Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} - 4126 x^{5} - 22759 x^{4} + 2997 x^{3} + 10504 x^{2} - 506 x - 1492 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-1.05309\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(5\) | 1.05309 | 0.470956 | 0.235478 | − | 0.971880i | \(-0.424334\pi\) | ||||
0.235478 | + | 0.971880i | \(0.424334\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.189425 | −0.0715957 | −0.0357979 | − | 0.999359i | \(-0.511397\pi\) | ||||
−0.0357979 | + | 0.999359i | \(0.511397\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.05309 | −0.333016 | ||||||||
\(11\) | −6.30119 | −1.89988 | −0.949941 | − | 0.312430i | \(-0.898857\pi\) | ||||
−0.949941 | + | 0.312430i | \(0.898857\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.189425 | 0.0506258 | ||||||||
\(15\) | −1.05309 | −0.271907 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.95903 | −1.20274 | −0.601371 | − | 0.798970i | \(-0.705379\pi\) | ||||
−0.601371 | + | 0.798970i | \(0.705379\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.89185 | −1.58110 | −0.790550 | − | 0.612398i | \(-0.790205\pi\) | ||||
−0.790550 | + | 0.612398i | \(0.790205\pi\) | |||||||
\(20\) | 1.05309 | 0.235478 | ||||||||
\(21\) | 0.189425 | 0.0413358 | ||||||||
\(22\) | 6.30119 | 1.34342 | ||||||||
\(23\) | 8.44585 | 1.76108 | 0.880541 | − | 0.473970i | \(-0.157179\pi\) | ||||
0.880541 | + | 0.473970i | \(0.157179\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.89100 | −0.778200 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.189425 | −0.0357979 | ||||||||
\(29\) | −2.48934 | −0.462259 | −0.231130 | − | 0.972923i | \(-0.574242\pi\) | ||||
−0.231130 | + | 0.972923i | \(0.574242\pi\) | |||||||
\(30\) | 1.05309 | 0.192267 | ||||||||
\(31\) | −6.01703 | −1.08069 | −0.540345 | − | 0.841443i | \(-0.681706\pi\) | ||||
−0.540345 | + | 0.841443i | \(0.681706\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.30119 | 1.09690 | ||||||||
\(34\) | 4.95903 | 0.850467 | ||||||||
\(35\) | −0.199481 | −0.0337185 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.704737 | 0.115858 | 0.0579290 | − | 0.998321i | \(-0.481550\pi\) | ||||
0.0579290 | + | 0.998321i | \(0.481550\pi\) | |||||||
\(38\) | 6.89185 | 1.11801 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.05309 | −0.166508 | ||||||||
\(41\) | −0.424853 | −0.0663509 | −0.0331754 | − | 0.999450i | \(-0.510562\pi\) | ||||
−0.0331754 | + | 0.999450i | \(0.510562\pi\) | |||||||
\(42\) | −0.189425 | −0.0292288 | ||||||||
\(43\) | −5.29921 | −0.808122 | −0.404061 | − | 0.914732i | \(-0.632402\pi\) | ||||
−0.404061 | + | 0.914732i | \(0.632402\pi\) | |||||||
\(44\) | −6.30119 | −0.949941 | ||||||||
\(45\) | 1.05309 | 0.156985 | ||||||||
\(46\) | −8.44585 | −1.24527 | ||||||||
\(47\) | 4.70034 | 0.685614 | 0.342807 | − | 0.939406i | \(-0.388622\pi\) | ||||
0.342807 | + | 0.939406i | \(0.388622\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.96412 | −0.994874 | ||||||||
\(50\) | 3.89100 | 0.550271 | ||||||||
\(51\) | 4.95903 | 0.694403 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −12.3270 | −1.69324 | −0.846621 | − | 0.532196i | \(-0.821367\pi\) | ||||
−0.846621 | + | 0.532196i | \(0.821367\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −6.63573 | −0.894761 | ||||||||
\(56\) | 0.189425 | 0.0253129 | ||||||||
\(57\) | 6.89185 | 0.912848 | ||||||||
\(58\) | 2.48934 | 0.326867 | ||||||||
\(59\) | −13.9362 | −1.81434 | −0.907171 | − | 0.420761i | \(-0.861763\pi\) | ||||
−0.907171 | + | 0.420761i | \(0.861763\pi\) | |||||||
\(60\) | −1.05309 | −0.135953 | ||||||||
\(61\) | 1.74461 | 0.223375 | 0.111687 | − | 0.993743i | \(-0.464374\pi\) | ||||
0.111687 | + | 0.993743i | \(0.464374\pi\) | |||||||
\(62\) | 6.01703 | 0.764164 | ||||||||
\(63\) | −0.189425 | −0.0238652 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.05309 | −0.130620 | ||||||||
\(66\) | −6.30119 | −0.775623 | ||||||||
\(67\) | 14.4705 | 1.76785 | 0.883925 | − | 0.467628i | \(-0.154891\pi\) | ||||
0.883925 | + | 0.467628i | \(0.154891\pi\) | |||||||
\(68\) | −4.95903 | −0.601371 | ||||||||
\(69\) | −8.44585 | −1.01676 | ||||||||
\(70\) | 0.199481 | 0.0238425 | ||||||||
\(71\) | 12.7428 | 1.51229 | 0.756146 | − | 0.654404i | \(-0.227080\pi\) | ||||
0.756146 | + | 0.654404i | \(0.227080\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 8.73221 | 1.02203 | 0.511014 | − | 0.859572i | \(-0.329270\pi\) | ||||
0.511014 | + | 0.859572i | \(0.329270\pi\) | |||||||
\(74\) | −0.704737 | −0.0819240 | ||||||||
\(75\) | 3.89100 | 0.449294 | ||||||||
\(76\) | −6.89185 | −0.790550 | ||||||||
\(77\) | 1.19360 | 0.136023 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 10.7464 | 1.20906 | 0.604531 | − | 0.796581i | \(-0.293360\pi\) | ||||
0.604531 | + | 0.796581i | \(0.293360\pi\) | |||||||
\(80\) | 1.05309 | 0.117739 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.424853 | 0.0469171 | ||||||||
\(83\) | −7.04418 | −0.773199 | −0.386600 | − | 0.922248i | \(-0.626350\pi\) | ||||
−0.386600 | + | 0.922248i | \(0.626350\pi\) | |||||||
\(84\) | 0.189425 | 0.0206679 | ||||||||
\(85\) | −5.22231 | −0.566439 | ||||||||
\(86\) | 5.29921 | 0.571429 | ||||||||
\(87\) | 2.48934 | 0.266885 | ||||||||
\(88\) | 6.30119 | 0.671710 | ||||||||
\(89\) | −11.5379 | −1.22301 | −0.611506 | − | 0.791240i | \(-0.709436\pi\) | ||||
−0.611506 | + | 0.791240i | \(0.709436\pi\) | |||||||
\(90\) | −1.05309 | −0.111005 | ||||||||
\(91\) | 0.189425 | 0.0198571 | ||||||||
\(92\) | 8.44585 | 0.880541 | ||||||||
\(93\) | 6.01703 | 0.623937 | ||||||||
\(94\) | −4.70034 | −0.484803 | ||||||||
\(95\) | −7.25774 | −0.744629 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −2.13606 | −0.216884 | −0.108442 | − | 0.994103i | \(-0.534586\pi\) | ||||
−0.108442 | + | 0.994103i | \(0.534586\pi\) | |||||||
\(98\) | 6.96412 | 0.703482 | ||||||||
\(99\) | −6.30119 | −0.633294 | ||||||||
\(100\) | −3.89100 | −0.389100 | ||||||||
\(101\) | −6.03888 | −0.600891 | −0.300445 | − | 0.953799i | \(-0.597135\pi\) | ||||
−0.300445 | + | 0.953799i | \(0.597135\pi\) | |||||||
\(102\) | −4.95903 | −0.491017 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0.199481 | 0.0194674 | ||||||||
\(106\) | 12.3270 | 1.19730 | ||||||||
\(107\) | 3.17310 | 0.306755 | 0.153378 | − | 0.988168i | \(-0.450985\pi\) | ||||
0.153378 | + | 0.988168i | \(0.450985\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 0.672224 | 0.0643873 | 0.0321937 | − | 0.999482i | \(-0.489751\pi\) | ||||
0.0321937 | + | 0.999482i | \(0.489751\pi\) | |||||||
\(110\) | 6.63573 | 0.632692 | ||||||||
\(111\) | −0.704737 | −0.0668907 | ||||||||
\(112\) | −0.189425 | −0.0178989 | ||||||||
\(113\) | −1.37079 | −0.128953 | −0.0644765 | − | 0.997919i | \(-0.520538\pi\) | ||||
−0.0644765 | + | 0.997919i | \(0.520538\pi\) | |||||||
\(114\) | −6.89185 | −0.645481 | ||||||||
\(115\) | 8.89424 | 0.829393 | ||||||||
\(116\) | −2.48934 | −0.231130 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 13.9362 | 1.28293 | ||||||||
\(119\) | 0.939362 | 0.0861112 | ||||||||
\(120\) | 1.05309 | 0.0961335 | ||||||||
