Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58531 | −1.12098 | −0.560491 | − | 0.828161i | \(-0.689387\pi\) | ||||
−0.560491 | + | 0.828161i | \(0.689387\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.513198 | 0.256599 | ||||||||
\(5\) | −0.0940015 | −0.0420388 | −0.0210194 | − | 0.999779i | \(-0.506691\pi\) | ||||
−0.0210194 | + | 0.999779i | \(0.506691\pi\) | |||||||
\(6\) | 1.58531 | 0.647199 | ||||||||
\(7\) | −1.19806 | −0.452824 | −0.226412 | − | 0.974032i | \(-0.572700\pi\) | ||||
−0.226412 | + | 0.974032i | \(0.572700\pi\) | |||||||
\(8\) | 2.35704 | 0.833339 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.149021 | 0.0471247 | ||||||||
\(11\) | −1.17843 | −0.355310 | −0.177655 | − | 0.984093i | \(-0.556851\pi\) | ||||
−0.177655 | + | 0.984093i | \(0.556851\pi\) | |||||||
\(12\) | −0.513198 | −0.148148 | ||||||||
\(13\) | 4.14850 | 1.15059 | 0.575293 | − | 0.817947i | \(-0.304888\pi\) | ||||
0.575293 | + | 0.817947i | \(0.304888\pi\) | |||||||
\(14\) | 1.89929 | 0.507607 | ||||||||
\(15\) | 0.0940015 | 0.0242711 | ||||||||
\(16\) | −4.76302 | −1.19076 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.58531 | −0.373660 | ||||||||
\(19\) | −1.35404 | −0.310638 | −0.155319 | − | 0.987864i | \(-0.549641\pi\) | ||||
−0.155319 | + | 0.987864i | \(0.549641\pi\) | |||||||
\(20\) | −0.0482414 | −0.0107871 | ||||||||
\(21\) | 1.19806 | 0.261438 | ||||||||
\(22\) | 1.86818 | 0.398296 | ||||||||
\(23\) | −6.52401 | −1.36035 | −0.680175 | − | 0.733050i | \(-0.738096\pi\) | ||||
−0.680175 | + | 0.733050i | \(0.738096\pi\) | |||||||
\(24\) | −2.35704 | −0.481128 | ||||||||
\(25\) | −4.99116 | −0.998233 | ||||||||
\(26\) | −6.57665 | −1.28979 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.614842 | −0.116194 | ||||||||
\(29\) | −0.853755 | −0.158538 | −0.0792692 | − | 0.996853i | \(-0.525259\pi\) | ||||
−0.0792692 | + | 0.996853i | \(0.525259\pi\) | |||||||
\(30\) | −0.149021 | −0.0272074 | ||||||||
\(31\) | −3.39872 | −0.610429 | −0.305214 | − | 0.952284i | \(-0.598728\pi\) | ||||
−0.305214 | + | 0.952284i | \(0.598728\pi\) | |||||||
\(32\) | 2.83678 | 0.501477 | ||||||||
\(33\) | 1.17843 | 0.205139 | ||||||||
\(34\) | −1.58531 | −0.271878 | ||||||||
\(35\) | 0.112619 | 0.0190362 | ||||||||
\(36\) | 0.513198 | 0.0855330 | ||||||||
\(37\) | 5.55666 | 0.913509 | 0.456754 | − | 0.889593i | \(-0.349012\pi\) | ||||
0.456754 | + | 0.889593i | \(0.349012\pi\) | |||||||
\(38\) | 2.14657 | 0.348219 | ||||||||
\(39\) | −4.14850 | −0.664292 | ||||||||
\(40\) | −0.221565 | −0.0350325 | ||||||||
\(41\) | −2.58240 | −0.403303 | −0.201652 | − | 0.979457i | \(-0.564631\pi\) | ||||
−0.201652 | + | 0.979457i | \(0.564631\pi\) | |||||||
\(42\) | −1.89929 | −0.293067 | ||||||||
\(43\) | 3.96282 | 0.604324 | 0.302162 | − | 0.953257i | \(-0.402292\pi\) | ||||
0.302162 | + | 0.953257i | \(0.402292\pi\) | |||||||
\(44\) | −0.604769 | −0.0911723 | ||||||||
\(45\) | −0.0940015 | −0.0140129 | ||||||||
\(46\) | 10.3426 | 1.52493 | ||||||||
\(47\) | 5.07300 | 0.739974 | 0.369987 | − | 0.929037i | \(-0.379362\pi\) | ||||
0.369987 | + | 0.929037i | \(0.379362\pi\) | |||||||
\(48\) | 4.76302 | 0.687483 | ||||||||
\(49\) | −5.56465 | −0.794950 | ||||||||
\(50\) | 7.91253 | 1.11900 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 2.12900 | 0.295240 | ||||||||
\(53\) | −4.08553 | −0.561191 | −0.280596 | − | 0.959826i | \(-0.590532\pi\) | ||||
−0.280596 | + | 0.959826i | \(0.590532\pi\) | |||||||
\(54\) | 1.58531 | 0.215733 | ||||||||
\(55\) | 0.110774 | 0.0149368 | ||||||||
\(56\) | −2.82387 | −0.377356 | ||||||||
\(57\) | 1.35404 | 0.179347 | ||||||||
\(58\) | 1.35346 | 0.177719 | ||||||||
\(59\) | 12.4715 | 1.62365 | 0.811823 | − | 0.583903i | \(-0.198475\pi\) | ||||
0.811823 | + | 0.583903i | \(0.198475\pi\) | |||||||
\(60\) | 0.0482414 | 0.00622794 | ||||||||
\(61\) | 4.03768 | 0.516972 | 0.258486 | − | 0.966015i | \(-0.416776\pi\) | ||||
0.258486 | + | 0.966015i | \(0.416776\pi\) | |||||||
\(62\) | 5.38802 | 0.684279 | ||||||||
\(63\) | −1.19806 | −0.150941 | ||||||||
\(64\) | 5.02888 | 0.628610 | ||||||||
\(65\) | −0.389965 | −0.0483693 | ||||||||
\(66\) | −1.86818 | −0.229957 | ||||||||
\(67\) | −7.06226 | −0.862792 | −0.431396 | − | 0.902163i | \(-0.641979\pi\) | ||||
−0.431396 | + | 0.902163i | \(0.641979\pi\) | |||||||
\(68\) | 0.513198 | 0.0622344 | ||||||||
\(69\) | 6.52401 | 0.785398 | ||||||||
\(70\) | −0.178536 | −0.0213392 | ||||||||
\(71\) | −3.45598 | −0.410149 | −0.205074 | − | 0.978746i | \(-0.565744\pi\) | ||||
−0.205074 | + | 0.978746i | \(0.565744\pi\) | |||||||
\(72\) | 2.35704 | 0.277780 | ||||||||
\(73\) | 4.62811 | 0.541680 | 0.270840 | − | 0.962624i | \(-0.412699\pi\) | ||||
0.270840 | + | 0.962624i | \(0.412699\pi\) | |||||||
\(74\) | −8.80901 | −1.02403 | ||||||||
\(75\) | 4.99116 | 0.576330 | ||||||||
\(76\) | −0.694890 | −0.0797094 | ||||||||
\(77\) | 1.41183 | 0.160893 | ||||||||
\(78\) | 6.57665 | 0.744659 | ||||||||
\(79\) | 10.1038 | 1.13676 | 0.568382 | − | 0.822765i | \(-0.307570\pi\) | ||||
0.568382 | + | 0.822765i | \(0.307570\pi\) | |||||||
\(80\) | 0.447732 | 0.0500579 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.09390 | 0.452096 | ||||||||
\(83\) | 2.57295 | 0.282418 | 0.141209 | − | 0.989980i | \(-0.454901\pi\) | ||||
0.141209 | + | 0.989980i | \(0.454901\pi\) | |||||||
\(84\) | 0.614842 | 0.0670848 | ||||||||
\(85\) | −0.0940015 | −0.0101959 | ||||||||
\(86\) | −6.28228 | −0.677436 | ||||||||
\(87\) | 0.853755 | 0.0915322 | ||||||||
\(88\) | −2.77761 | −0.296094 | ||||||||
\(89\) | 8.07859 | 0.856329 | 0.428165 | − | 0.903701i | \(-0.359160\pi\) | ||||
0.428165 | + | 0.903701i | \(0.359160\pi\) | |||||||
\(90\) | 0.149021 | 0.0157082 | ||||||||
\(91\) | −4.97015 | −0.521014 | ||||||||
\(92\) | −3.34811 | −0.349064 | ||||||||
\(93\) | 3.39872 | 0.352431 | ||||||||
\(94\) | −8.04227 | −0.829497 | ||||||||
\(95\) | 0.127282 | 0.0130588 | ||||||||
\(96\) | −2.83678 | −0.289528 | ||||||||
\(97\) | −4.60570 | −0.467638 | −0.233819 | − | 0.972280i | \(-0.575122\pi\) | ||||
−0.233819 | + | 0.972280i | \(0.575122\pi\) | |||||||
\(98\) | 8.82168 | 0.891124 | ||||||||
\(99\) | −1.17843 | −0.118437 | ||||||||
\(100\) | −2.56146 | −0.256146 | ||||||||
\(101\) | 0.944097 | 0.0939412 | 0.0469706 | − | 0.998896i | \(-0.485043\pi\) | ||||
0.0469706 | + | 0.998896i | \(0.485043\pi\) | |||||||
\(102\) | 1.58531 | 0.156969 | ||||||||
\(103\) | 1.99061 | 0.196141 | 0.0980704 | − | 0.995179i | \(-0.468733\pi\) | ||||
0.0980704 | + | 0.995179i | \(0.468733\pi\) | |||||||
\(104\) | 9.77817 | 0.958828 | ||||||||
\(105\) | −0.112619 | −0.0109905 | ||||||||
\(106\) | 6.47682 | 0.629085 | ||||||||
\(107\) | −13.6235 | −1.31703 | −0.658516 | − | 0.752567i | \(-0.728815\pi\) | ||||
−0.658516 | + | 0.752567i | \(0.728815\pi\) | |||||||
\(108\) | −0.513198 | −0.0493825 | ||||||||
\(109\) | 9.68033 | 0.927207 | 0.463604 | − | 0.886043i | \(-0.346556\pi\) | ||||
0.463604 | + | 0.886043i | \(0.346556\pi\) | |||||||
\(110\) | −0.175611 | −0.0167439 | ||||||||
\(111\) | −5.55666 | −0.527414 | ||||||||
\(112\) | 5.70639 | 0.539203 | ||||||||
\(113\) | −18.8489 | −1.77315 | −0.886576 | − | 0.462583i | \(-0.846923\pi\) | ||||
