Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.04892 | 1.36352 | 0.681759 | − | 0.731577i | \(-0.261215\pi\) | ||||
0.681759 | + | 0.731577i | \(0.261215\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.04892 | −0.964152 | ||||||||
\(11\) | −2.13706 | −0.644349 | −0.322174 | − | 0.946680i | \(-0.604414\pi\) | ||||
−0.322174 | + | 0.946680i | \(0.604414\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −3.04892 | −0.787227 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.40581 | −0.340960 | −0.170480 | − | 0.985361i | \(-0.554532\pi\) | ||||
−0.170480 | + | 0.985361i | \(0.554532\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.13706 | −0.490276 | −0.245138 | − | 0.969488i | \(-0.578833\pi\) | ||||
−0.245138 | + | 0.969488i | \(0.578833\pi\) | |||||||
\(20\) | 3.04892 | 0.681759 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 2.13706 | 0.455623 | ||||||||
\(23\) | −2.26875 | −0.473067 | −0.236534 | − | 0.971623i | \(-0.576011\pi\) | ||||
−0.236534 | + | 0.971623i | \(0.576011\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.29590 | 0.859179 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.58211 | −0.479485 | −0.239742 | − | 0.970837i | \(-0.577063\pi\) | ||||
−0.239742 | + | 0.970837i | \(0.577063\pi\) | |||||||
\(30\) | 3.04892 | 0.556654 | ||||||||
\(31\) | 6.34481 | 1.13956 | 0.569781 | − | 0.821796i | \(-0.307028\pi\) | ||||
0.569781 | + | 0.821796i | \(0.307028\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.13706 | 0.372015 | ||||||||
\(34\) | 1.40581 | 0.241095 | ||||||||
\(35\) | 3.04892 | 0.515361 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.6528 | −1.75131 | −0.875654 | − | 0.482939i | \(-0.839569\pi\) | ||||
−0.875654 | + | 0.482939i | \(0.839569\pi\) | |||||||
\(38\) | 2.13706 | 0.346677 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.04892 | −0.482076 | ||||||||
\(41\) | 4.43296 | 0.692312 | 0.346156 | − | 0.938177i | \(-0.387487\pi\) | ||||
0.346156 | + | 0.938177i | \(0.387487\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −9.55496 | −1.45712 | −0.728559 | − | 0.684983i | \(-0.759809\pi\) | ||||
−0.728559 | + | 0.684983i | \(0.759809\pi\) | |||||||
\(44\) | −2.13706 | −0.322174 | ||||||||
\(45\) | 3.04892 | 0.454506 | ||||||||
\(46\) | 2.26875 | 0.334509 | ||||||||
\(47\) | 3.98792 | 0.581698 | 0.290849 | − | 0.956769i | \(-0.406062\pi\) | ||||
0.290849 | + | 0.956769i | \(0.406062\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.29590 | −0.607532 | ||||||||
\(51\) | 1.40581 | 0.196853 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.46681 | 0.888285 | 0.444142 | − | 0.895956i | \(-0.353508\pi\) | ||||
0.444142 | + | 0.895956i | \(0.353508\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −6.51573 | −0.878581 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 2.13706 | 0.283061 | ||||||||
\(58\) | 2.58211 | 0.339047 | ||||||||
\(59\) | 3.44504 | 0.448506 | 0.224253 | − | 0.974531i | \(-0.428006\pi\) | ||||
0.224253 | + | 0.974531i | \(0.428006\pi\) | |||||||
\(60\) | −3.04892 | −0.393614 | ||||||||
\(61\) | 9.98792 | 1.27882 | 0.639411 | − | 0.768865i | \(-0.279178\pi\) | ||||
0.639411 | + | 0.768865i | \(0.279178\pi\) | |||||||
\(62\) | −6.34481 | −0.805792 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.13706 | −0.263054 | ||||||||
\(67\) | −11.3937 | −1.39197 | −0.695983 | − | 0.718058i | \(-0.745031\pi\) | ||||
−0.695983 | + | 0.718058i | \(0.745031\pi\) | |||||||
\(68\) | −1.40581 | −0.170480 | ||||||||
\(69\) | 2.26875 | 0.273125 | ||||||||
\(70\) | −3.04892 | −0.364415 | ||||||||
\(71\) | −4.21983 | −0.500802 | −0.250401 | − | 0.968142i | \(-0.580562\pi\) | ||||
−0.250401 | + | 0.968142i | \(0.580562\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −5.84548 | −0.684161 | −0.342081 | − | 0.939671i | \(-0.611132\pi\) | ||||
−0.342081 | + | 0.939671i | \(0.611132\pi\) | |||||||
\(74\) | 10.6528 | 1.23836 | ||||||||
\(75\) | −4.29590 | −0.496047 | ||||||||
\(76\) | −2.13706 | −0.245138 | ||||||||
\(77\) | −2.13706 | −0.243541 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.7071 | −1.20464 | −0.602321 | − | 0.798254i | \(-0.705757\pi\) | ||||
−0.602321 | + | 0.798254i | \(0.705757\pi\) | |||||||
\(80\) | 3.04892 | 0.340879 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.43296 | −0.489539 | ||||||||
\(83\) | −8.94869 | −0.982246 | −0.491123 | − | 0.871090i | \(-0.663414\pi\) | ||||
−0.491123 | + | 0.871090i | \(0.663414\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −4.28621 | −0.464905 | ||||||||
\(86\) | 9.55496 | 1.03034 | ||||||||
\(87\) | 2.58211 | 0.276831 | ||||||||
\(88\) | 2.13706 | 0.227812 | ||||||||
\(89\) | 3.73556 | 0.395969 | 0.197984 | − | 0.980205i | \(-0.436560\pi\) | ||||
0.197984 | + | 0.980205i | \(0.436560\pi\) | |||||||
\(90\) | −3.04892 | −0.321384 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.26875 | −0.236534 | ||||||||
\(93\) | −6.34481 | −0.657927 | ||||||||
\(94\) | −3.98792 | −0.411322 | ||||||||
\(95\) | −6.51573 | −0.668500 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 5.10321 | 0.518153 | 0.259076 | − | 0.965857i | \(-0.416582\pi\) | ||||
0.259076 | + | 0.965857i | \(0.416582\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −2.13706 | −0.214783 | ||||||||
\(100\) | 4.29590 | 0.429590 | ||||||||
\(101\) | −12.2174 | −1.21568 | −0.607840 | − | 0.794059i | \(-0.707964\pi\) | ||||
−0.607840 | + | 0.794059i | \(0.707964\pi\) | |||||||
\(102\) | −1.40581 | −0.139196 | ||||||||
\(103\) | −4.53319 | −0.446668 | −0.223334 | − | 0.974742i | \(-0.571694\pi\) | ||||
−0.223334 | + | 0.974742i | \(0.571694\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.04892 | −0.297544 | ||||||||
\(106\) | −6.46681 | −0.628112 | ||||||||
\(107\) | −12.5254 | −1.21088 | −0.605439 | − | 0.795892i | \(-0.707002\pi\) | ||||
−0.605439 | + | 0.795892i | \(0.707002\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 1.15883 | 0.110996 | 0.0554981 | − | 0.998459i | \(-0.482325\pi\) | ||||
0.0554981 | + | 0.998459i | \(0.482325\pi\) | |||||||
\(110\) | 6.51573 | 0.621250 | ||||||||
\(111\) | 10.6528 | 1.01112 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 4.34721 | 0.408951 | 0.204475 | − | 0.978872i | \(-0.434451\pi\) | ||||
0.204475 | + | 0.978872i | \(0.434451\pi\) | |||||||
\(114\) | −2.13706 | −0.200154 | ||||||||
\(115\) | −6.91723 | −0.645035 | ||||||||
\(116\) | −2.58211 | −0.239742 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.44504 | −0.317142 | ||||||||
\(119\) | −1.40581 | −0.128871 | ||||||||
\(120\) | 3.04892 | 0.278327 | ||||||||
\(121\) | −6.43296 | −0.584815 | ||||||||
\(122\) | −9.98792 | −0.904264 | ||||||||
\(123\) | −4.43296 | −0.399707 | ||||||||
\(124\) | 6.34481 | 0.569781 | ||||||||
\(125\) | −2.14675 | −0.192011 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 18.2959 | 1.62350 | 0.811749 | − | 0.584006i | \(-0.198516\pi\) | ||||