\(121\) | 28.7050 | 2.60955 | ||||||||
\(122\) | −1.74461 | −0.157950 | ||||||||
\(123\) | 0.424853 | 0.0383077 | ||||||||
\(124\) | −6.01703 | −0.540345 | ||||||||
\(125\) | −9.36303 | −0.837454 | ||||||||
\(126\) | 0.189425 | 0.0168753 | ||||||||
\(127\) | 17.8983 | 1.58822 | 0.794108 | − | 0.607777i | \(-0.207938\pi\) | ||||
0.794108 | + | 0.607777i | \(0.207938\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.29921 | 0.466570 | ||||||||
\(130\) | 1.05309 | 0.0923621 | ||||||||
\(131\) | −10.5649 | −0.923062 | −0.461531 | − | 0.887124i | \(-0.652700\pi\) | ||||
−0.461531 | + | 0.887124i | \(0.652700\pi\) | |||||||
\(132\) | 6.30119 | 0.548449 | ||||||||
\(133\) | 1.30549 | 0.113200 | ||||||||
\(134\) | −14.4705 | −1.25006 | ||||||||
\(135\) | −1.05309 | −0.0906356 | ||||||||
\(136\) | 4.95903 | 0.425233 | ||||||||
\(137\) | 20.2743 | 1.73215 | 0.866076 | − | 0.499912i | \(-0.166634\pi\) | ||||
0.866076 | + | 0.499912i | \(0.166634\pi\) | |||||||
\(138\) | 8.44585 | 0.718959 | ||||||||
\(139\) | 10.8071 | 0.916645 | 0.458323 | − | 0.888786i | \(-0.348450\pi\) | ||||
0.458323 | + | 0.888786i | \(0.348450\pi\) | |||||||
\(140\) | −0.199481 | −0.0168592 | ||||||||
\(141\) | −4.70034 | −0.395840 | ||||||||
\(142\) | −12.7428 | −1.06935 | ||||||||
\(143\) | 6.30119 | 0.526932 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.62150 | −0.217704 | ||||||||
\(146\) | −8.73221 | −0.722683 | ||||||||
\(147\) | 6.96412 | 0.574391 | ||||||||
\(148\) | 0.704737 | 0.0579290 | ||||||||
\(149\) | 16.2553 | 1.33168 | 0.665841 | − | 0.746094i | \(-0.268073\pi\) | ||||
0.665841 | + | 0.746094i | \(0.268073\pi\) | |||||||
\(150\) | −3.89100 | −0.317699 | ||||||||
\(151\) | 18.2933 | 1.48869 | 0.744344 | − | 0.667797i | \(-0.232762\pi\) | ||||
0.744344 | + | 0.667797i | \(0.232762\pi\) | |||||||
\(152\) | 6.89185 | 0.559003 | ||||||||
\(153\) | −4.95903 | −0.400914 | ||||||||
\(154\) | −1.19360 | −0.0961831 | ||||||||
\(155\) | −6.33648 | −0.508958 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −15.3375 | −1.22406 | −0.612032 | − | 0.790833i | \(-0.709648\pi\) | ||||
−0.612032 | + | 0.790833i | \(0.709648\pi\) | |||||||
\(158\) | −10.7464 | −0.854937 | ||||||||
\(159\) | 12.3270 | 0.977594 | ||||||||
\(160\) | −1.05309 | −0.0832541 | ||||||||
\(161\) | −1.59985 | −0.126086 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 19.0841 | 1.49478 | 0.747391 | − | 0.664384i | \(-0.231306\pi\) | ||||
0.747391 | + | 0.664384i | \(0.231306\pi\) | |||||||
\(164\) | −0.424853 | −0.0331754 | ||||||||
\(165\) | 6.63573 | 0.516591 | ||||||||
\(166\) | 7.04418 | 0.546734 | ||||||||
\(167\) | 10.4370 | 0.807640 | 0.403820 | − | 0.914838i | \(-0.367682\pi\) | ||||
0.403820 | + | 0.914838i | \(0.367682\pi\) | |||||||
\(168\) | −0.189425 | −0.0146144 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 5.22231 | 0.400533 | ||||||||
\(171\) | −6.89185 | −0.527033 | ||||||||
\(172\) | −5.29921 | −0.404061 | ||||||||
\(173\) | −2.06672 | −0.157130 | −0.0785650 | − | 0.996909i | \(-0.525034\pi\) | ||||
−0.0785650 | + | 0.996909i | \(0.525034\pi\) | |||||||
\(174\) | −2.48934 | −0.188716 | ||||||||
\(175\) | 0.737051 | 0.0557158 | ||||||||
\(176\) | −6.30119 | −0.474970 | ||||||||
\(177\) | 13.9362 | 1.04751 | ||||||||
\(178\) | 11.5379 | 0.864801 | ||||||||
\(179\) | −8.42487 | −0.629704 | −0.314852 | − | 0.949141i | \(-0.601955\pi\) | ||||
−0.314852 | + | 0.949141i | \(0.601955\pi\) | |||||||
\(180\) | 1.05309 | 0.0784927 | ||||||||
\(181\) | −10.7366 | −0.798045 | −0.399022 | − | 0.916941i | \(-0.630650\pi\) | ||||
−0.399022 | + | 0.916941i | \(0.630650\pi\) | |||||||
\(182\) | −0.189425 | −0.0140411 | ||||||||
\(183\) | −1.74461 | −0.128966 | ||||||||
\(184\) | −8.44585 | −0.622636 | ||||||||
\(185\) | 0.742151 | 0.0545640 | ||||||||
\(186\) | −6.01703 | −0.441190 | ||||||||
\(187\) | 31.2478 | 2.28507 | ||||||||
\(188\) | 4.70034 | 0.342807 | ||||||||
\(189\) | 0.189425 | 0.0137786 | ||||||||
\(190\) | 7.25774 | 0.526532 | ||||||||
\(191\) | −1.14807 | −0.0830715 | −0.0415358 | − | 0.999137i | \(-0.513225\pi\) | ||||
−0.0415358 | + | 0.999137i | \(0.513225\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 3.72614 | 0.268214 | 0.134107 | − | 0.990967i | \(-0.457183\pi\) | ||||
0.134107 | + | 0.990967i | \(0.457183\pi\) | |||||||
\(194\) | 2.13606 | 0.153360 | ||||||||
\(195\) | 1.05309 | 0.0754134 | ||||||||
\(196\) | −6.96412 | −0.497437 | ||||||||
\(197\) | −7.52027 | −0.535797 | −0.267898 | − | 0.963447i | \(-0.586329\pi\) | ||||
−0.267898 | + | 0.963447i | \(0.586329\pi\) | |||||||
\(198\) | 6.30119 | 0.447806 | ||||||||
\(199\) | −12.7348 | −0.902746 | −0.451373 | − | 0.892335i | \(-0.649066\pi\) | ||||
−0.451373 | + | 0.892335i | \(0.649066\pi\) | |||||||
\(200\) | 3.89100 | 0.275135 | ||||||||
\(201\) | −14.4705 | −1.02067 | ||||||||
\(202\) | 6.03888 | 0.424894 | ||||||||
\(203\) | 0.471542 | 0.0330958 | ||||||||
\(204\) | 4.95903 | 0.347202 | ||||||||
\(205\) | −0.447408 | −0.0312483 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 8.44585 | 0.587027 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 43.4269 | 3.00390 | ||||||||
\(210\) | −0.199481 | −0.0137655 | ||||||||
\(211\) | −13.2352 | −0.911147 | −0.455574 | − | 0.890198i | \(-0.650566\pi\) | ||||
−0.455574 | + | 0.890198i | \(0.650566\pi\) | |||||||
\(212\) | −12.3270 | −0.846621 | ||||||||
\(213\) | −12.7428 | −0.873122 | ||||||||
\(214\) | −3.17310 | −0.216909 | ||||||||
\(215\) | −5.58055 | −0.380590 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.13977 | 0.0773728 | ||||||||
\(218\) | −0.672224 | −0.0455287 | ||||||||
\(219\) | −8.73221 | −0.590068 | ||||||||
\(220\) | −6.63573 | −0.447381 | ||||||||
\(221\) | 4.95903 | 0.333580 | ||||||||
\(222\) | 0.704737 | 0.0472988 | ||||||||
\(223\) | 0.794330 | 0.0531923 | 0.0265961 | − | 0.999646i | \(-0.491533\pi\) | ||||
0.0265961 | + | 0.999646i | \(0.491533\pi\) | |||||||
\(224\) | 0.189425 | 0.0126565 | ||||||||
\(225\) | −3.89100 | −0.259400 | ||||||||
\(226\) | 1.37079 | 0.0911835 | ||||||||
\(227\) | −19.8316 | −1.31627 | −0.658134 | − | 0.752900i | \(-0.728654\pi\) | ||||
−0.658134 | + | 0.752900i | \(0.728654\pi\) | |||||||
\(228\) | 6.89185 | 0.456424 | ||||||||
\(229\) | 0.366382 | 0.0242112 | 0.0121056 | − | 0.999927i | \(-0.496147\pi\) | ||||
0.0121056 | + | 0.999927i | \(0.496147\pi\) | |||||||
\(230\) | −8.89424 | −0.586469 | ||||||||
\(231\) | −1.19360 | −0.0785331 | ||||||||
\(232\) | 2.48934 | 0.163433 | ||||||||
\(233\) | −19.6590 | −1.28790 | −0.643952 | − | 0.765066i | \(-0.722706\pi\) | ||||
−0.643952 | + | 0.765066i | \(0.722706\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 4.94988 | 0.322894 | ||||||||
\(236\) | −13.9362 | −0.907171 | ||||||||
\(237\) | −10.7464 | −0.698053 | ||||||||
\(238\) | −0.939362 | −0.0608898 | ||||||||
\(239\) | 10.2458 | 0.662747 | 0.331374 | − | 0.943500i | \(-0.392488\pi\) | ||||
0.331374 | + | 0.943500i | \(0.392488\pi\) | |||||||
\(240\) | −1.05309 | −0.0679767 | ||||||||
\(241\) | 4.66441 | 0.300461 | 0.150230 | − | 0.988651i | \(-0.451998\pi\) | ||||