−0.886576 | + | 0.462583i | \(0.846923\pi\) | |||||||
\(114\) | −2.14657 | −0.201044 | ||||||||
\(115\) | 0.613267 | 0.0571874 | ||||||||
\(116\) | −0.438146 | −0.0406808 | ||||||||
\(117\) | 4.14850 | 0.383529 | ||||||||
\(118\) | −19.7711 | −1.82008 | ||||||||
\(119\) | −1.19806 | −0.109826 | ||||||||
\(120\) | 0.221565 | 0.0202260 | ||||||||
\(121\) | −9.61130 | −0.873754 | ||||||||
\(122\) | −6.40096 | −0.579516 | ||||||||
\(123\) | 2.58240 | 0.232847 | ||||||||
\(124\) | −1.74422 | −0.156635 | ||||||||
\(125\) | 0.939185 | 0.0840032 | ||||||||
\(126\) | 1.89929 | 0.169202 | ||||||||
\(127\) | −15.5826 | −1.38273 | −0.691365 | − | 0.722506i | \(-0.742990\pi\) | ||||
−0.691365 | + | 0.722506i | \(0.742990\pi\) | |||||||
\(128\) | −13.6459 | −1.20614 | ||||||||
\(129\) | −3.96282 | −0.348907 | ||||||||
\(130\) | 0.618215 | 0.0542210 | ||||||||
\(131\) | −5.08877 | −0.444608 | −0.222304 | − | 0.974977i | \(-0.571358\pi\) | ||||
−0.222304 | + | 0.974977i | \(0.571358\pi\) | |||||||
\(132\) | 0.604769 | 0.0526384 | ||||||||
\(133\) | 1.62222 | 0.140664 | ||||||||
\(134\) | 11.1958 | 0.967174 | ||||||||
\(135\) | 0.0940015 | 0.00809036 | ||||||||
\(136\) | 2.35704 | 0.202114 | ||||||||
\(137\) | 2.45837 | 0.210032 | 0.105016 | − | 0.994471i | \(-0.466511\pi\) | ||||
0.105016 | + | 0.994471i | \(0.466511\pi\) | |||||||
\(138\) | −10.3426 | −0.880417 | ||||||||
\(139\) | 18.7419 | 1.58966 | 0.794832 | − | 0.606830i | \(-0.207559\pi\) | ||||
0.794832 | + | 0.606830i | \(0.207559\pi\) | |||||||
\(140\) | 0.0577961 | 0.00488466 | ||||||||
\(141\) | −5.07300 | −0.427224 | ||||||||
\(142\) | 5.47878 | 0.459769 | ||||||||
\(143\) | −4.88872 | −0.408816 | ||||||||
\(144\) | −4.76302 | −0.396919 | ||||||||
\(145\) | 0.0802543 | 0.00666476 | ||||||||
\(146\) | −7.33698 | −0.607213 | ||||||||
\(147\) | 5.56465 | 0.458965 | ||||||||
\(148\) | 2.85167 | 0.234405 | ||||||||
\(149\) | 12.2393 | 1.00269 | 0.501343 | − | 0.865249i | \(-0.332840\pi\) | ||||
0.501343 | + | 0.865249i | \(0.332840\pi\) | |||||||
\(150\) | −7.91253 | −0.646055 | ||||||||
\(151\) | −14.7731 | −1.20222 | −0.601109 | − | 0.799167i | \(-0.705274\pi\) | ||||
−0.601109 | + | 0.799167i | \(0.705274\pi\) | |||||||
\(152\) | −3.19152 | −0.258866 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −2.23819 | −0.180358 | ||||||||
\(155\) | 0.319485 | 0.0256617 | ||||||||
\(156\) | −2.12900 | −0.170457 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −16.0176 | −1.27429 | ||||||||
\(159\) | 4.08553 | 0.324004 | ||||||||
\(160\) | −0.266662 | −0.0210815 | ||||||||
\(161\) | 7.81615 | 0.615999 | ||||||||
\(162\) | −1.58531 | −0.124553 | ||||||||
\(163\) | 14.0288 | 1.09882 | 0.549412 | − | 0.835552i | \(-0.314852\pi\) | ||||
0.549412 | + | 0.835552i | \(0.314852\pi\) | |||||||
\(164\) | −1.32528 | −0.103487 | ||||||||
\(165\) | −0.110774 | −0.00862377 | ||||||||
\(166\) | −4.07892 | −0.316585 | ||||||||
\(167\) | −8.24775 | −0.638230 | −0.319115 | − | 0.947716i | \(-0.603386\pi\) | ||||
−0.319115 | + | 0.947716i | \(0.603386\pi\) | |||||||
\(168\) | 2.82387 | 0.217866 | ||||||||
\(169\) | 4.21005 | 0.323850 | ||||||||
\(170\) | 0.149021 | 0.0114294 | ||||||||
\(171\) | −1.35404 | −0.103546 | ||||||||
\(172\) | 2.03371 | 0.155069 | ||||||||
\(173\) | −15.5558 | −1.18268 | −0.591341 | − | 0.806421i | \(-0.701401\pi\) | ||||
−0.591341 | + | 0.806421i | \(0.701401\pi\) | |||||||
\(174\) | −1.35346 | −0.102606 | ||||||||
\(175\) | 5.97971 | 0.452024 | ||||||||
\(176\) | 5.61290 | 0.423088 | ||||||||
\(177\) | −12.4715 | −0.937413 | ||||||||
\(178\) | −12.8071 | −0.959929 | ||||||||
\(179\) | −3.00889 | −0.224895 | −0.112448 | − | 0.993658i | \(-0.535869\pi\) | ||||
−0.112448 | + | 0.993658i | \(0.535869\pi\) | |||||||
\(180\) | −0.0482414 | −0.00359570 | ||||||||
\(181\) | −0.214120 | −0.0159155 | −0.00795773 | − | 0.999968i | \(-0.502533\pi\) | ||||
−0.00795773 | + | 0.999968i | \(0.502533\pi\) | |||||||
\(182\) | 7.87922 | 0.584046 | ||||||||
\(183\) | −4.03768 | −0.298474 | ||||||||
\(184\) | −15.3773 | −1.13363 | ||||||||
\(185\) | −0.522334 | −0.0384028 | ||||||||
\(186\) | −5.38802 | −0.395069 | ||||||||
\(187\) | −1.17843 | −0.0861754 | ||||||||
\(188\) | 2.60346 | 0.189877 | ||||||||
\(189\) | 1.19806 | 0.0871461 | ||||||||
\(190\) | −0.201781 | −0.0146387 | ||||||||
\(191\) | −3.63746 | −0.263197 | −0.131599 | − | 0.991303i | \(-0.542011\pi\) | ||||
−0.131599 | + | 0.991303i | \(0.542011\pi\) | |||||||
\(192\) | −5.02888 | −0.362928 | ||||||||
\(193\) | −3.88554 | −0.279687 | −0.139844 | − | 0.990174i | \(-0.544660\pi\) | ||||
−0.139844 | + | 0.990174i | \(0.544660\pi\) | |||||||
\(194\) | 7.30144 | 0.524213 | ||||||||
\(195\) | 0.389965 | 0.0279260 | ||||||||
\(196\) | −2.85577 | −0.203984 | ||||||||
\(197\) | 4.76514 | 0.339502 | 0.169751 | − | 0.985487i | \(-0.445704\pi\) | ||||
0.169751 | + | 0.985487i | \(0.445704\pi\) | |||||||
\(198\) | 1.86818 | 0.132765 | ||||||||
\(199\) | −20.2641 | −1.43648 | −0.718242 | − | 0.695794i | \(-0.755053\pi\) | ||||
−0.718242 | + | 0.695794i | \(0.755053\pi\) | |||||||
\(200\) | −11.7644 | −0.831866 | ||||||||
\(201\) | 7.06226 | 0.498133 | ||||||||
\(202\) | −1.49668 | −0.105306 | ||||||||
\(203\) | 1.02285 | 0.0717900 | ||||||||
\(204\) | −0.513198 | −0.0359311 | ||||||||
\(205\) | 0.242750 | 0.0169544 | ||||||||
\(206\) | −3.15573 | −0.219870 | ||||||||
\(207\) | −6.52401 | −0.453450 | ||||||||
\(208\) | −19.7594 | −1.37007 | ||||||||
\(209\) | 1.59564 | 0.110373 | ||||||||
\(210\) | 0.178536 | 0.0123202 | ||||||||
\(211\) | −21.5453 | −1.48324 | −0.741618 | − | 0.670822i | \(-0.765941\pi\) | ||||
−0.741618 | + | 0.670822i | \(0.765941\pi\) | |||||||
\(212\) | −2.09669 | −0.144001 | ||||||||
\(213\) | 3.45598 | 0.236800 | ||||||||
\(214\) | 21.5974 | 1.47637 | ||||||||
\(215\) | −0.372511 | −0.0254050 | ||||||||
\(216\) | −2.35704 | −0.160376 | ||||||||
\(217\) | 4.07187 | 0.276417 | ||||||||
\(218\) | −15.3463 | −1.03938 | ||||||||
\(219\) | −4.62811 | −0.312739 | ||||||||
\(220\) | 0.0568492 | 0.00383277 | ||||||||
\(221\) | 4.14850 | 0.279058 | ||||||||
\(222\) | 8.80901 | 0.591222 | ||||||||
\(223\) | 24.5380 | 1.64318 | 0.821592 | − | 0.570077i | \(-0.193086\pi\) | ||||
0.821592 | + | 0.570077i | \(0.193086\pi\) | |||||||
\(224\) | −3.39863 | −0.227081 | ||||||||
\(225\) | −4.99116 | −0.332744 | ||||||||
\(226\) | 29.8812 | 1.98767 | ||||||||
\(227\) | −5.47778 | −0.363573 | −0.181786 | − | 0.983338i | \(-0.558188\pi\) | ||||
−0.181786 | + | 0.983338i | \(0.558188\pi\) | |||||||
\(228\) | 0.694890 | 0.0460202 | ||||||||
\(229\) | 17.0915 | 1.12944 | 0.564718 | − | 0.825284i | \(-0.308985\pi\) | ||||
0.564718 | + | 0.825284i | \(0.308985\pi\) | |||||||
\(230\) | −0.972216 | −0.0641060 | ||||||||
\(231\) | −1.41183 | −0.0928917 | ||||||||
\(232\) | −2.01233 | −0.132116 | ||||||||
\(233\) | 13.3891 | 0.877149 | 0.438574 | − | 0.898695i | \(-0.355484\pi\) | ||||
0.438574 | + | 0.898695i | \(0.355484\pi\) | |||||||
\(234\) | −6.57665 | −0.429929 | ||||||||
\(235\) | −0.476870 | −0.0311076 | ||||||||
\(236\) | 6.40033 | 0.416626 | ||||||||
\(237\) | −10.1038 | −0.656311 | ||||||||
\(238\) | 1.89929 | 0.123113 | ||||||||