0.811749 | + | 0.584006i | \(0.198516\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.55496 | 0.841267 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.52781 | 0.308226 | 0.154113 | − | 0.988053i | \(-0.450748\pi\) | ||||
0.154113 | + | 0.988053i | \(0.450748\pi\) | |||||||
\(132\) | 2.13706 | 0.186007 | ||||||||
\(133\) | −2.13706 | −0.185307 | ||||||||
\(134\) | 11.3937 | 0.984268 | ||||||||
\(135\) | −3.04892 | −0.262409 | ||||||||
\(136\) | 1.40581 | 0.120547 | ||||||||
\(137\) | −0.249373 | −0.0213053 | −0.0106527 | − | 0.999943i | \(-0.503391\pi\) | ||||
−0.0106527 | + | 0.999943i | \(0.503391\pi\) | |||||||
\(138\) | −2.26875 | −0.193129 | ||||||||
\(139\) | 0.168522 | 0.0142939 | 0.00714694 | − | 0.999974i | \(-0.497725\pi\) | ||||
0.00714694 | + | 0.999974i | \(0.497725\pi\) | |||||||
\(140\) | 3.04892 | 0.257681 | ||||||||
\(141\) | −3.98792 | −0.335843 | ||||||||
\(142\) | 4.21983 | 0.354120 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −7.87263 | −0.653786 | ||||||||
\(146\) | 5.84548 | 0.483775 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −10.6528 | −0.875654 | ||||||||
\(149\) | −16.3327 | −1.33803 | −0.669015 | − | 0.743249i | \(-0.733284\pi\) | ||||
−0.669015 | + | 0.743249i | \(0.733284\pi\) | |||||||
\(150\) | 4.29590 | 0.350759 | ||||||||
\(151\) | −24.3448 | −1.98115 | −0.990576 | − | 0.136961i | \(-0.956267\pi\) | ||||
−0.990576 | + | 0.136961i | \(0.956267\pi\) | |||||||
\(152\) | 2.13706 | 0.173339 | ||||||||
\(153\) | −1.40581 | −0.113653 | ||||||||
\(154\) | 2.13706 | 0.172209 | ||||||||
\(155\) | 19.3448 | 1.55381 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0978 | −0.965512 | −0.482756 | − | 0.875755i | \(-0.660364\pi\) | ||||
−0.482756 | + | 0.875755i | \(0.660364\pi\) | |||||||
\(158\) | 10.7071 | 0.851810 | ||||||||
\(159\) | −6.46681 | −0.512852 | ||||||||
\(160\) | −3.04892 | −0.241038 | ||||||||
\(161\) | −2.26875 | −0.178803 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −14.0707 | −1.10210 | −0.551051 | − | 0.834472i | \(-0.685773\pi\) | ||||
−0.551051 | + | 0.834472i | \(0.685773\pi\) | |||||||
\(164\) | 4.43296 | 0.346156 | ||||||||
\(165\) | 6.51573 | 0.507249 | ||||||||
\(166\) | 8.94869 | 0.694553 | ||||||||
\(167\) | −19.9541 | −1.54409 | −0.772046 | − | 0.635567i | \(-0.780767\pi\) | ||||
−0.772046 | + | 0.635567i | \(0.780767\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.28621 | 0.328737 | ||||||||
\(171\) | −2.13706 | −0.163425 | ||||||||
\(172\) | −9.55496 | −0.728559 | ||||||||
\(173\) | −6.61596 | −0.503002 | −0.251501 | − | 0.967857i | \(-0.580924\pi\) | ||||
−0.251501 | + | 0.967857i | \(0.580924\pi\) | |||||||
\(174\) | −2.58211 | −0.195749 | ||||||||
\(175\) | 4.29590 | 0.324739 | ||||||||
\(176\) | −2.13706 | −0.161087 | ||||||||
\(177\) | −3.44504 | −0.258945 | ||||||||
\(178\) | −3.73556 | −0.279992 | ||||||||
\(179\) | −7.49396 | −0.560125 | −0.280062 | − | 0.959982i | \(-0.590355\pi\) | ||||
−0.280062 | + | 0.959982i | \(0.590355\pi\) | |||||||
\(180\) | 3.04892 | 0.227253 | ||||||||
\(181\) | 19.1226 | 1.42137 | 0.710685 | − | 0.703510i | \(-0.248385\pi\) | ||||
0.710685 | + | 0.703510i | \(0.248385\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.98792 | −0.738328 | ||||||||
\(184\) | 2.26875 | 0.167254 | ||||||||
\(185\) | −32.4795 | −2.38794 | ||||||||
\(186\) | 6.34481 | 0.465224 | ||||||||
\(187\) | 3.00431 | 0.219697 | ||||||||
\(188\) | 3.98792 | 0.290849 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 6.51573 | 0.472701 | ||||||||
\(191\) | 23.2403 | 1.68161 | 0.840804 | − | 0.541340i | \(-0.182083\pi\) | ||||
0.840804 | + | 0.541340i | \(0.182083\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −4.00538 | −0.288313 | −0.144157 | − | 0.989555i | \(-0.546047\pi\) | ||||
−0.144157 | + | 0.989555i | \(0.546047\pi\) | |||||||
\(194\) | −5.10321 | −0.366389 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 7.75840 | 0.552763 | 0.276381 | − | 0.961048i | \(-0.410865\pi\) | ||||
0.276381 | + | 0.961048i | \(0.410865\pi\) | |||||||
\(198\) | 2.13706 | 0.151874 | ||||||||
\(199\) | 14.5526 | 1.03160 | 0.515802 | − | 0.856708i | \(-0.327494\pi\) | ||||
0.515802 | + | 0.856708i | \(0.327494\pi\) | |||||||
\(200\) | −4.29590 | −0.303766 | ||||||||
\(201\) | 11.3937 | 0.803652 | ||||||||
\(202\) | 12.2174 | 0.859616 | ||||||||
\(203\) | −2.58211 | −0.181228 | ||||||||
\(204\) | 1.40581 | 0.0984266 | ||||||||
\(205\) | 13.5157 | 0.943979 | ||||||||
\(206\) | 4.53319 | 0.315842 | ||||||||
\(207\) | −2.26875 | −0.157689 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.56704 | 0.315909 | ||||||||
\(210\) | 3.04892 | 0.210395 | ||||||||
\(211\) | 3.80194 | 0.261736 | 0.130868 | − | 0.991400i | \(-0.458224\pi\) | ||||
0.130868 | + | 0.991400i | \(0.458224\pi\) | |||||||
\(212\) | 6.46681 | 0.444142 | ||||||||
\(213\) | 4.21983 | 0.289138 | ||||||||
\(214\) | 12.5254 | 0.856220 | ||||||||
\(215\) | −29.1323 | −1.98680 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 6.34481 | 0.430714 | ||||||||
\(218\) | −1.15883 | −0.0784861 | ||||||||
\(219\) | 5.84548 | 0.395001 | ||||||||
\(220\) | −6.51573 | −0.439290 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.6528 | −0.714969 | ||||||||
\(223\) | 23.1347 | 1.54921 | 0.774606 | − | 0.632444i | \(-0.217948\pi\) | ||||
0.774606 | + | 0.632444i | \(0.217948\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 4.29590 | 0.286393 | ||||||||
\(226\) | −4.34721 | −0.289172 | ||||||||
\(227\) | 2.72348 | 0.180764 | 0.0903819 | − | 0.995907i | \(-0.471191\pi\) | ||||
0.0903819 | + | 0.995907i | \(0.471191\pi\) | |||||||
\(228\) | 2.13706 | 0.141530 | ||||||||
\(229\) | −11.7385 | −0.775705 | −0.387852 | − | 0.921721i | \(-0.626783\pi\) | ||||
−0.387852 | + | 0.921721i | \(0.626783\pi\) | |||||||
\(230\) | 6.91723 | 0.456109 | ||||||||
\(231\) | 2.13706 | 0.140608 | ||||||||
\(232\) | 2.58211 | 0.169524 | ||||||||
\(233\) | 9.92931 | 0.650491 | 0.325245 | − | 0.945630i | \(-0.394553\pi\) | ||||
0.325245 | + | 0.945630i | \(0.394553\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1588 | 0.793155 | ||||||||
\(236\) | 3.44504 | 0.224253 | ||||||||
\(237\) | 10.7071 | 0.695500 | ||||||||
\(238\) | 1.40581 | 0.0911253 | ||||||||
\(239\) | −22.1172 | −1.43064 | −0.715322 | − | 0.698795i | \(-0.753720\pi\) | ||||
−0.715322 | + | 0.698795i | \(0.753720\pi\) | |||||||
\(240\) | −3.04892 | −0.196807 | ||||||||
\(241\) | −24.5429 | −1.58095 | −0.790473 | − | 0.612497i | \(-0.790165\pi\) | ||||
−0.790473 | + | 0.612497i | \(0.790165\pi\) | |||||||
\(242\) | 6.43296 | 0.413526 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.98792 | 0.639411 | ||||||||
\(245\) | 3.04892 | 0.194788 | ||||||||
\(246\) | 4.43296 | 0.282635 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.34481 | −0.402896 | ||||||||
\(249\) | 8.94869 | 0.567100 | ||||||||
