0.0954771 | ||||||||
\(638\) | −7379.00 | −0.457896 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7275.00 | −0.449328 | ||||||||
\(641\) | −4830.00 | −0.297619 | −0.148809 | − | 0.988866i | \(-0.547544\pi\) | ||||
−0.148809 | + | 0.988866i | \(0.547544\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12549.0 | 0.769649 | 0.384824 | − | 0.922990i | \(-0.374262\pi\) | ||||
0.384824 | + | 0.922990i | \(0.374262\pi\) | |||||||
\(644\) | −126.000 | −0.00770978 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7336.00 | 0.446797 | ||||||||
\(647\) | −8164.00 | −0.496074 | −0.248037 | − | 0.968751i | \(-0.579785\pi\) | ||||
−0.248037 | + | 0.968751i | \(0.579785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35156.0 | −2.12634 | ||||||||
\(650\) | 125.000 | 0.00754293 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4991.00 | −0.299789 | ||||||||
\(653\) | −23768.0 | −1.42437 | −0.712185 | − | 0.701992i | \(-0.752294\pi\) | ||||
−0.712185 | + | 0.701992i | \(0.752294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9165.00 | −0.546727 | ||||||||
\(656\) | −5740.00 | −0.341630 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2082.00 | 0.123351 | ||||||||
\(659\) | −21472.0 | −1.26924 | −0.634621 | − | 0.772824i | \(-0.718844\pi\) | ||||
−0.634621 | + | 0.772824i | \(0.718844\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12982.0 | 0.763905 | 0.381953 | − | 0.924182i | \(-0.375252\pi\) | ||||
0.381953 | + | 0.924182i | \(0.375252\pi\) | |||||||
\(662\) | 4986.00 | 0.292729 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1530.00 | 0.0894210 | ||||||||
\(665\) | −1680.00 | −0.0979663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −471.000 | −0.0273421 | ||||||||
\(668\) | 11172.0 | 0.647092 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2460.00 | 0.141848 | ||||||||
\(671\) | −15886.0 | −0.913968 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6006.00 | −0.344003 | −0.172002 | − | 0.985097i | \(-0.555023\pi\) | ||||
−0.172002 | + | 0.985097i | \(0.555023\pi\) | |||||||
\(674\) | −904.000 | −0.0516629 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15204.0 | 0.865043 | ||||||||
\(677\) | −1164.00 | −0.0660800 | −0.0330400 | − | 0.999454i | \(-0.510519\pi\) | ||||
−0.0330400 | + | 0.999454i | \(0.510519\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5844.00 | −0.330298 | ||||||||
\(680\) | −9825.00 | −0.554076 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10575.0 | −0.593750 | ||||||||
\(683\) | −26496.0 | −1.48439 | −0.742197 | − | 0.670182i | \(-0.766216\pi\) | ||||
−0.742197 | + | 0.670182i | \(0.766216\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5490.00 | 0.306222 | ||||||||
\(686\) | −3900.00 | −0.217059 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16277.0 | 0.901969 | ||||||||
\(689\) | 20.0000 | 0.00110586 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17110.0 | 0.941961 | 0.470981 | − | 0.882144i | \(-0.343900\pi\) | ||||
0.470981 | + | 0.882144i | \(0.343900\pi\) | |||||||
\(692\) | 28938.0 | 1.58968 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8860.00 | 0.484612 | ||||||||
\(695\) | 5210.00 | 0.284355 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18340.0 | −0.996667 | ||||||||
\(698\) | 4454.00 | 0.241528 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1050.00 | 0.0566947 | ||||||||
\(701\) | −30251.0 | −1.62991 | −0.814953 | − | 0.579527i | \(-0.803237\pi\) | ||||
−0.814953 | + | 0.579527i | \(0.803237\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3920.00 | 0.210307 | ||||||||
\(704\) | −7849.00 | −0.420199 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8781.00 | −0.468098 | ||||||||
\(707\) | −8010.00 | −0.426092 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18820.0 | 0.996897 | 0.498448 | − | 0.866919i | \(-0.333903\pi\) | ||||
0.498448 | + | 0.866919i | \(0.333903\pi\) | |||||||
\(710\) | −160.000 | −0.00845731 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22320.0 | 1.17483 | ||||||||