\(239\) | −20.8431 | −1.34823 | −0.674115 | − | 0.738627i | \(-0.735475\pi\) | ||||
−0.674115 | + | 0.738627i | \(0.735475\pi\) | |||||||
\(240\) | −0.447732 | −0.0289009 | ||||||||
\(241\) | 4.56953 | 0.294349 | 0.147175 | − | 0.989111i | \(-0.452982\pi\) | ||||
0.147175 | + | 0.989111i | \(0.452982\pi\) | |||||||
\(242\) | 15.2369 | 0.979462 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.07213 | 0.132655 | ||||||||
\(245\) | 0.523086 | 0.0334187 | ||||||||
\(246\) | −4.09390 | −0.261017 | ||||||||
\(247\) | −5.61723 | −0.357416 | ||||||||
\(248\) | −8.01092 | −0.508694 | ||||||||
\(249\) | −2.57295 | −0.163054 | ||||||||
\(250\) | −1.48890 | −0.0941661 | ||||||||
\(251\) | 19.4588 | 1.22823 | 0.614114 | − | 0.789218i | \(-0.289514\pi\) | ||||
0.614114 | + | 0.789218i | \(0.289514\pi\) | |||||||
\(252\) | −0.614842 | −0.0387314 | ||||||||
\(253\) | 7.68810 | 0.483346 | ||||||||
\(254\) | 24.7031 | 1.55001 | ||||||||
\(255\) | 0.0940015 | 0.00588660 | ||||||||
\(256\) | 11.5751 | 0.723447 | ||||||||
\(257\) | −20.2944 | −1.26593 | −0.632964 | − | 0.774181i | \(-0.718162\pi\) | ||||
−0.632964 | + | 0.774181i | \(0.718162\pi\) | |||||||
\(258\) | 6.28228 | 0.391118 | ||||||||
\(259\) | −6.65721 | −0.413659 | ||||||||
\(260\) | −0.200130 | −0.0124115 | ||||||||
\(261\) | −0.853755 | −0.0528461 | ||||||||
\(262\) | 8.06727 | 0.498398 | ||||||||
\(263\) | −19.0181 | −1.17271 | −0.586353 | − | 0.810055i | \(-0.699437\pi\) | ||||
−0.586353 | + | 0.810055i | \(0.699437\pi\) | |||||||
\(264\) | 2.77761 | 0.170950 | ||||||||
\(265\) | 0.384046 | 0.0235918 | ||||||||
\(266\) | −2.57172 | −0.157682 | ||||||||
\(267\) | −8.07859 | −0.494402 | ||||||||
\(268\) | −3.62434 | −0.221392 | ||||||||
\(269\) | 7.11300 | 0.433687 | 0.216844 | − | 0.976206i | \(-0.430424\pi\) | ||||
0.216844 | + | 0.976206i | \(0.430424\pi\) | |||||||
\(270\) | −0.149021 | −0.00906915 | ||||||||
\(271\) | 29.2547 | 1.77710 | 0.888548 | − | 0.458784i | \(-0.151715\pi\) | ||||
0.888548 | + | 0.458784i | \(0.151715\pi\) | |||||||
\(272\) | −4.76302 | −0.288801 | ||||||||
\(273\) | 4.97015 | 0.300807 | ||||||||
\(274\) | −3.89727 | −0.235442 | ||||||||
\(275\) | 5.88174 | 0.354683 | ||||||||
\(276\) | 3.34811 | 0.201532 | ||||||||
\(277\) | 18.3881 | 1.10483 | 0.552416 | − | 0.833569i | \(-0.313706\pi\) | ||||
0.552416 | + | 0.833569i | \(0.313706\pi\) | |||||||
\(278\) | −29.7116 | −1.78198 | ||||||||
\(279\) | −3.39872 | −0.203476 | ||||||||
\(280\) | 0.265448 | 0.0158636 | ||||||||
\(281\) | 31.2096 | 1.86181 | 0.930904 | − | 0.365264i | \(-0.119021\pi\) | ||||
0.930904 | + | 0.365264i | \(0.119021\pi\) | |||||||
\(282\) | 8.04227 | 0.478910 | ||||||||
\(283\) | 13.6719 | 0.812710 | 0.406355 | − | 0.913715i | \(-0.366800\pi\) | ||||
0.406355 | + | 0.913715i | \(0.366800\pi\) | |||||||
\(284\) | −1.77360 | −0.105244 | ||||||||
\(285\) | −0.127282 | −0.00753952 | ||||||||
\(286\) | 7.75013 | 0.458275 | ||||||||
\(287\) | 3.09387 | 0.182626 | ||||||||
\(288\) | 2.83678 | 0.167159 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.127228 | −0.00747107 | ||||||||
\(291\) | 4.60570 | 0.269991 | ||||||||
\(292\) | 2.37514 | 0.138995 | ||||||||
\(293\) | 16.5597 | 0.967431 | 0.483715 | − | 0.875225i | \(-0.339287\pi\) | ||||
0.483715 | + | 0.875225i | \(0.339287\pi\) | |||||||
\(294\) | −8.82168 | −0.514491 | ||||||||
\(295\) | −1.17234 | −0.0682561 | ||||||||
\(296\) | 13.0972 | 0.761262 | ||||||||
\(297\) | 1.17843 | 0.0683795 | ||||||||
\(298\) | −19.4031 | −1.12399 | ||||||||
\(299\) | −27.0648 | −1.56520 | ||||||||
\(300\) | 2.56146 | 0.147886 | ||||||||
\(301\) | −4.74769 | −0.273652 | ||||||||
\(302\) | 23.4199 | 1.34766 | ||||||||
\(303\) | −0.944097 | −0.0542370 | ||||||||
\(304\) | 6.44932 | 0.369894 | ||||||||
\(305\) | −0.379548 | −0.0217329 | ||||||||
\(306\) | −1.58531 | −0.0906260 | ||||||||
\(307\) | 13.0778 | 0.746391 | 0.373195 | − | 0.927753i | \(-0.378262\pi\) | ||||
0.373195 | + | 0.927753i | \(0.378262\pi\) | |||||||
\(308\) | 0.724550 | 0.0412850 | ||||||||
\(309\) | −1.99061 | −0.113242 | ||||||||
\(310\) | −0.506482 | −0.0287662 | ||||||||
\(311\) | −11.7915 | −0.668632 | −0.334316 | − | 0.942461i | \(-0.608505\pi\) | ||||
−0.334316 | + | 0.942461i | \(0.608505\pi\) | |||||||
\(312\) | −9.77817 | −0.553580 | ||||||||
\(313\) | 27.2101 | 1.53800 | 0.769002 | − | 0.639247i | \(-0.220754\pi\) | ||||
0.769002 | + | 0.639247i | \(0.220754\pi\) | |||||||
\(314\) | 1.58531 | 0.0894640 | ||||||||
\(315\) | 0.112619 | 0.00634539 | ||||||||
\(316\) | 5.18524 | 0.291693 | ||||||||
\(317\) | 0.703267 | 0.0394994 | 0.0197497 | − | 0.999805i | \(-0.493713\pi\) | ||||
0.0197497 | + | 0.999805i | \(0.493713\pi\) | |||||||
\(318\) | −6.47682 | −0.363202 | ||||||||
\(319\) | 1.00609 | 0.0563303 | ||||||||
\(320\) | −0.472722 | −0.0264260 | ||||||||
\(321\) | 13.6235 | 0.760389 | ||||||||
\(322\) | −12.3910 | −0.690524 | ||||||||
\(323\) | −1.35404 | −0.0753407 | ||||||||
\(324\) | 0.513198 | 0.0285110 | ||||||||
\(325\) | −20.7058 | −1.14855 | ||||||||
\(326\) | −22.2400 | −1.23176 | ||||||||
\(327\) | −9.68033 | −0.535323 | ||||||||
\(328\) | −6.08682 | −0.336088 | ||||||||
\(329\) | −6.07776 | −0.335078 | ||||||||
\(330\) | 0.175611 | 0.00966709 | ||||||||
\(331\) | 1.49559 | 0.0822052 | 0.0411026 | − | 0.999155i | \(-0.486913\pi\) | ||||
0.0411026 | + | 0.999155i | \(0.486913\pi\) | |||||||
\(332\) | 1.32043 | 0.0724682 | ||||||||
\(333\) | 5.55666 | 0.304503 | ||||||||
\(334\) | 13.0752 | 0.715444 | ||||||||
\(335\) | 0.663863 | 0.0362707 | ||||||||
\(336\) | −5.70639 | −0.311309 | ||||||||
\(337\) | −21.5165 | −1.17208 | −0.586038 | − | 0.810284i | \(-0.699313\pi\) | ||||
−0.586038 | + | 0.810284i | \(0.699313\pi\) | |||||||
\(338\) | −6.67423 | −0.363030 | ||||||||
\(339\) | 18.8489 | 1.02373 | ||||||||
\(340\) | −0.0482414 | −0.00261626 | ||||||||
\(341\) | 4.00516 | 0.216892 | ||||||||
\(342\) | 2.14657 | 0.116073 | ||||||||
\(343\) | 15.0532 | 0.812797 | ||||||||
\(344\) | 9.34051 | 0.503606 | ||||||||
\(345\) | −0.613267 | −0.0330172 | ||||||||
\(346\) | 24.6607 | 1.32577 | ||||||||
\(347\) | −4.01777 | −0.215685 | −0.107843 | − | 0.994168i | \(-0.534394\pi\) | ||||
−0.107843 | + | 0.994168i | \(0.534394\pi\) | |||||||
\(348\) | 0.438146 | 0.0234871 | ||||||||
\(349\) | 0.308071 | 0.0164907 | 0.00824533 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824533 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(350\) | −9.47968 | −0.506710 | ||||||||
\(351\) | −4.14850 | −0.221431 | ||||||||
\(352\) | −3.34295 | −0.178180 | ||||||||
\(353\) | −16.4984 | −0.878122 | −0.439061 | − | 0.898457i | \(-0.644689\pi\) | ||||
−0.439061 | + | 0.898457i | \(0.644689\pi\) | |||||||
\(354\) | 19.7711 | 1.05082 | ||||||||
\(355\) | 0.324867 | 0.0172421 | ||||||||
\(356\) | 4.14592 | 0.219733 | ||||||||
\(357\) | 1.19806 | 0.0634081 | ||||||||
\(358\) | 4.77002 | 0.252103 | ||||||||
\(359\) | −10.1539 | −0.535902 | −0.267951 | − | 0.963433i | \(-0.586347\pi\) | ||||
−0.267951 | + | 0.963433i | \(0.586347\pi\) | |||||||
\(360\) | −0.221565 | −0.0116775 | ||||||||
\(361\) | −17.1666 | −0.903504 | ||||||||
\(362\) | 0.339447 | 0.0178409 | ||||||||