\(250\) | 2.14675 | 0.135773 | ||||||||
\(251\) | 27.2489 | 1.71994 | 0.859968 | − | 0.510349i | \(-0.170484\pi\) | ||||
0.859968 | + | 0.510349i | \(0.170484\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 4.84846 | 0.304820 | ||||||||
\(254\) | −18.2959 | −1.14799 | ||||||||
\(255\) | 4.28621 | 0.268413 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.2349 | 1.07508 | 0.537542 | − | 0.843237i | \(-0.319353\pi\) | ||||
0.537542 | + | 0.843237i | \(0.319353\pi\) | |||||||
\(258\) | −9.55496 | −0.594866 | ||||||||
\(259\) | −10.6528 | −0.661932 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.58211 | −0.159828 | ||||||||
\(262\) | −3.52781 | −0.217949 | ||||||||
\(263\) | 8.46011 | 0.521673 | 0.260836 | − | 0.965383i | \(-0.416002\pi\) | ||||
0.260836 | + | 0.965383i | \(0.416002\pi\) | |||||||
\(264\) | −2.13706 | −0.131527 | ||||||||
\(265\) | 19.7168 | 1.21119 | ||||||||
\(266\) | 2.13706 | 0.131032 | ||||||||
\(267\) | −3.73556 | −0.228613 | ||||||||
\(268\) | −11.3937 | −0.695983 | ||||||||
\(269\) | 1.29590 | 0.0790122 | 0.0395061 | − | 0.999219i | \(-0.487422\pi\) | ||||
0.0395061 | + | 0.999219i | \(0.487422\pi\) | |||||||
\(270\) | 3.04892 | 0.185551 | ||||||||
\(271\) | 5.46250 | 0.331823 | 0.165912 | − | 0.986141i | \(-0.446943\pi\) | ||||
0.165912 | + | 0.986141i | \(0.446943\pi\) | |||||||
\(272\) | −1.40581 | −0.0852399 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.249373 | 0.0150651 | ||||||||
\(275\) | −9.18060 | −0.553611 | ||||||||
\(276\) | 2.26875 | 0.136563 | ||||||||
\(277\) | 1.01746 | 0.0611332 | 0.0305666 | − | 0.999533i | \(-0.490269\pi\) | ||||
0.0305666 | + | 0.999533i | \(0.490269\pi\) | |||||||
\(278\) | −0.168522 | −0.0101073 | ||||||||
\(279\) | 6.34481 | 0.379854 | ||||||||
\(280\) | −3.04892 | −0.182208 | ||||||||
\(281\) | 23.7482 | 1.41670 | 0.708350 | − | 0.705861i | \(-0.249440\pi\) | ||||
0.708350 | + | 0.705861i | \(0.249440\pi\) | |||||||
\(282\) | 3.98792 | 0.237477 | ||||||||
\(283\) | −19.9148 | −1.18381 | −0.591907 | − | 0.806006i | \(-0.701625\pi\) | ||||
−0.591907 | + | 0.806006i | \(0.701625\pi\) | |||||||
\(284\) | −4.21983 | −0.250401 | ||||||||
\(285\) | 6.51573 | 0.385959 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.43296 | 0.261669 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.0237 | −0.883746 | ||||||||
\(290\) | 7.87263 | 0.462296 | ||||||||
\(291\) | −5.10321 | −0.299156 | ||||||||
\(292\) | −5.84548 | −0.342081 | ||||||||
\(293\) | −9.15213 | −0.534673 | −0.267337 | − | 0.963603i | \(-0.586144\pi\) | ||||
−0.267337 | + | 0.963603i | \(0.586144\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 10.5036 | 0.611546 | ||||||||
\(296\) | 10.6528 | 0.619181 | ||||||||
\(297\) | 2.13706 | 0.124005 | ||||||||
\(298\) | 16.3327 | 0.946130 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.29590 | −0.248024 | ||||||||
\(301\) | −9.55496 | −0.550739 | ||||||||
\(302\) | 24.3448 | 1.40089 | ||||||||
\(303\) | 12.2174 | 0.701874 | ||||||||
\(304\) | −2.13706 | −0.122569 | ||||||||
\(305\) | 30.4523 | 1.74370 | ||||||||
\(306\) | 1.40581 | 0.0803650 | ||||||||
\(307\) | −22.2784 | −1.27150 | −0.635749 | − | 0.771896i | \(-0.719309\pi\) | ||||
−0.635749 | + | 0.771896i | \(0.719309\pi\) | |||||||
\(308\) | −2.13706 | −0.121770 | ||||||||
\(309\) | 4.53319 | 0.257884 | ||||||||
\(310\) | −19.3448 | −1.09871 | ||||||||
\(311\) | −0.254749 | −0.0144455 | −0.00722275 | − | 0.999974i | \(-0.502299\pi\) | ||||
−0.00722275 | + | 0.999974i | \(0.502299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.1129 | 1.36294 | 0.681471 | − | 0.731845i | \(-0.261341\pi\) | ||||
0.681471 | + | 0.731845i | \(0.261341\pi\) | |||||||
\(314\) | 12.0978 | 0.682720 | ||||||||
\(315\) | 3.04892 | 0.171787 | ||||||||
\(316\) | −10.7071 | −0.602321 | ||||||||
\(317\) | 12.8321 | 0.720721 | 0.360360 | − | 0.932813i | \(-0.382654\pi\) | ||||
0.360360 | + | 0.932813i | \(0.382654\pi\) | |||||||
\(318\) | 6.46681 | 0.362641 | ||||||||
\(319\) | 5.51812 | 0.308956 | ||||||||
\(320\) | 3.04892 | 0.170440 | ||||||||
\(321\) | 12.5254 | 0.699101 | ||||||||
\(322\) | 2.26875 | 0.126432 | ||||||||
\(323\) | 3.00431 | 0.167164 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.0707 | 0.779303 | ||||||||
\(327\) | −1.15883 | −0.0640836 | ||||||||
\(328\) | −4.43296 | −0.244769 | ||||||||
\(329\) | 3.98792 | 0.219861 | ||||||||
\(330\) | −6.51573 | −0.358679 | ||||||||
\(331\) | −29.0707 | −1.59787 | −0.798935 | − | 0.601418i | \(-0.794603\pi\) | ||||
−0.798935 | + | 0.601418i | \(0.794603\pi\) | |||||||
\(332\) | −8.94869 | −0.491123 | ||||||||
\(333\) | −10.6528 | −0.583769 | ||||||||
\(334\) | 19.9541 | 1.09184 | ||||||||
\(335\) | −34.7385 | −1.89797 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 17.7821 | 0.968652 | 0.484326 | − | 0.874888i | \(-0.339065\pi\) | ||||
0.484326 | + | 0.874888i | \(0.339065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.34721 | −0.236108 | ||||||||
\(340\) | −4.28621 | −0.232452 | ||||||||
\(341\) | −13.5593 | −0.734276 | ||||||||
\(342\) | 2.13706 | 0.115559 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.55496 | 0.515169 | ||||||||
\(345\) | 6.91723 | 0.372411 | ||||||||
\(346\) | 6.61596 | 0.355676 | ||||||||
\(347\) | −10.5144 | −0.564443 | −0.282221 | − | 0.959349i | \(-0.591071\pi\) | ||||
−0.282221 | + | 0.959349i | \(0.591071\pi\) | |||||||
\(348\) | 2.58211 | 0.138415 | ||||||||
\(349\) | −18.1274 | −0.970336 | −0.485168 | − | 0.874421i | \(-0.661242\pi\) | ||||
−0.485168 | + | 0.874421i | \(0.661242\pi\) | |||||||
\(350\) | −4.29590 | −0.229625 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.13706 | 0.113906 | ||||||||
\(353\) | 16.1715 | 0.860722 | 0.430361 | − | 0.902657i | \(-0.358386\pi\) | ||||
0.430361 | + | 0.902657i | \(0.358386\pi\) | |||||||
\(354\) | 3.44504 | 0.183102 | ||||||||
\(355\) | −12.8659 | −0.682852 | ||||||||
\(356\) | 3.73556 | 0.197984 | ||||||||
\(357\) | 1.40581 | 0.0744035 | ||||||||
\(358\) | 7.49396 | 0.396068 | ||||||||
\(359\) | −7.77240 | −0.410211 | −0.205106 | − | 0.978740i | \(-0.565754\pi\) | ||||
−0.205106 | + | 0.978740i | \(0.565754\pi\) | |||||||
\(360\) | −3.04892 | −0.160692 | ||||||||
\(361\) | −14.4330 | −0.759629 | ||||||||
\(362\) | −19.1226 | −1.00506 | ||||||||
\(363\) | 6.43296 | 0.337643 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.8224 | −0.932866 | ||||||||
\(366\) | 9.98792 | 0.522077 | ||||||||
\(367\) | −2.07846 | −0.108495 | −0.0542473 | − | 0.998528i | \(-0.517276\pi\) | ||||
−0.0542473 | + | 0.998528i | \(0.517276\pi\) | |||||||
\(368\) | −2.26875 | −0.118267 | ||||||||
\(369\) | 4.43296 | 0.230771 | ||||||||
\(370\) | 32.4795 | 1.68853 | ||||||||
\(371\) | 6.46681 | 0.335740 | ||||||||
\(372\) | −6.34481 | −0.328963 | ||||||||
\(373\) | 8.10752 | 0.419792 | 0.209896 | − | 0.977724i | \(-0.432688\pi\) | ||||