\(713\) | −675.000 | −0.0354543 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1175.00 | 0.0614581 | ||||||||
\(716\) | 12796.0 | 0.667890 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2928.00 | 0.152189 | ||||||||
\(719\) | −31890.0 | −1.65410 | −0.827049 | − | 0.562130i | \(-0.809982\pi\) | ||||
−0.827049 | + | 0.562130i | \(0.809982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4116.00 | −0.212605 | ||||||||
\(722\) | 3723.00 | 0.191905 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3640.00 | 0.186850 | ||||||||
\(725\) | 3925.00 | 0.201063 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11452.0 | −0.584224 | −0.292112 | − | 0.956384i | \(-0.594358\pi\) | ||||
−0.292112 | + | 0.956384i | \(0.594358\pi\) | |||||||
\(728\) | 450.000 | 0.0229095 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4850.00 | 0.245899 | ||||||||
\(731\) | 52007.0 | 2.63139 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7094.00 | 0.357466 | 0.178733 | − | 0.983898i | \(-0.442800\pi\) | ||||
0.178733 | + | 0.983898i | \(0.442800\pi\) | |||||||
\(734\) | −9102.00 | −0.457712 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 483.000 | 0.0241897 | ||||||||
\(737\) | 23124.0 | 1.15574 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3200.00 | −0.159288 | −0.0796440 | − | 0.996823i | \(-0.525378\pi\) | ||||
−0.0796440 | + | 0.996823i | \(0.525378\pi\) | |||||||
\(740\) | −2450.00 | −0.121708 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24.0000 | −0.00118742 | ||||||||
\(743\) | 20831.0 | 1.02855 | 0.514277 | − | 0.857624i | \(-0.328060\pi\) | ||||
0.514277 | + | 0.857624i | \(0.328060\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14705.0 | −0.723154 | ||||||||
\(746\) | 8183.00 | 0.401610 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −43099.0 | −2.10676 | ||||||||
\(749\) | −6588.00 | −0.321389 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15605.0 | −0.758235 | −0.379118 | − | 0.925349i | \(-0.623772\pi\) | ||||
−0.379118 | + | 0.925349i | \(0.623772\pi\) | |||||||
\(752\) | 14227.0 | 0.689901 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 785.000 | 0.0379151 | ||||||||
\(755\) | −2555.00 | −0.123160 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21349.0 | 1.02502 | 0.512512 | − | 0.858680i | \(-0.328715\pi\) | ||||
0.512512 | + | 0.858680i | \(0.328715\pi\) | |||||||
\(758\) | −6136.00 | −0.294023 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4200.00 | 0.200461 | ||||||||
\(761\) | −3702.00 | −0.176343 | −0.0881717 | − | 0.996105i | \(-0.528102\pi\) | ||||
−0.0881717 | + | 0.996105i | \(0.528102\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4200.00 | 0.199279 | ||||||||
\(764\) | 33782.0 | 1.59972 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5643.00 | 0.266175 | ||||||||
\(767\) | 3740.00 | 0.176067 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1393.00 | −0.0653223 | −0.0326612 | − | 0.999466i | \(-0.510398\pi\) | ||||
−0.0326612 | + | 0.999466i | \(0.510398\pi\) | |||||||
\(770\) | −1410.00 | −0.0659907 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11690.0 | −0.544990 | ||||||||
\(773\) | 6906.00 | 0.321334 | 0.160667 | − | 0.987009i | \(-0.448635\pi\) | ||||
0.160667 | + | 0.987009i | \(0.448635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5625.00 | 0.260717 | ||||||||
\(776\) | 14610.0 | 0.675861 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8991.00 | 0.414323 | ||||||||
\(779\) | 7840.00 | 0.360587 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1504.00 | −0.0689083 | ||||||||
\(782\) | 393.000 | 0.0179714 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12587.0 | −0.573387 | ||||||||
\(785\) | 2855.00 | 0.129808 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30493.0 | 1.38114 | 0.690571 | − | 0.723265i | \(-0.257359\pi\) | ||||
0.690571 | + | 0.723265i | \(0.257359\pi\) | |||||||
\(788\) | −9660.00 | −0.436705 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6285.00 | −0.283051 | ||||||||