\(363\) | 9.61130 | 0.504462 | ||||||||
\(364\) | −2.55067 | −0.133692 | ||||||||
\(365\) | −0.435050 | −0.0227716 | ||||||||
\(366\) | 6.40096 | 0.334584 | ||||||||
\(367\) | 13.0341 | 0.680375 | 0.340188 | − | 0.940358i | \(-0.389509\pi\) | ||||
0.340188 | + | 0.940358i | \(0.389509\pi\) | |||||||
\(368\) | 31.0740 | 1.61984 | ||||||||
\(369\) | −2.58240 | −0.134434 | ||||||||
\(370\) | 0.828060 | 0.0430488 | ||||||||
\(371\) | 4.89471 | 0.254121 | ||||||||
\(372\) | 1.74422 | 0.0904335 | ||||||||
\(373\) | 32.2015 | 1.66733 | 0.833666 | − | 0.552269i | \(-0.186238\pi\) | ||||
0.833666 | + | 0.552269i | \(0.186238\pi\) | |||||||
\(374\) | 1.86818 | 0.0966011 | ||||||||
\(375\) | −0.939185 | −0.0484993 | ||||||||
\(376\) | 11.9573 | 0.616649 | ||||||||
\(377\) | −3.54180 | −0.182412 | ||||||||
\(378\) | −1.89929 | −0.0976891 | ||||||||
\(379\) | −24.5671 | −1.26193 | −0.630963 | − | 0.775813i | \(-0.717340\pi\) | ||||
−0.630963 | + | 0.775813i | \(0.717340\pi\) | |||||||
\(380\) | 0.0653207 | 0.00335088 | ||||||||
\(381\) | 15.5826 | 0.798319 | ||||||||
\(382\) | 5.76649 | 0.295039 | ||||||||
\(383\) | −12.8825 | −0.658267 | −0.329134 | − | 0.944283i | \(-0.606757\pi\) | ||||
−0.329134 | + | 0.944283i | \(0.606757\pi\) | |||||||
\(384\) | 13.6459 | 0.696363 | ||||||||
\(385\) | −0.132714 | −0.00676375 | ||||||||
\(386\) | 6.15977 | 0.313524 | ||||||||
\(387\) | 3.96282 | 0.201441 | ||||||||
\(388\) | −2.36364 | −0.119995 | ||||||||
\(389\) | −22.0471 | −1.11783 | −0.558915 | − | 0.829225i | \(-0.688782\pi\) | ||||
−0.558915 | + | 0.829225i | \(0.688782\pi\) | |||||||
\(390\) | −0.618215 | −0.0313045 | ||||||||
\(391\) | −6.52401 | −0.329933 | ||||||||
\(392\) | −13.1161 | −0.662463 | ||||||||
\(393\) | 5.08877 | 0.256695 | ||||||||
\(394\) | −7.55421 | −0.380575 | ||||||||
\(395\) | −0.949771 | −0.0477881 | ||||||||
\(396\) | −0.604769 | −0.0303908 | ||||||||
\(397\) | 7.25640 | 0.364188 | 0.182094 | − | 0.983281i | \(-0.441712\pi\) | ||||
0.182094 | + | 0.983281i | \(0.441712\pi\) | |||||||
\(398\) | 32.1248 | 1.61027 | ||||||||
\(399\) | −1.62222 | −0.0812126 | ||||||||
\(400\) | 23.7730 | 1.18865 | ||||||||
\(401\) | 29.2533 | 1.46084 | 0.730420 | − | 0.682998i | \(-0.239324\pi\) | ||||
0.730420 | + | 0.682998i | \(0.239324\pi\) | |||||||
\(402\) | −11.1958 | −0.558398 | ||||||||
\(403\) | −14.0996 | −0.702351 | ||||||||
\(404\) | 0.484509 | 0.0241052 | ||||||||
\(405\) | −0.0940015 | −0.00467097 | ||||||||
\(406\) | −1.62153 | −0.0804753 | ||||||||
\(407\) | −6.54814 | −0.324579 | ||||||||
\(408\) | −2.35704 | −0.116691 | ||||||||
\(409\) | −2.46448 | −0.121861 | −0.0609303 | − | 0.998142i | \(-0.519407\pi\) | ||||
−0.0609303 | + | 0.998142i | \(0.519407\pi\) | |||||||
\(410\) | −0.384833 | −0.0190055 | ||||||||
\(411\) | −2.45837 | −0.121262 | ||||||||
\(412\) | 1.02158 | 0.0503295 | ||||||||
\(413\) | −14.9416 | −0.735226 | ||||||||
\(414\) | 10.3426 | 0.508309 | ||||||||
\(415\) | −0.241861 | −0.0118725 | ||||||||
\(416\) | 11.7684 | 0.576993 | ||||||||
\(417\) | −18.7419 | −0.917793 | ||||||||
\(418\) | −2.52958 | −0.123726 | ||||||||
\(419\) | −22.7859 | −1.11316 | −0.556582 | − | 0.830793i | \(-0.687888\pi\) | ||||
−0.556582 | + | 0.830793i | \(0.687888\pi\) | |||||||
\(420\) | −0.0577961 | −0.00282016 | ||||||||
\(421\) | 18.3479 | 0.894222 | 0.447111 | − | 0.894479i | \(-0.352453\pi\) | ||||
0.447111 | + | 0.894479i | \(0.352453\pi\) | |||||||
\(422\) | 34.1558 | 1.66268 | ||||||||
\(423\) | 5.07300 | 0.246658 | ||||||||
\(424\) | −9.62975 | −0.467662 | ||||||||
\(425\) | −4.99116 | −0.242107 | ||||||||
\(426\) | −5.47878 | −0.265448 | ||||||||
\(427\) | −4.83738 | −0.234097 | ||||||||
\(428\) | −6.99155 | −0.337949 | ||||||||
\(429\) | 4.88872 | 0.236030 | ||||||||
\(430\) | 0.590544 | 0.0284786 | ||||||||
\(431\) | −10.7821 | −0.519356 | −0.259678 | − | 0.965695i | \(-0.583617\pi\) | ||||
−0.259678 | + | 0.965695i | \(0.583617\pi\) | |||||||
\(432\) | 4.76302 | 0.229161 | ||||||||
\(433\) | 21.1233 | 1.01512 | 0.507560 | − | 0.861617i | \(-0.330548\pi\) | ||||
0.507560 | + | 0.861617i | \(0.330548\pi\) | |||||||
\(434\) | −6.45517 | −0.309858 | ||||||||
\(435\) | −0.0802543 | −0.00384790 | ||||||||
\(436\) | 4.96793 | 0.237921 | ||||||||
\(437\) | 8.83376 | 0.422576 | ||||||||
\(438\) | 7.33698 | 0.350575 | ||||||||
\(439\) | 31.4087 | 1.49905 | 0.749527 | − | 0.661974i | \(-0.230281\pi\) | ||||
0.749527 | + | 0.661974i | \(0.230281\pi\) | |||||||
\(440\) | 0.261099 | 0.0124474 | ||||||||
\(441\) | −5.56465 | −0.264983 | ||||||||
\(442\) | −6.57665 | −0.312819 | ||||||||
\(443\) | −32.7680 | −1.55685 | −0.778426 | − | 0.627736i | \(-0.783982\pi\) | ||||
−0.778426 | + | 0.627736i | \(0.783982\pi\) | |||||||
\(444\) | −2.85167 | −0.135334 | ||||||||
\(445\) | −0.759400 | −0.0359990 | ||||||||
\(446\) | −38.9002 | −1.84198 | ||||||||
\(447\) | −12.2393 | −0.578901 | ||||||||
\(448\) | −6.02490 | −0.284650 | ||||||||
\(449\) | −17.6554 | −0.833209 | −0.416604 | − | 0.909088i | \(-0.636780\pi\) | ||||
−0.416604 | + | 0.909088i | \(0.636780\pi\) | |||||||
\(450\) | 7.91253 | 0.373000 | ||||||||
\(451\) | 3.04318 | 0.143298 | ||||||||
\(452\) | −9.67320 | −0.454989 | ||||||||
\(453\) | 14.7731 | 0.694101 | ||||||||
\(454\) | 8.68396 | 0.407558 | ||||||||
\(455\) | 0.467202 | 0.0219028 | ||||||||
\(456\) | 3.19152 | 0.149457 | ||||||||
\(457\) | 9.67664 | 0.452654 | 0.226327 | − | 0.974051i | \(-0.427328\pi\) | ||||
0.226327 | + | 0.974051i | \(0.427328\pi\) | |||||||
\(458\) | −27.0952 | −1.26608 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0.314727 | 0.0146742 | ||||||||
\(461\) | 36.3672 | 1.69379 | 0.846894 | − | 0.531762i | \(-0.178470\pi\) | ||||
0.846894 | + | 0.531762i | \(0.178470\pi\) | |||||||
\(462\) | 2.23819 | 0.104130 | ||||||||
\(463\) | −27.7149 | −1.28802 | −0.644011 | − | 0.765016i | \(-0.722731\pi\) | ||||
−0.644011 | + | 0.765016i | \(0.722731\pi\) | |||||||
\(464\) | 4.06646 | 0.188781 | ||||||||
\(465\) | −0.319485 | −0.0148158 | ||||||||
\(466\) | −21.2258 | −0.983267 | ||||||||
\(467\) | 11.4205 | 0.528478 | 0.264239 | − | 0.964457i | \(-0.414879\pi\) | ||||
0.264239 | + | 0.964457i | \(0.414879\pi\) | |||||||
\(468\) | 2.12900 | 0.0984132 | ||||||||
\(469\) | 8.46101 | 0.390693 | ||||||||
\(470\) | 0.755986 | 0.0348710 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 29.3957 | 1.35305 | ||||||||
\(473\) | −4.66991 | −0.214723 | ||||||||
\(474\) | 16.0176 | 0.735712 | ||||||||
\(475\) | 6.75823 | 0.310089 | ||||||||
\(476\) | −0.614842 | −0.0281813 | ||||||||
\(477\) | −4.08553 | −0.187064 | ||||||||
\(478\) | 33.0427 | 1.51134 | ||||||||
\(479\) | 5.96685 | 0.272632 | 0.136316 | − | 0.990665i | \(-0.456474\pi\) | ||||
0.136316 | + | 0.990665i | \(0.456474\pi\) | |||||||
\(480\) | 0.266662 | 0.0121714 | ||||||||
\(481\) | 23.0518 | 1.05107 | ||||||||
\(482\) | −7.24411 | −0.329960 | ||||||||
\(483\) | −7.81615 | −0.355647 | ||||||||
\(484\) | −4.93250 | −0.224205 | ||||||||
\(485\) | 0.432943 | 0.0196589 | ||||||||
\(486\) | 1.58531 | 0.0719110 | ||||||||
\(487\) | −7.19615 | −0.326089 | −0.163044 | − | 0.986619i | \(-0.552131\pi\) | ||||
−0.163044 | + | 0.986619i | \(0.552131\pi\) | |||||||