0.150230 | + | 0.988651i | \(0.451998\pi\) | |||||||
\(242\) | −28.7050 | −1.84523 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.74461 | 0.111687 | ||||||||
\(245\) | −7.33384 | −0.468542 | ||||||||
\(246\) | −0.424853 | −0.0270876 | ||||||||
\(247\) | 6.89185 | 0.438518 | ||||||||
\(248\) | 6.01703 | 0.382082 | ||||||||
\(249\) | 7.04418 | 0.446407 | ||||||||
\(250\) | 9.36303 | 0.592170 | ||||||||
\(251\) | 8.36406 | 0.527935 | 0.263968 | − | 0.964532i | \(-0.414969\pi\) | ||||
0.263968 | + | 0.964532i | \(0.414969\pi\) | |||||||
\(252\) | −0.189425 | −0.0119326 | ||||||||
\(253\) | −53.2190 | −3.34585 | ||||||||
\(254\) | −17.8983 | −1.12304 | ||||||||
\(255\) | 5.22231 | 0.327033 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.3987 | −0.711030 | −0.355515 | − | 0.934671i | \(-0.615695\pi\) | ||||
−0.355515 | + | 0.934671i | \(0.615695\pi\) | |||||||
\(258\) | −5.29921 | −0.329914 | ||||||||
\(259\) | −0.133494 | −0.00829494 | ||||||||
\(260\) | −1.05309 | −0.0653099 | ||||||||
\(261\) | −2.48934 | −0.154086 | ||||||||
\(262\) | 10.5649 | 0.652703 | ||||||||
\(263\) | −4.13508 | −0.254980 | −0.127490 | − | 0.991840i | \(-0.540692\pi\) | ||||
−0.127490 | + | 0.991840i | \(0.540692\pi\) | |||||||
\(264\) | −6.30119 | −0.387812 | ||||||||
\(265\) | −12.9814 | −0.797443 | ||||||||
\(266\) | −1.30549 | −0.0800445 | ||||||||
\(267\) | 11.5379 | 0.706107 | ||||||||
\(268\) | 14.4705 | 0.883925 | ||||||||
\(269\) | −27.1252 | −1.65385 | −0.826927 | − | 0.562309i | \(-0.809913\pi\) | ||||
−0.826927 | + | 0.562309i | \(0.809913\pi\) | |||||||
\(270\) | 1.05309 | 0.0640890 | ||||||||
\(271\) | 15.3612 | 0.933127 | 0.466563 | − | 0.884488i | \(-0.345492\pi\) | ||||
0.466563 | + | 0.884488i | \(0.345492\pi\) | |||||||
\(272\) | −4.95903 | −0.300685 | ||||||||
\(273\) | −0.189425 | −0.0114645 | ||||||||
\(274\) | −20.2743 | −1.22482 | ||||||||
\(275\) | 24.5180 | 1.47849 | ||||||||
\(276\) | −8.44585 | −0.508381 | ||||||||
\(277\) | −11.8077 | −0.709453 | −0.354727 | − | 0.934970i | \(-0.615426\pi\) | ||||
−0.354727 | + | 0.934970i | \(0.615426\pi\) | |||||||
\(278\) | −10.8071 | −0.648166 | ||||||||
\(279\) | −6.01703 | −0.360230 | ||||||||
\(280\) | 0.199481 | 0.0119213 | ||||||||
\(281\) | 11.4689 | 0.684174 | 0.342087 | − | 0.939668i | \(-0.388866\pi\) | ||||
0.342087 | + | 0.939668i | \(0.388866\pi\) | |||||||
\(282\) | 4.70034 | 0.279901 | ||||||||
\(283\) | 25.0579 | 1.48954 | 0.744770 | − | 0.667321i | \(-0.232559\pi\) | ||||
0.744770 | + | 0.667321i | \(0.232559\pi\) | |||||||
\(284\) | 12.7428 | 0.756146 | ||||||||
\(285\) | 7.25774 | 0.429912 | ||||||||
\(286\) | −6.30119 | −0.372597 | ||||||||
\(287\) | 0.0804775 | 0.00475044 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 7.59198 | 0.446587 | ||||||||
\(290\) | 2.62150 | 0.153940 | ||||||||
\(291\) | 2.13606 | 0.125218 | ||||||||
\(292\) | 8.73221 | 0.511014 | ||||||||
\(293\) | 0.545131 | 0.0318469 | 0.0159234 | − | 0.999873i | \(-0.494931\pi\) | ||||
0.0159234 | + | 0.999873i | \(0.494931\pi\) | |||||||
\(294\) | −6.96412 | −0.406156 | ||||||||
\(295\) | −14.6761 | −0.854476 | ||||||||
\(296\) | −0.704737 | −0.0409620 | ||||||||
\(297\) | 6.30119 | 0.365632 | ||||||||
\(298\) | −16.2553 | −0.941642 | ||||||||
\(299\) | −8.44585 | −0.488436 | ||||||||
\(300\) | 3.89100 | 0.224647 | ||||||||
\(301\) | 1.00380 | 0.0578581 | ||||||||
\(302\) | −18.2933 | −1.05266 | ||||||||
\(303\) | 6.03888 | 0.346924 | ||||||||
\(304\) | −6.89185 | −0.395275 | ||||||||
\(305\) | 1.83724 | 0.105200 | ||||||||
\(306\) | 4.95903 | 0.283489 | ||||||||
\(307\) | 25.4222 | 1.45092 | 0.725460 | − | 0.688265i | \(-0.241627\pi\) | ||||
0.725460 | + | 0.688265i | \(0.241627\pi\) | |||||||
\(308\) | 1.19360 | 0.0680117 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 6.33648 | 0.359888 | ||||||||
\(311\) | −31.7263 | −1.79903 | −0.899516 | − | 0.436888i | \(-0.856081\pi\) | ||||
−0.899516 | + | 0.436888i | \(0.856081\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −13.1655 | −0.744156 | −0.372078 | − | 0.928201i | \(-0.621355\pi\) | ||||
−0.372078 | + | 0.928201i | \(0.621355\pi\) | |||||||
\(314\) | 15.3375 | 0.865544 | ||||||||
\(315\) | −0.199481 | −0.0112395 | ||||||||
\(316\) | 10.7464 | 0.604531 | ||||||||
\(317\) | 24.2733 | 1.36332 | 0.681661 | − | 0.731668i | \(-0.261258\pi\) | ||||
0.681661 | + | 0.731668i | \(0.261258\pi\) | |||||||
\(318\) | −12.3270 | −0.691263 | ||||||||
\(319\) | 15.6858 | 0.878238 | ||||||||
\(320\) | 1.05309 | 0.0588695 | ||||||||
\(321\) | −3.17310 | −0.177105 | ||||||||
\(322\) | 1.59985 | 0.0891562 | ||||||||
\(323\) | 34.1769 | 1.90165 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.89100 | 0.215834 | ||||||||
\(326\) | −19.0841 | −1.05697 | ||||||||
\(327\) | −0.672224 | −0.0371741 | ||||||||
\(328\) | 0.424853 | 0.0234586 | ||||||||
\(329\) | −0.890359 | −0.0490871 | ||||||||
\(330\) | −6.63573 | −0.365285 | ||||||||
\(331\) | −14.0156 | −0.770367 | −0.385183 | − | 0.922840i | \(-0.625862\pi\) | ||||
−0.385183 | + | 0.922840i | \(0.625862\pi\) | |||||||
\(332\) | −7.04418 | −0.386600 | ||||||||
\(333\) | 0.704737 | 0.0386193 | ||||||||
\(334\) | −10.4370 | −0.571088 | ||||||||
\(335\) | 15.2387 | 0.832580 | ||||||||
\(336\) | 0.189425 | 0.0103340 | ||||||||
\(337\) | −33.6272 | −1.83179 | −0.915895 | − | 0.401418i | \(-0.868517\pi\) | ||||
−0.915895 | + | 0.401418i | \(0.868517\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 1.37079 | 0.0744510 | ||||||||
\(340\) | −5.22231 | −0.283219 | ||||||||
\(341\) | 37.9145 | 2.05318 | ||||||||
\(342\) | 6.89185 | 0.372669 | ||||||||
\(343\) | 2.64515 | 0.142824 | ||||||||
\(344\) | 5.29921 | 0.285714 | ||||||||
\(345\) | −8.89424 | −0.478850 | ||||||||
\(346\) | 2.06672 | 0.111108 | ||||||||
\(347\) | −8.14151 | −0.437059 | −0.218530 | − | 0.975830i | \(-0.570126\pi\) | ||||
−0.218530 | + | 0.975830i | \(0.570126\pi\) | |||||||
\(348\) | 2.48934 | 0.133443 | ||||||||
\(349\) | 27.9084 | 1.49390 | 0.746952 | − | 0.664878i | \(-0.231517\pi\) | ||||
0.746952 | + | 0.664878i | \(0.231517\pi\) | |||||||
\(350\) | −0.737051 | −0.0393970 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 6.30119 | 0.335855 | ||||||||
\(353\) | −9.11644 | −0.485219 | −0.242610 | − | 0.970124i | \(-0.578003\pi\) | ||||
−0.242610 | + | 0.970124i | \(0.578003\pi\) | |||||||
\(354\) | −13.9362 | −0.740702 | ||||||||
\(355\) | 13.4193 | 0.712223 | ||||||||
\(356\) | −11.5379 | −0.611506 | ||||||||
\(357\) | −0.939362 | −0.0497163 | ||||||||
\(358\) | 8.42487 | 0.445268 | ||||||||
\(359\) | −16.4159 | −0.866398 | −0.433199 | − | 0.901298i | \(-0.642615\pi\) | ||||
−0.433199 | + | 0.901298i | \(0.642615\pi\) | |||||||
\(360\) | −1.05309 | −0.0555027 | ||||||||
\(361\) | 28.4976 | 1.49988 | ||||||||
\(362\) | 10.7366 | 0.564303 | ||||||||
\(363\) | −28.7050 | −1.50662 | ||||||||
\(364\) | 0.189425 | 0.00992854 | ||||||||
\(365\) | 9.19581 | 0.481331 | ||||||||
\(366\) | 1.74461 | 0.0911925 | ||||||||
\(367\) | −33.3974 | −1.74333 | −0.871666 | − | 0.490101i | \(-0.836960\pi\) | ||||