\(791\) | −6330.00 | −0.284537 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1690.00 | 0.0756793 | ||||||||
\(794\) | 12449.0 | 0.556421 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30499.0 | −1.35805 | ||||||||
\(797\) | −33488.0 | −1.48834 | −0.744169 | − | 0.667991i | \(-0.767154\pi\) | ||||
−0.744169 | + | 0.667991i | \(0.767154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45457.0 | 2.01271 | ||||||||
\(800\) | −4025.00 | −0.177882 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8076.00 | 0.355578 | ||||||||
\(803\) | 45590.0 | 2.00353 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −90.0000 | −0.00394048 | ||||||||
\(806\) | 1125.00 | 0.0491643 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20025.0 | 0.871878 | ||||||||
\(809\) | 15304.0 | 0.665093 | 0.332546 | − | 0.943087i | \(-0.392092\pi\) | ||||
0.332546 | + | 0.943087i | \(0.392092\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40122.0 | −1.73721 | −0.868603 | − | 0.495509i | \(-0.834982\pi\) | ||||
−0.868603 | + | 0.495509i | \(0.834982\pi\) | |||||||
\(812\) | 6594.00 | 0.284980 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3290.00 | 0.141664 | ||||||||
\(815\) | −3565.00 | −0.153223 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22232.0 | −0.952019 | ||||||||
\(818\) | 2833.00 | 0.121092 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4900.00 | −0.208677 | ||||||||
\(821\) | −25098.0 | −1.06690 | −0.533451 | − | 0.845831i | \(-0.679105\pi\) | ||||
−0.533451 | + | 0.845831i | \(0.679105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43492.0 | −1.84208 | −0.921042 | − | 0.389462i | \(-0.872661\pi\) | ||||
−0.921042 | + | 0.389462i | \(0.872661\pi\) | |||||||
\(824\) | 10290.0 | 0.435035 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4488.00 | −0.189053 | ||||||||
\(827\) | −11206.0 | −0.471186 | −0.235593 | − | 0.971852i | \(-0.575703\pi\) | ||||
−0.235593 | + | 0.971852i | \(0.575703\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23964.0 | −1.00399 | −0.501993 | − | 0.864872i | \(-0.667400\pi\) | ||||
−0.501993 | + | 0.864872i | \(0.667400\pi\) | |||||||
\(830\) | 510.000 | 0.0213281 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 835.000 | 0.0347938 | ||||||||
\(833\) | −40217.0 | −1.67279 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7980.00 | 0.330730 | ||||||||
\(836\) | 18424.0 | 0.762210 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4777.00 | −0.196920 | ||||||||
\(839\) | 34606.0 | 1.42399 | 0.711997 | − | 0.702182i | \(-0.247791\pi\) | ||||
0.711997 | + | 0.702182i | \(0.247791\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 260.000 | 0.0106605 | ||||||||
\(842\) | 6464.00 | 0.264566 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29134.0 | 1.18819 | ||||||||
\(845\) | 10860.0 | 0.442125 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5268.00 | −0.213708 | ||||||||
\(848\) | −164.000 | −0.00664125 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3275.00 | −0.132155 | ||||||||
\(851\) | 210.000 | 0.00845912 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18477.0 | −0.741665 | −0.370833 | − | 0.928700i | \(-0.620928\pi\) | ||||
−0.370833 | + | 0.928700i | \(0.620928\pi\) | |||||||
\(854\) | −2028.00 | −0.0812608 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16470.0 | 0.657632 | ||||||||
\(857\) | 41342.0 | 1.64786 | 0.823930 | − | 0.566692i | \(-0.191777\pi\) | ||||
0.823930 | + | 0.566692i | \(0.191777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21898.0 | 0.869791 | 0.434895 | − | 0.900481i | \(-0.356785\pi\) | ||||
0.434895 | + | 0.900481i | \(0.356785\pi\) | |||||||
\(860\) | 13895.0 | 0.550948 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10680.0 | 0.421998 | ||||||||
\(863\) | 18487.0 | 0.729206 | 0.364603 | − | 0.931163i | \(-0.381205\pi\) | ||||
0.364603 | + | 0.931163i | \(0.381205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20670.0 | 0.812487 | ||||||||