\(488\) | 9.51696 | 0.430813 | ||||||||
\(489\) | −14.0288 | −0.634406 | ||||||||
\(490\) | −0.829252 | −0.0374618 | ||||||||
\(491\) | −18.7626 | −0.846743 | −0.423371 | − | 0.905956i | \(-0.639153\pi\) | ||||
−0.423371 | + | 0.905956i | \(0.639153\pi\) | |||||||
\(492\) | 1.32528 | 0.0597484 | ||||||||
\(493\) | −0.853755 | −0.0384512 | ||||||||
\(494\) | 8.90503 | 0.400656 | ||||||||
\(495\) | 0.110774 | 0.00497894 | ||||||||
\(496\) | 16.1882 | 0.726872 | ||||||||
\(497\) | 4.14047 | 0.185725 | ||||||||
\(498\) | 4.07892 | 0.182781 | ||||||||
\(499\) | −0.0189266 | −0.000847271 0 | −0.000423635 | − | 1.00000i | \(-0.500135\pi\) | ||||
−0.000423635 | 1.00000i | \(0.500135\pi\) | ||||||||
\(500\) | 0.481988 | 0.0215552 | ||||||||
\(501\) | 8.24775 | 0.368483 | ||||||||
\(502\) | −30.8481 | −1.37682 | ||||||||
\(503\) | −13.4502 | −0.599715 | −0.299857 | − | 0.953984i | \(-0.596939\pi\) | ||||
−0.299857 | + | 0.953984i | \(0.596939\pi\) | |||||||
\(504\) | −2.82387 | −0.125785 | ||||||||
\(505\) | −0.0887466 | −0.00394917 | ||||||||
\(506\) | −12.1880 | −0.541822 | ||||||||
\(507\) | −4.21005 | −0.186975 | ||||||||
\(508\) | −7.99694 | −0.354807 | ||||||||
\(509\) | −8.21896 | −0.364299 | −0.182149 | − | 0.983271i | \(-0.558305\pi\) | ||||
−0.182149 | + | 0.983271i | \(0.558305\pi\) | |||||||
\(510\) | −0.149021 | −0.00659877 | ||||||||
\(511\) | −5.54476 | −0.245286 | ||||||||
\(512\) | 8.94160 | 0.395166 | ||||||||
\(513\) | 1.35404 | 0.0597823 | ||||||||
\(514\) | 32.1728 | 1.41908 | ||||||||
\(515\) | −0.187120 | −0.00824551 | ||||||||
\(516\) | −2.03371 | −0.0895291 | ||||||||
\(517\) | −5.97819 | −0.262920 | ||||||||
\(518\) | 10.5537 | 0.463704 | ||||||||
\(519\) | 15.5558 | 0.682822 | ||||||||
\(520\) | −0.919163 | −0.0403080 | ||||||||
\(521\) | −6.46434 | −0.283208 | −0.141604 | − | 0.989923i | \(-0.545226\pi\) | ||||
−0.141604 | + | 0.989923i | \(0.545226\pi\) | |||||||
\(522\) | 1.35346 | 0.0592395 | ||||||||
\(523\) | 21.0407 | 0.920046 | 0.460023 | − | 0.887907i | \(-0.347841\pi\) | ||||
0.460023 | + | 0.887907i | \(0.347841\pi\) | |||||||
\(524\) | −2.61155 | −0.114086 | ||||||||
\(525\) | −5.97971 | −0.260976 | ||||||||
\(526\) | 30.1495 | 1.31458 | ||||||||
\(527\) | −3.39872 | −0.148051 | ||||||||
\(528\) | −5.61290 | −0.244270 | ||||||||
\(529\) | 19.5627 | 0.850551 | ||||||||
\(530\) | −0.608831 | −0.0264459 | ||||||||
\(531\) | 12.4715 | 0.541216 | ||||||||
\(532\) | 0.832520 | 0.0360943 | ||||||||
\(533\) | −10.7131 | −0.464036 | ||||||||
\(534\) | 12.8071 | 0.554215 | ||||||||
\(535\) | 1.28063 | 0.0553664 | ||||||||
\(536\) | −16.6460 | −0.718998 | ||||||||
\(537\) | 3.00889 | 0.129843 | ||||||||
\(538\) | −11.2763 | −0.486155 | ||||||||
\(539\) | 6.55756 | 0.282454 | ||||||||
\(540\) | 0.0482414 | 0.00207598 | ||||||||
\(541\) | 5.74195 | 0.246866 | 0.123433 | − | 0.992353i | \(-0.460610\pi\) | ||||
0.123433 | + | 0.992353i | \(0.460610\pi\) | |||||||
\(542\) | −46.3777 | −1.99209 | ||||||||
\(543\) | 0.214120 | 0.00918879 | ||||||||
\(544\) | 2.83678 | 0.121626 | ||||||||
\(545\) | −0.909966 | −0.0389787 | ||||||||
\(546\) | −7.87922 | −0.337199 | ||||||||
\(547\) | 37.9788 | 1.62385 | 0.811927 | − | 0.583759i | \(-0.198419\pi\) | ||||
0.811927 | + | 0.583759i | \(0.198419\pi\) | |||||||
\(548\) | 1.26163 | 0.0538941 | ||||||||
\(549\) | 4.03768 | 0.172324 | ||||||||
\(550\) | −9.32437 | −0.397592 | ||||||||
\(551\) | 1.15602 | 0.0492480 | ||||||||
\(552\) | 15.3773 | 0.654503 | ||||||||
\(553\) | −12.1049 | −0.514754 | ||||||||
\(554\) | −29.1507 | −1.23850 | ||||||||
\(555\) | 0.522334 | 0.0221719 | ||||||||
\(556\) | 9.61829 | 0.407906 | ||||||||
\(557\) | 45.6129 | 1.93268 | 0.966341 | − | 0.257266i | \(-0.0828216\pi\) | ||||
0.966341 | + | 0.257266i | \(0.0828216\pi\) | |||||||
\(558\) | 5.38802 | 0.228093 | ||||||||
\(559\) | 16.4397 | 0.695327 | ||||||||
\(560\) | −0.536409 | −0.0226674 | ||||||||
\(561\) | 1.17843 | 0.0497534 | ||||||||
\(562\) | −49.4768 | −2.08705 | ||||||||
\(563\) | 1.55663 | 0.0656043 | 0.0328022 | − | 0.999462i | \(-0.489557\pi\) | ||||
0.0328022 | + | 0.999462i | \(0.489557\pi\) | |||||||
\(564\) | −2.60346 | −0.109625 | ||||||||
\(565\) | 1.77182 | 0.0745411 | ||||||||
\(566\) | −21.6742 | −0.911033 | ||||||||
\(567\) | −1.19806 | −0.0503138 | ||||||||
\(568\) | −8.14586 | −0.341793 | ||||||||
\(569\) | −24.6347 | −1.03274 | −0.516371 | − | 0.856365i | \(-0.672717\pi\) | ||||
−0.516371 | + | 0.856365i | \(0.672717\pi\) | |||||||
\(570\) | 0.201781 | 0.00845166 | ||||||||
\(571\) | −13.0800 | −0.547382 | −0.273691 | − | 0.961818i | \(-0.588245\pi\) | ||||
−0.273691 | + | 0.961818i | \(0.588245\pi\) | |||||||
\(572\) | −2.50888 | −0.104902 | ||||||||
\(573\) | 3.63746 | 0.151957 | ||||||||
\(574\) | −4.90474 | −0.204720 | ||||||||
\(575\) | 32.5624 | 1.35795 | ||||||||
\(576\) | 5.02888 | 0.209537 | ||||||||
\(577\) | 23.9952 | 0.998932 | 0.499466 | − | 0.866333i | \(-0.333529\pi\) | ||||
0.499466 | + | 0.866333i | \(0.333529\pi\) | |||||||
\(578\) | −1.58531 | −0.0659401 | ||||||||
\(579\) | 3.88554 | 0.161477 | ||||||||
\(580\) | 0.0411864 | 0.00171017 | ||||||||
\(581\) | −3.08255 | −0.127886 | ||||||||
\(582\) | −7.30144 | −0.302655 | ||||||||
\(583\) | 4.81452 | 0.199397 | ||||||||
\(584\) | 10.9086 | 0.451403 | ||||||||
\(585\) | −0.389965 | −0.0161231 | ||||||||
\(586\) | −26.2523 | −1.08447 | ||||||||
\(587\) | 16.7954 | 0.693218 | 0.346609 | − | 0.938010i | \(-0.387333\pi\) | ||||
0.346609 | + | 0.938010i | \(0.387333\pi\) | |||||||
\(588\) | 2.85577 | 0.117770 | ||||||||
\(589\) | 4.60200 | 0.189622 | ||||||||
\(590\) | 1.85851 | 0.0765138 | ||||||||
\(591\) | −4.76514 | −0.196012 | ||||||||
\(592\) | −26.4665 | −1.08777 | ||||||||
\(593\) | 45.7288 | 1.87786 | 0.938929 | − | 0.344110i | \(-0.111819\pi\) | ||||
0.938929 | + | 0.344110i | \(0.111819\pi\) | |||||||
\(594\) | −1.86818 | −0.0766522 | ||||||||
\(595\) | 0.112619 | 0.00461695 | ||||||||
\(596\) | 6.28121 | 0.257288 | ||||||||
\(597\) | 20.2641 | 0.829354 | ||||||||
\(598\) | 42.9061 | 1.75456 | ||||||||
\(599\) | 2.07274 | 0.0846897 | 0.0423449 | − | 0.999103i | \(-0.486517\pi\) | ||||
0.0423449 | + | 0.999103i | \(0.486517\pi\) | |||||||
\(600\) | 11.7644 | 0.480278 | ||||||||
\(601\) | −13.3066 | −0.542787 | −0.271393 | − | 0.962468i | \(-0.587484\pi\) | ||||
−0.271393 | + | 0.962468i | \(0.587484\pi\) | |||||||
\(602\) | 7.52655 | 0.306759 | ||||||||
\(603\) | −7.06226 | −0.287597 | ||||||||
\(604\) | −7.58153 | −0.308488 | ||||||||
\(605\) | 0.903477 | 0.0367316 | ||||||||
\(606\) | 1.49668 | 0.0607986 | ||||||||
\(607\) | 47.8341 | 1.94153 | 0.970763 | − | 0.240040i | \(-0.0771607\pi\) | ||||
0.970763 | + | 0.240040i | \(0.0771607\pi\) | |||||||
\(608\) | −3.84111 | −0.155778 | ||||||||
\(609\) | −1.02285 | −0.0414480 | ||||||||
\(610\) | 0.601700 | 0.0243621 | ||||||||
\(611\) | 21.0454 | 0.851404 | ||||||||
\(612\) | 0.513198 | 0.0207448 | ||||||||
\(613\) | 30.6114 | 1.23638 | 0.618191 | − | 0.786028i | \(-0.287866\pi\) | ||||
0.618191 | + | 0.786028i | \(0.287866\pi\) | |||||||
\(614\) | −20.7324 | −0.836690 | ||||||||
\(615\) | −0.242750 | −0.00978861 | ||||||||