0.209896 | + | 0.977724i | \(0.432688\pi\) | |||||||
\(374\) | −3.00431 | −0.155349 | ||||||||
\(375\) | 2.14675 | 0.110858 | ||||||||
\(376\) | −3.98792 | −0.205661 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −13.4222 | −0.689452 | −0.344726 | − | 0.938703i | \(-0.612028\pi\) | ||||
−0.344726 | + | 0.938703i | \(0.612028\pi\) | |||||||
\(380\) | −6.51573 | −0.334250 | ||||||||
\(381\) | −18.2959 | −0.937327 | ||||||||
\(382\) | −23.2403 | −1.18908 | ||||||||
\(383\) | −12.4209 | −0.634677 | −0.317339 | − | 0.948312i | \(-0.602789\pi\) | ||||
−0.317339 | + | 0.948312i | \(0.602789\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −6.51573 | −0.332072 | ||||||||
\(386\) | 4.00538 | 0.203868 | ||||||||
\(387\) | −9.55496 | −0.485706 | ||||||||
\(388\) | 5.10321 | 0.259076 | ||||||||
\(389\) | 37.5666 | 1.90470 | 0.952350 | − | 0.305007i | \(-0.0986587\pi\) | ||||
0.952350 | + | 0.305007i | \(0.0986587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.18944 | 0.161297 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −3.52781 | −0.177955 | ||||||||
\(394\) | −7.75840 | −0.390862 | ||||||||
\(395\) | −32.6450 | −1.64255 | ||||||||
\(396\) | −2.13706 | −0.107391 | ||||||||
\(397\) | −36.1159 | −1.81260 | −0.906302 | − | 0.422630i | \(-0.861107\pi\) | ||||
−0.906302 | + | 0.422630i | \(0.861107\pi\) | |||||||
\(398\) | −14.5526 | −0.729454 | ||||||||
\(399\) | 2.13706 | 0.106987 | ||||||||
\(400\) | 4.29590 | 0.214795 | ||||||||
\(401\) | 9.82610 | 0.490692 | 0.245346 | − | 0.969436i | \(-0.421098\pi\) | ||||
0.245346 | + | 0.969436i | \(0.421098\pi\) | |||||||
\(402\) | −11.3937 | −0.568268 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.2174 | −0.607840 | ||||||||
\(405\) | 3.04892 | 0.151502 | ||||||||
\(406\) | 2.58211 | 0.128148 | ||||||||
\(407\) | 22.7657 | 1.12845 | ||||||||
\(408\) | −1.40581 | −0.0695981 | ||||||||
\(409\) | 3.09352 | 0.152965 | 0.0764824 | − | 0.997071i | \(-0.475631\pi\) | ||||
0.0764824 | + | 0.997071i | \(0.475631\pi\) | |||||||
\(410\) | −13.5157 | −0.667494 | ||||||||
\(411\) | 0.249373 | 0.0123006 | ||||||||
\(412\) | −4.53319 | −0.223334 | ||||||||
\(413\) | 3.44504 | 0.169519 | ||||||||
\(414\) | 2.26875 | 0.111503 | ||||||||
\(415\) | −27.2838 | −1.33931 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.168522 | −0.00825257 | ||||||||
\(418\) | −4.56704 | −0.223381 | ||||||||
\(419\) | −20.1535 | −0.984561 | −0.492280 | − | 0.870437i | \(-0.663837\pi\) | ||||
−0.492280 | + | 0.870437i | \(0.663837\pi\) | |||||||
\(420\) | −3.04892 | −0.148772 | ||||||||
\(421\) | −11.2034 | −0.546022 | −0.273011 | − | 0.962011i | \(-0.588020\pi\) | ||||
−0.273011 | + | 0.962011i | \(0.588020\pi\) | |||||||
\(422\) | −3.80194 | −0.185075 | ||||||||
\(423\) | 3.98792 | 0.193899 | ||||||||
\(424\) | −6.46681 | −0.314056 | ||||||||
\(425\) | −6.03923 | −0.292946 | ||||||||
\(426\) | −4.21983 | −0.204452 | ||||||||
\(427\) | 9.98792 | 0.483349 | ||||||||
\(428\) | −12.5254 | −0.605439 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 29.1323 | 1.40488 | ||||||||
\(431\) | 38.9898 | 1.87807 | 0.939037 | − | 0.343816i | \(-0.111720\pi\) | ||||
0.939037 | + | 0.343816i | \(0.111720\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 23.4426 | 1.12658 | 0.563291 | − | 0.826259i | \(-0.309535\pi\) | ||||
0.563291 | + | 0.826259i | \(0.309535\pi\) | |||||||
\(434\) | −6.34481 | −0.304561 | ||||||||
\(435\) | 7.87263 | 0.377463 | ||||||||
\(436\) | 1.15883 | 0.0554981 | ||||||||
\(437\) | 4.84846 | 0.231933 | ||||||||
\(438\) | −5.84548 | −0.279308 | ||||||||
\(439\) | −26.8592 | −1.28192 | −0.640960 | − | 0.767574i | \(-0.721464\pi\) | ||||
−0.640960 | + | 0.767574i | \(0.721464\pi\) | |||||||
\(440\) | 6.51573 | 0.310625 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.1347 | −0.529024 | −0.264512 | − | 0.964382i | \(-0.585211\pi\) | ||||
−0.264512 | + | 0.964382i | \(0.585211\pi\) | |||||||
\(444\) | 10.6528 | 0.505559 | ||||||||
\(445\) | 11.3894 | 0.539910 | ||||||||
\(446\) | −23.1347 | −1.09546 | ||||||||
\(447\) | 16.3327 | 0.772512 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −27.0858 | −1.27826 | −0.639128 | − | 0.769100i | \(-0.720705\pi\) | ||||
−0.639128 | + | 0.769100i | \(0.720705\pi\) | |||||||
\(450\) | −4.29590 | −0.202511 | ||||||||
\(451\) | −9.47352 | −0.446090 | ||||||||
\(452\) | 4.34721 | 0.204475 | ||||||||
\(453\) | 24.3448 | 1.14382 | ||||||||
\(454\) | −2.72348 | −0.127819 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.13706 | −0.100077 | ||||||||
\(457\) | −3.40880 | −0.159457 | −0.0797284 | − | 0.996817i | \(-0.525405\pi\) | ||||
−0.0797284 | + | 0.996817i | \(0.525405\pi\) | |||||||
\(458\) | 11.7385 | 0.548506 | ||||||||
\(459\) | 1.40581 | 0.0656177 | ||||||||
\(460\) | −6.91723 | −0.322518 | ||||||||
\(461\) | 30.9178 | 1.43999 | 0.719993 | − | 0.693981i | \(-0.244145\pi\) | ||||
0.719993 | + | 0.693981i | \(0.244145\pi\) | |||||||
\(462\) | −2.13706 | −0.0994252 | ||||||||
\(463\) | −35.0465 | −1.62875 | −0.814375 | − | 0.580339i | \(-0.802920\pi\) | ||||
−0.814375 | + | 0.580339i | \(0.802920\pi\) | |||||||
\(464\) | −2.58211 | −0.119871 | ||||||||
\(465\) | −19.3448 | −0.897094 | ||||||||
\(466\) | −9.92931 | −0.459967 | ||||||||
\(467\) | 4.04652 | 0.187251 | 0.0936254 | − | 0.995607i | \(-0.470154\pi\) | ||||
0.0936254 | + | 0.995607i | \(0.470154\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.3937 | −0.526114 | ||||||||
\(470\) | −12.1588 | −0.560845 | ||||||||
\(471\) | 12.0978 | 0.557439 | ||||||||
\(472\) | −3.44504 | −0.158571 | ||||||||
\(473\) | 20.4196 | 0.938892 | ||||||||
\(474\) | −10.7071 | −0.491793 | ||||||||
\(475\) | −9.18060 | −0.421235 | ||||||||
\(476\) | −1.40581 | −0.0644353 | ||||||||
\(477\) | 6.46681 | 0.296095 | ||||||||
\(478\) | 22.1172 | 1.01162 | ||||||||
\(479\) | 16.0411 | 0.732939 | 0.366469 | − | 0.930430i | \(-0.380566\pi\) | ||||
0.366469 | + | 0.930430i | \(0.380566\pi\) | |||||||
\(480\) | 3.04892 | 0.139163 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 24.5429 | 1.11790 | ||||||||
\(483\) | 2.26875 | 0.103232 | ||||||||
\(484\) | −6.43296 | −0.292407 | ||||||||
\(485\) | 15.5593 | 0.706510 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −36.7724 | −1.66632 | −0.833158 | − | 0.553035i | \(-0.813470\pi\) | ||||
−0.833158 | + | 0.553035i | \(0.813470\pi\) | |||||||
\(488\) | −9.98792 | −0.452132 | ||||||||
\(489\) | 14.0707 | 0.636298 | ||||||||
\(490\) | −3.04892 | −0.137736 | ||||||||
\(491\) | −7.69069 | −0.347076 | −0.173538 | − | 0.984827i | \(-0.555520\pi\) | ||||
−0.173538 | + | 0.984827i | \(0.555520\pi\) | |||||||
\(492\) | −4.43296 | −0.199853 | ||||||||
\(493\) | 3.62996 | 0.163485 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.51573 | −0.292860 | ||||||||
\(496\) | 6.34481 | 0.284891 | ||||||||
\(497\) | −4.21983 | −0.189285 | ||||||||
