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: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32783 | −0.938917 | −0.469459 | − | 0.882954i | \(-0.655551\pi\) | ||||
−0.469459 | + | 0.882954i | \(0.655551\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.236868 | −0.118434 | ||||||||
\(5\) | 2.41386 | 1.07951 | 0.539755 | − | 0.841822i | \(-0.318517\pi\) | ||||
0.539755 | + | 0.841822i | \(0.318517\pi\) | |||||||
\(6\) | −1.32783 | −0.542084 | ||||||||
\(7\) | 0.553664 | 0.209265 | 0.104633 | − | 0.994511i | \(-0.466633\pi\) | ||||
0.104633 | + | 0.994511i | \(0.466633\pi\) | |||||||
\(8\) | 2.97018 | 1.05012 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.20519 | −1.01357 | ||||||||
\(11\) | −0.0504547 | −0.0152127 | −0.00760633 | − | 0.999971i | \(-0.502421\pi\) | ||||
−0.00760633 | + | 0.999971i | \(0.502421\pi\) | |||||||
\(12\) | −0.236868 | −0.0683780 | ||||||||
\(13\) | −2.00996 | −0.557462 | −0.278731 | − | 0.960369i | \(-0.589914\pi\) | ||||
−0.278731 | + | 0.960369i | \(0.589914\pi\) | |||||||
\(14\) | −0.735171 | −0.196483 | ||||||||
\(15\) | 2.41386 | 0.623255 | ||||||||
\(16\) | −3.47016 | −0.867539 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.32783 | −0.312972 | ||||||||
\(19\) | −7.25787 | −1.66507 | −0.832535 | − | 0.553973i | \(-0.813111\pi\) | ||||
−0.832535 | + | 0.553973i | \(0.813111\pi\) | |||||||
\(20\) | −0.571766 | −0.127851 | ||||||||
\(21\) | 0.553664 | 0.120819 | ||||||||
\(22\) | 0.0669952 | 0.0142834 | ||||||||
\(23\) | 3.59294 | 0.749180 | 0.374590 | − | 0.927191i | \(-0.377783\pi\) | ||||
0.374590 | + | 0.927191i | \(0.377783\pi\) | |||||||
\(24\) | 2.97018 | 0.606285 | ||||||||
\(25\) | 0.826709 | 0.165342 | ||||||||
\(26\) | 2.66888 | 0.523410 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.131145 | −0.0247841 | ||||||||
\(29\) | −1.61089 | −0.299134 | −0.149567 | − | 0.988752i | \(-0.547788\pi\) | ||||
−0.149567 | + | 0.988752i | \(0.547788\pi\) | |||||||
\(30\) | −3.20519 | −0.585185 | ||||||||
\(31\) | −1.39126 | −0.249878 | −0.124939 | − | 0.992164i | \(-0.539873\pi\) | ||||
−0.124939 | + | 0.992164i | \(0.539873\pi\) | |||||||
\(32\) | −1.33258 | −0.235570 | ||||||||
\(33\) | −0.0504547 | −0.00878303 | ||||||||
\(34\) | −1.32783 | −0.227721 | ||||||||
\(35\) | 1.33647 | 0.225904 | ||||||||
\(36\) | −0.236868 | −0.0394780 | ||||||||
\(37\) | −9.04760 | −1.48742 | −0.743708 | − | 0.668505i | \(-0.766935\pi\) | ||||
−0.743708 | + | 0.668505i | \(0.766935\pi\) | |||||||
\(38\) | 9.63722 | 1.56336 | ||||||||
\(39\) | −2.00996 | −0.321851 | ||||||||
\(40\) | 7.16959 | 1.13361 | ||||||||
\(41\) | 3.56543 | 0.556827 | 0.278413 | − | 0.960461i | \(-0.410191\pi\) | ||||
0.278413 | + | 0.960461i | \(0.410191\pi\) | |||||||
\(42\) | −0.735171 | −0.113439 | ||||||||
\(43\) | 3.35313 | 0.511348 | 0.255674 | − | 0.966763i | \(-0.417703\pi\) | ||||
0.255674 | + | 0.966763i | \(0.417703\pi\) | |||||||
\(44\) | 0.0119511 | 0.00180170 | ||||||||
\(45\) | 2.41386 | 0.359837 | ||||||||
\(46\) | −4.77081 | −0.703418 | ||||||||
\(47\) | 2.01172 | 0.293439 | 0.146720 | − | 0.989178i | \(-0.453128\pi\) | ||||
0.146720 | + | 0.989178i | \(0.453128\pi\) | |||||||
\(48\) | −3.47016 | −0.500874 | ||||||||
\(49\) | −6.69346 | −0.956208 | ||||||||
\(50\) | −1.09773 | −0.155242 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0.476095 | 0.0660225 | ||||||||
