Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 32 x^{11} - 5 x^{10} + 376 x^{9} + 100 x^{8} - 1985 x^{7} - 576 x^{6} + 4708 x^{5} + 889 x^{4} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-2.15443\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 | 0.707107 | ||||||||
\(3\) | 2.15443 | 1.24386 | 0.621932 | − | 0.783071i | \(-0.286348\pi\) | ||||
0.621932 | + | 0.783071i | \(0.286348\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.15443 | 0.879544 | ||||||||
\(7\) | 5.20049 | 1.96560 | 0.982800 | − | 0.184674i | \(-0.0591230\pi\) | ||||
0.982800 | + | 0.184674i | \(0.0591230\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.64159 | 0.547196 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.15443 | 0.621932 | ||||||||
\(13\) | −3.69356 | −1.02441 | −0.512204 | − | 0.858864i | \(-0.671171\pi\) | ||||
−0.512204 | + | 0.858864i | \(0.671171\pi\) | |||||||
\(14\) | 5.20049 | 1.38989 | ||||||||
\(15\) | −2.15443 | −0.556273 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.28911 | 0.555190 | 0.277595 | − | 0.960698i | \(-0.410463\pi\) | ||||
0.277595 | + | 0.960698i | \(0.410463\pi\) | |||||||
\(18\) | 1.64159 | 0.386926 | ||||||||
\(19\) | 3.91291 | 0.897684 | 0.448842 | − | 0.893611i | \(-0.351837\pi\) | ||||
0.448842 | + | 0.893611i | \(0.351837\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 11.2041 | 2.44494 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −7.46477 | −1.55651 | −0.778256 | − | 0.627948i | \(-0.783895\pi\) | ||||
−0.778256 | + | 0.627948i | \(0.783895\pi\) | |||||||
\(24\) | 2.15443 | 0.439772 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.69356 | −0.724366 | ||||||||
\(27\) | −2.92661 | −0.563226 | ||||||||
\(28\) | 5.20049 | 0.982800 | ||||||||
\(29\) | 8.04319 | 1.49358 | 0.746791 | − | 0.665058i | \(-0.231593\pi\) | ||||
0.746791 | + | 0.665058i | \(0.231593\pi\) | |||||||
\(30\) | −2.15443 | −0.393344 | ||||||||
\(31\) | −2.87929 | −0.517136 | −0.258568 | − | 0.965993i | \(-0.583251\pi\) | ||||
−0.258568 | + | 0.965993i | \(0.583251\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.15443 | 0.375039 | ||||||||
\(34\) | 2.28911 | 0.392579 | ||||||||
\(35\) | −5.20049 | −0.879043 | ||||||||
\(36\) | 1.64159 | 0.273598 | ||||||||
\(37\) | 10.2217 | 1.68043 | 0.840216 | − | 0.542253i | \(-0.182428\pi\) | ||||
0.840216 | + | 0.542253i | \(0.182428\pi\) | |||||||
\(38\) | 3.91291 | 0.634758 | ||||||||
\(39\) | −7.95753 | −1.27422 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 3.12737 | 0.488413 | 0.244206 | − | 0.969723i | \(-0.421473\pi\) | ||||
0.244206 | + | 0.969723i | \(0.421473\pi\) | |||||||
\(42\) | 11.2041 | 1.72883 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −1.64159 | −0.244714 | ||||||||
\(46\) | −7.46477 | −1.10062 | ||||||||
\(47\) | −9.31889 | −1.35930 | −0.679650 | − | 0.733536i | \(-0.737868\pi\) | ||||
−0.679650 | + | 0.733536i | \(0.737868\pi\) | |||||||
\(48\) | 2.15443 | 0.310966 | ||||||||
\(49\) | 20.0451 | 2.86358 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 4.93173 | 0.690581 | ||||||||
\(52\) | −3.69356 | −0.512204 | ||||||||
\(53\) | −0.670647 | −0.0921205 | −0.0460602 | − | 0.998939i | \(-0.514667\pi\) | ||||
−0.0460602 | + | 0.998939i | \(0.514667\pi\) | |||||||
\(54\) | −2.92661 | −0.398261 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 5.20049 | 0.694944 | ||||||||
\(57\) | 8.43011 | 1.11660 | ||||||||
\(58\) | 8.04319 | 1.05612 | ||||||||
\(59\) | 6.55249 | 0.853062 | 0.426531 | − | 0.904473i | \(-0.359736\pi\) | ||||
0.426531 | + | 0.904473i | \(0.359736\pi\) | |||||||
\(60\) | −2.15443 | −0.278136 | ||||||||
\(61\) | 7.70264 | 0.986221 | 0.493111 | − | 0.869967i | \(-0.335860\pi\) | ||||
0.493111 | + | 0.869967i | \(0.335860\pi\) | |||||||
\(62\) | −2.87929 | −0.365671 | ||||||||
\(63\) | 8.53706 | 1.07557 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.69356 | 0.458129 | ||||||||
\(66\) | 2.15443 | 0.265193 | ||||||||
\(67\) | −4.29126 | −0.524261 | −0.262131 | − | 0.965032i | \(-0.584425\pi\) | ||||
−0.262131 | + | 0.965032i | \(0.584425\pi\) | |||||||
\(68\) | 2.28911 | 0.277595 | ||||||||
\(69\) | −16.0824 | −1.93609 | ||||||||
\(70\) | −5.20049 | −0.621577 | ||||||||
\(71\) | −8.54294 | −1.01386 | −0.506930 | − | 0.861987i | \(-0.669220\pi\) | ||||
−0.506930 | + | 0.861987i | \(0.669220\pi\) | |||||||
\(72\) | 1.64159 | 0.193463 | ||||||||
\(73\) | −9.80369 | −1.14743 | −0.573717 | − | 0.819053i | \(-0.694499\pi\) | ||||
−0.573717 | + | 0.819053i | \(0.694499\pi\) | |||||||
\(74\) | 10.2217 | 1.18824 | ||||||||
\(75\) | 2.15443 | 0.248773 | ||||||||
\(76\) | 3.91291 | 0.448842 | ||||||||
\(77\) | 5.20049 | 0.592651 | ||||||||
\(78\) | −7.95753 | −0.901012 | ||||||||
\(79\) | 11.4945 | 1.29323 | 0.646614 | − | 0.762818i | \(-0.276185\pi\) | ||||
0.646614 | + | 0.762818i | \(0.276185\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −11.2300 | −1.24777 | ||||||||
\(82\) | 3.12737 | 0.345360 | ||||||||
\(83\) | −6.18517 | −0.678910 | −0.339455 | − | 0.940622i | \(-0.610243\pi\) | ||||
−0.339455 | + | 0.940622i | \(0.610243\pi\) | |||||||
\(84\) | 11.2041 | 1.22247 | ||||||||
\(85\) | −2.28911 | −0.248289 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | 17.3285 | 1.85781 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −5.34397 | −0.566460 | −0.283230 | − | 0.959052i | \(-0.591406\pi\) | ||||
−0.283230 | + | 0.959052i | \(0.591406\pi\) | |||||||
\(90\) | −1.64159 | −0.173039 | ||||||||
\(91\) | −19.2083 | −2.01358 | ||||||||
\(92\) | −7.46477 | −0.778256 | ||||||||
\(93\) | −6.20325 | −0.643247 | ||||||||
\(94\) | −9.31889 | −0.961170 | ||||||||
\(95\) | −3.91291 | −0.401456 | ||||||||
\(96\) | 2.15443 | 0.219886 | ||||||||
\(97\) | 5.40206 | 0.548496 | 0.274248 | − | 0.961659i | \(-0.411571\pi\) | ||||
0.274248 | + | 0.961659i | \(0.411571\pi\) | |||||||
\(98\) | 20.0451 | 2.02486 | ||||||||
\(99\) | 1.64159 | 0.164986 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 16.4334 | 1.63518 | 0.817591 | − | 0.575799i | \(-0.195309\pi\) | ||||
0.817591 | + | 0.575799i | \(0.195309\pi\) | |||||||
\(102\) | 4.93173 | 0.488314 | ||||||||
\(103\) | −12.9541 | −1.27640 | −0.638201 | − | 0.769870i | \(-0.720321\pi\) | ||||
−0.638201 | + | 0.769870i | \(0.720321\pi\) | |||||||
\(104\) | −3.69356 | −0.362183 | ||||||||
\(105\) | −11.2041 | −1.09341 | ||||||||
\(106\) | −0.670647 | −0.0651390 | ||||||||
\(107\) | −16.3514 | −1.58075 | −0.790373 | − | 0.612626i | \(-0.790113\pi\) | ||||
−0.790373 | + | 0.612626i | \(0.790113\pi\) | |||||||
\(108\) | −2.92661 | −0.281613 | ||||||||
\(109\) | 16.8177 | 1.61084 | 0.805419 | − | 0.592705i | \(-0.201940\pi\) | ||||
0.805419 | + | 0.592705i | \(0.201940\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 22.0219 | 2.09023 | ||||||||
\(112\) | 5.20049 | 0.491400 | ||||||||
\(113\) | −5.65787 | −0.532248 | −0.266124 | − | 0.963939i | \(-0.585743\pi\) | ||||
−0.266124 | + | 0.963939i | \(0.585743\pi\) | |||||||
\(114\) | 8.43011 | 0.789553 | ||||||||
\(115\) | 7.46477 | 0.696093 | ||||||||
\(116\) | 8.04319 | 0.746791 | ||||||||