\(498\) | −8.94869 | −0.401000 | ||||||||
\(499\) | 21.8213 | 0.976856 | 0.488428 | − | 0.872604i | \(-0.337570\pi\) | ||||
0.488428 | + | 0.872604i | \(0.337570\pi\) | |||||||
\(500\) | −2.14675 | −0.0960057 | ||||||||
\(501\) | 19.9541 | 0.891482 | ||||||||
\(502\) | −27.2489 | −1.21618 | ||||||||
\(503\) | 0.875018 | 0.0390151 | 0.0195076 | − | 0.999810i | \(-0.493790\pi\) | ||||
0.0195076 | + | 0.999810i | \(0.493790\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −37.2500 | −1.65760 | ||||||||
\(506\) | −4.84846 | −0.215540 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.2959 | 0.811749 | ||||||||
\(509\) | 40.2043 | 1.78202 | 0.891012 | − | 0.453980i | \(-0.149996\pi\) | ||||
0.891012 | + | 0.453980i | \(0.149996\pi\) | |||||||
\(510\) | −4.28621 | −0.189796 | ||||||||
\(511\) | −5.84548 | −0.258589 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.13706 | 0.0943537 | ||||||||
\(514\) | −17.2349 | −0.760199 | ||||||||
\(515\) | −13.8213 | −0.609040 | ||||||||
\(516\) | 9.55496 | 0.420634 | ||||||||
\(517\) | −8.52243 | −0.374816 | ||||||||
\(518\) | 10.6528 | 0.468057 | ||||||||
\(519\) | 6.61596 | 0.290408 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.36898 | −0.191408 | −0.0957042 | − | 0.995410i | \(-0.530510\pi\) | ||||
−0.0957042 | + | 0.995410i | \(0.530510\pi\) | |||||||
\(522\) | 2.58211 | 0.113016 | ||||||||
\(523\) | −9.54958 | −0.417574 | −0.208787 | − | 0.977961i | \(-0.566952\pi\) | ||||
−0.208787 | + | 0.977961i | \(0.566952\pi\) | |||||||
\(524\) | 3.52781 | 0.154113 | ||||||||
\(525\) | −4.29590 | −0.187488 | ||||||||
\(526\) | −8.46011 | −0.368878 | ||||||||
\(527\) | −8.91962 | −0.388545 | ||||||||
\(528\) | 2.13706 | 0.0930037 | ||||||||
\(529\) | −17.8528 | −0.776208 | ||||||||
\(530\) | −19.7168 | −0.856442 | ||||||||
\(531\) | 3.44504 | 0.149502 | ||||||||
\(532\) | −2.13706 | −0.0926534 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.73556 | 0.161654 | ||||||||
\(535\) | −38.1890 | −1.65105 | ||||||||
\(536\) | 11.3937 | 0.492134 | ||||||||
\(537\) | 7.49396 | 0.323388 | ||||||||
\(538\) | −1.29590 | −0.0558701 | ||||||||
\(539\) | −2.13706 | −0.0920498 | ||||||||
\(540\) | −3.04892 | −0.131205 | ||||||||
\(541\) | −4.13813 | −0.177912 | −0.0889560 | − | 0.996036i | \(-0.528353\pi\) | ||||
−0.0889560 | + | 0.996036i | \(0.528353\pi\) | |||||||
\(542\) | −5.46250 | −0.234634 | ||||||||
\(543\) | −19.1226 | −0.820629 | ||||||||
\(544\) | 1.40581 | 0.0602737 | ||||||||
\(545\) | 3.53319 | 0.151345 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.0242 | −0.727901 | −0.363950 | − | 0.931418i | \(-0.618572\pi\) | ||||
−0.363950 | + | 0.931418i | \(0.618572\pi\) | |||||||
\(548\) | −0.249373 | −0.0106527 | ||||||||
\(549\) | 9.98792 | 0.426274 | ||||||||
\(550\) | 9.18060 | 0.391462 | ||||||||
\(551\) | 5.51812 | 0.235080 | ||||||||
\(552\) | −2.26875 | −0.0965644 | ||||||||
\(553\) | −10.7071 | −0.455312 | ||||||||
\(554\) | −1.01746 | −0.0432277 | ||||||||
\(555\) | 32.4795 | 1.37868 | ||||||||
\(556\) | 0.168522 | 0.00714694 | ||||||||
\(557\) | 18.9778 | 0.804113 | 0.402057 | − | 0.915615i | \(-0.368295\pi\) | ||||
0.402057 | + | 0.915615i | \(0.368295\pi\) | |||||||
\(558\) | −6.34481 | −0.268597 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.04892 | 0.128840 | ||||||||
\(561\) | −3.00431 | −0.126842 | ||||||||
\(562\) | −23.7482 | −1.00176 | ||||||||
\(563\) | −31.3840 | −1.32268 | −0.661340 | − | 0.750086i | \(-0.730012\pi\) | ||||
−0.661340 | + | 0.750086i | \(0.730012\pi\) | |||||||
\(564\) | −3.98792 | −0.167922 | ||||||||
\(565\) | 13.2543 | 0.557612 | ||||||||
\(566\) | 19.9148 | 0.837083 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 4.21983 | 0.177060 | ||||||||
\(569\) | 30.4196 | 1.27525 | 0.637627 | − | 0.770345i | \(-0.279916\pi\) | ||||
0.637627 | + | 0.770345i | \(0.279916\pi\) | |||||||
\(570\) | −6.51573 | −0.272914 | ||||||||
\(571\) | −26.4534 | −1.10704 | −0.553520 | − | 0.832836i | \(-0.686716\pi\) | ||||
−0.553520 | + | 0.832836i | \(0.686716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.2403 | −0.970876 | ||||||||
\(574\) | −4.43296 | −0.185028 | ||||||||
\(575\) | −9.74632 | −0.406449 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 6.25667 | 0.260469 | 0.130234 | − | 0.991483i | \(-0.458427\pi\) | ||||
0.130234 | + | 0.991483i | \(0.458427\pi\) | |||||||
\(578\) | 15.0237 | 0.624903 | ||||||||
\(579\) | 4.00538 | 0.166458 | ||||||||
\(580\) | −7.87263 | −0.326893 | ||||||||
\(581\) | −8.94869 | −0.371254 | ||||||||
\(582\) | 5.10321 | 0.211535 | ||||||||
\(583\) | −13.8200 | −0.572365 | ||||||||
\(584\) | 5.84548 | 0.241888 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.15213 | 0.378071 | ||||||||
\(587\) | 16.9028 | 0.697651 | 0.348826 | − | 0.937188i | \(-0.386581\pi\) | ||||
0.348826 | + | 0.937188i | \(0.386581\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −13.5593 | −0.558700 | ||||||||
\(590\) | −10.5036 | −0.432428 | ||||||||
\(591\) | −7.75840 | −0.319138 | ||||||||
\(592\) | −10.6528 | −0.437827 | ||||||||
\(593\) | −8.60089 | −0.353196 | −0.176598 | − | 0.984283i | \(-0.556509\pi\) | ||||
−0.176598 | + | 0.984283i | \(0.556509\pi\) | |||||||
\(594\) | −2.13706 | −0.0876848 | ||||||||
\(595\) | −4.28621 | −0.175717 | ||||||||
\(596\) | −16.3327 | −0.669015 | ||||||||
\(597\) | −14.5526 | −0.595597 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.3744 | −1.15934 | −0.579672 | − | 0.814850i | \(-0.696819\pi\) | ||||
−0.579672 | + | 0.814850i | \(0.696819\pi\) | |||||||
\(600\) | 4.29590 | 0.175379 | ||||||||
\(601\) | 30.3394 | 1.23757 | 0.618786 | − | 0.785560i | \(-0.287625\pi\) | ||||
0.618786 | + | 0.785560i | \(0.287625\pi\) | |||||||
\(602\) | 9.55496 | 0.389431 | ||||||||
\(603\) | −11.3937 | −0.463989 | ||||||||
\(604\) | −24.3448 | −0.990576 | ||||||||
\(605\) | −19.6136 | −0.797405 | ||||||||
\(606\) | −12.2174 | −0.496300 | ||||||||
\(607\) | 9.64609 | 0.391523 | 0.195761 | − | 0.980652i | \(-0.437282\pi\) | ||||
0.195761 | + | 0.980652i | \(0.437282\pi\) | |||||||
\(608\) | 2.13706 | 0.0866694 | ||||||||
\(609\) | 2.58211 | 0.104632 | ||||||||
\(610\) | −30.4523 | −1.23298 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.40581 | −0.0568266 | ||||||||
\(613\) | −27.1444 | −1.09635 | −0.548175 | − | 0.836364i | \(-0.684677\pi\) | ||||
−0.548175 | + | 0.836364i | \(0.684677\pi\) | |||||||
\(614\) | 22.2784 | 0.899085 | ||||||||
\(615\) | −13.5157 | −0.545007 | ||||||||
\(616\) | 2.13706 | 0.0861047 | ||||||||
\(617\) | −30.4510 | −1.22591 | −0.612956 | − | 0.790117i | \(-0.710020\pi\) | ||||
−0.612956 | + | 0.790117i | \(0.710020\pi\) | |||||||
\(618\) | −4.53319 | −0.182352 | ||||||||
\(619\) | −3.06578 | −0.123224 | −0.0616121 | − | 0.998100i | \(-0.519624\pi\) | ||||
−0.0616121 | + | 0.998100i | \(0.519624\pi\) | |||||||
\(620\) | 19.3448 | 0.776906 | ||||||||