\(53\) | 13.0015 | 1.78589 | 0.892945 | − | 0.450166i | \(-0.148635\pi\) | ||||
0.892945 | + | 0.450166i | \(0.148635\pi\) | |||||||
\(54\) | −1.32783 | −0.180695 | ||||||||
\(55\) | −0.121790 | −0.0164222 | ||||||||
\(56\) | 1.64448 | 0.219753 | ||||||||
\(57\) | −7.25787 | −0.961328 | ||||||||
\(58\) | 2.13898 | 0.280862 | ||||||||
\(59\) | −6.27918 | −0.817480 | −0.408740 | − | 0.912651i | \(-0.634032\pi\) | ||||
−0.408740 | + | 0.912651i | \(0.634032\pi\) | |||||||
\(60\) | −0.571766 | −0.0738147 | ||||||||
\(61\) | −4.50894 | −0.577311 | −0.288656 | − | 0.957433i | \(-0.593208\pi\) | ||||
−0.288656 | + | 0.957433i | \(0.593208\pi\) | |||||||
\(62\) | 1.84736 | 0.234615 | ||||||||
\(63\) | 0.553664 | 0.0697551 | ||||||||
\(64\) | 8.70976 | 1.08872 | ||||||||
\(65\) | −4.85175 | −0.601785 | ||||||||
\(66\) | 0.0669952 | 0.00824654 | ||||||||
\(67\) | −11.0415 | −1.34894 | −0.674469 | − | 0.738303i | \(-0.735627\pi\) | ||||
−0.674469 | + | 0.738303i | \(0.735627\pi\) | |||||||
\(68\) | −0.236868 | −0.0287245 | ||||||||
\(69\) | 3.59294 | 0.432539 | ||||||||
\(70\) | −1.77460 | −0.212105 | ||||||||
\(71\) | −9.22355 | −1.09463 | −0.547317 | − | 0.836925i | \(-0.684351\pi\) | ||||
−0.547317 | + | 0.836925i | \(0.684351\pi\) | |||||||
\(72\) | 2.97018 | 0.350039 | ||||||||
\(73\) | −4.15599 | −0.486422 | −0.243211 | − | 0.969973i | \(-0.578201\pi\) | ||||
−0.243211 | + | 0.969973i | \(0.578201\pi\) | |||||||
\(74\) | 12.0137 | 1.39656 | ||||||||
\(75\) | 0.826709 | 0.0954602 | ||||||||
\(76\) | 1.71916 | 0.197201 | ||||||||
\(77\) | −0.0279349 | −0.00318348 | ||||||||
\(78\) | 2.66888 | 0.302191 | ||||||||
\(79\) | −4.22154 | −0.474961 | −0.237480 | − | 0.971392i | \(-0.576322\pi\) | ||||
−0.237480 | + | 0.971392i | \(0.576322\pi\) | |||||||
\(80\) | −8.37647 | −0.936517 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.73429 | −0.522814 | ||||||||
\(83\) | 7.35373 | 0.807177 | 0.403588 | − | 0.914941i | \(-0.367763\pi\) | ||||
0.403588 | + | 0.914941i | \(0.367763\pi\) | |||||||
\(84\) | −0.131145 | −0.0143091 | ||||||||
\(85\) | 2.41386 | 0.261820 | ||||||||
\(86\) | −4.45239 | −0.480114 | ||||||||
\(87\) | −1.61089 | −0.172705 | ||||||||
\(88\) | −0.149860 | −0.0159751 | ||||||||
\(89\) | −17.7277 | −1.87913 | −0.939566 | − | 0.342368i | \(-0.888771\pi\) | ||||
−0.939566 | + | 0.342368i | \(0.888771\pi\) | |||||||
\(90\) | −3.20519 | −0.337857 | ||||||||
\(91\) | −1.11284 | −0.116657 | ||||||||
\(92\) | −0.851054 | −0.0887285 | ||||||||
\(93\) | −1.39126 | −0.144267 | ||||||||
\(94\) | −2.67122 | −0.275515 | ||||||||
\(95\) | −17.5195 | −1.79746 | ||||||||
\(96\) | −1.33258 | −0.136006 | ||||||||
\(97\) | −6.12639 | −0.622041 | −0.311021 | − | 0.950403i | \(-0.600671\pi\) | ||||
−0.311021 | + | 0.950403i | \(0.600671\pi\) | |||||||
\(98\) | 8.88777 | 0.897800 | ||||||||
\(99\) | −0.0504547 | −0.00507089 | ||||||||
\(100\) | −0.195821 | −0.0195821 | ||||||||
\(101\) | −3.55682 | −0.353917 | −0.176958 | − | 0.984218i | \(-0.556626\pi\) | ||||
−0.176958 | + | 0.984218i | \(0.556626\pi\) | |||||||
\(102\) | −1.32783 | −0.131475 | ||||||||
\(103\) | 7.38321 | 0.727489 | 0.363745 | − | 0.931499i | \(-0.381498\pi\) | ||||
0.363745 | + | 0.931499i | \(0.381498\pi\) | |||||||
\(104\) | −5.96993 | −0.585400 | ||||||||
\(105\) | 1.33647 | 0.130426 | ||||||||