\(117\) | −6.06330 | −0.560552 | ||||||||
\(118\) | 6.55249 | 0.603206 | ||||||||
\(119\) | 11.9045 | 1.09128 | ||||||||
\(120\) | −2.15443 | −0.196672 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.70264 | 0.697364 | ||||||||
\(123\) | 6.73771 | 0.607519 | ||||||||
\(124\) | −2.87929 | −0.258568 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 8.53706 | 0.760542 | ||||||||
\(127\) | −17.6856 | −1.56934 | −0.784670 | − | 0.619914i | \(-0.787167\pi\) | ||||
−0.784670 | + | 0.619914i | \(0.787167\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.15443 | 0.189687 | ||||||||
\(130\) | 3.69356 | 0.323946 | ||||||||
\(131\) | −16.4398 | −1.43635 | −0.718176 | − | 0.695861i | \(-0.755023\pi\) | ||||
−0.718176 | + | 0.695861i | \(0.755023\pi\) | |||||||
\(132\) | 2.15443 | 0.187519 | ||||||||
\(133\) | 20.3491 | 1.76449 | ||||||||
\(134\) | −4.29126 | −0.370709 | ||||||||
\(135\) | 2.92661 | 0.251882 | ||||||||
\(136\) | 2.28911 | 0.196289 | ||||||||
\(137\) | −4.54096 | −0.387960 | −0.193980 | − | 0.981005i | \(-0.562140\pi\) | ||||
−0.193980 | + | 0.981005i | \(0.562140\pi\) | |||||||
\(138\) | −16.0824 | −1.36902 | ||||||||
\(139\) | 17.7324 | 1.50404 | 0.752021 | − | 0.659139i | \(-0.229079\pi\) | ||||
0.752021 | + | 0.659139i | \(0.229079\pi\) | |||||||
\(140\) | −5.20049 | −0.439521 | ||||||||
\(141\) | −20.0769 | −1.69078 | ||||||||
\(142\) | −8.54294 | −0.716908 | ||||||||
\(143\) | −3.69356 | −0.308871 | ||||||||
\(144\) | 1.64159 | 0.136799 | ||||||||
\(145\) | −8.04319 | −0.667950 | ||||||||
\(146\) | −9.80369 | −0.811359 | ||||||||
\(147\) | 43.1858 | 3.56190 | ||||||||
\(148\) | 10.2217 | 0.840216 | ||||||||
\(149\) | −2.59038 | −0.212212 | −0.106106 | − | 0.994355i | \(-0.533838\pi\) | ||||
−0.106106 | + | 0.994355i | \(0.533838\pi\) | |||||||
\(150\) | 2.15443 | 0.175909 | ||||||||
\(151\) | 20.9220 | 1.70261 | 0.851304 | − | 0.524673i | \(-0.175813\pi\) | ||||
0.851304 | + | 0.524673i | \(0.175813\pi\) | |||||||
\(152\) | 3.91291 | 0.317379 | ||||||||
\(153\) | 3.75777 | 0.303798 | ||||||||
\(154\) | 5.20049 | 0.419067 | ||||||||
\(155\) | 2.87929 | 0.231270 | ||||||||
\(156\) | −7.95753 | −0.637112 | ||||||||
\(157\) | −13.6347 | −1.08817 | −0.544083 | − | 0.839031i | \(-0.683122\pi\) | ||||
−0.544083 | + | 0.839031i | \(0.683122\pi\) | |||||||
\(158\) | 11.4945 | 0.914450 | ||||||||
\(159\) | −1.44487 | −0.114585 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −38.8204 | −3.05948 | ||||||||
\(162\) | −11.2300 | −0.882308 | ||||||||
\(163\) | −18.6569 | −1.46133 | −0.730663 | − | 0.682739i | \(-0.760789\pi\) | ||||
−0.730663 | + | 0.682739i | \(0.760789\pi\) | |||||||
\(164\) | 3.12737 | 0.244206 | ||||||||
\(165\) | −2.15443 | −0.167723 | ||||||||
\(166\) | −6.18517 | −0.480062 | ||||||||
\(167\) | 2.47973 | 0.191887 | 0.0959435 | − | 0.995387i | \(-0.469413\pi\) | ||||
0.0959435 | + | 0.995387i | \(0.469413\pi\) | |||||||
\(168\) | 11.2041 | 0.864416 | ||||||||
\(169\) | 0.642357 | 0.0494121 | ||||||||
\(170\) | −2.28911 | −0.175567 | ||||||||
\(171\) | 6.42339 | 0.491209 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | −2.91913 | −0.221937 | −0.110968 | − | 0.993824i | \(-0.535395\pi\) | ||||
−0.110968 | + | 0.993824i | \(0.535395\pi\) | |||||||
\(174\) | 17.3285 | 1.31367 | ||||||||
\(175\) | 5.20049 | 0.393120 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 14.1169 | 1.06109 | ||||||||
\(178\) | −5.34397 | −0.400548 | ||||||||
\(179\) | −13.7699 | −1.02921 | −0.514606 | − | 0.857427i | \(-0.672062\pi\) | ||||
−0.514606 | + | 0.857427i | \(0.672062\pi\) | |||||||
\(180\) | −1.64159 | −0.122357 | ||||||||
\(181\) | −9.50722 | −0.706666 | −0.353333 | − | 0.935498i | \(-0.614952\pi\) | ||||
−0.353333 | + | 0.935498i | \(0.614952\pi\) | |||||||
\(182\) | −19.2083 | −1.42381 | ||||||||
\(183\) | 16.5948 | 1.22672 | ||||||||
\(184\) | −7.46477 | −0.550310 | ||||||||
\(185\) | −10.2217 | −0.751512 | ||||||||
\(186\) | −6.20325 | −0.454844 | ||||||||
\(187\) | 2.28911 | 0.167396 | ||||||||
\(188\) | −9.31889 | −0.679650 | ||||||||
\(189\) | −15.2198 | −1.10708 | ||||||||
\(190\) | −3.91291 | −0.283873 | ||||||||
\(191\) | 22.3373 | 1.61627 | 0.808134 | − | 0.588998i | \(-0.200477\pi\) | ||||
0.808134 | + | 0.588998i | \(0.200477\pi\) | |||||||
\(192\) | 2.15443 | 0.155483 | ||||||||
\(193\) | 5.77134 | 0.415430 | 0.207715 | − | 0.978189i | \(-0.433397\pi\) | ||||
0.207715 | + | 0.978189i | \(0.433397\pi\) | |||||||
\(194\) | 5.40206 | 0.387845 | ||||||||
\(195\) | 7.95753 | 0.569850 | ||||||||
\(196\) | 20.0451 | 1.43179 | ||||||||
\(197\) | 7.78147 | 0.554407 | 0.277203 | − | 0.960811i | \(-0.410592\pi\) | ||||
0.277203 | + | 0.960811i | \(0.410592\pi\) | |||||||
\(198\) | 1.64159 | 0.116663 | ||||||||
\(199\) | −17.2211 | −1.22077 | −0.610387 | − | 0.792104i | \(-0.708986\pi\) | ||||
−0.610387 | + | 0.792104i | \(0.708986\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −9.24525 | −0.652109 | ||||||||
\(202\) | 16.4334 | 1.15625 | ||||||||
\(203\) | 41.8285 | 2.93579 | ||||||||
\(204\) | 4.93173 | 0.345290 | ||||||||
\(205\) | −3.12737 | −0.218425 | ||||||||
\(206\) | −12.9541 | −0.902552 | ||||||||
\(207\) | −12.2541 | −0.851717 | ||||||||
\(208\) | −3.69356 | −0.256102 | ||||||||
\(209\) | 3.91291 | 0.270662 | ||||||||
\(210\) | −11.2041 | −0.773157 | ||||||||
\(211\) | −2.25780 | −0.155434 | −0.0777168 | − | 0.996975i | \(-0.524763\pi\) | ||||
−0.0777168 | + | 0.996975i | \(0.524763\pi\) | |||||||
\(212\) | −0.670647 | −0.0460602 | ||||||||
\(213\) | −18.4052 | −1.26110 | ||||||||
\(214\) | −16.3514 | −1.11776 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | −2.92661 | −0.199131 | ||||||||
\(217\) | −14.9737 | −1.01648 | ||||||||
\(218\) | 16.8177 | 1.13904 | ||||||||
\(219\) | −21.1214 | −1.42725 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −8.45495 | −0.568741 | ||||||||
\(222\) | 22.0219 | 1.47801 | ||||||||
\(223\) | −5.70292 | −0.381896 | −0.190948 | − | 0.981600i | \(-0.561156\pi\) | ||||
−0.190948 | + | 0.981600i | \(0.561156\pi\) | |||||||
\(224\) | 5.20049 | 0.347472 | ||||||||
\(225\) | 1.64159 | 0.109439 | ||||||||
\(226\) | −5.65787 | −0.376356 | ||||||||
\(227\) | −1.85378 | −0.123040 | −0.0615199 | − | 0.998106i | \(-0.519595\pi\) | ||||
−0.0615199 | + | 0.998106i | \(0.519595\pi\) | |||||||
\(228\) | 8.43011 | 0.558298 | ||||||||
\(229\) | −12.0610 | −0.797014 | −0.398507 | − | 0.917165i | \(-0.630472\pi\) | ||||
−0.398507 | + | 0.917165i | \(0.630472\pi\) | |||||||
\(230\) | 7.46477 | 0.492212 | ||||||||
\(231\) | 11.2041 | 0.737176 | ||||||||
\(232\) | 8.04319 | 0.528061 | ||||||||
\(233\) | 6.65456 | 0.435955 | 0.217977 | − | 0.975954i | \(-0.430054\pi\) | ||||
0.217977 | + | 0.975954i | \(0.430054\pi\) | |||||||
\(234\) | −6.06330 | −0.396370 | ||||||||
\(235\) | 9.31889 | 0.607898 | ||||||||
\(236\) | 6.55249 | 0.426531 | ||||||||
\(237\) | 24.7641 | 1.60860 | ||||||||
\(238\) | 11.9045 | 0.771653 | ||||||||
\(239\) | −15.6396 | −1.01164 | −0.505819 | − | 0.862639i | \(-0.668810\pi\) | ||||
−0.505819 | + | 0.862639i | \(0.668810\pi\) | |||||||