\(866\) | −11566.0 | −0.453844 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9450.00 | 0.369532 | ||||||||
\(869\) | −59079.0 | −2.30623 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2460.00 | −0.0956991 | ||||||||
\(872\) | −10500.0 | −0.407769 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −168.000 | −0.00650193 | ||||||||
\(875\) | 750.000 | 0.0289767 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7593.00 | 0.292357 | 0.146179 | − | 0.989258i | \(-0.453303\pi\) | ||||
0.146179 | + | 0.989258i | \(0.453303\pi\) | |||||||
\(878\) | 1448.00 | 0.0556579 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9635.00 | −0.369086 | ||||||||
\(881\) | 3038.00 | 0.116178 | 0.0580890 | − | 0.998311i | \(-0.481499\pi\) | ||||
0.0580890 | + | 0.998311i | \(0.481499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16732.0 | −0.637686 | −0.318843 | − | 0.947808i | \(-0.603294\pi\) | ||||
−0.318843 | + | 0.947808i | \(0.603294\pi\) | |||||||
\(884\) | 4585.00 | 0.174446 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2376.00 | −0.0900940 | ||||||||
\(887\) | 8031.00 | 0.304007 | 0.152004 | − | 0.988380i | \(-0.451427\pi\) | ||||
0.152004 | + | 0.988380i | \(0.451427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9876.00 | 0.372588 | ||||||||
\(890\) | 7440.00 | 0.280213 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41692.0 | 1.56497 | ||||||||
\(893\) | −19432.0 | −0.728183 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9140.00 | 0.341359 | ||||||||
\(896\) | −8730.00 | −0.325501 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14894.0 | −0.553474 | ||||||||
\(899\) | 35325.0 | 1.31052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −524.000 | −0.0193751 | ||||||||
\(902\) | 6580.00 | 0.242894 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15825.0 | 0.582225 | ||||||||
\(905\) | 2600.00 | 0.0954994 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38487.0 | −1.40897 | −0.704487 | − | 0.709717i | \(-0.748823\pi\) | ||||
−0.704487 | + | 0.709717i | \(0.748823\pi\) | |||||||
\(908\) | 34580.0 | 1.26385 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 150.000 | 0.00546423 | ||||||||
\(911\) | 5120.00 | 0.186205 | 0.0931027 | − | 0.995657i | \(-0.470321\pi\) | ||||
0.0931027 | + | 0.995657i | \(0.470321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4794.00 | 0.173777 | ||||||||
\(914\) | −16204.0 | −0.586412 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30408.0 | −1.09684 | ||||||||
\(917\) | −10998.0 | −0.396059 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28075.0 | 1.00774 | 0.503868 | − | 0.863781i | \(-0.331910\pi\) | ||||
0.503868 | + | 0.863781i | \(0.331910\pi\) | |||||||
\(920\) | 225.000 | 0.00806308 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5082.00 | −0.181526 | ||||||||
\(923\) | 160.000 | 0.00570581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1750.00 | −0.0622050 | ||||||||
\(926\) | 10326.0 | 0.366451 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25277.0 | −0.894136 | ||||||||
\(929\) | 12856.0 | 0.454028 | 0.227014 | − | 0.973892i | \(-0.427104\pi\) | ||||
0.227014 | + | 0.973892i | \(0.427104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17192.0 | 0.605204 | ||||||||
\(932\) | −36414.0 | −1.27981 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4184.00 | 0.146579 | ||||||||
\(935\) | −30785.0 | −1.07677 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1374.00 | −0.0479046 | −0.0239523 | − | 0.999713i | \(-0.507625\pi\) | ||||
−0.0239523 | + | 0.999713i | \(0.507625\pi\) | |||||||
\(938\) | 2952.00 | 0.102757 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12145.0 | 0.421411 | ||||||||
\(941\) | −8543.00 | −0.295955 | −0.147978 | − | 0.988991i | \(-0.547276\pi\) | ||||
−0.147978 | + | 0.988991i | \(0.547276\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 420.000 | 0.0145038 | ||||||||
\(944\) | −30668.0 | −1.05737 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18659.0 | −0.641286 | ||||||||