\(616\) | 3.32774 | 0.134078 | ||||||||
\(617\) | 2.25525 | 0.0907928 | 0.0453964 | − | 0.998969i | \(-0.485545\pi\) | ||||
0.0453964 | + | 0.998969i | \(0.485545\pi\) | |||||||
\(618\) | 3.15573 | 0.126942 | ||||||||
\(619\) | −14.0837 | −0.566071 | −0.283035 | − | 0.959109i | \(-0.591341\pi\) | ||||
−0.283035 | + | 0.959109i | \(0.591341\pi\) | |||||||
\(620\) | 0.163959 | 0.00658476 | ||||||||
\(621\) | 6.52401 | 0.261799 | ||||||||
\(622\) | 18.6931 | 0.749524 | ||||||||
\(623\) | −9.67864 | −0.387767 | ||||||||
\(624\) | 19.7594 | 0.791009 | ||||||||
\(625\) | 24.8675 | 0.994701 | ||||||||
\(626\) | −43.1363 | −1.72407 | ||||||||
\(627\) | −1.59564 | −0.0637238 | ||||||||
\(628\) | −0.513198 | −0.0204788 | ||||||||
\(629\) | 5.55666 | 0.221558 | ||||||||
\(630\) | −0.178536 | −0.00711306 | ||||||||
\(631\) | 10.2104 | 0.406471 | 0.203236 | − | 0.979130i | \(-0.434854\pi\) | ||||
0.203236 | + | 0.979130i | \(0.434854\pi\) | |||||||
\(632\) | 23.8150 | 0.947309 | ||||||||
\(633\) | 21.5453 | 0.856347 | ||||||||
\(634\) | −1.11489 | −0.0442781 | ||||||||
\(635\) | 1.46479 | 0.0581282 | ||||||||
\(636\) | 2.09669 | 0.0831391 | ||||||||
\(637\) | −23.0850 | −0.914659 | ||||||||
\(638\) | −1.59496 | −0.0631453 | ||||||||
\(639\) | −3.45598 | −0.136716 | ||||||||
\(640\) | 1.28273 | 0.0507045 | ||||||||
\(641\) | −15.1851 | −0.599774 | −0.299887 | − | 0.953975i | \(-0.596949\pi\) | ||||
−0.299887 | + | 0.953975i | \(0.596949\pi\) | |||||||
\(642\) | −21.5974 | −0.852381 | ||||||||
\(643\) | −31.7845 | −1.25346 | −0.626728 | − | 0.779238i | \(-0.715606\pi\) | ||||
−0.626728 | + | 0.779238i | \(0.715606\pi\) | |||||||
\(644\) | 4.01124 | 0.158065 | ||||||||
\(645\) | 0.372511 | 0.0146676 | ||||||||
\(646\) | 2.14657 | 0.0844555 | ||||||||
\(647\) | −39.6248 | −1.55781 | −0.778906 | − | 0.627141i | \(-0.784225\pi\) | ||||
−0.778906 | + | 0.627141i | \(0.784225\pi\) | |||||||
\(648\) | 2.35704 | 0.0925932 | ||||||||
\(649\) | −14.6968 | −0.576899 | ||||||||
\(650\) | 32.8251 | 1.28751 | ||||||||
\(651\) | −4.07187 | −0.159589 | ||||||||
\(652\) | 7.19957 | 0.281957 | ||||||||
\(653\) | −5.10534 | −0.199787 | −0.0998937 | − | 0.994998i | \(-0.531850\pi\) | ||||
−0.0998937 | + | 0.994998i | \(0.531850\pi\) | |||||||
\(654\) | 15.3463 | 0.600088 | ||||||||
\(655\) | 0.478353 | 0.0186908 | ||||||||
\(656\) | 12.3000 | 0.480236 | ||||||||
\(657\) | 4.62811 | 0.180560 | ||||||||
\(658\) | 9.63512 | 0.375616 | ||||||||
\(659\) | 23.2663 | 0.906326 | 0.453163 | − | 0.891428i | \(-0.350296\pi\) | ||||
0.453163 | + | 0.891428i | \(0.350296\pi\) | |||||||
\(660\) | −0.0568492 | −0.00221285 | ||||||||
\(661\) | 1.49758 | 0.0582491 | 0.0291246 | − | 0.999576i | \(-0.490728\pi\) | ||||
0.0291246 | + | 0.999576i | \(0.490728\pi\) | |||||||
\(662\) | −2.37097 | −0.0921505 | ||||||||
\(663\) | −4.14850 | −0.161114 | ||||||||
\(664\) | 6.06454 | 0.235350 | ||||||||
\(665\) | −0.152491 | −0.00591335 | ||||||||
\(666\) | −8.80901 | −0.341342 | ||||||||
\(667\) | 5.56991 | 0.215668 | ||||||||
\(668\) | −4.23273 | −0.163769 | ||||||||
\(669\) | −24.5380 | −0.948692 | ||||||||
\(670\) | −1.05243 | −0.0406588 | ||||||||
\(671\) | −4.75813 | −0.183686 | ||||||||
\(672\) | 3.39863 | 0.131105 | ||||||||
\(673\) | 29.8941 | 1.15233 | 0.576167 | − | 0.817332i | \(-0.304548\pi\) | ||||
0.576167 | + | 0.817332i | \(0.304548\pi\) | |||||||
\(674\) | 34.1102 | 1.31388 | ||||||||
\(675\) | 4.99116 | 0.192110 | ||||||||
\(676\) | 2.16059 | 0.0830997 | ||||||||
\(677\) | 47.9436 | 1.84262 | 0.921311 | − | 0.388827i | \(-0.127120\pi\) | ||||
0.921311 | + | 0.388827i | \(0.127120\pi\) | |||||||
\(678\) | −29.8812 | −1.14758 | ||||||||
\(679\) | 5.51790 | 0.211758 | ||||||||
\(680\) | −0.221565 | −0.00849663 | ||||||||
\(681\) | 5.47778 | 0.209909 | ||||||||
\(682\) | −6.34941 | −0.243131 | ||||||||
\(683\) | 11.4373 | 0.437636 | 0.218818 | − | 0.975766i | \(-0.429780\pi\) | ||||
0.218818 | + | 0.975766i | \(0.429780\pi\) | |||||||
\(684\) | −0.694890 | −0.0265698 | ||||||||
\(685\) | −0.231090 | −0.00882950 | ||||||||
\(686\) | −23.8640 | −0.911130 | ||||||||
\(687\) | −17.0915 | −0.652080 | ||||||||
\(688\) | −18.8750 | −0.719602 | ||||||||
\(689\) | −16.9488 | −0.645699 | ||||||||
\(690\) | 0.972216 | 0.0370116 | ||||||||
\(691\) | −5.89264 | −0.224166 | −0.112083 | − | 0.993699i | \(-0.535752\pi\) | ||||
−0.112083 | + | 0.993699i | \(0.535752\pi\) | |||||||
\(692\) | −7.98319 | −0.303475 | ||||||||
\(693\) | 1.41183 | 0.0536311 | ||||||||
\(694\) | 6.36940 | 0.241779 | ||||||||
\(695\) | −1.76176 | −0.0668275 | ||||||||
\(696\) | 2.01233 | 0.0762773 | ||||||||
\(697\) | −2.58240 | −0.0978154 | ||||||||
\(698\) | −0.488387 | −0.0184857 | ||||||||
\(699\) | −13.3891 | −0.506422 | ||||||||
\(700\) | 3.06878 | 0.115989 | ||||||||
\(701\) | −13.1328 | −0.496019 | −0.248009 | − | 0.968758i | \(-0.579776\pi\) | ||||
−0.248009 | + | 0.968758i | \(0.579776\pi\) | |||||||
\(702\) | 6.57665 | 0.248220 | ||||||||
\(703\) | −7.52393 | −0.283770 | ||||||||
\(704\) | −5.92619 | −0.223352 | ||||||||
\(705\) | 0.476870 | 0.0179600 | ||||||||
\(706\) | 26.1551 | 0.984359 | ||||||||
\(707\) | −1.13109 | −0.0425388 | ||||||||
\(708\) | −6.40033 | −0.240539 | ||||||||
\(709\) | −5.19511 | −0.195106 | −0.0975532 | − | 0.995230i | \(-0.531102\pi\) | ||||
−0.0975532 | + | 0.995230i | \(0.531102\pi\) | |||||||
\(710\) | −0.515014 | −0.0193281 | ||||||||
\(711\) | 10.1038 | 0.378921 | ||||||||
\(712\) | 19.0415 | 0.713612 | ||||||||
\(713\) | 22.1733 | 0.830396 | ||||||||
\(714\) | −1.89929 | −0.0710793 | ||||||||
\(715\) | 0.459547 | 0.0171861 | ||||||||
\(716\) | −1.54416 | −0.0577079 | ||||||||
\(717\) | 20.8431 | 0.778401 | ||||||||
\(718\) | 16.0970 | 0.600736 | ||||||||
\(719\) | −19.0009 | −0.708614 | −0.354307 | − | 0.935129i | \(-0.615283\pi\) | ||||
−0.354307 | + | 0.935129i | \(0.615283\pi\) | |||||||
\(720\) | 0.447732 | 0.0166860 | ||||||||
\(721\) | −2.38487 | −0.0888173 | ||||||||
\(722\) | 27.2143 | 1.01281 | ||||||||
\(723\) | −4.56953 | −0.169943 | ||||||||
\(724\) | −0.109886 | −0.00408389 | ||||||||
\(725\) | 4.26123 | 0.158258 | ||||||||
\(726\) | −15.2369 | −0.565493 | ||||||||
\(727\) | 34.0186 | 1.26168 | 0.630841 | − | 0.775912i | \(-0.282710\pi\) | ||||
0.630841 | + | 0.775912i | \(0.282710\pi\) | |||||||
\(728\) | −11.7148 | −0.434181 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.689688 | 0.0255265 | ||||||||
\(731\) | 3.96282 | 0.146570 | ||||||||
\(732\) | −2.07213 | −0.0765881 | ||||||||
\(733\) | 15.1993 | 0.561398 | 0.280699 | − | 0.959796i | \(-0.409434\pi\) | ||||
0.280699 | + | 0.959796i | \(0.409434\pi\) | |||||||
\(734\) | −20.6631 | −0.762688 | ||||||||
\(735\) | −0.523086 | −0.0192943 | ||||||||
\(736\) | −18.5072 | −0.682184 | ||||||||
\(737\) | 8.32239 | 0.306559 | ||||||||
\(738\) | 4.09390 | 0.150699 | ||||||||
\(739\) | 22.5626 | 0.829980 | 0.414990 | − | 0.909826i | \(-0.363785\pi\) | ||||
0.414990 | + | 0.909826i | \(0.363785\pi\) | |||||||
\(740\) | −0.268061 | −0.00985412 | ||||||||
\(741\) | 5.61723 | 0.206354 | ||||||||
\(742\) | −7.75962 | −0.284865 | ||||||||
\(743\) | −17.1847 | −0.630445 | −0.315223 | − | 0.949018i | \(-0.602079\pi\) | ||||