\(240\) | −2.15443 | −0.139068 | ||||||||
\(241\) | −0.896388 | −0.0577414 | −0.0288707 | − | 0.999583i | \(-0.509191\pi\) | ||||
−0.0288707 | + | 0.999583i | \(0.509191\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −15.4144 | −0.988832 | ||||||||
\(244\) | 7.70264 | 0.493111 | ||||||||
\(245\) | −20.0451 | −1.28063 | ||||||||
\(246\) | 6.73771 | 0.429581 | ||||||||
\(247\) | −14.4526 | −0.919595 | ||||||||
\(248\) | −2.87929 | −0.182835 | ||||||||
\(249\) | −13.3255 | −0.844471 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 3.71338 | 0.234387 | 0.117193 | − | 0.993109i | \(-0.462610\pi\) | ||||
0.117193 | + | 0.993109i | \(0.462610\pi\) | |||||||
\(252\) | 8.53706 | 0.537784 | ||||||||
\(253\) | −7.46477 | −0.469306 | ||||||||
\(254\) | −17.6856 | −1.10969 | ||||||||
\(255\) | −4.93173 | −0.308837 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.07711 | 0.316701 | 0.158351 | − | 0.987383i | \(-0.449382\pi\) | ||||
0.158351 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(258\) | 2.15443 | 0.134129 | ||||||||
\(259\) | 53.1576 | 3.30305 | ||||||||
\(260\) | 3.69356 | 0.229065 | ||||||||
\(261\) | 13.2036 | 0.817283 | ||||||||
\(262\) | −16.4398 | −1.01565 | ||||||||
\(263\) | 27.1172 | 1.67212 | 0.836058 | − | 0.548641i | \(-0.184855\pi\) | ||||
0.836058 | + | 0.548641i | \(0.184855\pi\) | |||||||
\(264\) | 2.15443 | 0.132596 | ||||||||
\(265\) | 0.670647 | 0.0411975 | ||||||||
\(266\) | 20.3491 | 1.24768 | ||||||||
\(267\) | −11.5132 | −0.704599 | ||||||||
\(268\) | −4.29126 | −0.262131 | ||||||||
\(269\) | −2.78067 | −0.169540 | −0.0847702 | − | 0.996401i | \(-0.527016\pi\) | ||||
−0.0847702 | + | 0.996401i | \(0.527016\pi\) | |||||||
\(270\) | 2.92661 | 0.178108 | ||||||||
\(271\) | −12.6460 | −0.768189 | −0.384094 | − | 0.923294i | \(-0.625486\pi\) | ||||
−0.384094 | + | 0.923294i | \(0.625486\pi\) | |||||||
\(272\) | 2.28911 | 0.138798 | ||||||||
\(273\) | −41.3830 | −2.50461 | ||||||||
\(274\) | −4.54096 | −0.274329 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −16.0824 | −0.968044 | ||||||||
\(277\) | −6.74725 | −0.405403 | −0.202701 | − | 0.979241i | \(-0.564972\pi\) | ||||
−0.202701 | + | 0.979241i | \(0.564972\pi\) | |||||||
\(278\) | 17.7324 | 1.06352 | ||||||||
\(279\) | −4.72661 | −0.282975 | ||||||||
\(280\) | −5.20049 | −0.310789 | ||||||||
\(281\) | −5.29405 | −0.315816 | −0.157908 | − | 0.987454i | \(-0.550475\pi\) | ||||
−0.157908 | + | 0.987454i | \(0.550475\pi\) | |||||||
\(282\) | −20.0769 | −1.19556 | ||||||||
\(283\) | −0.938443 | −0.0557846 | −0.0278923 | − | 0.999611i | \(-0.508880\pi\) | ||||
−0.0278923 | + | 0.999611i | \(0.508880\pi\) | |||||||
\(284\) | −8.54294 | −0.506930 | ||||||||
\(285\) | −8.43011 | −0.499357 | ||||||||
\(286\) | −3.69356 | −0.218405 | ||||||||
\(287\) | 16.2638 | 0.960024 | ||||||||
\(288\) | 1.64159 | 0.0967315 | ||||||||
\(289\) | −11.7600 | −0.691764 | ||||||||
\(290\) | −8.04319 | −0.472312 | ||||||||
\(291\) | 11.6384 | 0.682254 | ||||||||
\(292\) | −9.80369 | −0.573717 | ||||||||
\(293\) | 25.1151 | 1.46724 | 0.733620 | − | 0.679560i | \(-0.237829\pi\) | ||||
0.733620 | + | 0.679560i | \(0.237829\pi\) | |||||||
\(294\) | 43.1858 | 2.51865 | ||||||||
\(295\) | −6.55249 | −0.381501 | ||||||||
\(296\) | 10.2217 | 0.594122 | ||||||||
\(297\) | −2.92661 | −0.169819 | ||||||||
\(298\) | −2.59038 | −0.150057 | ||||||||
\(299\) | 27.5715 | 1.59450 | ||||||||
\(300\) | 2.15443 | 0.124386 | ||||||||
\(301\) | 5.20049 | 0.299751 | ||||||||
\(302\) | 20.9220 | 1.20393 | ||||||||
\(303\) | 35.4046 | 2.03394 | ||||||||
\(304\) | 3.91291 | 0.224421 | ||||||||
\(305\) | −7.70264 | −0.441052 | ||||||||
\(306\) | 3.75777 | 0.214818 | ||||||||
\(307\) | −11.3935 | −0.650262 | −0.325131 | − | 0.945669i | \(-0.605408\pi\) | ||||
−0.325131 | + | 0.945669i | \(0.605408\pi\) | |||||||
\(308\) | 5.20049 | 0.296325 | ||||||||
\(309\) | −27.9087 | −1.58767 | ||||||||
\(310\) | 2.87929 | 0.163533 | ||||||||
\(311\) | −4.64254 | −0.263254 | −0.131627 | − | 0.991299i | \(-0.542020\pi\) | ||||
−0.131627 | + | 0.991299i | \(0.542020\pi\) | |||||||
\(312\) | −7.95753 | −0.450506 | ||||||||
\(313\) | −7.23924 | −0.409186 | −0.204593 | − | 0.978847i | \(-0.565587\pi\) | ||||
−0.204593 | + | 0.978847i | \(0.565587\pi\) | |||||||
\(314\) | −13.6347 | −0.769450 | ||||||||
\(315\) | −8.53706 | −0.481009 | ||||||||
\(316\) | 11.4945 | 0.646614 | ||||||||
\(317\) | 13.1816 | 0.740353 | 0.370176 | − | 0.928961i | \(-0.379297\pi\) | ||||
0.370176 | + | 0.928961i | \(0.379297\pi\) | |||||||
\(318\) | −1.44487 | −0.0810240 | ||||||||
\(319\) | 8.04319 | 0.450332 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −35.2280 | −1.96623 | ||||||||
\(322\) | −38.8204 | −2.16338 | ||||||||
\(323\) | 8.95708 | 0.498385 | ||||||||
\(324\) | −11.2300 | −0.623886 | ||||||||
\(325\) | −3.69356 | −0.204882 | ||||||||
\(326\) | −18.6569 | −1.03331 | ||||||||
\(327\) | 36.2325 | 2.00366 | ||||||||
\(328\) | 3.12737 | 0.172680 | ||||||||
\(329\) | −48.4628 | −2.67184 | ||||||||
\(330\) | −2.15443 | −0.118598 | ||||||||
\(331\) | 5.45659 | 0.299921 | 0.149961 | − | 0.988692i | \(-0.452085\pi\) | ||||
0.149961 | + | 0.988692i | \(0.452085\pi\) | |||||||
\(332\) | −6.18517 | −0.339455 | ||||||||
\(333\) | 16.7798 | 0.919525 | ||||||||
\(334\) | 2.47973 | 0.135685 | ||||||||
\(335\) | 4.29126 | 0.234457 | ||||||||
\(336\) | 11.2041 | 0.611234 | ||||||||
\(337\) | 23.7542 | 1.29397 | 0.646987 | − | 0.762501i | \(-0.276029\pi\) | ||||
0.646987 | + | 0.762501i | \(0.276029\pi\) | |||||||
\(338\) | 0.642357 | 0.0349396 | ||||||||
\(339\) | −12.1895 | −0.662044 | ||||||||
\(340\) | −2.28911 | −0.124144 | ||||||||
\(341\) | −2.87929 | −0.155922 | ||||||||
\(342\) | 6.42339 | 0.347337 | ||||||||
\(343\) | 67.8407 | 3.66306 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | 16.0824 | 0.865845 | ||||||||
\(346\) | −2.91913 | −0.156933 | ||||||||
\(347\) | −27.5506 | −1.47899 | −0.739497 | − | 0.673160i | \(-0.764937\pi\) | ||||
−0.739497 | + | 0.673160i | \(0.764937\pi\) | |||||||
\(348\) | 17.3285 | 0.928906 | ||||||||
\(349\) | 19.1046 | 1.02264 | 0.511322 | − | 0.859389i | \(-0.329156\pi\) | ||||
0.511322 | + | 0.859389i | \(0.329156\pi\) | |||||||
\(350\) | 5.20049 | 0.277978 | ||||||||
\(351\) | 10.8096 | 0.576973 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −19.9199 | −1.06023 | −0.530114 | − | 0.847926i | \(-0.677851\pi\) | ||||
−0.530114 | + | 0.847926i | \(0.677851\pi\) | |||||||
\(354\) | 14.1169 | 0.750306 | ||||||||
\(355\) | 8.54294 | 0.453412 | ||||||||
\(356\) | −5.34397 | −0.283230 | ||||||||
\(357\) | 25.6474 | 1.35741 | ||||||||
\(358\) | −13.7699 | −0.727763 | ||||||||
\(359\) | −6.69249 | −0.353216 | −0.176608 | − | 0.984281i | \(-0.556512\pi\) | ||||
−0.176608 | + | 0.984281i | \(0.556512\pi\) | |||||||
\(360\) | −1.64159 | −0.0865193 | ||||||||
\(361\) | −3.68911 | −0.194164 | ||||||||
\(362\) | −9.50722 | −0.499688 | ||||||||
\(363\) | 2.15443 | 0.113078 | ||||||||
\(364\) | −19.2083 | −1.00679 | ||||||||
\(365\) | 9.80369 | 0.513149 | ||||||||