−0.871666 | + | 0.490101i | \(0.836960\pi\) | |||||||
\(368\) | 8.44585 | 0.440270 | ||||||||
\(369\) | −0.424853 | −0.0221170 | ||||||||
\(370\) | −0.742151 | −0.0385826 | ||||||||
\(371\) | 2.33503 | 0.121229 | ||||||||
\(372\) | 6.01703 | 0.311968 | ||||||||
\(373\) | 9.39484 | 0.486446 | 0.243223 | − | 0.969970i | \(-0.421795\pi\) | ||||
0.243223 | + | 0.969970i | \(0.421795\pi\) | |||||||
\(374\) | −31.2478 | −1.61579 | ||||||||
\(375\) | 9.36303 | 0.483505 | ||||||||
\(376\) | −4.70034 | −0.242401 | ||||||||
\(377\) | 2.48934 | 0.128208 | ||||||||
\(378\) | −0.189425 | −0.00974295 | ||||||||
\(379\) | 18.9930 | 0.975607 | 0.487803 | − | 0.872953i | \(-0.337798\pi\) | ||||
0.487803 | + | 0.872953i | \(0.337798\pi\) | |||||||
\(380\) | −7.25774 | −0.372314 | ||||||||
\(381\) | −17.8983 | −0.916957 | ||||||||
\(382\) | 1.14807 | 0.0587404 | ||||||||
\(383\) | 11.2538 | 0.575044 | 0.287522 | − | 0.957774i | \(-0.407169\pi\) | ||||
0.287522 | + | 0.957774i | \(0.407169\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.25697 | 0.0640611 | ||||||||
\(386\) | −3.72614 | −0.189656 | ||||||||
\(387\) | −5.29921 | −0.269374 | ||||||||
\(388\) | −2.13606 | −0.108442 | ||||||||
\(389\) | 25.8266 | 1.30946 | 0.654730 | − | 0.755863i | \(-0.272782\pi\) | ||||
0.654730 | + | 0.755863i | \(0.272782\pi\) | |||||||
\(390\) | −1.05309 | −0.0533253 | ||||||||
\(391\) | −41.8832 | −2.11813 | ||||||||
\(392\) | 6.96412 | 0.351741 | ||||||||
\(393\) | 10.5649 | 0.532930 | ||||||||
\(394\) | 7.52027 | 0.378866 | ||||||||
\(395\) | 11.3169 | 0.569416 | ||||||||
\(396\) | −6.30119 | −0.316647 | ||||||||
\(397\) | 4.09534 | 0.205539 | 0.102770 | − | 0.994705i | \(-0.467230\pi\) | ||||
0.102770 | + | 0.994705i | \(0.467230\pi\) | |||||||
\(398\) | 12.7348 | 0.638338 | ||||||||
\(399\) | −1.30549 | −0.0653560 | ||||||||
\(400\) | −3.89100 | −0.194550 | ||||||||
\(401\) | 4.12362 | 0.205924 | 0.102962 | − | 0.994685i | \(-0.467168\pi\) | ||||
0.102962 | + | 0.994685i | \(0.467168\pi\) | |||||||
\(402\) | 14.4705 | 0.721722 | ||||||||
\(403\) | 6.01703 | 0.299730 | ||||||||
\(404\) | −6.03888 | −0.300445 | ||||||||
\(405\) | 1.05309 | 0.0523285 | ||||||||
\(406\) | −0.471542 | −0.0234022 | ||||||||
\(407\) | −4.44068 | −0.220116 | ||||||||
\(408\) | −4.95903 | −0.245509 | ||||||||
\(409\) | −28.7895 | −1.42355 | −0.711773 | − | 0.702409i | \(-0.752108\pi\) | ||||
−0.711773 | + | 0.702409i | \(0.752108\pi\) | |||||||
\(410\) | 0.447408 | 0.0220959 | ||||||||
\(411\) | −20.2743 | −1.00006 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 2.63986 | 0.129899 | ||||||||
\(414\) | −8.44585 | −0.415091 | ||||||||
\(415\) | −7.41816 | −0.364143 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −10.8071 | −0.529225 | ||||||||
\(418\) | −43.4269 | −2.12408 | ||||||||
\(419\) | 2.93488 | 0.143378 | 0.0716891 | − | 0.997427i | \(-0.477161\pi\) | ||||
0.0716891 | + | 0.997427i | \(0.477161\pi\) | |||||||
\(420\) | 0.199481 | 0.00973368 | ||||||||
\(421\) | 17.2512 | 0.840771 | 0.420386 | − | 0.907346i | \(-0.361895\pi\) | ||||
0.420386 | + | 0.907346i | \(0.361895\pi\) | |||||||
\(422\) | 13.2352 | 0.644278 | ||||||||
\(423\) | 4.70034 | 0.228538 | ||||||||
\(424\) | 12.3270 | 0.598652 | ||||||||
\(425\) | 19.2956 | 0.935974 | ||||||||
\(426\) | 12.7428 | 0.617390 | ||||||||
\(427\) | −0.330473 | −0.0159927 | ||||||||
\(428\) | 3.17310 | 0.153378 | ||||||||
\(429\) | −6.30119 | −0.304225 | ||||||||
\(430\) | 5.58055 | 0.269118 | ||||||||
\(431\) | 28.0145 | 1.34941 | 0.674706 | − | 0.738087i | \(-0.264270\pi\) | ||||
0.674706 | + | 0.738087i | \(0.264270\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −0.102646 | −0.00493285 | −0.00246642 | − | 0.999997i | \(-0.500785\pi\) | ||||
−0.00246642 | + | 0.999997i | \(0.500785\pi\) | |||||||
\(434\) | −1.13977 | −0.0547109 | ||||||||
\(435\) | 2.62150 | 0.125691 | ||||||||
\(436\) | 0.672224 | 0.0321937 | ||||||||
\(437\) | −58.2076 | −2.78445 | ||||||||
\(438\) | 8.73221 | 0.417241 | ||||||||
\(439\) | 23.1977 | 1.10716 | 0.553582 | − | 0.832795i | \(-0.313261\pi\) | ||||
0.553582 | + | 0.832795i | \(0.313261\pi\) | |||||||
\(440\) | 6.63573 | 0.316346 | ||||||||
\(441\) | −6.96412 | −0.331625 | ||||||||
\(442\) | −4.95903 | −0.235877 | ||||||||
\(443\) | 5.64862 | 0.268374 | 0.134187 | − | 0.990956i | \(-0.457158\pi\) | ||||
0.134187 | + | 0.990956i | \(0.457158\pi\) | |||||||
\(444\) | −0.704737 | −0.0334453 | ||||||||
\(445\) | −12.1504 | −0.575985 | ||||||||
\(446\) | −0.794330 | −0.0376126 | ||||||||
\(447\) | −16.2553 | −0.768847 | ||||||||
\(448\) | −0.189425 | −0.00894947 | ||||||||
\(449\) | −12.3808 | −0.584288 | −0.292144 | − | 0.956374i | \(-0.594369\pi\) | ||||
−0.292144 | + | 0.956374i | \(0.594369\pi\) | |||||||
\(450\) | 3.89100 | 0.183424 | ||||||||
\(451\) | 2.67708 | 0.126059 | ||||||||
\(452\) | −1.37079 | −0.0644765 | ||||||||
\(453\) | −18.2933 | −0.859494 | ||||||||
\(454\) | 19.8316 | 0.930743 | ||||||||
\(455\) | 0.199481 | 0.00935182 | ||||||||
\(456\) | −6.89185 | −0.322741 | ||||||||
\(457\) | 19.3974 | 0.907372 | 0.453686 | − | 0.891162i | \(-0.350109\pi\) | ||||
0.453686 | + | 0.891162i | \(0.350109\pi\) | |||||||
\(458\) | −0.366382 | −0.0171199 | ||||||||
\(459\) | 4.95903 | 0.231468 | ||||||||
\(460\) | 8.89424 | 0.414696 | ||||||||
\(461\) | −36.2967 | −1.69051 | −0.845253 | − | 0.534366i | \(-0.820551\pi\) | ||||
−0.845253 | + | 0.534366i | \(0.820551\pi\) | |||||||
\(462\) | 1.19360 | 0.0555313 | ||||||||
\(463\) | −27.7766 | −1.29089 | −0.645445 | − | 0.763807i | \(-0.723328\pi\) | ||||
−0.645445 | + | 0.763807i | \(0.723328\pi\) | |||||||
\(464\) | −2.48934 | −0.115565 | ||||||||
\(465\) | 6.33648 | 0.293847 | ||||||||
\(466\) | 19.6590 | 0.910686 | ||||||||
\(467\) | −24.9476 | −1.15444 | −0.577218 | − | 0.816590i | \(-0.695862\pi\) | ||||
−0.577218 | + | 0.816590i | \(0.695862\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −2.74106 | −0.126571 | ||||||||
\(470\) | −4.94988 | −0.228321 | ||||||||
\(471\) | 15.3375 | 0.706714 | ||||||||
\(472\) | 13.9362 | 0.641467 | ||||||||
\(473\) | 33.3914 | 1.53534 | ||||||||
\(474\) | 10.7464 | 0.493598 | ||||||||
\(475\) | 26.8162 | 1.23041 | ||||||||
\(476\) | 0.939362 | 0.0430556 | ||||||||
\(477\) | −12.3270 | −0.564414 | ||||||||
\(478\) | −10.2458 | −0.468633 | ||||||||
\(479\) | 20.9084 | 0.955328 | 0.477664 | − | 0.878543i | \(-0.341484\pi\) | ||||
0.477664 | + | 0.878543i | \(0.341484\pi\) | |||||||
\(480\) | 1.05309 | 0.0480668 | ||||||||
\(481\) | −0.704737 | −0.0321332 | ||||||||
\(482\) | −4.66441 | −0.212458 | ||||||||
\(483\) | 1.59985 | 0.0727958 | ||||||||
\(484\) | 28.7050 | 1.30477 | ||||||||
\(485\) | −2.24947 | −0.102143 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −8.35360 | −0.378538 | −0.189269 | − | 0.981925i | \(-0.560612\pi\) | ||||
−0.189269 | + | 0.981925i | \(0.560612\pi\) | |||||||
\(488\) | −1.74461 | −0.0789750 | ||||||||
\(489\) | −19.0841 | −0.863013 | ||||||||
\(490\) | 7.33384 | 0.331309 | ||||||||
\(491\) | 15.5291 | 0.700817 | 0.350408 | − | 0.936597i | \(-0.386043\pi\) | ||||