\(621\) | 2.26875 | 0.0910418 | ||||||||
\(622\) | 0.254749 | 0.0102145 | ||||||||
\(623\) | 3.73556 | 0.149662 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.0248 | −1.12099 | ||||||||
\(626\) | −24.1129 | −0.963745 | ||||||||
\(627\) | −4.56704 | −0.182390 | ||||||||
\(628\) | −12.0978 | −0.482756 | ||||||||
\(629\) | 14.9758 | 0.597126 | ||||||||
\(630\) | −3.04892 | −0.121472 | ||||||||
\(631\) | −17.7791 | −0.707775 | −0.353887 | − | 0.935288i | \(-0.615140\pi\) | ||||
−0.353887 | + | 0.935288i | \(0.615140\pi\) | |||||||
\(632\) | 10.7071 | 0.425905 | ||||||||
\(633\) | −3.80194 | −0.151113 | ||||||||
\(634\) | −12.8321 | −0.509627 | ||||||||
\(635\) | 55.7827 | 2.21367 | ||||||||
\(636\) | −6.46681 | −0.256426 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.51812 | −0.218465 | ||||||||
\(639\) | −4.21983 | −0.166934 | ||||||||
\(640\) | −3.04892 | −0.120519 | ||||||||
\(641\) | −41.9754 | −1.65793 | −0.828964 | − | 0.559303i | \(-0.811069\pi\) | ||||
−0.828964 | + | 0.559303i | \(0.811069\pi\) | |||||||
\(642\) | −12.5254 | −0.494339 | ||||||||
\(643\) | 26.7222 | 1.05382 | 0.526909 | − | 0.849921i | \(-0.323351\pi\) | ||||
0.526909 | + | 0.849921i | \(0.323351\pi\) | |||||||
\(644\) | −2.26875 | −0.0894013 | ||||||||
\(645\) | 29.1323 | 1.14708 | ||||||||
\(646\) | −3.00431 | −0.118203 | ||||||||
\(647\) | −33.7399 | −1.32645 | −0.663226 | − | 0.748419i | \(-0.730813\pi\) | ||||
−0.663226 | + | 0.748419i | \(0.730813\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −7.36227 | −0.288994 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.34481 | −0.248673 | ||||||||
\(652\) | −14.0707 | −0.551051 | ||||||||
\(653\) | −14.8374 | −0.580634 | −0.290317 | − | 0.956931i | \(-0.593761\pi\) | ||||
−0.290317 | + | 0.956931i | \(0.593761\pi\) | |||||||
\(654\) | 1.15883 | 0.0453140 | ||||||||
\(655\) | 10.7560 | 0.420272 | ||||||||
\(656\) | 4.43296 | 0.173078 | ||||||||
\(657\) | −5.84548 | −0.228054 | ||||||||
\(658\) | −3.98792 | −0.155465 | ||||||||
\(659\) | −25.0508 | −0.975842 | −0.487921 | − | 0.872888i | \(-0.662245\pi\) | ||||
−0.487921 | + | 0.872888i | \(0.662245\pi\) | |||||||
\(660\) | 6.51573 | 0.253624 | ||||||||
\(661\) | −34.5816 | −1.34507 | −0.672535 | − | 0.740066i | \(-0.734794\pi\) | ||||
−0.672535 | + | 0.740066i | \(0.734794\pi\) | |||||||
\(662\) | 29.0707 | 1.12986 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.94869 | 0.347277 | ||||||||
\(665\) | −6.51573 | −0.252669 | ||||||||
\(666\) | 10.6528 | 0.412787 | ||||||||
\(667\) | 5.85815 | 0.226829 | ||||||||
\(668\) | −19.9541 | −0.772046 | ||||||||
\(669\) | −23.1347 | −0.894438 | ||||||||
\(670\) | 34.7385 | 1.34207 | ||||||||
\(671\) | −21.3448 | −0.824007 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 24.7791 | 0.955164 | 0.477582 | − | 0.878587i | \(-0.341513\pi\) | ||||
0.477582 | + | 0.878587i | \(0.341513\pi\) | |||||||
\(674\) | −17.7821 | −0.684940 | ||||||||
\(675\) | −4.29590 | −0.165349 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.1347 | −1.46563 | −0.732817 | − | 0.680426i | \(-0.761795\pi\) | ||||
−0.732817 | + | 0.680426i | \(0.761795\pi\) | |||||||
\(678\) | 4.34721 | 0.166953 | ||||||||
\(679\) | 5.10321 | 0.195843 | ||||||||
\(680\) | 4.28621 | 0.164369 | ||||||||
\(681\) | −2.72348 | −0.104364 | ||||||||
\(682\) | 13.5593 | 0.519211 | ||||||||
\(683\) | 38.6407 | 1.47855 | 0.739273 | − | 0.673406i | \(-0.235169\pi\) | ||||
0.739273 | + | 0.673406i | \(0.235169\pi\) | |||||||
\(684\) | −2.13706 | −0.0817127 | ||||||||
\(685\) | −0.760316 | −0.0290502 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 11.7385 | 0.447853 | ||||||||
\(688\) | −9.55496 | −0.364279 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.91723 | −0.263334 | ||||||||
\(691\) | −6.00969 | −0.228619 | −0.114310 | − | 0.993445i | \(-0.536466\pi\) | ||||
−0.114310 | + | 0.993445i | \(0.536466\pi\) | |||||||
\(692\) | −6.61596 | −0.251501 | ||||||||
\(693\) | −2.13706 | −0.0811803 | ||||||||
\(694\) | 10.5144 | 0.399121 | ||||||||
\(695\) | 0.513811 | 0.0194899 | ||||||||
\(696\) | −2.58211 | −0.0978744 | ||||||||
\(697\) | −6.23191 | −0.236051 | ||||||||
\(698\) | 18.1274 | 0.686131 | ||||||||
\(699\) | −9.92931 | −0.375561 | ||||||||
\(700\) | 4.29590 | 0.162370 | ||||||||
\(701\) | 24.3642 | 0.920223 | 0.460111 | − | 0.887861i | \(-0.347809\pi\) | ||||
0.460111 | + | 0.887861i | \(0.347809\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.7657 | 0.858624 | ||||||||
\(704\) | −2.13706 | −0.0805436 | ||||||||
\(705\) | −12.1588 | −0.457928 | ||||||||
\(706\) | −16.1715 | −0.608623 | ||||||||
\(707\) | −12.2174 | −0.459484 | ||||||||
\(708\) | −3.44504 | −0.129473 | ||||||||
\(709\) | 26.1239 | 0.981104 | 0.490552 | − | 0.871412i | \(-0.336795\pi\) | ||||
0.490552 | + | 0.871412i | \(0.336795\pi\) | |||||||
\(710\) | 12.8659 | 0.482849 | ||||||||
\(711\) | −10.7071 | −0.401547 | ||||||||
\(712\) | −3.73556 | −0.139996 | ||||||||
\(713\) | −14.3948 | −0.539089 | ||||||||
\(714\) | −1.40581 | −0.0526112 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.49396 | −0.280062 | ||||||||
\(717\) | 22.1172 | 0.825982 | ||||||||
\(718\) | 7.77240 | 0.290063 | ||||||||
\(719\) | −4.64981 | −0.173409 | −0.0867043 | − | 0.996234i | \(-0.527634\pi\) | ||||
−0.0867043 | + | 0.996234i | \(0.527634\pi\) | |||||||
\(720\) | 3.04892 | 0.113626 | ||||||||
\(721\) | −4.53319 | −0.168825 | ||||||||
\(722\) | 14.4330 | 0.537139 | ||||||||
\(723\) | 24.5429 | 0.912759 | ||||||||
\(724\) | 19.1226 | 0.710685 | ||||||||
\(725\) | −11.0925 | −0.411964 | ||||||||
\(726\) | −6.43296 | −0.238750 | ||||||||
\(727\) | −28.4292 | −1.05438 | −0.527191 | − | 0.849747i | \(-0.676755\pi\) | ||||
−0.527191 | + | 0.849747i | \(0.676755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 17.8224 | 0.659636 | ||||||||
\(731\) | 13.4325 | 0.496818 | ||||||||
\(732\) | −9.98792 | −0.369164 | ||||||||
\(733\) | −9.99356 | −0.369120 | −0.184560 | − | 0.982821i | \(-0.559086\pi\) | ||||
−0.184560 | + | 0.982821i | \(0.559086\pi\) | |||||||
\(734\) | 2.07846 | 0.0767173 | ||||||||
\(735\) | −3.04892 | −0.112461 | ||||||||
\(736\) | 2.26875 | 0.0836272 | ||||||||
\(737\) | 24.3491 | 0.896912 | ||||||||
\(738\) | −4.43296 | −0.163180 | ||||||||
\(739\) | 13.5101 | 0.496977 | 0.248488 | − | 0.968635i | \(-0.420066\pi\) | ||||
0.248488 | + | 0.968635i | \(0.420066\pi\) | |||||||
\(740\) | −32.4795 | −1.19397 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.46681 | −0.237404 | ||||||||
\(743\) | −38.1540 | −1.39974 | −0.699868 | − | 0.714272i | \(-0.746758\pi\) | ||||
−0.699868 | + | 0.714272i | \(0.746758\pi\) | |||||||
\(744\) | 6.34481 | 0.232612 | ||||||||
\(745\) | −49.7972 | −1.82443 | ||||||||
\(746\) | −8.10752 | −0.296838 | ||||||||
\(747\) | −8.94869 | −0.327415 | ||||||||
\(748\) | 3.00431 | 0.109849 | ||||||||