\(366\) | 16.5948 | 0.867425 | ||||||||
\(367\) | −10.2267 | −0.533827 | −0.266914 | − | 0.963720i | \(-0.586004\pi\) | ||||
−0.266914 | + | 0.963720i | \(0.586004\pi\) | |||||||
\(368\) | −7.46477 | −0.389128 | ||||||||
\(369\) | 5.13385 | 0.267258 | ||||||||
\(370\) | −10.2217 | −0.531399 | ||||||||
\(371\) | −3.48769 | −0.181072 | ||||||||
\(372\) | −6.20325 | −0.321623 | ||||||||
\(373\) | 18.4363 | 0.954594 | 0.477297 | − | 0.878742i | \(-0.341617\pi\) | ||||
0.477297 | + | 0.878742i | \(0.341617\pi\) | |||||||
\(374\) | 2.28911 | 0.118367 | ||||||||
\(375\) | −2.15443 | −0.111255 | ||||||||
\(376\) | −9.31889 | −0.480585 | ||||||||
\(377\) | −29.7080 | −1.53004 | ||||||||
\(378\) | −15.2198 | −0.782822 | ||||||||
\(379\) | 2.83712 | 0.145733 | 0.0728666 | − | 0.997342i | \(-0.476785\pi\) | ||||
0.0728666 | + | 0.997342i | \(0.476785\pi\) | |||||||
\(380\) | −3.91291 | −0.200728 | ||||||||
\(381\) | −38.1024 | −1.95204 | ||||||||
\(382\) | 22.3373 | 1.14287 | ||||||||
\(383\) | 13.9972 | 0.715223 | 0.357612 | − | 0.933870i | \(-0.383591\pi\) | ||||
0.357612 | + | 0.933870i | \(0.383591\pi\) | |||||||
\(384\) | 2.15443 | 0.109943 | ||||||||
\(385\) | −5.20049 | −0.265041 | ||||||||
\(386\) | 5.77134 | 0.293753 | ||||||||
\(387\) | 1.64159 | 0.0834466 | ||||||||
\(388\) | 5.40206 | 0.274248 | ||||||||
\(389\) | −3.40004 | −0.172389 | −0.0861944 | − | 0.996278i | \(-0.527471\pi\) | ||||
−0.0861944 | + | 0.996278i | \(0.527471\pi\) | |||||||
\(390\) | 7.95753 | 0.402945 | ||||||||
\(391\) | −17.0877 | −0.864160 | ||||||||
\(392\) | 20.0451 | 1.01243 | ||||||||
\(393\) | −35.4185 | −1.78663 | ||||||||
\(394\) | 7.78147 | 0.392025 | ||||||||
\(395\) | −11.4945 | −0.578349 | ||||||||
\(396\) | 1.64159 | 0.0824929 | ||||||||
\(397\) | 19.0532 | 0.956251 | 0.478125 | − | 0.878292i | \(-0.341316\pi\) | ||||
0.478125 | + | 0.878292i | \(0.341316\pi\) | |||||||
\(398\) | −17.2211 | −0.863217 | ||||||||
\(399\) | 43.8407 | 2.19478 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 6.62751 | 0.330962 | 0.165481 | − | 0.986213i | \(-0.447082\pi\) | ||||
0.165481 | + | 0.986213i | \(0.447082\pi\) | |||||||
\(402\) | −9.24525 | −0.461111 | ||||||||
\(403\) | 10.6348 | 0.529759 | ||||||||
\(404\) | 16.4334 | 0.817591 | ||||||||
\(405\) | 11.2300 | 0.558021 | ||||||||
\(406\) | 41.8285 | 2.07591 | ||||||||
\(407\) | 10.2217 | 0.506669 | ||||||||
\(408\) | 4.93173 | 0.244157 | ||||||||
\(409\) | −26.0155 | −1.28638 | −0.643192 | − | 0.765705i | \(-0.722390\pi\) | ||||
−0.643192 | + | 0.765705i | \(0.722390\pi\) | |||||||
\(410\) | −3.12737 | −0.154450 | ||||||||
\(411\) | −9.78319 | −0.482569 | ||||||||
\(412\) | −12.9541 | −0.638201 | ||||||||
\(413\) | 34.0762 | 1.67678 | ||||||||
\(414\) | −12.2541 | −0.602255 | ||||||||
\(415\) | 6.18517 | 0.303618 | ||||||||
\(416\) | −3.69356 | −0.181091 | ||||||||
\(417\) | 38.2033 | 1.87082 | ||||||||
\(418\) | 3.91291 | 0.191387 | ||||||||
\(419\) | 17.7419 | 0.866747 | 0.433373 | − | 0.901214i | \(-0.357323\pi\) | ||||
0.433373 | + | 0.901214i | \(0.357323\pi\) | |||||||
\(420\) | −11.2041 | −0.546705 | ||||||||
\(421\) | 7.77410 | 0.378886 | 0.189443 | − | 0.981892i | \(-0.439332\pi\) | ||||
0.189443 | + | 0.981892i | \(0.439332\pi\) | |||||||
\(422\) | −2.25780 | −0.109908 | ||||||||
\(423\) | −15.2978 | −0.743804 | ||||||||
\(424\) | −0.670647 | −0.0325695 | ||||||||
\(425\) | 2.28911 | 0.111038 | ||||||||
\(426\) | −18.4052 | −0.891735 | ||||||||
\(427\) | 40.0575 | 1.93852 | ||||||||
\(428\) | −16.3514 | −0.790373 | ||||||||
\(429\) | −7.95753 | −0.384193 | ||||||||
\(430\) | −1.00000 | −0.0482243 | ||||||||
\(431\) | 24.8823 | 1.19854 | 0.599270 | − | 0.800547i | \(-0.295458\pi\) | ||||
0.599270 | + | 0.800547i | \(0.295458\pi\) | |||||||
\(432\) | −2.92661 | −0.140807 | ||||||||
\(433\) | 32.3003 | 1.55226 | 0.776128 | − | 0.630576i | \(-0.217181\pi\) | ||||
0.776128 | + | 0.630576i | \(0.217181\pi\) | |||||||
\(434\) | −14.9737 | −0.718762 | ||||||||
\(435\) | −17.3285 | −0.830839 | ||||||||
\(436\) | 16.8177 | 0.805419 | ||||||||
\(437\) | −29.2090 | −1.39725 | ||||||||
\(438\) | −21.1214 | −1.00922 | ||||||||
\(439\) | −33.5844 | −1.60290 | −0.801448 | − | 0.598064i | \(-0.795937\pi\) | ||||
−0.801448 | + | 0.598064i | \(0.795937\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 32.9058 | 1.56694 | ||||||||
\(442\) | −8.45495 | −0.402161 | ||||||||
\(443\) | −26.5635 | −1.26207 | −0.631036 | − | 0.775754i | \(-0.717370\pi\) | ||||
−0.631036 | + | 0.775754i | \(0.717370\pi\) | |||||||
\(444\) | 22.0219 | 1.04511 | ||||||||
\(445\) | 5.34397 | 0.253329 | ||||||||
\(446\) | −5.70292 | −0.270041 | ||||||||
\(447\) | −5.58080 | −0.263963 | ||||||||
\(448\) | 5.20049 | 0.245700 | ||||||||
\(449\) | 36.7589 | 1.73476 | 0.867379 | − | 0.497648i | \(-0.165803\pi\) | ||||
0.867379 | + | 0.497648i | \(0.165803\pi\) | |||||||
\(450\) | 1.64159 | 0.0773852 | ||||||||
\(451\) | 3.12737 | 0.147262 | ||||||||
\(452\) | −5.65787 | −0.266124 | ||||||||
\(453\) | 45.0751 | 2.11781 | ||||||||
\(454\) | −1.85378 | −0.0870022 | ||||||||
\(455\) | 19.2083 | 0.900499 | ||||||||
\(456\) | 8.43011 | 0.394776 | ||||||||
\(457\) | 24.9793 | 1.16848 | 0.584241 | − | 0.811581i | \(-0.301392\pi\) | ||||
0.584241 | + | 0.811581i | \(0.301392\pi\) | |||||||
\(458\) | −12.0610 | −0.563574 | ||||||||
\(459\) | −6.69932 | −0.312698 | ||||||||
\(460\) | 7.46477 | 0.348047 | ||||||||
\(461\) | −28.6874 | −1.33610 | −0.668052 | − | 0.744115i | \(-0.732872\pi\) | ||||
−0.668052 | + | 0.744115i | \(0.732872\pi\) | |||||||
\(462\) | 11.2041 | 0.521262 | ||||||||
\(463\) | −6.94892 | −0.322944 | −0.161472 | − | 0.986877i | \(-0.551624\pi\) | ||||
−0.161472 | + | 0.986877i | \(0.551624\pi\) | |||||||
\(464\) | 8.04319 | 0.373396 | ||||||||
\(465\) | 6.20325 | 0.287669 | ||||||||
\(466\) | 6.65456 | 0.308267 | ||||||||
\(467\) | −25.0640 | −1.15982 | −0.579911 | − | 0.814680i | \(-0.696913\pi\) | ||||
−0.579911 | + | 0.814680i | \(0.696913\pi\) | |||||||
\(468\) | −6.06330 | −0.280276 | ||||||||
\(469\) | −22.3167 | −1.03049 | ||||||||
\(470\) | 9.31889 | 0.429848 | ||||||||
\(471\) | −29.3750 | −1.35353 | ||||||||
\(472\) | 6.55249 | 0.301603 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 24.7641 | 1.13745 | ||||||||
\(475\) | 3.91291 | 0.179537 | ||||||||
\(476\) | 11.9045 | 0.545641 | ||||||||
\(477\) | −1.10093 | −0.0504080 | ||||||||
\(478\) | −15.6396 | −0.715337 | ||||||||
\(479\) | −24.7063 | −1.12886 | −0.564429 | − | 0.825482i | \(-0.690904\pi\) | ||||
−0.564429 | + | 0.825482i | \(0.690904\pi\) | |||||||
\(480\) | −2.15443 | −0.0983360 | ||||||||
\(481\) | −37.7543 | −1.72145 | ||||||||
\(482\) | −0.896388 | −0.0408294 | ||||||||
\(483\) | −83.6361 | −3.80557 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −5.40206 | −0.245295 | ||||||||
\(486\) | −15.4144 | −0.699210 | ||||||||
\(487\) | −27.4194 | −1.24249 | −0.621245 | − | 0.783617i | \(-0.713373\pi\) | ||||
−0.621245 | + | 0.783617i | \(0.713373\pi\) | |||||||
\(488\) | 7.70264 | 0.348682 | ||||||||
\(489\) | −40.1952 | −1.81769 | ||||||||