0.350408 | + | 0.936597i | \(0.386043\pi\) | |||||||
\(492\) | 0.424853 | 0.0191538 | ||||||||
\(493\) | 12.3447 | 0.555978 | ||||||||
\(494\) | −6.89185 | −0.310079 | ||||||||
\(495\) | −6.63573 | −0.298254 | ||||||||
\(496\) | −6.01703 | −0.270173 | ||||||||
\(497\) | −2.41380 | −0.108274 | ||||||||
\(498\) | −7.04418 | −0.315657 | ||||||||
\(499\) | −2.73506 | −0.122438 | −0.0612190 | − | 0.998124i | \(-0.519499\pi\) | ||||
−0.0612190 | + | 0.998124i | \(0.519499\pi\) | |||||||
\(500\) | −9.36303 | −0.418727 | ||||||||
\(501\) | −10.4370 | −0.466291 | ||||||||
\(502\) | −8.36406 | −0.373306 | ||||||||
\(503\) | 1.42393 | 0.0634897 | 0.0317448 | − | 0.999496i | \(-0.489894\pi\) | ||||
0.0317448 | + | 0.999496i | \(0.489894\pi\) | |||||||
\(504\) | 0.189425 | 0.00843764 | ||||||||
\(505\) | −6.35948 | −0.282993 | ||||||||
\(506\) | 53.2190 | 2.36587 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 17.8983 | 0.794108 | ||||||||
\(509\) | 14.0771 | 0.623957 | 0.311978 | − | 0.950089i | \(-0.399008\pi\) | ||||
0.311978 | + | 0.950089i | \(0.399008\pi\) | |||||||
\(510\) | −5.22231 | −0.231248 | ||||||||
\(511\) | −1.65410 | −0.0731729 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.89185 | 0.304283 | ||||||||
\(514\) | 11.3987 | 0.502774 | ||||||||
\(515\) | 1.05309 | 0.0464047 | ||||||||
\(516\) | 5.29921 | 0.233285 | ||||||||
\(517\) | −29.6177 | −1.30259 | ||||||||
\(518\) | 0.133494 | 0.00586541 | ||||||||
\(519\) | 2.06672 | 0.0907191 | ||||||||
\(520\) | 1.05309 | 0.0461811 | ||||||||
\(521\) | −31.7922 | −1.39284 | −0.696421 | − | 0.717633i | \(-0.745225\pi\) | ||||
−0.696421 | + | 0.717633i | \(0.745225\pi\) | |||||||
\(522\) | 2.48934 | 0.108956 | ||||||||
\(523\) | 41.2495 | 1.80371 | 0.901857 | − | 0.432035i | \(-0.142204\pi\) | ||||
0.901857 | + | 0.432035i | \(0.142204\pi\) | |||||||
\(524\) | −10.5649 | −0.461531 | ||||||||
\(525\) | −0.737051 | −0.0321675 | ||||||||
\(526\) | 4.13508 | 0.180298 | ||||||||
\(527\) | 29.8386 | 1.29979 | ||||||||
\(528\) | 6.30119 | 0.274224 | ||||||||
\(529\) | 48.3324 | 2.10141 | ||||||||
\(530\) | 12.9814 | 0.563877 | ||||||||
\(531\) | −13.9362 | −0.604781 | ||||||||
\(532\) | 1.30549 | 0.0566000 | ||||||||
\(533\) | 0.424853 | 0.0184024 | ||||||||
\(534\) | −11.5379 | −0.499293 | ||||||||
\(535\) | 3.34156 | 0.144468 | ||||||||
\(536\) | −14.4705 | −0.625030 | ||||||||
\(537\) | 8.42487 | 0.363560 | ||||||||
\(538\) | 27.1252 | 1.16945 | ||||||||
\(539\) | 43.8823 | 1.89014 | ||||||||
\(540\) | −1.05309 | −0.0453178 | ||||||||
\(541\) | −19.3016 | −0.829843 | −0.414921 | − | 0.909857i | \(-0.636191\pi\) | ||||
−0.414921 | + | 0.909857i | \(0.636191\pi\) | |||||||
\(542\) | −15.3612 | −0.659820 | ||||||||
\(543\) | 10.7366 | 0.460751 | ||||||||
\(544\) | 4.95903 | 0.212617 | ||||||||
\(545\) | 0.707912 | 0.0303236 | ||||||||
\(546\) | 0.189425 | 0.00810662 | ||||||||
\(547\) | 37.9160 | 1.62117 | 0.810584 | − | 0.585622i | \(-0.199150\pi\) | ||||
0.810584 | + | 0.585622i | \(0.199150\pi\) | |||||||
\(548\) | 20.2743 | 0.866076 | ||||||||
\(549\) | 1.74461 | 0.0744583 | ||||||||
\(550\) | −24.5180 | −1.04545 | ||||||||
\(551\) | 17.1562 | 0.730878 | ||||||||
\(552\) | 8.44585 | 0.359479 | ||||||||
\(553\) | −2.03563 | −0.0865637 | ||||||||
\(554\) | 11.8077 | 0.501659 | ||||||||
\(555\) | −0.742151 | −0.0315026 | ||||||||
\(556\) | 10.8071 | 0.458323 | ||||||||
\(557\) | −38.2536 | −1.62086 | −0.810428 | − | 0.585838i | \(-0.800766\pi\) | ||||
−0.810428 | + | 0.585838i | \(0.800766\pi\) | |||||||
\(558\) | 6.01703 | 0.254721 | ||||||||
\(559\) | 5.29921 | 0.224133 | ||||||||
\(560\) | −0.199481 | −0.00842961 | ||||||||
\(561\) | −31.2478 | −1.31928 | ||||||||
\(562\) | −11.4689 | −0.483784 | ||||||||
\(563\) | −33.2804 | −1.40260 | −0.701301 | − | 0.712866i | \(-0.747397\pi\) | ||||
−0.701301 | + | 0.712866i | \(0.747397\pi\) | |||||||
\(564\) | −4.70034 | −0.197920 | ||||||||
\(565\) | −1.44356 | −0.0607312 | ||||||||
\(566\) | −25.0579 | −1.05326 | ||||||||
\(567\) | −0.189425 | −0.00795508 | ||||||||
\(568\) | −12.7428 | −0.534676 | ||||||||
\(569\) | 34.3452 | 1.43983 | 0.719913 | − | 0.694064i | \(-0.244181\pi\) | ||||
0.719913 | + | 0.694064i | \(0.244181\pi\) | |||||||
\(570\) | −7.25774 | −0.303993 | ||||||||
\(571\) | 3.88244 | 0.162475 | 0.0812376 | − | 0.996695i | \(-0.474113\pi\) | ||||
0.0812376 | + | 0.996695i | \(0.474113\pi\) | |||||||
\(572\) | 6.30119 | 0.263466 | ||||||||
\(573\) | 1.14807 | 0.0479614 | ||||||||
\(574\) | −0.0804775 | −0.00335907 | ||||||||
\(575\) | −32.8628 | −1.37047 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 36.7291 | 1.52905 | 0.764527 | − | 0.644592i | \(-0.222973\pi\) | ||||
0.764527 | + | 0.644592i | \(0.222973\pi\) | |||||||
\(578\) | −7.59198 | −0.315785 | ||||||||
\(579\) | −3.72614 | −0.154853 | ||||||||
\(580\) | −2.62150 | −0.108852 | ||||||||
\(581\) | 1.33434 | 0.0553578 | ||||||||
\(582\) | −2.13606 | −0.0885426 | ||||||||
\(583\) | 77.6748 | 3.21696 | ||||||||
\(584\) | −8.73221 | −0.361342 | ||||||||
\(585\) | −1.05309 | −0.0435399 | ||||||||
\(586\) | −0.545131 | −0.0225191 | ||||||||
\(587\) | 18.4319 | 0.760767 | 0.380384 | − | 0.924829i | \(-0.375792\pi\) | ||||
0.380384 | + | 0.924829i | \(0.375792\pi\) | |||||||
\(588\) | 6.96412 | 0.287195 | ||||||||
\(589\) | 41.4685 | 1.70868 | ||||||||
\(590\) | 14.6761 | 0.604206 | ||||||||
\(591\) | 7.52027 | 0.309342 | ||||||||
\(592\) | 0.704737 | 0.0289645 | ||||||||
\(593\) | 18.8293 | 0.773228 | 0.386614 | − | 0.922242i | \(-0.373645\pi\) | ||||
0.386614 | + | 0.922242i | \(0.373645\pi\) | |||||||
\(594\) | −6.30119 | −0.258541 | ||||||||
\(595\) | 0.989233 | 0.0405546 | ||||||||
\(596\) | 16.2553 | 0.665841 | ||||||||
\(597\) | 12.7348 | 0.521201 | ||||||||
\(598\) | 8.44585 | 0.345377 | ||||||||
\(599\) | −19.8400 | −0.810641 | −0.405320 | − | 0.914175i | \(-0.632840\pi\) | ||||
−0.405320 | + | 0.914175i | \(0.632840\pi\) | |||||||
\(600\) | −3.89100 | −0.158849 | ||||||||
\(601\) | −40.2792 | −1.64302 | −0.821512 | − | 0.570192i | \(-0.806869\pi\) | ||||
−0.821512 | + | 0.570192i | \(0.806869\pi\) | |||||||
\(602\) | −1.00380 | −0.0409119 | ||||||||
\(603\) | 14.4705 | 0.589284 | ||||||||
\(604\) | 18.2933 | 0.744344 | ||||||||
\(605\) | 30.2290 | 1.22898 | ||||||||
\(606\) | −6.03888 | −0.245313 | ||||||||
\(607\) | −22.1552 | −0.899253 | −0.449626 | − | 0.893217i | \(-0.648443\pi\) | ||||
−0.449626 | + | 0.893217i | \(0.648443\pi\) | |||||||
\(608\) | 6.89185 | 0.279502 | ||||||||
\(609\) | −0.471542 | −0.0191079 | ||||||||
\(610\) | −1.83724 | −0.0743875 | ||||||||
\(611\) | −4.70034 | −0.190155 | ||||||||
\(612\) | −4.95903 | −0.200457 | ||||||||
\(613\) | −15.1016 | −0.609946 | −0.304973 | − | 0.952361i | \(-0.598647\pi\) | ||||
−0.304973 | + | 0.952361i | \(0.598647\pi\) | |||||||
\(614\) | −25.4222 | −1.02595 | ||||||||
\(615\) | 0.447408 | 0.0180412 | ||||||||
\(616\) | −1.19360 | −0.0480915 | ||||||||
\(617\) | −7.10984 | −0.286231 | −0.143116 | − | 0.989706i | \(-0.545712\pi\) | ||||