−0.315223 | + | 0.949018i | \(0.602079\pi\) | |||||||
\(744\) | 8.01092 | 0.293694 | ||||||||
\(745\) | −1.15052 | −0.0421517 | ||||||||
\(746\) | −51.0493 | −1.86905 | ||||||||
\(747\) | 2.57295 | 0.0941393 | ||||||||
\(748\) | −0.604769 | −0.0221125 | ||||||||
\(749\) | 16.3218 | 0.596384 | ||||||||
\(750\) | 1.48890 | 0.0543668 | ||||||||
\(751\) | 9.63721 | 0.351667 | 0.175833 | − | 0.984420i | \(-0.443738\pi\) | ||||
0.175833 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(752\) | −24.1628 | −0.881128 | ||||||||
\(753\) | −19.4588 | −0.709117 | ||||||||
\(754\) | 5.61485 | 0.204481 | ||||||||
\(755\) | 1.38869 | 0.0505398 | ||||||||
\(756\) | 0.614842 | 0.0223616 | ||||||||
\(757\) | 52.4796 | 1.90740 | 0.953702 | − | 0.300754i | \(-0.0972382\pi\) | ||||
0.953702 | + | 0.300754i | \(0.0972382\pi\) | |||||||
\(758\) | 38.9463 | 1.41459 | ||||||||
\(759\) | −7.68810 | −0.279060 | ||||||||
\(760\) | 0.300008 | 0.0108824 | ||||||||
\(761\) | 12.8888 | 0.467217 | 0.233609 | − | 0.972331i | \(-0.424947\pi\) | ||||
0.233609 | + | 0.972331i | \(0.424947\pi\) | |||||||
\(762\) | −24.7031 | −0.894901 | ||||||||
\(763\) | −11.5976 | −0.419862 | ||||||||
\(764\) | −1.86674 | −0.0675362 | ||||||||
\(765\) | −0.0940015 | −0.00339863 | ||||||||
\(766\) | 20.4228 | 0.737905 | ||||||||
\(767\) | 51.7379 | 1.86815 | ||||||||
\(768\) | −11.5751 | −0.417682 | ||||||||
\(769\) | 44.8067 | 1.61577 | 0.807886 | − | 0.589339i | \(-0.200612\pi\) | ||||
0.807886 | + | 0.589339i | \(0.200612\pi\) | |||||||
\(770\) | 0.210393 | 0.00758204 | ||||||||
\(771\) | 20.2944 | 0.730884 | ||||||||
\(772\) | −1.99405 | −0.0717675 | ||||||||
\(773\) | −9.47075 | −0.340639 | −0.170320 | − | 0.985389i | \(-0.554480\pi\) | ||||
−0.170320 | + | 0.985389i | \(0.554480\pi\) | |||||||
\(774\) | −6.28228 | −0.225812 | ||||||||
\(775\) | 16.9636 | 0.609350 | ||||||||
\(776\) | −10.8558 | −0.389701 | ||||||||
\(777\) | 6.65721 | 0.238826 | ||||||||
\(778\) | 34.9514 | 1.25307 | ||||||||
\(779\) | 3.49667 | 0.125281 | ||||||||
\(780\) | 0.200130 | 0.00716579 | ||||||||
\(781\) | 4.07263 | 0.145730 | ||||||||
\(782\) | 10.3426 | 0.369849 | ||||||||
\(783\) | 0.853755 | 0.0305107 | ||||||||
\(784\) | 26.5046 | 0.946592 | ||||||||
\(785\) | 0.0940015 | 0.00335506 | ||||||||
\(786\) | −8.06727 | −0.287750 | ||||||||
\(787\) | 10.9358 | 0.389820 | 0.194910 | − | 0.980821i | \(-0.437559\pi\) | ||||
0.194910 | + | 0.980821i | \(0.437559\pi\) | |||||||
\(788\) | 2.44546 | 0.0871159 | ||||||||
\(789\) | 19.0181 | 0.677063 | ||||||||
\(790\) | 1.50568 | 0.0535696 | ||||||||
\(791\) | 22.5821 | 0.802926 | ||||||||
\(792\) | −2.77761 | −0.0986980 | ||||||||
\(793\) | 16.7503 | 0.594821 | ||||||||
\(794\) | −11.5036 | −0.408248 | ||||||||
\(795\) | −0.384046 | −0.0136207 | ||||||||
\(796\) | −10.3995 | −0.368600 | ||||||||
\(797\) | −0.490880 | −0.0173879 | −0.00869393 | − | 0.999962i | \(-0.502767\pi\) | ||||
−0.00869393 | + | 0.999962i | \(0.502767\pi\) | |||||||
\(798\) | 2.57172 | 0.0910378 | ||||||||
\(799\) | 5.07300 | 0.179470 | ||||||||
\(800\) | −14.1588 | −0.500590 | ||||||||
\(801\) | 8.07859 | 0.285443 | ||||||||
\(802\) | −46.3755 | −1.63757 | ||||||||
\(803\) | −5.45392 | −0.192465 | ||||||||
\(804\) | 3.62434 | 0.127821 | ||||||||
\(805\) | −0.734730 | −0.0258958 | ||||||||
\(806\) | 22.3522 | 0.787323 | ||||||||
\(807\) | −7.11300 | −0.250389 | ||||||||
\(808\) | 2.22527 | 0.0782848 | ||||||||
\(809\) | 8.86525 | 0.311686 | 0.155843 | − | 0.987782i | \(-0.450191\pi\) | ||||
0.155843 | + | 0.987782i | \(0.450191\pi\) | |||||||
\(810\) | 0.149021 | 0.00523607 | ||||||||
\(811\) | −14.8785 | −0.522456 | −0.261228 | − | 0.965277i | \(-0.584127\pi\) | ||||
−0.261228 | + | 0.965277i | \(0.584127\pi\) | |||||||
\(812\) | 0.524925 | 0.0184213 | ||||||||
\(813\) | −29.2547 | −1.02601 | ||||||||
\(814\) | 10.3808 | 0.363847 | ||||||||
\(815\) | −1.31873 | −0.0461932 | ||||||||
\(816\) | 4.76302 | 0.166739 | ||||||||
\(817\) | −5.36581 | −0.187726 | ||||||||
\(818\) | 3.90696 | 0.136604 | ||||||||
\(819\) | −4.97015 | −0.173671 | ||||||||
\(820\) | 0.124579 | 0.00435048 | ||||||||
\(821\) | 35.2954 | 1.23182 | 0.615909 | − | 0.787817i | \(-0.288789\pi\) | ||||
0.615909 | + | 0.787817i | \(0.288789\pi\) | |||||||
\(822\) | 3.89727 | 0.135933 | ||||||||
\(823\) | −26.2260 | −0.914181 | −0.457091 | − | 0.889420i | \(-0.651108\pi\) | ||||
−0.457091 | + | 0.889420i | \(0.651108\pi\) | |||||||
\(824\) | 4.69194 | 0.163452 | ||||||||
\(825\) | −5.88174 | −0.204776 | ||||||||
\(826\) | 23.6870 | 0.824175 | ||||||||
\(827\) | 12.8288 | 0.446100 | 0.223050 | − | 0.974807i | \(-0.428399\pi\) | ||||
0.223050 | + | 0.974807i | \(0.428399\pi\) | |||||||
\(828\) | −3.34811 | −0.116355 | ||||||||
\(829\) | −38.9339 | −1.35223 | −0.676116 | − | 0.736795i | \(-0.736338\pi\) | ||||
−0.676116 | + | 0.736795i | \(0.736338\pi\) | |||||||
\(830\) | 0.383424 | 0.0133089 | ||||||||
\(831\) | −18.3881 | −0.637875 | ||||||||
\(832\) | 20.8623 | 0.723270 | ||||||||
\(833\) | −5.56465 | −0.192804 | ||||||||
\(834\) | 29.7116 | 1.02883 | ||||||||
\(835\) | 0.775302 | 0.0268304 | ||||||||
\(836\) | 0.818880 | 0.0283216 | ||||||||
\(837\) | 3.39872 | 0.117477 | ||||||||
\(838\) | 36.1227 | 1.24784 | ||||||||
\(839\) | −4.52967 | −0.156382 | −0.0781908 | − | 0.996938i | \(-0.524914\pi\) | ||||
−0.0781908 | + | 0.996938i | \(0.524914\pi\) | |||||||
\(840\) | −0.265448 | −0.00915884 | ||||||||
\(841\) | −28.2711 | −0.974866 | ||||||||
\(842\) | −29.0870 | −1.00241 | ||||||||
\(843\) | −31.2096 | −1.07492 | ||||||||
\(844\) | −11.0570 | −0.380597 | ||||||||
\(845\) | −0.395751 | −0.0136143 | ||||||||
\(846\) | −8.04227 | −0.276499 | ||||||||
\(847\) | 11.5149 | 0.395657 | ||||||||
\(848\) | 19.4595 | 0.668242 | ||||||||
\(849\) | −13.6719 | −0.469219 | ||||||||
\(850\) | 7.91253 | 0.271397 | ||||||||
\(851\) | −36.2517 | −1.24269 | ||||||||
\(852\) | 1.77360 | 0.0607625 | ||||||||
\(853\) | 33.1425 | 1.13478 | 0.567388 | − | 0.823451i | \(-0.307954\pi\) | ||||
0.567388 | + | 0.823451i | \(0.307954\pi\) | |||||||
\(854\) | 7.66874 | 0.262419 | ||||||||
\(855\) | 0.127282 | 0.00435294 | ||||||||
\(856\) | −32.1111 | −1.09753 | ||||||||
\(857\) | 30.3101 | 1.03537 | 0.517687 | − | 0.855570i | \(-0.326793\pi\) | ||||
0.517687 | + | 0.855570i | \(0.326793\pi\) | |||||||
\(858\) | −7.75013 | −0.264585 | ||||||||
\(859\) | 13.9450 | 0.475799 | 0.237899 | − | 0.971290i | \(-0.423541\pi\) | ||||
0.237899 | + | 0.971290i | \(0.423541\pi\) | |||||||
\(860\) | −0.191172 | −0.00651891 | ||||||||
\(861\) | −3.09387 | −0.105439 | ||||||||
\(862\) | 17.0930 | 0.582189 | ||||||||
\(863\) | −7.77055 | −0.264512 | −0.132256 | − | 0.991216i | \(-0.542222\pi\) | ||||
−0.132256 | + | 0.991216i | \(0.542222\pi\) | |||||||
\(864\) | −2.83678 | −0.0965092 | ||||||||
\(865\) | 1.46227 | 0.0497185 | ||||||||
\(866\) | −33.4868 | −1.13793 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 2.08968 | 0.0709283 | ||||||||
\(869\) | −11.9066 | −0.403904 | ||||||||
\(870\) | 0.127228 | 0.00431342 | ||||||||
\(871\) | −29.2978 | −0.992717 | ||||||||
\(872\) | 22.8169 | 0.772678 | ||||||||
\(873\) | −4.60570 | −0.155879 | ||||||||