\(490\) | −20.0451 | −0.905544 | ||||||||
\(491\) | −26.8303 | −1.21084 | −0.605418 | − | 0.795907i | \(-0.706994\pi\) | ||||
−0.605418 | + | 0.795907i | \(0.706994\pi\) | |||||||
\(492\) | 6.73771 | 0.303759 | ||||||||
\(493\) | 18.4117 | 0.829223 | ||||||||
\(494\) | −14.4526 | −0.650252 | ||||||||
\(495\) | −1.64159 | −0.0737839 | ||||||||
\(496\) | −2.87929 | −0.129284 | ||||||||
\(497\) | −44.4275 | −1.99284 | ||||||||
\(498\) | −13.3255 | −0.597131 | ||||||||
\(499\) | −19.6464 | −0.879495 | −0.439748 | − | 0.898121i | \(-0.644932\pi\) | ||||
−0.439748 | + | 0.898121i | \(0.644932\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 5.34241 | 0.238681 | ||||||||
\(502\) | 3.71338 | 0.165736 | ||||||||
\(503\) | −21.2482 | −0.947409 | −0.473705 | − | 0.880684i | \(-0.657084\pi\) | ||||
−0.473705 | + | 0.880684i | \(0.657084\pi\) | |||||||
\(504\) | 8.53706 | 0.380271 | ||||||||
\(505\) | −16.4334 | −0.731276 | ||||||||
\(506\) | −7.46477 | −0.331849 | ||||||||
\(507\) | 1.38392 | 0.0614619 | ||||||||
\(508\) | −17.6856 | −0.784670 | ||||||||
\(509\) | −13.9210 | −0.617036 | −0.308518 | − | 0.951219i | \(-0.599833\pi\) | ||||
−0.308518 | + | 0.951219i | \(0.599833\pi\) | |||||||
\(510\) | −4.93173 | −0.218381 | ||||||||
\(511\) | −50.9840 | −2.25540 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −11.4516 | −0.505599 | ||||||||
\(514\) | 5.07711 | 0.223942 | ||||||||
\(515\) | 12.9541 | 0.570824 | ||||||||
\(516\) | 2.15443 | 0.0948437 | ||||||||
\(517\) | −9.31889 | −0.409844 | ||||||||
\(518\) | 53.1576 | 2.33561 | ||||||||
\(519\) | −6.28906 | −0.276059 | ||||||||
\(520\) | 3.69356 | 0.161973 | ||||||||
\(521\) | 40.9486 | 1.79399 | 0.896995 | − | 0.442041i | \(-0.145745\pi\) | ||||
0.896995 | + | 0.442041i | \(0.145745\pi\) | |||||||
\(522\) | 13.2036 | 0.577906 | ||||||||
\(523\) | 21.5173 | 0.940887 | 0.470444 | − | 0.882430i | \(-0.344094\pi\) | ||||
0.470444 | + | 0.882430i | \(0.344094\pi\) | |||||||
\(524\) | −16.4398 | −0.718176 | ||||||||
\(525\) | 11.2041 | 0.488987 | ||||||||
\(526\) | 27.1172 | 1.18236 | ||||||||
\(527\) | −6.59101 | −0.287109 | ||||||||
\(528\) | 2.15443 | 0.0937597 | ||||||||
\(529\) | 32.7227 | 1.42273 | ||||||||
\(530\) | 0.670647 | 0.0291310 | ||||||||
\(531\) | 10.7565 | 0.466792 | ||||||||
\(532\) | 20.3491 | 0.882243 | ||||||||
\(533\) | −11.5511 | −0.500334 | ||||||||
\(534\) | −11.5132 | −0.498227 | ||||||||
\(535\) | 16.3514 | 0.706931 | ||||||||
\(536\) | −4.29126 | −0.185354 | ||||||||
\(537\) | −29.6664 | −1.28020 | ||||||||
\(538\) | −2.78067 | −0.119883 | ||||||||
\(539\) | 20.0451 | 0.863402 | ||||||||
\(540\) | 2.92661 | 0.125941 | ||||||||
\(541\) | 25.3884 | 1.09153 | 0.545766 | − | 0.837938i | \(-0.316239\pi\) | ||||
0.545766 | + | 0.837938i | \(0.316239\pi\) | |||||||
\(542\) | −12.6460 | −0.543191 | ||||||||
\(543\) | −20.4827 | −0.878996 | ||||||||
\(544\) | 2.28911 | 0.0981447 | ||||||||
\(545\) | −16.8177 | −0.720389 | ||||||||
\(546\) | −41.3830 | −1.77103 | ||||||||
\(547\) | −27.2451 | −1.16492 | −0.582458 | − | 0.812861i | \(-0.697909\pi\) | ||||
−0.582458 | + | 0.812861i | \(0.697909\pi\) | |||||||
\(548\) | −4.54096 | −0.193980 | ||||||||
\(549\) | 12.6446 | 0.539657 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 31.4723 | 1.34076 | ||||||||
\(552\) | −16.0824 | −0.684510 | ||||||||
\(553\) | 59.7768 | 2.54197 | ||||||||
\(554\) | −6.74725 | −0.286663 | ||||||||
\(555\) | −22.0219 | −0.934778 | ||||||||
\(556\) | 17.7324 | 0.752021 | ||||||||
\(557\) | −38.6556 | −1.63789 | −0.818945 | − | 0.573872i | \(-0.805441\pi\) | ||||
−0.818945 | + | 0.573872i | \(0.805441\pi\) | |||||||
\(558\) | −4.72661 | −0.200094 | ||||||||
\(559\) | −3.69356 | −0.156221 | ||||||||
\(560\) | −5.20049 | −0.219761 | ||||||||
\(561\) | 4.93173 | 0.208218 | ||||||||
\(562\) | −5.29405 | −0.223316 | ||||||||
\(563\) | −10.9047 | −0.459579 | −0.229790 | − | 0.973240i | \(-0.573804\pi\) | ||||
−0.229790 | + | 0.973240i | \(0.573804\pi\) | |||||||
\(564\) | −20.0769 | −0.845392 | ||||||||
\(565\) | 5.65787 | 0.238028 | ||||||||
\(566\) | −0.938443 | −0.0394457 | ||||||||
\(567\) | −58.4012 | −2.45262 | ||||||||
\(568\) | −8.54294 | −0.358454 | ||||||||
\(569\) | −42.4101 | −1.77792 | −0.888961 | − | 0.457982i | \(-0.848572\pi\) | ||||
−0.888961 | + | 0.457982i | \(0.848572\pi\) | |||||||
\(570\) | −8.43011 | −0.353099 | ||||||||
\(571\) | 0.618946 | 0.0259021 | 0.0129510 | − | 0.999916i | \(-0.495877\pi\) | ||||
0.0129510 | + | 0.999916i | \(0.495877\pi\) | |||||||
\(572\) | −3.69356 | −0.154435 | ||||||||
\(573\) | 48.1242 | 2.01042 | ||||||||
\(574\) | 16.2638 | 0.678839 | ||||||||
\(575\) | −7.46477 | −0.311302 | ||||||||
\(576\) | 1.64159 | 0.0683995 | ||||||||
\(577\) | −27.3660 | −1.13926 | −0.569630 | − | 0.821901i | \(-0.692914\pi\) | ||||
−0.569630 | + | 0.821901i | \(0.692914\pi\) | |||||||
\(578\) | −11.7600 | −0.489151 | ||||||||
\(579\) | 12.4340 | 0.516738 | ||||||||
\(580\) | −8.04319 | −0.333975 | ||||||||
\(581\) | −32.1659 | −1.33447 | ||||||||
\(582\) | 11.6384 | 0.482426 | ||||||||
\(583\) | −0.670647 | −0.0277754 | ||||||||
\(584\) | −9.80369 | −0.405680 | ||||||||
\(585\) | 6.06330 | 0.250687 | ||||||||
\(586\) | 25.1151 | 1.03750 | ||||||||
\(587\) | 3.63605 | 0.150076 | 0.0750380 | − | 0.997181i | \(-0.476092\pi\) | ||||
0.0750380 | + | 0.997181i | \(0.476092\pi\) | |||||||
\(588\) | 43.1858 | 1.78095 | ||||||||
\(589\) | −11.2664 | −0.464225 | ||||||||
\(590\) | −6.55249 | −0.269762 | ||||||||
\(591\) | 16.7647 | 0.689606 | ||||||||
\(592\) | 10.2217 | 0.420108 | ||||||||
\(593\) | 2.40157 | 0.0986206 | 0.0493103 | − | 0.998784i | \(-0.484298\pi\) | ||||
0.0493103 | + | 0.998784i | \(0.484298\pi\) | |||||||
\(594\) | −2.92661 | −0.120080 | ||||||||
\(595\) | −11.9045 | −0.488036 | ||||||||
\(596\) | −2.59038 | −0.106106 | ||||||||
\(597\) | −37.1018 | −1.51848 | ||||||||
\(598\) | 27.5715 | 1.12748 | ||||||||
\(599\) | −21.5690 | −0.881284 | −0.440642 | − | 0.897683i | \(-0.645249\pi\) | ||||
−0.440642 | + | 0.897683i | \(0.645249\pi\) | |||||||
\(600\) | 2.15443 | 0.0879544 | ||||||||
\(601\) | 25.5815 | 1.04349 | 0.521745 | − | 0.853101i | \(-0.325281\pi\) | ||||
0.521745 | + | 0.853101i | \(0.325281\pi\) | |||||||
\(602\) | 5.20049 | 0.211956 | ||||||||
\(603\) | −7.04449 | −0.286874 | ||||||||
\(604\) | 20.9220 | 0.851304 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 35.4046 | 1.43822 | ||||||||
\(607\) | −16.2877 | −0.661097 | −0.330548 | − | 0.943789i | \(-0.607234\pi\) | ||||
−0.330548 | + | 0.943789i | \(0.607234\pi\) | |||||||
\(608\) | 3.91291 | 0.158690 | ||||||||
\(609\) | 90.1168 | 3.65172 | ||||||||
\(610\) | −7.70264 | −0.311871 | ||||||||
\(611\) | 34.4199 | 1.39248 | ||||||||
\(612\) | 3.75777 | 0.151899 | ||||||||
\(613\) | −4.91861 | −0.198661 | −0.0993304 | − | 0.995055i | \(-0.531670\pi\) | ||||
−0.0993304 | + | 0.995055i | \(0.531670\pi\) | |||||||
\(614\) | −11.3935 | −0.459805 | ||||||||
\(615\) | −6.73771 | −0.271691 | ||||||||
\(616\) | 5.20049 | 0.209534 | ||||||||