−0.143116 | + | 0.989706i | \(0.545712\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 38.9573 | 1.56582 | 0.782912 | − | 0.622132i | \(-0.213733\pi\) | ||||
0.782912 | + | 0.622132i | \(0.213733\pi\) | |||||||
\(620\) | −6.33648 | −0.254479 | ||||||||
\(621\) | −8.44585 | −0.338920 | ||||||||
\(622\) | 31.7263 | 1.27211 | ||||||||
\(623\) | 2.18556 | 0.0875625 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 9.59490 | 0.383796 | ||||||||
\(626\) | 13.1655 | 0.526198 | ||||||||
\(627\) | −43.4269 | −1.73430 | ||||||||
\(628\) | −15.3375 | −0.612032 | ||||||||
\(629\) | −3.49481 | −0.139347 | ||||||||
\(630\) | 0.199481 | 0.00794752 | ||||||||
\(631\) | −18.8358 | −0.749839 | −0.374920 | − | 0.927057i | \(-0.622330\pi\) | ||||
−0.374920 | + | 0.927057i | \(0.622330\pi\) | |||||||
\(632\) | −10.7464 | −0.427468 | ||||||||
\(633\) | 13.2352 | 0.526051 | ||||||||
\(634\) | −24.2733 | −0.964014 | ||||||||
\(635\) | 18.8485 | 0.747980 | ||||||||
\(636\) | 12.3270 | 0.488797 | ||||||||
\(637\) | 6.96412 | 0.275928 | ||||||||
\(638\) | −15.6858 | −0.621008 | ||||||||
\(639\) | 12.7428 | 0.504097 | ||||||||
\(640\) | −1.05309 | −0.0416270 | ||||||||
\(641\) | 48.3133 | 1.90826 | 0.954130 | − | 0.299392i | \(-0.0967838\pi\) | ||||
0.954130 | + | 0.299392i | \(0.0967838\pi\) | |||||||
\(642\) | 3.17310 | 0.125232 | ||||||||
\(643\) | −11.6209 | −0.458284 | −0.229142 | − | 0.973393i | \(-0.573592\pi\) | ||||
−0.229142 | + | 0.973393i | \(0.573592\pi\) | |||||||
\(644\) | −1.59985 | −0.0630430 | ||||||||
\(645\) | 5.58055 | 0.219734 | ||||||||
\(646\) | −34.1769 | −1.34467 | ||||||||
\(647\) | 40.7120 | 1.60055 | 0.800277 | − | 0.599630i | \(-0.204686\pi\) | ||||
0.800277 | + | 0.599630i | \(0.204686\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 87.8149 | 3.44704 | ||||||||
\(650\) | −3.89100 | −0.152618 | ||||||||
\(651\) | −1.13977 | −0.0446712 | ||||||||
\(652\) | 19.0841 | 0.747391 | ||||||||
\(653\) | −15.4355 | −0.604037 | −0.302018 | − | 0.953302i | \(-0.597660\pi\) | ||||
−0.302018 | + | 0.953302i | \(0.597660\pi\) | |||||||
\(654\) | 0.672224 | 0.0262860 | ||||||||
\(655\) | −11.1258 | −0.434722 | ||||||||
\(656\) | −0.424853 | −0.0165877 | ||||||||
\(657\) | 8.73221 | 0.340676 | ||||||||
\(658\) | 0.890359 | 0.0347098 | ||||||||
\(659\) | −35.0061 | −1.36364 | −0.681821 | − | 0.731519i | \(-0.738812\pi\) | ||||
−0.681821 | + | 0.731519i | \(0.738812\pi\) | |||||||
\(660\) | 6.63573 | 0.258295 | ||||||||
\(661\) | −5.46991 | −0.212755 | −0.106377 | − | 0.994326i | \(-0.533925\pi\) | ||||
−0.106377 | + | 0.994326i | \(0.533925\pi\) | |||||||
\(662\) | 14.0156 | 0.544732 | ||||||||
\(663\) | −4.95903 | −0.192593 | ||||||||
\(664\) | 7.04418 | 0.273367 | ||||||||
\(665\) | 1.37479 | 0.0533122 | ||||||||
\(666\) | −0.704737 | −0.0273080 | ||||||||
\(667\) | −21.0246 | −0.814076 | ||||||||
\(668\) | 10.4370 | 0.403820 | ||||||||
\(669\) | −0.794330 | −0.0307106 | ||||||||
\(670\) | −15.2387 | −0.588723 | ||||||||
\(671\) | −10.9932 | −0.424386 | ||||||||
\(672\) | −0.189425 | −0.00730721 | ||||||||
\(673\) | 9.16405 | 0.353248 | 0.176624 | − | 0.984278i | \(-0.443482\pi\) | ||||
0.176624 | + | 0.984278i | \(0.443482\pi\) | |||||||
\(674\) | 33.6272 | 1.29527 | ||||||||
\(675\) | 3.89100 | 0.149765 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 41.6779 | 1.60181 | 0.800906 | − | 0.598789i | \(-0.204351\pi\) | ||||
0.800906 | + | 0.598789i | \(0.204351\pi\) | |||||||
\(678\) | −1.37079 | −0.0526448 | ||||||||
\(679\) | 0.404622 | 0.0155280 | ||||||||
\(680\) | 5.22231 | 0.200266 | ||||||||
\(681\) | 19.8316 | 0.759948 | ||||||||
\(682\) | −37.9145 | −1.45182 | ||||||||
\(683\) | −22.7126 | −0.869072 | −0.434536 | − | 0.900654i | \(-0.643088\pi\) | ||||
−0.434536 | + | 0.900654i | \(0.643088\pi\) | |||||||
\(684\) | −6.89185 | −0.263517 | ||||||||
\(685\) | 21.3507 | 0.815768 | ||||||||
\(686\) | −2.64515 | −0.100992 | ||||||||
\(687\) | −0.366382 | −0.0139784 | ||||||||
\(688\) | −5.29921 | −0.202031 | ||||||||
\(689\) | 12.3270 | 0.469621 | ||||||||
\(690\) | 8.89424 | 0.338598 | ||||||||
\(691\) | 18.2678 | 0.694938 | 0.347469 | − | 0.937691i | \(-0.387041\pi\) | ||||
0.347469 | + | 0.937691i | \(0.387041\pi\) | |||||||
\(692\) | −2.06672 | −0.0785650 | ||||||||
\(693\) | 1.19360 | 0.0453411 | ||||||||
\(694\) | 8.14151 | 0.309048 | ||||||||
\(695\) | 11.3808 | 0.431700 | ||||||||
\(696\) | −2.48934 | −0.0943582 | ||||||||
\(697\) | 2.10686 | 0.0798029 | ||||||||
\(698\) | −27.9084 | −1.05635 | ||||||||
\(699\) | 19.6590 | 0.743572 | ||||||||
\(700\) | 0.737051 | 0.0278579 | ||||||||
\(701\) | −6.76574 | −0.255538 | −0.127769 | − | 0.991804i | \(-0.540782\pi\) | ||||
−0.127769 | + | 0.991804i | \(0.540782\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −4.85694 | −0.183183 | ||||||||
\(704\) | −6.30119 | −0.237485 | ||||||||
\(705\) | −4.94988 | −0.186423 | ||||||||
\(706\) | 9.11644 | 0.343102 | ||||||||
\(707\) | 1.14391 | 0.0430212 | ||||||||
\(708\) | 13.9362 | 0.523756 | ||||||||
\(709\) | 15.1334 | 0.568348 | 0.284174 | − | 0.958773i | \(-0.408281\pi\) | ||||
0.284174 | + | 0.958773i | \(0.408281\pi\) | |||||||
\(710\) | −13.4193 | −0.503618 | ||||||||
\(711\) | 10.7464 | 0.403021 | ||||||||
\(712\) | 11.5379 | 0.432400 | ||||||||
\(713\) | −50.8189 | −1.90318 | ||||||||
\(714\) | 0.939362 | 0.0351547 | ||||||||
\(715\) | 6.63573 | 0.248162 | ||||||||
\(716\) | −8.42487 | −0.314852 | ||||||||
\(717\) | −10.2458 | −0.382637 | ||||||||
\(718\) | 16.4159 | 0.612636 | ||||||||
\(719\) | −4.18830 | −0.156197 | −0.0780987 | − | 0.996946i | \(-0.524885\pi\) | ||||
−0.0780987 | + | 0.996946i | \(0.524885\pi\) | |||||||
\(720\) | 1.05309 | 0.0392464 | ||||||||
\(721\) | −0.189425 | −0.00705454 | ||||||||
\(722\) | −28.4976 | −1.06057 | ||||||||
\(723\) | −4.66441 | −0.173471 | ||||||||
\(724\) | −10.7366 | −0.399022 | ||||||||
\(725\) | 9.68603 | 0.359730 | ||||||||
\(726\) | 28.7050 | 1.06534 | ||||||||
\(727\) | 24.6242 | 0.913262 | 0.456631 | − | 0.889656i | \(-0.349056\pi\) | ||||
0.456631 | + | 0.889656i | \(0.349056\pi\) | |||||||
\(728\) | −0.189425 | −0.00702054 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.19581 | −0.340352 | ||||||||
\(731\) | 26.2789 | 0.971962 | ||||||||
\(732\) | −1.74461 | −0.0644828 | ||||||||
\(733\) | 17.7081 | 0.654065 | 0.327032 | − | 0.945013i | \(-0.393951\pi\) | ||||
0.327032 | + | 0.945013i | \(0.393951\pi\) | |||||||
\(734\) | 33.3974 | 1.23272 | ||||||||
\(735\) | 7.33384 | 0.270513 | ||||||||
\(736\) | −8.44585 | −0.311318 | ||||||||
\(737\) | −91.1813 | −3.35871 | ||||||||
\(738\) | 0.424853 | 0.0156390 | ||||||||
\(739\) | −32.5190 | −1.19623 | −0.598114 | − | 0.801411i | \(-0.704083\pi\) | ||||
−0.598114 | + | 0.801411i | \(0.704083\pi\) | |||||||
\(740\) | 0.742151 | 0.0272820 | ||||||||
\(741\) | −6.89185 | −0.253179 | ||||||||
\(742\) | −2.33503 | −0.0857218 | ||||||||
\(743\) | 44.1268 | 1.61886 | 0.809428 | − | 0.587219i | \(-0.199777\pi\) | ||||
0.809428 | + | 0.587219i | \(0.199777\pi\) | |||||||
\(744\) | −6.01703 | −0.220595 | ||||||||