\(874\) | −14.0042 | −0.473700 | ||||||||
\(875\) | −1.12520 | −0.0380387 | ||||||||
\(876\) | −2.37514 | −0.0802485 | ||||||||
\(877\) | 24.2895 | 0.820198 | 0.410099 | − | 0.912041i | \(-0.365494\pi\) | ||||
0.410099 | + | 0.912041i | \(0.365494\pi\) | |||||||
\(878\) | −49.7924 | −1.68041 | ||||||||
\(879\) | −16.5597 | −0.558546 | ||||||||
\(880\) | −0.527621 | −0.0177861 | ||||||||
\(881\) | −12.0254 | −0.405146 | −0.202573 | − | 0.979267i | \(-0.564930\pi\) | ||||
−0.202573 | + | 0.979267i | \(0.564930\pi\) | |||||||
\(882\) | 8.82168 | 0.297041 | ||||||||
\(883\) | −6.17274 | −0.207729 | −0.103865 | − | 0.994591i | \(-0.533121\pi\) | ||||
−0.103865 | + | 0.994591i | \(0.533121\pi\) | |||||||
\(884\) | 2.12900 | 0.0716061 | ||||||||
\(885\) | 1.17234 | 0.0394077 | ||||||||
\(886\) | 51.9473 | 1.74520 | ||||||||
\(887\) | −27.6016 | −0.926772 | −0.463386 | − | 0.886157i | \(-0.653366\pi\) | ||||
−0.463386 | + | 0.886157i | \(0.653366\pi\) | |||||||
\(888\) | −13.0972 | −0.439515 | ||||||||
\(889\) | 18.6688 | 0.626133 | ||||||||
\(890\) | 1.20388 | 0.0403542 | ||||||||
\(891\) | −1.17843 | −0.0394789 | ||||||||
\(892\) | 12.5928 | 0.421639 | ||||||||
\(893\) | −6.86904 | −0.229864 | ||||||||
\(894\) | 19.4031 | 0.648937 | ||||||||
\(895\) | 0.282841 | 0.00945432 | ||||||||
\(896\) | 16.3486 | 0.546168 | ||||||||
\(897\) | 27.0648 | 0.903669 | ||||||||
\(898\) | 27.9892 | 0.934012 | ||||||||
\(899\) | 2.90168 | 0.0967764 | ||||||||
\(900\) | −2.56146 | −0.0853819 | ||||||||
\(901\) | −4.08553 | −0.136109 | ||||||||
\(902\) | −4.82438 | −0.160634 | ||||||||
\(903\) | 4.74769 | 0.157993 | ||||||||
\(904\) | −44.4275 | −1.47764 | ||||||||
\(905\) | 0.0201277 | 0.000669066 0 | ||||||||
\(906\) | −23.4199 | −0.778074 | ||||||||
\(907\) | −35.2935 | −1.17190 | −0.585951 | − | 0.810346i | \(-0.699279\pi\) | ||||
−0.585951 | + | 0.810346i | \(0.699279\pi\) | |||||||
\(908\) | −2.81118 | −0.0932924 | ||||||||
\(909\) | 0.944097 | 0.0313137 | ||||||||
\(910\) | −0.740659 | −0.0245526 | ||||||||
\(911\) | 22.4896 | 0.745113 | 0.372557 | − | 0.928009i | \(-0.378481\pi\) | ||||
0.372557 | + | 0.928009i | \(0.378481\pi\) | |||||||
\(912\) | −6.44932 | −0.213558 | ||||||||
\(913\) | −3.03204 | −0.100346 | ||||||||
\(914\) | −15.3404 | −0.507417 | ||||||||
\(915\) | 0.379548 | 0.0125475 | ||||||||
\(916\) | 8.77131 | 0.289812 | ||||||||
\(917\) | 6.09666 | 0.201329 | ||||||||
\(918\) | 1.58531 | 0.0523229 | ||||||||
\(919\) | −7.59835 | −0.250646 | −0.125323 | − | 0.992116i | \(-0.539997\pi\) | ||||
−0.125323 | + | 0.992116i | \(0.539997\pi\) | |||||||
\(920\) | 1.44549 | 0.0476565 | ||||||||
\(921\) | −13.0778 | −0.430929 | ||||||||
\(922\) | −57.6531 | −1.89870 | ||||||||
\(923\) | −14.3371 | −0.471912 | ||||||||
\(924\) | −0.724550 | −0.0238359 | ||||||||
\(925\) | −27.7342 | −0.911894 | ||||||||
\(926\) | 43.9367 | 1.44385 | ||||||||
\(927\) | 1.99061 | 0.0653802 | ||||||||
\(928\) | −2.42192 | −0.0795033 | ||||||||
\(929\) | 8.66415 | 0.284261 | 0.142131 | − | 0.989848i | \(-0.454605\pi\) | ||||
0.142131 | + | 0.989848i | \(0.454605\pi\) | |||||||
\(930\) | 0.506482 | 0.0166082 | ||||||||
\(931\) | 7.53475 | 0.246942 | ||||||||
\(932\) | 6.87126 | 0.225076 | ||||||||
\(933\) | 11.7915 | 0.386035 | ||||||||
\(934\) | −18.1050 | −0.592414 | ||||||||
\(935\) | 0.110774 | 0.00362271 | ||||||||
\(936\) | 9.77817 | 0.319609 | ||||||||
\(937\) | 31.5936 | 1.03212 | 0.516059 | − | 0.856553i | \(-0.327399\pi\) | ||||
0.516059 | + | 0.856553i | \(0.327399\pi\) | |||||||
\(938\) | −13.4133 | −0.437960 | ||||||||
\(939\) | −27.2101 | −0.887967 | ||||||||
\(940\) | −0.244729 | −0.00798218 | ||||||||
\(941\) | −46.0415 | −1.50091 | −0.750455 | − | 0.660921i | \(-0.770166\pi\) | ||||
−0.750455 | + | 0.660921i | \(0.770166\pi\) | |||||||
\(942\) | −1.58531 | −0.0516521 | ||||||||
\(943\) | 16.8476 | 0.548634 | ||||||||
\(944\) | −59.4019 | −1.93337 | ||||||||
\(945\) | −0.112619 | −0.00366351 | ||||||||
\(946\) | 7.40324 | 0.240700 | ||||||||
\(947\) | 30.4961 | 0.990990 | 0.495495 | − | 0.868611i | \(-0.334987\pi\) | ||||
0.495495 | + | 0.868611i | \(0.334987\pi\) | |||||||
\(948\) | −5.18524 | −0.168409 | ||||||||
\(949\) | 19.1997 | 0.623250 | ||||||||
\(950\) | −10.7139 | −0.347604 | ||||||||
\(951\) | −0.703267 | −0.0228050 | ||||||||
\(952\) | −2.82387 | −0.0915222 | ||||||||
\(953\) | 34.4385 | 1.11557 | 0.557786 | − | 0.829985i | \(-0.311651\pi\) | ||||
0.557786 | + | 0.829985i | \(0.311651\pi\) | |||||||
\(954\) | 6.47682 | 0.209695 | ||||||||
\(955\) | 0.341927 | 0.0110645 | ||||||||
\(956\) | −10.6967 | −0.345954 | ||||||||
\(957\) | −1.00609 | −0.0325223 | ||||||||
\(958\) | −9.45929 | −0.305616 | ||||||||
\(959\) | −2.94527 | −0.0951078 | ||||||||
\(960\) | 0.472722 | 0.0152571 | ||||||||
\(961\) | −19.4487 | −0.627377 | ||||||||
\(962\) | −36.5442 | −1.17823 | ||||||||
\(963\) | −13.6235 | −0.439011 | ||||||||
\(964\) | 2.34507 | 0.0755298 | ||||||||
\(965\) | 0.365247 | 0.0117577 | ||||||||
\(966\) | 12.3910 | 0.398674 | ||||||||
\(967\) | −16.7249 | −0.537837 | −0.268918 | − | 0.963163i | \(-0.586666\pi\) | ||||
−0.268918 | + | 0.963163i | \(0.586666\pi\) | |||||||
\(968\) | −22.6542 | −0.728133 | ||||||||
\(969\) | 1.35404 | 0.0434980 | ||||||||
\(970\) | −0.686347 | −0.0220373 | ||||||||
\(971\) | 13.5678 | 0.435411 | 0.217706 | − | 0.976014i | \(-0.430143\pi\) | ||||
0.217706 | + | 0.976014i | \(0.430143\pi\) | |||||||
\(972\) | −0.513198 | −0.0164608 | ||||||||
\(973\) | −22.4539 | −0.719838 | ||||||||
\(974\) | 11.4081 | 0.365539 | ||||||||
\(975\) | 20.7058 | 0.663118 | ||||||||
\(976\) | −19.2316 | −0.615587 | ||||||||
\(977\) | −2.41584 | −0.0772895 | −0.0386448 | − | 0.999253i | \(-0.512304\pi\) | ||||
−0.0386448 | + | 0.999253i | \(0.512304\pi\) | |||||||
\(978\) | 22.2400 | 0.711157 | ||||||||
\(979\) | −9.52007 | −0.304263 | ||||||||
\(980\) | 0.268447 | 0.00857522 | ||||||||
\(981\) | 9.68033 | 0.309069 | ||||||||
\(982\) | 29.7444 | 0.949183 | ||||||||
\(983\) | −3.62934 | −0.115758 | −0.0578790 | − | 0.998324i | \(-0.518434\pi\) | ||||
−0.0578790 | + | 0.998324i | \(0.518434\pi\) | |||||||
\(984\) | 6.08682 | 0.194041 | ||||||||
\(985\) | −0.447930 | −0.0142722 | ||||||||
\(986\) | 1.35346 | 0.0431031 | ||||||||
\(987\) | 6.07776 | 0.193457 | ||||||||
\(988\) | −2.88275 | −0.0917126 | ||||||||
\(989\) | −25.8534 | −0.822092 | ||||||||
\(990\) | −0.175611 | −0.00558130 | ||||||||
\(991\) | 53.7197 | 1.70646 | 0.853231 | − | 0.521533i | \(-0.174640\pi\) | ||||
0.853231 | + | 0.521533i | \(0.174640\pi\) | |||||||
\(992\) | −9.64143 | −0.306116 | ||||||||
\(993\) | −1.49559 | −0.0474612 | ||||||||
\(994\) | −6.56391 | −0.208195 | ||||||||
\(995\) | 1.90486 | 0.0603880 | ||||||||
\(996\) | −1.32043 | −0.0418395 | ||||||||
\(997\) | 28.0904 | 0.889633 | 0.444816 | − | 0.895622i | \(-0.353269\pi\) | ||||
0.444816 | + | 0.895622i | \(0.353269\pi\) | |||||||
\(998\) | 0.0300045 | 0.000949775 0 | ||||||||
\(999\) | −5.55666 | −0.175805 |
(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 | 8007.2.a.j.1.17 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.17 | ✓ | 64 | 1.1 | even | 1 | trivial |