\(617\) | −18.4337 | −0.742114 | −0.371057 | − | 0.928610i | \(-0.621004\pi\) | ||||
−0.371057 | + | 0.928610i | \(0.621004\pi\) | |||||||
\(618\) | −27.9087 | −1.12265 | ||||||||
\(619\) | 26.7959 | 1.07702 | 0.538509 | − | 0.842620i | \(-0.318988\pi\) | ||||
0.538509 | + | 0.842620i | \(0.318988\pi\) | |||||||
\(620\) | 2.87929 | 0.115635 | ||||||||
\(621\) | 21.8464 | 0.876668 | ||||||||
\(622\) | −4.64254 | −0.186149 | ||||||||
\(623\) | −27.7913 | −1.11343 | ||||||||
\(624\) | −7.95753 | −0.318556 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.23924 | −0.289338 | ||||||||
\(627\) | 8.43011 | 0.336666 | ||||||||
\(628\) | −13.6347 | −0.544083 | ||||||||
\(629\) | 23.3985 | 0.932959 | ||||||||
\(630\) | −8.53706 | −0.340125 | ||||||||
\(631\) | −3.76933 | −0.150055 | −0.0750273 | − | 0.997181i | \(-0.523904\pi\) | ||||
−0.0750273 | + | 0.997181i | \(0.523904\pi\) | |||||||
\(632\) | 11.4945 | 0.457225 | ||||||||
\(633\) | −4.86429 | −0.193338 | ||||||||
\(634\) | 13.1816 | 0.523508 | ||||||||
\(635\) | 17.6856 | 0.701830 | ||||||||
\(636\) | −1.44487 | −0.0572926 | ||||||||
\(637\) | −74.0376 | −2.93348 | ||||||||
\(638\) | 8.04319 | 0.318433 | ||||||||
\(639\) | −14.0240 | −0.554781 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 33.5915 | 1.32678 | 0.663392 | − | 0.748272i | \(-0.269116\pi\) | ||||
0.663392 | + | 0.748272i | \(0.269116\pi\) | |||||||
\(642\) | −35.2280 | −1.39034 | ||||||||
\(643\) | −25.2666 | −0.996417 | −0.498208 | − | 0.867057i | \(-0.666009\pi\) | ||||
−0.498208 | + | 0.867057i | \(0.666009\pi\) | |||||||
\(644\) | −38.8204 | −1.52974 | ||||||||
\(645\) | −2.15443 | −0.0848308 | ||||||||
\(646\) | 8.95708 | 0.352412 | ||||||||
\(647\) | 38.3656 | 1.50831 | 0.754154 | − | 0.656698i | \(-0.228047\pi\) | ||||
0.754154 | + | 0.656698i | \(0.228047\pi\) | |||||||
\(648\) | −11.2300 | −0.441154 | ||||||||
\(649\) | 6.55249 | 0.257208 | ||||||||
\(650\) | −3.69356 | −0.144873 | ||||||||
\(651\) | −32.2599 | −1.26437 | ||||||||
\(652\) | −18.6569 | −0.730663 | ||||||||
\(653\) | −13.4101 | −0.524777 | −0.262388 | − | 0.964962i | \(-0.584510\pi\) | ||||
−0.262388 | + | 0.964962i | \(0.584510\pi\) | |||||||
\(654\) | 36.2325 | 1.41680 | ||||||||
\(655\) | 16.4398 | 0.642357 | ||||||||
\(656\) | 3.12737 | 0.122103 | ||||||||
\(657\) | −16.0936 | −0.627872 | ||||||||
\(658\) | −48.4628 | −1.88928 | ||||||||
\(659\) | −13.5960 | −0.529624 | −0.264812 | − | 0.964300i | \(-0.585310\pi\) | ||||
−0.264812 | + | 0.964300i | \(0.585310\pi\) | |||||||
\(660\) | −2.15443 | −0.0838613 | ||||||||
\(661\) | −14.5741 | −0.566868 | −0.283434 | − | 0.958992i | \(-0.591474\pi\) | ||||
−0.283434 | + | 0.958992i | \(0.591474\pi\) | |||||||
\(662\) | 5.45659 | 0.212076 | ||||||||
\(663\) | −18.2156 | −0.707437 | ||||||||
\(664\) | −6.18517 | −0.240031 | ||||||||
\(665\) | −20.3491 | −0.789102 | ||||||||
\(666\) | 16.7798 | 0.650203 | ||||||||
\(667\) | −60.0405 | −2.32478 | ||||||||
\(668\) | 2.47973 | 0.0959435 | ||||||||
\(669\) | −12.2866 | −0.475026 | ||||||||
\(670\) | 4.29126 | 0.165786 | ||||||||
\(671\) | 7.70264 | 0.297357 | ||||||||
\(672\) | 11.2041 | 0.432208 | ||||||||
\(673\) | 20.4531 | 0.788408 | 0.394204 | − | 0.919023i | \(-0.371020\pi\) | ||||
0.394204 | + | 0.919023i | \(0.371020\pi\) | |||||||
\(674\) | 23.7542 | 0.914978 | ||||||||
\(675\) | −2.92661 | −0.112645 | ||||||||
\(676\) | 0.642357 | 0.0247061 | ||||||||
\(677\) | −23.6276 | −0.908082 | −0.454041 | − | 0.890981i | \(-0.650018\pi\) | ||||
−0.454041 | + | 0.890981i | \(0.650018\pi\) | |||||||
\(678\) | −12.1895 | −0.468136 | ||||||||
\(679\) | 28.0933 | 1.07812 | ||||||||
\(680\) | −2.28911 | −0.0877833 | ||||||||
\(681\) | −3.99385 | −0.153045 | ||||||||
\(682\) | −2.87929 | −0.110254 | ||||||||
\(683\) | −20.3160 | −0.777371 | −0.388685 | − | 0.921371i | \(-0.627071\pi\) | ||||
−0.388685 | + | 0.921371i | \(0.627071\pi\) | |||||||
\(684\) | 6.42339 | 0.245605 | ||||||||
\(685\) | 4.54096 | 0.173501 | ||||||||
\(686\) | 67.8407 | 2.59017 | ||||||||
\(687\) | −25.9847 | −0.991376 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 2.47707 | 0.0943690 | ||||||||
\(690\) | 16.0824 | 0.612245 | ||||||||
\(691\) | −33.7100 | −1.28239 | −0.641194 | − | 0.767379i | \(-0.721561\pi\) | ||||
−0.641194 | + | 0.767379i | \(0.721561\pi\) | |||||||
\(692\) | −2.91913 | −0.110968 | ||||||||
\(693\) | 8.53706 | 0.324296 | ||||||||
\(694\) | −27.5506 | −1.04581 | ||||||||
\(695\) | −17.7324 | −0.672628 | ||||||||
\(696\) | 17.3285 | 0.656836 | ||||||||
\(697\) | 7.15888 | 0.271162 | ||||||||
\(698\) | 19.1046 | 0.723119 | ||||||||
\(699\) | 14.3368 | 0.542268 | ||||||||
\(700\) | 5.20049 | 0.196560 | ||||||||
\(701\) | −25.8681 | −0.977025 | −0.488513 | − | 0.872557i | \(-0.662460\pi\) | ||||
−0.488513 | + | 0.872557i | \(0.662460\pi\) | |||||||
\(702\) | 10.8096 | 0.407982 | ||||||||
\(703\) | 39.9965 | 1.50850 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 20.0769 | 0.756141 | ||||||||
\(706\) | −19.9199 | −0.749694 | ||||||||
\(707\) | 85.4616 | 3.21411 | ||||||||
\(708\) | 14.1169 | 0.530546 | ||||||||
\(709\) | 31.4230 | 1.18012 | 0.590058 | − | 0.807361i | \(-0.299105\pi\) | ||||
0.590058 | + | 0.807361i | \(0.299105\pi\) | |||||||
\(710\) | 8.54294 | 0.320611 | ||||||||
\(711\) | 18.8692 | 0.707649 | ||||||||
\(712\) | −5.34397 | −0.200274 | ||||||||
\(713\) | 21.4933 | 0.804929 | ||||||||
\(714\) | 25.6474 | 0.959831 | ||||||||
\(715\) | 3.69356 | 0.138131 | ||||||||
\(716\) | −13.7699 | −0.514606 | ||||||||
\(717\) | −33.6944 | −1.25834 | ||||||||
\(718\) | −6.69249 | −0.249761 | ||||||||
\(719\) | −9.03068 | −0.336787 | −0.168394 | − | 0.985720i | \(-0.553858\pi\) | ||||
−0.168394 | + | 0.985720i | \(0.553858\pi\) | |||||||
\(720\) | −1.64159 | −0.0611784 | ||||||||
\(721\) | −67.3674 | −2.50889 | ||||||||
\(722\) | −3.68911 | −0.137295 | ||||||||
\(723\) | −1.93121 | −0.0718225 | ||||||||
\(724\) | −9.50722 | −0.353333 | ||||||||
\(725\) | 8.04319 | 0.298717 | ||||||||
\(726\) | 2.15443 | 0.0799586 | ||||||||
\(727\) | −3.98733 | −0.147882 | −0.0739410 | − | 0.997263i | \(-0.523558\pi\) | ||||
−0.0739410 | + | 0.997263i | \(0.523558\pi\) | |||||||
\(728\) | −19.2083 | −0.711907 | ||||||||
\(729\) | 0.480600 | 0.0178000 | ||||||||
\(730\) | 9.80369 | 0.362851 | ||||||||
\(731\) | 2.28911 | 0.0846657 | ||||||||
\(732\) | 16.5948 | 0.613362 | ||||||||
\(733\) | −22.6962 | −0.838303 | −0.419151 | − | 0.907916i | \(-0.637672\pi\) | ||||
−0.419151 | + | 0.907916i | \(0.637672\pi\) | |||||||
\(734\) | −10.2267 | −0.377473 | ||||||||
\(735\) | −43.1858 | −1.59293 | ||||||||
\(736\) | −7.46477 | −0.275155 | ||||||||
\(737\) | −4.29126 | −0.158071 | ||||||||
\(738\) | 5.13385 | 0.188980 | ||||||||
\(739\) | 33.6588 | 1.23816 | 0.619079 | − | 0.785328i | \(-0.287506\pi\) | ||||
0.619079 | + | 0.785328i | \(0.287506\pi\) | |||||||
\(740\) | −10.2217 | −0.375756 | ||||||||
\(741\) | −31.1371 | −1.14385 | ||||||||
\(742\) | −3.48769 | −0.128037 | ||||||||
\(743\) | −9.34944 | −0.342998 | −0.171499 | − | 0.985184i | \(-0.554861\pi\) | ||||