\(745\) | 17.1182 | 0.627164 | ||||||||
\(746\) | −9.39484 | −0.343970 | ||||||||
\(747\) | −7.04418 | −0.257733 | ||||||||
\(748\) | 31.2478 | 1.14253 | ||||||||
\(749\) | −0.601063 | −0.0219624 | ||||||||
\(750\) | −9.36303 | −0.341889 | ||||||||
\(751\) | 35.2019 | 1.28453 | 0.642267 | − | 0.766481i | \(-0.277994\pi\) | ||||
0.642267 | + | 0.766481i | \(0.277994\pi\) | |||||||
\(752\) | 4.70034 | 0.171404 | ||||||||
\(753\) | −8.36406 | −0.304803 | ||||||||
\(754\) | −2.48934 | −0.0906565 | ||||||||
\(755\) | 19.2645 | 0.701107 | ||||||||
\(756\) | 0.189425 | 0.00688930 | ||||||||
\(757\) | −8.50362 | −0.309069 | −0.154535 | − | 0.987987i | \(-0.549388\pi\) | ||||
−0.154535 | + | 0.987987i | \(0.549388\pi\) | |||||||
\(758\) | −18.9930 | −0.689858 | ||||||||
\(759\) | 53.2190 | 1.93173 | ||||||||
\(760\) | 7.25774 | 0.263266 | ||||||||
\(761\) | 20.9888 | 0.760845 | 0.380422 | − | 0.924813i | \(-0.375779\pi\) | ||||
0.380422 | + | 0.924813i | \(0.375779\pi\) | |||||||
\(762\) | 17.8983 | 0.648387 | ||||||||
\(763\) | −0.127336 | −0.00460986 | ||||||||
\(764\) | −1.14807 | −0.0415358 | ||||||||
\(765\) | −5.22231 | −0.188813 | ||||||||
\(766\) | −11.2538 | −0.406618 | ||||||||
\(767\) | 13.9362 | 0.503208 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −19.0681 | −0.687614 | −0.343807 | − | 0.939040i | \(-0.611717\pi\) | ||||
−0.343807 | + | 0.939040i | \(0.611717\pi\) | |||||||
\(770\) | −1.25697 | −0.0452980 | ||||||||
\(771\) | 11.3987 | 0.410514 | ||||||||
\(772\) | 3.72614 | 0.134107 | ||||||||
\(773\) | −29.6344 | −1.06587 | −0.532937 | − | 0.846155i | \(-0.678912\pi\) | ||||
−0.532937 | + | 0.846155i | \(0.678912\pi\) | |||||||
\(774\) | 5.29921 | 0.190476 | ||||||||
\(775\) | 23.4123 | 0.840994 | ||||||||
\(776\) | 2.13606 | 0.0766801 | ||||||||
\(777\) | 0.133494 | 0.00478909 | ||||||||
\(778\) | −25.8266 | −0.925928 | ||||||||
\(779\) | 2.92802 | 0.104907 | ||||||||
\(780\) | 1.05309 | 0.0377067 | ||||||||
\(781\) | −80.2948 | −2.87317 | ||||||||
\(782\) | 41.8832 | 1.49774 | ||||||||
\(783\) | 2.48934 | 0.0889618 | ||||||||
\(784\) | −6.96412 | −0.248719 | ||||||||
\(785\) | −16.1518 | −0.576481 | ||||||||
\(786\) | −10.5649 | −0.376838 | ||||||||
\(787\) | −28.8046 | −1.02677 | −0.513387 | − | 0.858157i | \(-0.671609\pi\) | ||||
−0.513387 | + | 0.858157i | \(0.671609\pi\) | |||||||
\(788\) | −7.52027 | −0.267898 | ||||||||
\(789\) | 4.13508 | 0.147213 | ||||||||
\(790\) | −11.3169 | −0.402638 | ||||||||
\(791\) | 0.259661 | 0.00923248 | ||||||||
\(792\) | 6.30119 | 0.223903 | ||||||||
\(793\) | −1.74461 | −0.0619531 | ||||||||
\(794\) | −4.09534 | −0.145338 | ||||||||
\(795\) | 12.9814 | 0.460404 | ||||||||
\(796\) | −12.7348 | −0.451373 | ||||||||
\(797\) | −44.8138 | −1.58739 | −0.793693 | − | 0.608319i | \(-0.791844\pi\) | ||||
−0.793693 | + | 0.608319i | \(0.791844\pi\) | |||||||
\(798\) | 1.30549 | 0.0462137 | ||||||||
\(799\) | −23.3091 | −0.824617 | ||||||||
\(800\) | 3.89100 | 0.137568 | ||||||||
\(801\) | −11.5379 | −0.407671 | ||||||||
\(802\) | −4.12362 | −0.145610 | ||||||||
\(803\) | −55.0234 | −1.94173 | ||||||||
\(804\) | −14.4705 | −0.510335 | ||||||||
\(805\) | −1.68479 | −0.0593810 | ||||||||
\(806\) | −6.01703 | −0.211941 | ||||||||
\(807\) | 27.1252 | 0.954853 | ||||||||
\(808\) | 6.03888 | 0.212447 | ||||||||
\(809\) | 50.2362 | 1.76621 | 0.883105 | − | 0.469175i | \(-0.155449\pi\) | ||||
0.883105 | + | 0.469175i | \(0.155449\pi\) | |||||||
\(810\) | −1.05309 | −0.0370018 | ||||||||
\(811\) | 19.0399 | 0.668581 | 0.334290 | − | 0.942470i | \(-0.391503\pi\) | ||||
0.334290 | + | 0.942470i | \(0.391503\pi\) | |||||||
\(812\) | 0.471542 | 0.0165479 | ||||||||
\(813\) | −15.3612 | −0.538741 | ||||||||
\(814\) | 4.44068 | 0.155646 | ||||||||
\(815\) | 20.0973 | 0.703977 | ||||||||
\(816\) | 4.95903 | 0.173601 | ||||||||
\(817\) | 36.5214 | 1.27772 | ||||||||
\(818\) | 28.7895 | 1.00660 | ||||||||
\(819\) | 0.189425 | 0.00661903 | ||||||||
\(820\) | −0.447408 | −0.0156242 | ||||||||
\(821\) | 37.2395 | 1.29967 | 0.649834 | − | 0.760076i | \(-0.274838\pi\) | ||||
0.649834 | + | 0.760076i | \(0.274838\pi\) | |||||||
\(822\) | 20.2743 | 0.707148 | ||||||||
\(823\) | −5.46725 | −0.190576 | −0.0952882 | − | 0.995450i | \(-0.530377\pi\) | ||||
−0.0952882 | + | 0.995450i | \(0.530377\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −24.5180 | −0.853606 | ||||||||
\(826\) | −2.63986 | −0.0918526 | ||||||||
\(827\) | 38.4335 | 1.33647 | 0.668233 | − | 0.743952i | \(-0.267051\pi\) | ||||
0.668233 | + | 0.743952i | \(0.267051\pi\) | |||||||
\(828\) | 8.44585 | 0.293514 | ||||||||
\(829\) | −7.35497 | −0.255449 | −0.127724 | − | 0.991810i | \(-0.540767\pi\) | ||||
−0.127724 | + | 0.991810i | \(0.540767\pi\) | |||||||
\(830\) | 7.41816 | 0.257488 | ||||||||
\(831\) | 11.8077 | 0.409603 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 34.5353 | 1.19658 | ||||||||
\(834\) | 10.8071 | 0.374219 | ||||||||
\(835\) | 10.9911 | 0.380363 | ||||||||
\(836\) | 43.4269 | 1.50195 | ||||||||
\(837\) | 6.01703 | 0.207979 | ||||||||
\(838\) | −2.93488 | −0.101384 | ||||||||
\(839\) | −50.6337 | −1.74807 | −0.874035 | − | 0.485862i | \(-0.838506\pi\) | ||||
−0.874035 | + | 0.485862i | \(0.838506\pi\) | |||||||
\(840\) | −0.199481 | −0.00688275 | ||||||||
\(841\) | −22.8032 | −0.786317 | ||||||||
\(842\) | −17.2512 | −0.594515 | ||||||||
\(843\) | −11.4689 | −0.395008 | ||||||||
\(844\) | −13.2352 | −0.455574 | ||||||||
\(845\) | 1.05309 | 0.0362274 | ||||||||
\(846\) | −4.70034 | −0.161601 | ||||||||
\(847\) | −5.43744 | −0.186833 | ||||||||
\(848\) | −12.3270 | −0.423311 | ||||||||
\(849\) | −25.0579 | −0.859986 | ||||||||
\(850\) | −19.2956 | −0.661833 | ||||||||
\(851\) | 5.95210 | 0.204035 | ||||||||
\(852\) | −12.7428 | −0.436561 | ||||||||
\(853\) | −5.22926 | −0.179046 | −0.0895232 | − | 0.995985i | \(-0.528534\pi\) | ||||
−0.0895232 | + | 0.995985i | \(0.528534\pi\) | |||||||
\(854\) | 0.330473 | 0.0113085 | ||||||||
\(855\) | −7.25774 | −0.248210 | ||||||||
\(856\) | −3.17310 | −0.108454 | ||||||||
\(857\) | 4.92641 | 0.168283 | 0.0841415 | − | 0.996454i | \(-0.473185\pi\) | ||||
0.0841415 | + | 0.996454i | \(0.473185\pi\) | |||||||
\(858\) | 6.30119 | 0.215119 | ||||||||
\(859\) | −17.2776 | −0.589506 | −0.294753 | − | 0.955574i | \(-0.595237\pi\) | ||||
−0.294753 | + | 0.955574i | \(0.595237\pi\) | |||||||
\(860\) | −5.58055 | −0.190295 | ||||||||
\(861\) | −0.0804775 | −0.00274267 | ||||||||
\(862\) | −28.0145 | −0.954178 | ||||||||
\(863\) | −48.6896 | −1.65741 | −0.828707 | − | 0.559682i | \(-0.810923\pi\) | ||||
−0.828707 | + | 0.559682i | \(0.810923\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −2.17645 | −0.0740014 | ||||||||
\(866\) | 0.102646 | 0.00348805 | ||||||||
\(867\) | −7.59198 | −0.257837 | ||||||||
\(868\) | 1.13977 | 0.0386864 | ||||||||
\(869\) | −67.7151 | −2.29708 | ||||||||
\(870\) | −2.62150 | −0.0888772 | ||||||||
\(871\) | −14.4705 | −0.490314 | ||||||||
\(872\) | −0.672224 | −0.0227644 | ||||||||
\(873\) | −2.13606 | −0.0722947 | ||||||||