\(947\) | −13506.0 | −0.463449 | −0.231724 | − | 0.972781i | \(-0.574437\pi\) | ||||
−0.231724 | + | 0.972781i | \(0.574437\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4850.00 | −0.165898 | ||||||||
\(950\) | 1400.00 | 0.0478126 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11790.0 | −0.401382 | ||||||||
\(953\) | −21775.0 | −0.740148 | −0.370074 | − | 0.929002i | \(-0.620668\pi\) | ||||
−0.370074 | + | 0.929002i | \(0.620668\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24130.0 | 0.817621 | ||||||||
\(956\) | 10822.0 | 0.366118 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15576.0 | −0.525300 | ||||||||
\(959\) | 6588.00 | 0.221833 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20834.0 | 0.699339 | ||||||||
\(962\) | −350.000 | −0.0117302 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25613.0 | 0.855746 | ||||||||
\(965\) | −8350.00 | −0.278545 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3854.00 | 0.128166 | 0.0640829 | − | 0.997945i | \(-0.479588\pi\) | ||||
0.0640829 | + | 0.997945i | \(0.479588\pi\) | |||||||
\(968\) | 13170.0 | 0.437293 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4870.00 | 0.161202 | ||||||||
\(971\) | −12933.0 | −0.427435 | −0.213718 | − | 0.976895i | \(-0.568557\pi\) | ||||
−0.213718 | + | 0.976895i | \(0.568557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6252.00 | 0.205992 | ||||||||
\(974\) | −10220.0 | −0.336211 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13858.0 | −0.454492 | ||||||||
\(977\) | −17521.0 | −0.573743 | −0.286871 | − | 0.957969i | \(-0.592615\pi\) | ||||
−0.286871 | + | 0.957969i | \(0.592615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 69936.0 | 2.28311 | ||||||||
\(980\) | −10745.0 | −0.350241 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2692.00 | −0.0874798 | ||||||||
\(983\) | 12573.0 | 0.407952 | 0.203976 | − | 0.978976i | \(-0.434614\pi\) | ||||
0.203976 | + | 0.978976i | \(0.434614\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6900.00 | −0.223200 | ||||||||
\(986\) | −20567.0 | −0.664287 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1960.00 | −0.0631133 | ||||||||
\(989\) | −1191.00 | −0.0382928 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8945.00 | 0.286728 | 0.143364 | − | 0.989670i | \(-0.454208\pi\) | ||||
0.143364 | + | 0.989670i | \(0.454208\pi\) | |||||||
\(992\) | −36225.0 | −1.15942 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −192.000 | −0.00612663 | ||||||||
\(995\) | −21785.0 | −0.694101 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58179.0 | −1.84809 | −0.924046 | − | 0.382282i | \(-0.875138\pi\) | ||||
−0.924046 | + | 0.382282i | \(0.875138\pi\) | |||||||
\(998\) | −5764.00 | −0.182822 | ||||||||
\(999\) | 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 | 135.4.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 135.4.a.c.1.1 | yes | 1 | ||
4.3 | odd | 2 | 2160.4.a.f.1.1 | 1 | |||
5.2 | odd | 4 | 675.4.b.f.649.1 | 2 | |||
5.3 | odd | 4 | 675.4.b.f.649.2 | 2 | |||
5.4 | even | 2 | 675.4.a.h.1.1 | 1 | |||
9.2 | odd | 6 | 405.4.e.f.271.1 | 2 | |||
9.4 | even | 3 | 405.4.e.h.136.1 | 2 | |||
9.5 | odd | 6 | 405.4.e.f.136.1 | 2 | |||
9.7 | even | 3 | 405.4.e.h.271.1 | 2 | |||
12.11 | even | 2 | 2160.4.a.p.1.1 | 1 | |||
15.2 | even | 4 | 675.4.b.e.649.2 | 2 | |||
15.8 | even | 4 | 675.4.b.e.649.1 | 2 | |||
15.14 | odd | 2 | 675.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
135.4.a.c.1.1 | yes | 1 | 3.2 | odd | 2 | ||
405.4.e.f.136.1 | 2 | 9.5 | odd | 6 | |||
405.4.e.f.271.1 | 2 | 9.2 | odd | 6 | |||
405.4.e.h.136.1 | 2 | 9.4 | even | 3 | |||
405.4.e.h.271.1 | 2 | 9.7 | even | 3 | |||
675.4.a.c.1.1 | 1 | 15.14 | odd | 2 | |||
675.4.a.h.1.1 | 1 | 5.4 | even | 2 | |||
675.4.b.e.649.1 | 2 | 15.8 | even | 4 | |||
675.4.b.e.649.2 | 2 | 15.2 | even | 4 | |||
675.4.b.f.649.1 | 2 | 5.2 | odd | 4 | |||
675.4.b.f.649.2 | 2 | 5.3 | odd | 4 | |||
2160.4.a.f.1.1 | 1 | 4.3 | odd | 2 | |||
2160.4.a.p.1.1 | 1 | 12.11 | even | 2 |