−0.171499 | + | 0.985184i | \(0.554861\pi\) | |||||||
\(744\) | −6.20325 | −0.227422 | ||||||||
\(745\) | 2.59038 | 0.0949042 | ||||||||
\(746\) | 18.4363 | 0.675000 | ||||||||
\(747\) | −10.1535 | −0.371497 | ||||||||
\(748\) | 2.28911 | 0.0836981 | ||||||||
\(749\) | −85.0351 | −3.10711 | ||||||||
\(750\) | −2.15443 | −0.0786688 | ||||||||
\(751\) | 52.3542 | 1.91043 | 0.955216 | − | 0.295908i | \(-0.0956223\pi\) | ||||
0.955216 | + | 0.295908i | \(0.0956223\pi\) | |||||||
\(752\) | −9.31889 | −0.339825 | ||||||||
\(753\) | 8.00024 | 0.291545 | ||||||||
\(754\) | −29.7080 | −1.08190 | ||||||||
\(755\) | −20.9220 | −0.761429 | ||||||||
\(756\) | −15.2198 | −0.553539 | ||||||||
\(757\) | 38.6890 | 1.40618 | 0.703088 | − | 0.711103i | \(-0.251804\pi\) | ||||
0.703088 | + | 0.711103i | \(0.251804\pi\) | |||||||
\(758\) | 2.83712 | 0.103049 | ||||||||
\(759\) | −16.0824 | −0.583752 | ||||||||
\(760\) | −3.91291 | −0.141936 | ||||||||
\(761\) | −20.6832 | −0.749765 | −0.374882 | − | 0.927072i | \(-0.622317\pi\) | ||||
−0.374882 | + | 0.927072i | \(0.622317\pi\) | |||||||
\(762\) | −38.1024 | −1.38030 | ||||||||
\(763\) | 87.4600 | 3.16626 | ||||||||
\(764\) | 22.3373 | 0.808134 | ||||||||
\(765\) | −3.75777 | −0.135863 | ||||||||
\(766\) | 13.9972 | 0.505739 | ||||||||
\(767\) | −24.2020 | −0.873884 | ||||||||
\(768\) | 2.15443 | 0.0777415 | ||||||||
\(769\) | 6.62323 | 0.238840 | 0.119420 | − | 0.992844i | \(-0.461897\pi\) | ||||
0.119420 | + | 0.992844i | \(0.461897\pi\) | |||||||
\(770\) | −5.20049 | −0.187413 | ||||||||
\(771\) | 10.9383 | 0.393933 | ||||||||
\(772\) | 5.77134 | 0.207715 | ||||||||
\(773\) | −44.9087 | −1.61525 | −0.807627 | − | 0.589694i | \(-0.799248\pi\) | ||||
−0.807627 | + | 0.589694i | \(0.799248\pi\) | |||||||
\(774\) | 1.64159 | 0.0590057 | ||||||||
\(775\) | −2.87929 | −0.103427 | ||||||||
\(776\) | 5.40206 | 0.193923 | ||||||||
\(777\) | 114.525 | 4.10855 | ||||||||
\(778\) | −3.40004 | −0.121897 | ||||||||
\(779\) | 12.2371 | 0.438440 | ||||||||
\(780\) | 7.95753 | 0.284925 | ||||||||
\(781\) | −8.54294 | −0.305690 | ||||||||
\(782\) | −17.0877 | −0.611053 | ||||||||
\(783\) | −23.5393 | −0.841225 | ||||||||
\(784\) | 20.0451 | 0.715895 | ||||||||
\(785\) | 13.6347 | 0.486643 | ||||||||
\(786\) | −35.4185 | −1.26334 | ||||||||
\(787\) | 10.4312 | 0.371832 | 0.185916 | − | 0.982566i | \(-0.440475\pi\) | ||||
0.185916 | + | 0.982566i | \(0.440475\pi\) | |||||||
\(788\) | 7.78147 | 0.277203 | ||||||||
\(789\) | 58.4222 | 2.07988 | ||||||||
\(790\) | −11.4945 | −0.408954 | ||||||||
\(791\) | −29.4237 | −1.04619 | ||||||||
\(792\) | 1.64159 | 0.0583313 | ||||||||
\(793\) | −28.4501 | −1.01029 | ||||||||
\(794\) | 19.0532 | 0.676172 | ||||||||
\(795\) | 1.44487 | 0.0512441 | ||||||||
\(796\) | −17.2211 | −0.610387 | ||||||||
\(797\) | 32.0697 | 1.13597 | 0.567983 | − | 0.823040i | \(-0.307724\pi\) | ||||
0.567983 | + | 0.823040i | \(0.307724\pi\) | |||||||
\(798\) | 43.8407 | 1.55194 | ||||||||
\(799\) | −21.3320 | −0.754670 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −8.77260 | −0.309965 | ||||||||
\(802\) | 6.62751 | 0.234026 | ||||||||
\(803\) | −9.80369 | −0.345965 | ||||||||
\(804\) | −9.24525 | −0.326055 | ||||||||
\(805\) | 38.8204 | 1.36824 | ||||||||
\(806\) | 10.6348 | 0.374596 | ||||||||
\(807\) | −5.99077 | −0.210885 | ||||||||
\(808\) | 16.4334 | 0.578124 | ||||||||
\(809\) | −10.9308 | −0.384308 | −0.192154 | − | 0.981365i | \(-0.561547\pi\) | ||||
−0.192154 | + | 0.981365i | \(0.561547\pi\) | |||||||
\(810\) | 11.2300 | 0.394580 | ||||||||
\(811\) | 9.65584 | 0.339063 | 0.169531 | − | 0.985525i | \(-0.445775\pi\) | ||||
0.169531 | + | 0.985525i | \(0.445775\pi\) | |||||||
\(812\) | 41.8285 | 1.46789 | ||||||||
\(813\) | −27.2449 | −0.955522 | ||||||||
\(814\) | 10.2217 | 0.358269 | ||||||||
\(815\) | 18.6569 | 0.653524 | ||||||||
\(816\) | 4.93173 | 0.172645 | ||||||||
\(817\) | 3.91291 | 0.136895 | ||||||||
\(818\) | −26.0155 | −0.909611 | ||||||||
\(819\) | −31.5321 | −1.10182 | ||||||||
\(820\) | −3.12737 | −0.109212 | ||||||||
\(821\) | −27.9243 | −0.974565 | −0.487283 | − | 0.873244i | \(-0.662012\pi\) | ||||
−0.487283 | + | 0.873244i | \(0.662012\pi\) | |||||||
\(822\) | −9.78319 | −0.341228 | ||||||||
\(823\) | −18.5996 | −0.648341 | −0.324170 | − | 0.945999i | \(-0.605085\pi\) | ||||
−0.324170 | + | 0.945999i | \(0.605085\pi\) | |||||||
\(824\) | −12.9541 | −0.451276 | ||||||||
\(825\) | 2.15443 | 0.0750078 | ||||||||
\(826\) | 34.0762 | 1.18566 | ||||||||
\(827\) | 45.5295 | 1.58322 | 0.791608 | − | 0.611030i | \(-0.209244\pi\) | ||||
0.791608 | + | 0.611030i | \(0.209244\pi\) | |||||||
\(828\) | −12.2541 | −0.425859 | ||||||||
\(829\) | 44.6185 | 1.54967 | 0.774833 | − | 0.632166i | \(-0.217834\pi\) | ||||
0.774833 | + | 0.632166i | \(0.217834\pi\) | |||||||
\(830\) | 6.18517 | 0.214690 | ||||||||
\(831\) | −14.5365 | −0.504266 | ||||||||
\(832\) | −3.69356 | −0.128051 | ||||||||
\(833\) | 45.8853 | 1.58983 | ||||||||
\(834\) | 38.2033 | 1.32287 | ||||||||
\(835\) | −2.47973 | −0.0858145 | ||||||||
\(836\) | 3.91291 | 0.135331 | ||||||||
\(837\) | 8.42656 | 0.291265 | ||||||||
\(838\) | 17.7419 | 0.612883 | ||||||||
\(839\) | −6.02623 | −0.208048 | −0.104024 | − | 0.994575i | \(-0.533172\pi\) | ||||
−0.104024 | + | 0.994575i | \(0.533172\pi\) | |||||||
\(840\) | −11.2041 | −0.386579 | ||||||||
\(841\) | 35.6929 | 1.23079 | ||||||||
\(842\) | 7.77410 | 0.267913 | ||||||||
\(843\) | −11.4057 | −0.392832 | ||||||||
\(844\) | −2.25780 | −0.0777168 | ||||||||
\(845\) | −0.642357 | −0.0220978 | ||||||||
\(846\) | −15.2978 | −0.525949 | ||||||||
\(847\) | 5.20049 | 0.178691 | ||||||||
\(848\) | −0.670647 | −0.0230301 | ||||||||
\(849\) | −2.02181 | −0.0693884 | ||||||||
\(850\) | 2.28911 | 0.0785158 | ||||||||
\(851\) | −76.3023 | −2.61561 | ||||||||
\(852\) | −18.4052 | −0.630552 | ||||||||
\(853\) | 37.9163 | 1.29823 | 0.649116 | − | 0.760690i | \(-0.275139\pi\) | ||||
0.649116 | + | 0.760690i | \(0.275139\pi\) | |||||||
\(854\) | 40.0575 | 1.37074 | ||||||||
\(855\) | −6.42339 | −0.219675 | ||||||||
\(856\) | −16.3514 | −0.558878 | ||||||||
\(857\) | 9.15268 | 0.312650 | 0.156325 | − | 0.987706i | \(-0.450035\pi\) | ||||
0.156325 | + | 0.987706i | \(0.450035\pi\) | |||||||
\(858\) | −7.95753 | −0.271665 | ||||||||
\(859\) | −6.50679 | −0.222009 | −0.111004 | − | 0.993820i | \(-0.535407\pi\) | ||||
−0.111004 | + | 0.993820i | \(0.535407\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | 35.0394 | 1.19414 | ||||||||
\(862\) | 24.8823 | 0.847495 | ||||||||
\(863\) | −12.9822 | −0.441918 | −0.220959 | − | 0.975283i | \(-0.570919\pi\) | ||||
−0.220959 | + | 0.975283i | \(0.570919\pi\) | |||||||
\(864\) | −2.92661 | −0.0995653 | ||||||||
\(865\) | 2.91913 | 0.0992532 | ||||||||
\(866\) | 32.3003 | 1.09761 | ||||||||
\(867\) | −25.3361 | −0.860460 | ||||||||
\(868\) | −14.9737 | −0.508242 | ||||||||
\(869\) | 11.4945 | 0.389923 | ||||||||
\(870\) | −17.3285 | −0.587492 | ||||||||
\(871\) | 15.8500 | 0.537057 | ||||||||
\(872\) | 16.8177 | 0.569518 | ||||||||
\(873\) | 8.86796 | 0.300135 | ||||||||