\(874\) | 58.2076 | 1.96890 | ||||||||
\(875\) | 1.77359 | 0.0599582 | ||||||||
\(876\) | −8.73221 | −0.295034 | ||||||||
\(877\) | −34.5015 | −1.16503 | −0.582516 | − | 0.812819i | \(-0.697932\pi\) | ||||
−0.582516 | + | 0.812819i | \(0.697932\pi\) | |||||||
\(878\) | −23.1977 | −0.782883 | ||||||||
\(879\) | −0.545131 | −0.0183868 | ||||||||
\(880\) | −6.63573 | −0.223690 | ||||||||
\(881\) | 23.8168 | 0.802408 | 0.401204 | − | 0.915989i | \(-0.368592\pi\) | ||||
0.401204 | + | 0.915989i | \(0.368592\pi\) | |||||||
\(882\) | 6.96412 | 0.234494 | ||||||||
\(883\) | 41.0927 | 1.38288 | 0.691440 | − | 0.722434i | \(-0.256977\pi\) | ||||
0.691440 | + | 0.722434i | \(0.256977\pi\) | |||||||
\(884\) | 4.95903 | 0.166790 | ||||||||
\(885\) | 14.6761 | 0.493332 | ||||||||
\(886\) | −5.64862 | −0.189769 | ||||||||
\(887\) | 45.8192 | 1.53846 | 0.769229 | − | 0.638973i | \(-0.220640\pi\) | ||||
0.769229 | + | 0.638973i | \(0.220640\pi\) | |||||||
\(888\) | 0.704737 | 0.0236494 | ||||||||
\(889\) | −3.39037 | −0.113709 | ||||||||
\(890\) | 12.1504 | 0.407283 | ||||||||
\(891\) | −6.30119 | −0.211098 | ||||||||
\(892\) | 0.794330 | 0.0265961 | ||||||||
\(893\) | −32.3940 | −1.08402 | ||||||||
\(894\) | 16.2553 | 0.543657 | ||||||||
\(895\) | −8.87214 | −0.296563 | ||||||||
\(896\) | 0.189425 | 0.00632823 | ||||||||
\(897\) | 8.44585 | 0.281999 | ||||||||
\(898\) | 12.3808 | 0.413154 | ||||||||
\(899\) | 14.9784 | 0.499559 | ||||||||
\(900\) | −3.89100 | −0.129700 | ||||||||
\(901\) | 61.1299 | 2.03653 | ||||||||
\(902\) | −2.67708 | −0.0891370 | ||||||||
\(903\) | −1.00380 | −0.0334044 | ||||||||
\(904\) | 1.37079 | 0.0455918 | ||||||||
\(905\) | −11.3066 | −0.375844 | ||||||||
\(906\) | 18.2933 | 0.607754 | ||||||||
\(907\) | 21.1713 | 0.702980 | 0.351490 | − | 0.936192i | \(-0.385675\pi\) | ||||
0.351490 | + | 0.936192i | \(0.385675\pi\) | |||||||
\(908\) | −19.8316 | −0.658134 | ||||||||
\(909\) | −6.03888 | −0.200297 | ||||||||
\(910\) | −0.199481 | −0.00661273 | ||||||||
\(911\) | −43.2041 | −1.43142 | −0.715708 | − | 0.698400i | \(-0.753896\pi\) | ||||
−0.715708 | + | 0.698400i | \(0.753896\pi\) | |||||||
\(912\) | 6.89185 | 0.228212 | ||||||||
\(913\) | 44.3867 | 1.46899 | ||||||||
\(914\) | −19.3974 | −0.641609 | ||||||||
\(915\) | −1.83724 | −0.0607372 | ||||||||
\(916\) | 0.366382 | 0.0121056 | ||||||||
\(917\) | 2.00126 | 0.0660873 | ||||||||
\(918\) | −4.95903 | −0.163672 | ||||||||
\(919\) | 54.5527 | 1.79953 | 0.899764 | − | 0.436378i | \(-0.143739\pi\) | ||||
0.899764 | + | 0.436378i | \(0.143739\pi\) | |||||||
\(920\) | −8.89424 | −0.293235 | ||||||||
\(921\) | −25.4222 | −0.837689 | ||||||||
\(922\) | 36.2967 | 1.19537 | ||||||||
\(923\) | −12.7428 | −0.419434 | ||||||||
\(924\) | −1.19360 | −0.0392666 | ||||||||
\(925\) | −2.74213 | −0.0901607 | ||||||||
\(926\) | 27.7766 | 0.912797 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 2.48934 | 0.0817166 | ||||||||
\(929\) | −15.0501 | −0.493778 | −0.246889 | − | 0.969044i | \(-0.579408\pi\) | ||||
−0.246889 | + | 0.969044i | \(0.579408\pi\) | |||||||
\(930\) | −6.33648 | −0.207781 | ||||||||
\(931\) | 47.9957 | 1.57299 | ||||||||
\(932\) | −19.6590 | −0.643952 | ||||||||
\(933\) | 31.7263 | 1.03867 | ||||||||
\(934\) | 24.9476 | 0.816310 | ||||||||
\(935\) | 32.9068 | 1.07617 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 8.25479 | 0.269672 | 0.134836 | − | 0.990868i | \(-0.456949\pi\) | ||||
0.134836 | + | 0.990868i | \(0.456949\pi\) | |||||||
\(938\) | 2.74106 | 0.0894989 | ||||||||
\(939\) | 13.1655 | 0.429639 | ||||||||
\(940\) | 4.94988 | 0.161447 | ||||||||
\(941\) | −34.1684 | −1.11386 | −0.556928 | − | 0.830561i | \(-0.688020\pi\) | ||||
−0.556928 | + | 0.830561i | \(0.688020\pi\) | |||||||
\(942\) | −15.3375 | −0.499722 | ||||||||
\(943\) | −3.58824 | −0.116849 | ||||||||
\(944\) | −13.9362 | −0.453586 | ||||||||
\(945\) | 0.199481 | 0.00648912 | ||||||||
\(946\) | −33.3914 | −1.08565 | ||||||||
\(947\) | 16.4384 | 0.534175 | 0.267087 | − | 0.963672i | \(-0.413939\pi\) | ||||
0.267087 | + | 0.963672i | \(0.413939\pi\) | |||||||
\(948\) | −10.7464 | −0.349026 | ||||||||
\(949\) | −8.73221 | −0.283460 | ||||||||
\(950\) | −26.8162 | −0.870033 | ||||||||
\(951\) | −24.2733 | −0.787114 | ||||||||
\(952\) | −0.939362 | −0.0304449 | ||||||||
\(953\) | 49.3439 | 1.59840 | 0.799202 | − | 0.601062i | \(-0.205256\pi\) | ||||
0.799202 | + | 0.601062i | \(0.205256\pi\) | |||||||
\(954\) | 12.3270 | 0.399101 | ||||||||
\(955\) | −1.20902 | −0.0391231 | ||||||||
\(956\) | 10.2458 | 0.331374 | ||||||||
\(957\) | −15.6858 | −0.507051 | ||||||||
\(958\) | −20.9084 | −0.675519 | ||||||||
\(959\) | −3.84045 | −0.124015 | ||||||||
\(960\) | −1.05309 | −0.0339883 | ||||||||
\(961\) | 5.20465 | 0.167892 | ||||||||
\(962\) | 0.704737 | 0.0227216 | ||||||||
\(963\) | 3.17310 | 0.102252 | ||||||||
\(964\) | 4.66441 | 0.150230 | ||||||||
\(965\) | 3.92396 | 0.126317 | ||||||||
\(966\) | −1.59985 | −0.0514744 | ||||||||
\(967\) | −33.3715 | −1.07316 | −0.536578 | − | 0.843851i | \(-0.680283\pi\) | ||||
−0.536578 | + | 0.843851i | \(0.680283\pi\) | |||||||
\(968\) | −28.7050 | −0.922615 | ||||||||
\(969\) | −34.1769 | −1.09792 | ||||||||
\(970\) | 2.24947 | 0.0722260 | ||||||||
\(971\) | −32.1683 | −1.03233 | −0.516165 | − | 0.856489i | \(-0.672641\pi\) | ||||
−0.516165 | + | 0.856489i | \(0.672641\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −2.04713 | −0.0656279 | ||||||||
\(974\) | 8.35360 | 0.267667 | ||||||||
\(975\) | −3.89100 | −0.124612 | ||||||||
\(976\) | 1.74461 | 0.0558437 | ||||||||
\(977\) | −42.1490 | −1.34847 | −0.674233 | − | 0.738519i | \(-0.735526\pi\) | ||||
−0.674233 | + | 0.738519i | \(0.735526\pi\) | |||||||
\(978\) | 19.0841 | 0.610242 | ||||||||
\(979\) | 72.7024 | 2.32358 | ||||||||
\(980\) | −7.33384 | −0.234271 | ||||||||
\(981\) | 0.672224 | 0.0214624 | ||||||||
\(982\) | −15.5291 | −0.495552 | ||||||||
\(983\) | −6.49059 | −0.207018 | −0.103509 | − | 0.994629i | \(-0.533007\pi\) | ||||
−0.103509 | + | 0.994629i | \(0.533007\pi\) | |||||||
\(984\) | −0.424853 | −0.0135438 | ||||||||
\(985\) | −7.91952 | −0.252337 | ||||||||
\(986\) | −12.3447 | −0.393136 | ||||||||
\(987\) | 0.890359 | 0.0283404 | ||||||||
\(988\) | 6.89185 | 0.219259 | ||||||||
\(989\) | −44.7564 | −1.42317 | ||||||||
\(990\) | 6.63573 | 0.210897 | ||||||||
\(991\) | 32.1833 | 1.02233 | 0.511167 | − | 0.859481i | \(-0.329213\pi\) | ||||
0.511167 | + | 0.859481i | \(0.329213\pi\) | |||||||
\(992\) | 6.01703 | 0.191041 | ||||||||
\(993\) | 14.0156 | 0.444772 | ||||||||
\(994\) | 2.41380 | 0.0765610 | ||||||||
\(995\) | −13.4109 | −0.425154 | ||||||||
\(996\) | 7.04418 | 0.223203 | ||||||||
\(997\) | 30.7553 | 0.974032 | 0.487016 | − | 0.873393i | \(-0.338085\pi\) | ||||
0.487016 | + | 0.873393i | \(0.338085\pi\) | |||||||
\(998\) | 2.73506 | 0.0865767 | ||||||||
\(999\) | −0.704737 | −0.0222969 |
(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 | 8034.2.a.ba.1.10 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.ba.1.10 | ✓ | 14 | 1.1 | even | 1 | trivial |