\(749\) | −12.5254 | −0.457669 | ||||||||
\(750\) | −2.14675 | −0.0783883 | ||||||||
\(751\) | −24.1473 | −0.881149 | −0.440575 | − | 0.897716i | \(-0.645225\pi\) | ||||
−0.440575 | + | 0.897716i | \(0.645225\pi\) | |||||||
\(752\) | 3.98792 | 0.145424 | ||||||||
\(753\) | −27.2489 | −0.993005 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −74.2253 | −2.70134 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −7.27173 | −0.264296 | −0.132148 | − | 0.991230i | \(-0.542187\pi\) | ||||
−0.132148 | + | 0.991230i | \(0.542187\pi\) | |||||||
\(758\) | 13.4222 | 0.487516 | ||||||||
\(759\) | −4.84846 | −0.175988 | ||||||||
\(760\) | 6.51573 | 0.236350 | ||||||||
\(761\) | −27.7894 | −1.00736 | −0.503682 | − | 0.863889i | \(-0.668022\pi\) | ||||
−0.503682 | + | 0.863889i | \(0.668022\pi\) | |||||||
\(762\) | 18.2959 | 0.662790 | ||||||||
\(763\) | 1.15883 | 0.0419526 | ||||||||
\(764\) | 23.2403 | 0.840804 | ||||||||
\(765\) | −4.28621 | −0.154968 | ||||||||
\(766\) | 12.4209 | 0.448785 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 12.5894 | 0.453985 | 0.226993 | − | 0.973896i | \(-0.427111\pi\) | ||||
0.226993 | + | 0.973896i | \(0.427111\pi\) | |||||||
\(770\) | 6.51573 | 0.234811 | ||||||||
\(771\) | −17.2349 | −0.620700 | ||||||||
\(772\) | −4.00538 | −0.144157 | ||||||||
\(773\) | −42.4935 | −1.52838 | −0.764192 | − | 0.644989i | \(-0.776862\pi\) | ||||
−0.764192 | + | 0.644989i | \(0.776862\pi\) | |||||||
\(774\) | 9.55496 | 0.343446 | ||||||||
\(775\) | 27.2567 | 0.979088 | ||||||||
\(776\) | −5.10321 | −0.183195 | ||||||||
\(777\) | 10.6528 | 0.382167 | ||||||||
\(778\) | −37.5666 | −1.34683 | ||||||||
\(779\) | −9.47352 | −0.339424 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.01805 | 0.322691 | ||||||||
\(782\) | −3.18944 | −0.114054 | ||||||||
\(783\) | 2.58211 | 0.0922769 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −36.8853 | −1.31649 | ||||||||
\(786\) | 3.52781 | 0.125833 | ||||||||
\(787\) | 30.9017 | 1.10153 | 0.550763 | − | 0.834662i | \(-0.314337\pi\) | ||||
0.550763 | + | 0.834662i | \(0.314337\pi\) | |||||||
\(788\) | 7.75840 | 0.276381 | ||||||||
\(789\) | −8.46011 | −0.301188 | ||||||||
\(790\) | 32.6450 | 1.16146 | ||||||||
\(791\) | 4.34721 | 0.154569 | ||||||||
\(792\) | 2.13706 | 0.0759372 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 36.1159 | 1.28170 | ||||||||
\(795\) | −19.7168 | −0.699282 | ||||||||
\(796\) | 14.5526 | 0.515802 | ||||||||
\(797\) | 52.3038 | 1.85270 | 0.926348 | − | 0.376670i | \(-0.122931\pi\) | ||||
0.926348 | + | 0.376670i | \(0.122931\pi\) | |||||||
\(798\) | −2.13706 | −0.0756512 | ||||||||
\(799\) | −5.60627 | −0.198336 | ||||||||
\(800\) | −4.29590 | −0.151883 | ||||||||
\(801\) | 3.73556 | 0.131990 | ||||||||
\(802\) | −9.82610 | −0.346972 | ||||||||
\(803\) | 12.4922 | 0.440839 | ||||||||
\(804\) | 11.3937 | 0.401826 | ||||||||
\(805\) | −6.91723 | −0.243800 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.29590 | −0.0456177 | ||||||||
\(808\) | 12.2174 | 0.429808 | ||||||||
\(809\) | 31.7942 | 1.11782 | 0.558912 | − | 0.829227i | \(-0.311219\pi\) | ||||
0.558912 | + | 0.829227i | \(0.311219\pi\) | |||||||
\(810\) | −3.04892 | −0.107128 | ||||||||
\(811\) | 12.3196 | 0.432599 | 0.216300 | − | 0.976327i | \(-0.430601\pi\) | ||||
0.216300 | + | 0.976327i | \(0.430601\pi\) | |||||||
\(812\) | −2.58211 | −0.0906141 | ||||||||
\(813\) | −5.46250 | −0.191578 | ||||||||
\(814\) | −22.7657 | −0.797937 | ||||||||
\(815\) | −42.9004 | −1.50273 | ||||||||
\(816\) | 1.40581 | 0.0492133 | ||||||||
\(817\) | 20.4196 | 0.714390 | ||||||||
\(818\) | −3.09352 | −0.108162 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5157 | 0.471990 | ||||||||
\(821\) | 41.0901 | 1.43405 | 0.717027 | − | 0.697046i | \(-0.245503\pi\) | ||||
0.717027 | + | 0.697046i | \(0.245503\pi\) | |||||||
\(822\) | −0.249373 | −0.00869787 | ||||||||
\(823\) | −2.76164 | −0.0962649 | −0.0481324 | − | 0.998841i | \(-0.515327\pi\) | ||||
−0.0481324 | + | 0.998841i | \(0.515327\pi\) | |||||||
\(824\) | 4.53319 | 0.157921 | ||||||||
\(825\) | 9.18060 | 0.319628 | ||||||||
\(826\) | −3.44504 | −0.119868 | ||||||||
\(827\) | −28.6098 | −0.994862 | −0.497431 | − | 0.867504i | \(-0.665723\pi\) | ||||
−0.497431 | + | 0.867504i | \(0.665723\pi\) | |||||||
\(828\) | −2.26875 | −0.0788445 | ||||||||
\(829\) | −50.4741 | −1.75304 | −0.876519 | − | 0.481367i | \(-0.840140\pi\) | ||||
−0.876519 | + | 0.481367i | \(0.840140\pi\) | |||||||
\(830\) | 27.2838 | 0.947035 | ||||||||
\(831\) | −1.01746 | −0.0352952 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.40581 | −0.0487085 | ||||||||
\(834\) | 0.168522 | 0.00583545 | ||||||||
\(835\) | −60.8383 | −2.10540 | ||||||||
\(836\) | 4.56704 | 0.157954 | ||||||||
\(837\) | −6.34481 | −0.219309 | ||||||||
\(838\) | 20.1535 | 0.696190 | ||||||||
\(839\) | 38.4185 | 1.32635 | 0.663177 | − | 0.748463i | \(-0.269208\pi\) | ||||
0.663177 | + | 0.748463i | \(0.269208\pi\) | |||||||
\(840\) | 3.04892 | 0.105198 | ||||||||
\(841\) | −22.3327 | −0.770094 | ||||||||
\(842\) | 11.2034 | 0.386096 | ||||||||
\(843\) | −23.7482 | −0.817933 | ||||||||
\(844\) | 3.80194 | 0.130868 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.98792 | −0.137107 | ||||||||
\(847\) | −6.43296 | −0.221039 | ||||||||
\(848\) | 6.46681 | 0.222071 | ||||||||
\(849\) | 19.9148 | 0.683475 | ||||||||
\(850\) | 6.03923 | 0.207144 | ||||||||
\(851\) | 24.1685 | 0.828486 | ||||||||
\(852\) | 4.21983 | 0.144569 | ||||||||
\(853\) | 7.09677 | 0.242989 | 0.121494 | − | 0.992592i | \(-0.461231\pi\) | ||||
0.121494 | + | 0.992592i | \(0.461231\pi\) | |||||||
\(854\) | −9.98792 | −0.341780 | ||||||||
\(855\) | −6.51573 | −0.222833 | ||||||||
\(856\) | 12.5254 | 0.428110 | ||||||||
\(857\) | −37.8901 | −1.29430 | −0.647150 | − | 0.762362i | \(-0.724039\pi\) | ||||
−0.647150 | + | 0.762362i | \(0.724039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.9329 | 1.12366 | 0.561828 | − | 0.827254i | \(-0.310098\pi\) | ||||
0.561828 | + | 0.827254i | \(0.310098\pi\) | |||||||
\(860\) | −29.1323 | −0.993402 | ||||||||
\(861\) | −4.43296 | −0.151075 | ||||||||
\(862\) | −38.9898 | −1.32800 | ||||||||
\(863\) | 27.3400 | 0.930665 | 0.465333 | − | 0.885136i | \(-0.345935\pi\) | ||||
0.465333 | + | 0.885136i | \(0.345935\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −20.1715 | −0.685852 | ||||||||
\(866\) | −23.4426 | −0.796614 | ||||||||
\(867\) | 15.0237 | 0.510231 | ||||||||
\(868\) | 6.34481 | 0.215357 | ||||||||
\(869\) | 22.8817 | 0.776209 | ||||||||
\(870\) | −7.87263 | −0.266907 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.15883 | −0.0392431 | ||||||||
\(873\) | 5.10321 | 0.172718 | ||||||||
\(874\) | −4.84846 | −0.164002 | ||||||||
\(875\) | −2.14675 | −0.0725735 | ||||||||
\(876\) | 5.84548 | 0.197500 | ||||||||
\(877\) | −7.54852 | −0.254895 | −0.127448 | − | 0.991845i | \(-0.540678\pi\) | ||||