\(874\) | −29.2090 | −0.988008 | ||||||||
\(875\) | −5.20049 | −0.175809 | ||||||||
\(876\) | −21.1214 | −0.713626 | ||||||||
\(877\) | −15.6834 | −0.529592 | −0.264796 | − | 0.964305i | \(-0.585305\pi\) | ||||
−0.264796 | + | 0.964305i | \(0.585305\pi\) | |||||||
\(878\) | −33.5844 | −1.13342 | ||||||||
\(879\) | 54.1089 | 1.82505 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | −33.4494 | −1.12694 | −0.563469 | − | 0.826137i | \(-0.690533\pi\) | ||||
−0.563469 | + | 0.826137i | \(0.690533\pi\) | |||||||
\(882\) | 32.9058 | 1.10799 | ||||||||
\(883\) | −57.8360 | −1.94634 | −0.973168 | − | 0.230098i | \(-0.926095\pi\) | ||||
−0.973168 | + | 0.230098i | \(0.926095\pi\) | |||||||
\(884\) | −8.45495 | −0.284371 | ||||||||
\(885\) | −14.1169 | −0.474535 | ||||||||
\(886\) | −26.5635 | −0.892419 | ||||||||
\(887\) | 9.92486 | 0.333244 | 0.166622 | − | 0.986021i | \(-0.446714\pi\) | ||||
0.166622 | + | 0.986021i | \(0.446714\pi\) | |||||||
\(888\) | 22.0219 | 0.739007 | ||||||||
\(889\) | −91.9735 | −3.08469 | ||||||||
\(890\) | 5.34397 | 0.179130 | ||||||||
\(891\) | −11.2300 | −0.376218 | ||||||||
\(892\) | −5.70292 | −0.190948 | ||||||||
\(893\) | −36.4640 | −1.22022 | ||||||||
\(894\) | −5.58080 | −0.186650 | ||||||||
\(895\) | 13.7699 | 0.460278 | ||||||||
\(896\) | 5.20049 | 0.173736 | ||||||||
\(897\) | 59.4011 | 1.98334 | ||||||||
\(898\) | 36.7589 | 1.22666 | ||||||||
\(899\) | −23.1587 | −0.772386 | ||||||||
\(900\) | 1.64159 | 0.0547196 | ||||||||
\(901\) | −1.53518 | −0.0511444 | ||||||||
\(902\) | 3.12737 | 0.104130 | ||||||||
\(903\) | 11.2041 | 0.372849 | ||||||||
\(904\) | −5.65787 | −0.188178 | ||||||||
\(905\) | 9.50722 | 0.316031 | ||||||||
\(906\) | 45.0751 | 1.49752 | ||||||||
\(907\) | 48.1403 | 1.59847 | 0.799236 | − | 0.601017i | \(-0.205238\pi\) | ||||
0.799236 | + | 0.601017i | \(0.205238\pi\) | |||||||
\(908\) | −1.85378 | −0.0615199 | ||||||||
\(909\) | 26.9768 | 0.894765 | ||||||||
\(910\) | 19.2083 | 0.636749 | ||||||||
\(911\) | 40.6760 | 1.34766 | 0.673829 | − | 0.738888i | \(-0.264649\pi\) | ||||
0.673829 | + | 0.738888i | \(0.264649\pi\) | |||||||
\(912\) | 8.43011 | 0.279149 | ||||||||
\(913\) | −6.18517 | −0.204699 | ||||||||
\(914\) | 24.9793 | 0.826241 | ||||||||
\(915\) | −16.5948 | −0.548608 | ||||||||
\(916\) | −12.0610 | −0.398507 | ||||||||
\(917\) | −85.4950 | −2.82329 | ||||||||
\(918\) | −6.69932 | −0.221111 | ||||||||
\(919\) | 33.9679 | 1.12050 | 0.560249 | − | 0.828324i | \(-0.310705\pi\) | ||||
0.560249 | + | 0.828324i | \(0.310705\pi\) | |||||||
\(920\) | 7.46477 | 0.246106 | ||||||||
\(921\) | −24.5466 | −0.808837 | ||||||||
\(922\) | −28.6874 | −0.944768 | ||||||||
\(923\) | 31.5538 | 1.03861 | ||||||||
\(924\) | 11.2041 | 0.368588 | ||||||||
\(925\) | 10.2217 | 0.336086 | ||||||||
\(926\) | −6.94892 | −0.228356 | ||||||||
\(927\) | −21.2652 | −0.698442 | ||||||||
\(928\) | 8.04319 | 0.264031 | ||||||||
\(929\) | 10.5337 | 0.345600 | 0.172800 | − | 0.984957i | \(-0.444718\pi\) | ||||
0.172800 | + | 0.984957i | \(0.444718\pi\) | |||||||
\(930\) | 6.20325 | 0.203413 | ||||||||
\(931\) | 78.4346 | 2.57059 | ||||||||
\(932\) | 6.65456 | 0.217977 | ||||||||
\(933\) | −10.0021 | −0.327453 | ||||||||
\(934\) | −25.0640 | −0.820118 | ||||||||
\(935\) | −2.28911 | −0.0748618 | ||||||||
\(936\) | −6.06330 | −0.198185 | ||||||||
\(937\) | 5.91694 | 0.193298 | 0.0966490 | − | 0.995319i | \(-0.469188\pi\) | ||||
0.0966490 | + | 0.995319i | \(0.469188\pi\) | |||||||
\(938\) | −22.3167 | −0.728665 | ||||||||
\(939\) | −15.5965 | −0.508972 | ||||||||
\(940\) | 9.31889 | 0.303949 | ||||||||
\(941\) | −26.3145 | −0.857829 | −0.428914 | − | 0.903345i | \(-0.641104\pi\) | ||||
−0.428914 | + | 0.903345i | \(0.641104\pi\) | |||||||
\(942\) | −29.3750 | −0.957090 | ||||||||
\(943\) | −23.3451 | −0.760220 | ||||||||
\(944\) | 6.55249 | 0.213265 | ||||||||
\(945\) | 15.2198 | 0.495100 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | −44.4225 | −1.44354 | −0.721769 | − | 0.692134i | \(-0.756671\pi\) | ||||
−0.721769 | + | 0.692134i | \(0.756671\pi\) | |||||||
\(948\) | 24.7641 | 0.804299 | ||||||||
\(949\) | 36.2105 | 1.17544 | ||||||||
\(950\) | 3.91291 | 0.126952 | ||||||||
\(951\) | 28.3989 | 0.920898 | ||||||||
\(952\) | 11.9045 | 0.385826 | ||||||||
\(953\) | 31.1009 | 1.00746 | 0.503729 | − | 0.863862i | \(-0.331961\pi\) | ||||
0.503729 | + | 0.863862i | \(0.331961\pi\) | |||||||
\(954\) | −1.10093 | −0.0356438 | ||||||||
\(955\) | −22.3373 | −0.722817 | ||||||||
\(956\) | −15.6396 | −0.505819 | ||||||||
\(957\) | 17.3285 | 0.560152 | ||||||||
\(958\) | −24.7063 | −0.798223 | ||||||||
\(959\) | −23.6152 | −0.762574 | ||||||||
\(960\) | −2.15443 | −0.0695341 | ||||||||
\(961\) | −22.7097 | −0.732570 | ||||||||
\(962\) | −37.7543 | −1.21725 | ||||||||
\(963\) | −26.8422 | −0.864979 | ||||||||
\(964\) | −0.896388 | −0.0288707 | ||||||||
\(965\) | −5.77134 | −0.185786 | ||||||||
\(966\) | −83.6361 | −2.69095 | ||||||||
\(967\) | 42.4769 | 1.36596 | 0.682982 | − | 0.730435i | \(-0.260683\pi\) | ||||
0.682982 | + | 0.730435i | \(0.260683\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 19.2974 | 0.619923 | ||||||||
\(970\) | −5.40206 | −0.173450 | ||||||||
\(971\) | −17.2183 | −0.552562 | −0.276281 | − | 0.961077i | \(-0.589102\pi\) | ||||
−0.276281 | + | 0.961077i | \(0.589102\pi\) | |||||||
\(972\) | −15.4144 | −0.494416 | ||||||||
\(973\) | 92.2171 | 2.95635 | ||||||||
\(974\) | −27.4194 | −0.878573 | ||||||||
\(975\) | −7.95753 | −0.254845 | ||||||||
\(976\) | 7.70264 | 0.246555 | ||||||||
\(977\) | 9.75852 | 0.312203 | 0.156101 | − | 0.987741i | \(-0.450107\pi\) | ||||
0.156101 | + | 0.987741i | \(0.450107\pi\) | |||||||
\(978\) | −40.1952 | −1.28530 | ||||||||
\(979\) | −5.34397 | −0.170794 | ||||||||
\(980\) | −20.0451 | −0.640316 | ||||||||
\(981\) | 27.6077 | 0.881445 | ||||||||
\(982\) | −26.8303 | −0.856191 | ||||||||
\(983\) | 45.8749 | 1.46318 | 0.731591 | − | 0.681744i | \(-0.238778\pi\) | ||||
0.731591 | + | 0.681744i | \(0.238778\pi\) | |||||||
\(984\) | 6.73771 | 0.214790 | ||||||||
\(985\) | −7.78147 | −0.247938 | ||||||||
\(986\) | 18.4117 | 0.586349 | ||||||||
\(987\) | −104.410 | −3.32340 | ||||||||
\(988\) | −14.4526 | −0.459797 | ||||||||
\(989\) | −7.46477 | −0.237366 | ||||||||
\(990\) | −1.64159 | −0.0521731 | ||||||||
\(991\) | −14.7351 | −0.468077 | −0.234039 | − | 0.972227i | \(-0.575194\pi\) | ||||
−0.234039 | + | 0.972227i | \(0.575194\pi\) | |||||||
\(992\) | −2.87929 | −0.0914177 | ||||||||
\(993\) | 11.7559 | 0.373061 | ||||||||
\(994\) | −44.4275 | −1.40915 | ||||||||
\(995\) | 17.2211 | 0.545946 | ||||||||
\(996\) | −13.3255 | −0.422236 | ||||||||
\(997\) | 11.3414 | 0.359185 | 0.179592 | − | 0.983741i | \(-0.442522\pi\) | ||||
0.179592 | + | 0.983741i | \(0.442522\pi\) | |||||||
\(998\) | −19.6464 | −0.621897 | ||||||||
\(999\) | −29.9148 | −0.946463 |
(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 | 4730.2.a.bf.1.10 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.bf.1.10 | ✓ | 13 | 1.1 | even | 1 | trivial |