−0.127448 | + | 0.991845i | \(0.540678\pi\) | |||||||
\(878\) | 26.8592 | 0.906455 | ||||||||
\(879\) | 9.15213 | 0.308694 | ||||||||
\(880\) | −6.51573 | −0.219645 | ||||||||
\(881\) | −9.14138 | −0.307981 | −0.153990 | − | 0.988072i | \(-0.549212\pi\) | ||||
−0.153990 | + | 0.988072i | \(0.549212\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 31.5838 | 1.06288 | 0.531439 | − | 0.847097i | \(-0.321651\pi\) | ||||
0.531439 | + | 0.847097i | \(0.321651\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.5036 | −0.353076 | ||||||||
\(886\) | 11.1347 | 0.374077 | ||||||||
\(887\) | 57.3159 | 1.92448 | 0.962239 | − | 0.272205i | \(-0.0877530\pi\) | ||||
0.962239 | + | 0.272205i | \(0.0877530\pi\) | |||||||
\(888\) | −10.6528 | −0.357484 | ||||||||
\(889\) | 18.2959 | 0.613625 | ||||||||
\(890\) | −11.3894 | −0.381774 | ||||||||
\(891\) | −2.13706 | −0.0715943 | ||||||||
\(892\) | 23.1347 | 0.774606 | ||||||||
\(893\) | −8.52243 | −0.285192 | ||||||||
\(894\) | −16.3327 | −0.546248 | ||||||||
\(895\) | −22.8485 | −0.763740 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27.0858 | 0.903863 | ||||||||
\(899\) | −16.3830 | −0.546403 | ||||||||
\(900\) | 4.29590 | 0.143197 | ||||||||
\(901\) | −9.09113 | −0.302869 | ||||||||
\(902\) | 9.47352 | 0.315434 | ||||||||
\(903\) | 9.55496 | 0.317969 | ||||||||
\(904\) | −4.34721 | −0.144586 | ||||||||
\(905\) | 58.3032 | 1.93806 | ||||||||
\(906\) | −24.3448 | −0.808802 | ||||||||
\(907\) | −35.9963 | −1.19524 | −0.597618 | − | 0.801781i | \(-0.703886\pi\) | ||||
−0.597618 | + | 0.801781i | \(0.703886\pi\) | |||||||
\(908\) | 2.72348 | 0.0903819 | ||||||||
\(909\) | −12.2174 | −0.405227 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.76569 | −0.290420 | −0.145210 | − | 0.989401i | \(-0.546386\pi\) | ||||
−0.145210 | + | 0.989401i | \(0.546386\pi\) | |||||||
\(912\) | 2.13706 | 0.0707652 | ||||||||
\(913\) | 19.1239 | 0.632909 | ||||||||
\(914\) | 3.40880 | 0.112753 | ||||||||
\(915\) | −30.4523 | −1.00672 | ||||||||
\(916\) | −11.7385 | −0.387852 | ||||||||
\(917\) | 3.52781 | 0.116499 | ||||||||
\(918\) | −1.40581 | −0.0463987 | ||||||||
\(919\) | 28.5695 | 0.942422 | 0.471211 | − | 0.882020i | \(-0.343817\pi\) | ||||
0.471211 | + | 0.882020i | \(0.343817\pi\) | |||||||
\(920\) | 6.91723 | 0.228054 | ||||||||
\(921\) | 22.2784 | 0.734100 | ||||||||
\(922\) | −30.9178 | −1.01822 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.13706 | 0.0703042 | ||||||||
\(925\) | −45.7633 | −1.50469 | ||||||||
\(926\) | 35.0465 | 1.15170 | ||||||||
\(927\) | −4.53319 | −0.148889 | ||||||||
\(928\) | 2.58211 | 0.0847618 | ||||||||
\(929\) | 23.2644 | 0.763281 | 0.381641 | − | 0.924311i | \(-0.375359\pi\) | ||||
0.381641 | + | 0.924311i | \(0.375359\pi\) | |||||||
\(930\) | 19.3448 | 0.634341 | ||||||||
\(931\) | −2.13706 | −0.0700394 | ||||||||
\(932\) | 9.92931 | 0.325245 | ||||||||
\(933\) | 0.254749 | 0.00834012 | ||||||||
\(934\) | −4.04652 | −0.132406 | ||||||||
\(935\) | 9.15990 | 0.299561 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.3491 | 1.87351 | 0.936757 | − | 0.349980i | \(-0.113812\pi\) | ||||
0.936757 | + | 0.349980i | \(0.113812\pi\) | |||||||
\(938\) | 11.3937 | 0.372019 | ||||||||
\(939\) | −24.1129 | −0.786895 | ||||||||
\(940\) | 12.1588 | 0.396577 | ||||||||
\(941\) | −50.8840 | −1.65877 | −0.829385 | − | 0.558677i | \(-0.811309\pi\) | ||||
−0.829385 | + | 0.558677i | \(0.811309\pi\) | |||||||
\(942\) | −12.0978 | −0.394169 | ||||||||
\(943\) | −10.0573 | −0.327510 | ||||||||
\(944\) | 3.44504 | 0.112127 | ||||||||
\(945\) | −3.04892 | −0.0991813 | ||||||||
\(946\) | −20.4196 | −0.663897 | ||||||||
\(947\) | 9.63593 | 0.313126 | 0.156563 | − | 0.987668i | \(-0.449959\pi\) | ||||
0.156563 | + | 0.987668i | \(0.449959\pi\) | |||||||
\(948\) | 10.7071 | 0.347750 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 9.18060 | 0.297858 | ||||||||
\(951\) | −12.8321 | −0.416108 | ||||||||
\(952\) | 1.40581 | 0.0455627 | ||||||||
\(953\) | −6.38345 | −0.206780 | −0.103390 | − | 0.994641i | \(-0.532969\pi\) | ||||
−0.103390 | + | 0.994641i | \(0.532969\pi\) | |||||||
\(954\) | −6.46681 | −0.209371 | ||||||||
\(955\) | 70.8577 | 2.29290 | ||||||||
\(956\) | −22.1172 | −0.715322 | ||||||||
\(957\) | −5.51812 | −0.178376 | ||||||||
\(958\) | −16.0411 | −0.518266 | ||||||||
\(959\) | −0.249373 | −0.00805266 | ||||||||
\(960\) | −3.04892 | −0.0984034 | ||||||||
\(961\) | 9.25667 | 0.298602 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.5254 | −0.403626 | ||||||||
\(964\) | −24.5429 | −0.790473 | ||||||||
\(965\) | −12.2121 | −0.393120 | ||||||||
\(966\) | −2.26875 | −0.0729958 | ||||||||
\(967\) | 28.8692 | 0.928370 | 0.464185 | − | 0.885738i | \(-0.346347\pi\) | ||||
0.464185 | + | 0.885738i | \(0.346347\pi\) | |||||||
\(968\) | 6.43296 | 0.206763 | ||||||||
\(969\) | −3.00431 | −0.0965124 | ||||||||
\(970\) | −15.5593 | −0.499578 | ||||||||
\(971\) | −35.9661 | −1.15421 | −0.577104 | − | 0.816670i | \(-0.695817\pi\) | ||||
−0.577104 | + | 0.816670i | \(0.695817\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0.168522 | 0.00540258 | ||||||||
\(974\) | 36.7724 | 1.17826 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.98792 | 0.319705 | ||||||||
\(977\) | −42.2664 | −1.35222 | −0.676110 | − | 0.736800i | \(-0.736336\pi\) | ||||
−0.676110 | + | 0.736800i | \(0.736336\pi\) | |||||||
\(978\) | −14.0707 | −0.449931 | ||||||||
\(979\) | −7.98313 | −0.255142 | ||||||||
\(980\) | 3.04892 | 0.0973941 | ||||||||
\(981\) | 1.15883 | 0.0369987 | ||||||||
\(982\) | 7.69069 | 0.245420 | ||||||||
\(983\) | −39.2435 | −1.25167 | −0.625837 | − | 0.779954i | \(-0.715242\pi\) | ||||
−0.625837 | + | 0.779954i | \(0.715242\pi\) | |||||||
\(984\) | 4.43296 | 0.141318 | ||||||||
\(985\) | 23.6547 | 0.753702 | ||||||||
\(986\) | −3.62996 | −0.115601 | ||||||||
\(987\) | −3.98792 | −0.126937 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.6778 | 0.689314 | ||||||||
\(990\) | 6.51573 | 0.207083 | ||||||||
\(991\) | 31.1892 | 0.990758 | 0.495379 | − | 0.868677i | \(-0.335029\pi\) | ||||
0.495379 | + | 0.868677i | \(0.335029\pi\) | |||||||
\(992\) | −6.34481 | −0.201448 | ||||||||
\(993\) | 29.0707 | 0.922530 | ||||||||
\(994\) | 4.21983 | 0.133845 | ||||||||
\(995\) | 44.3696 | 1.40661 | ||||||||
\(996\) | 8.94869 | 0.283550 | ||||||||
\(997\) | −23.7275 | −0.751458 | −0.375729 | − | 0.926730i | \(-0.622608\pi\) | ||||
−0.375729 | + | 0.926730i | \(0.622608\pi\) | |||||||
\(998\) | −21.8213 | −0.690742 | ||||||||
\(999\) | 10.6528 | 0.337039 |
(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 | 7098.2.a.cd.1.3 | ✓ | 3 | |
13.12 | even | 2 | 7098.2.a.ci.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cd.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7098.2.a.ci.1.1 | yes | 3 | 13.12 | even | 2 |