\(106\) | −17.2637 | −1.67680 | ||||||||
\(107\) | −3.10591 | −0.300260 | −0.150130 | − | 0.988666i | \(-0.547969\pi\) | ||||
−0.150130 | + | 0.988666i | \(0.547969\pi\) | |||||||
\(108\) | −0.236868 | −0.0227927 | ||||||||
\(109\) | 0.250085 | 0.0239538 | 0.0119769 | − | 0.999928i | \(-0.496188\pi\) | ||||
0.0119769 | + | 0.999928i | \(0.496188\pi\) | |||||||
\(110\) | 0.161717 | 0.0154191 | ||||||||
\(111\) | −9.04760 | −0.858760 | ||||||||
\(112\) | −1.92130 | −0.181546 | ||||||||
\(113\) | 18.2101 | 1.71307 | 0.856533 | − | 0.516092i | \(-0.172614\pi\) | ||||
0.856533 | + | 0.516092i | \(0.172614\pi\) | |||||||
\(114\) | 9.63722 | 0.902608 | ||||||||
\(115\) | 8.67285 | 0.808747 | ||||||||
\(116\) | 0.381568 | 0.0354277 | ||||||||
\(117\) | −2.00996 | −0.185821 | ||||||||
\(118\) | 8.33768 | 0.767546 | ||||||||
\(119\) | 0.553664 | 0.0507543 | ||||||||
\(120\) | 7.16959 | 0.654491 | ||||||||
\(121\) | −10.9975 | −0.999769 | ||||||||
\(122\) | 5.98711 | 0.542048 | ||||||||
\(123\) | 3.56543 | 0.321484 | ||||||||
\(124\) | 0.329545 | 0.0295941 | ||||||||
\(125\) | −10.0737 | −0.901022 | ||||||||
\(126\) | −0.735171 | −0.0654943 | ||||||||
\(127\) | −13.3376 | −1.18352 | −0.591761 | − | 0.806113i | \(-0.701567\pi\) | ||||
−0.591761 | + | 0.806113i | \(0.701567\pi\) | |||||||
\(128\) | −8.89991 | −0.786648 | ||||||||
\(129\) | 3.35313 | 0.295227 | ||||||||
\(130\) | 6.44230 | 0.565027 | ||||||||
\(131\) | 1.77550 | 0.155126 | 0.0775631 | − | 0.996987i | \(-0.475286\pi\) | ||||
0.0775631 | + | 0.996987i | \(0.475286\pi\) | |||||||
\(132\) | 0.0119511 | 0.00104021 | ||||||||
\(133\) | −4.01842 | −0.348441 | ||||||||
\(134\) | 14.6613 | 1.26654 | ||||||||
\(135\) | 2.41386 | 0.207752 | ||||||||
\(136\) | 2.97018 | 0.254691 | ||||||||
\(137\) | 3.07784 | 0.262957 | 0.131479 | − | 0.991319i | \(-0.458028\pi\) | ||||
0.131479 | + | 0.991319i | \(0.458028\pi\) | |||||||
\(138\) | −4.77081 | −0.406119 | ||||||||
\(139\) | −9.18804 | −0.779319 | −0.389660 | − | 0.920959i | \(-0.627407\pi\) | ||||
−0.389660 | + | 0.920959i | \(0.627407\pi\) | |||||||
\(140\) | −0.316566 | −0.0267547 | ||||||||
\(141\) | 2.01172 | 0.169417 | ||||||||
\(142\) | 12.2473 | 1.02777 | ||||||||
\(143\) | 0.101412 | 0.00848048 | ||||||||
\(144\) | −3.47016 | −0.289180 | ||||||||
\(145\) | −3.88845 | −0.322918 | ||||||||
\(146\) | 5.51845 | 0.456710 | ||||||||
\(147\) | −6.69346 | −0.552067 | ||||||||
\(148\) | 2.14309 | 0.176161 | ||||||||
\(149\) | −8.11168 | −0.664535 | −0.332267 | − | 0.943185i | \(-0.607814\pi\) | ||||
−0.332267 | + | 0.943185i | \(0.607814\pi\) | |||||||
\(150\) | −1.09773 | −0.0896292 | ||||||||
\(151\) | −3.85015 | −0.313321 | −0.156661 | − | 0.987653i | \(-0.550073\pi\) | ||||
−0.156661 | + | 0.987653i | \(0.550073\pi\) | |||||||
\(152\) | −21.5572 | −1.74852 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 0.0370928 | 0.00298903 | ||||||||
\(155\) | −3.35831 | −0.269746 | ||||||||
\(156\) | 0.476095 | 0.0381181 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 5.60549 | 0.445949 | ||||||||
\(159\) | 13.0015 | 1.03108 | ||||||||
\(160\) | −3.21667 | −0.254300 | ||||||||
\(161\) | 1.98928 | 0.156777 | ||||||||
\(162\) | −1.32783 | −0.104324 | ||||||||
\(163\) | 5.57276 | 0.436492 | 0.218246 | − | 0.975894i | \(-0.429966\pi\) | ||||
0.218246 | + | 0.975894i | \(0.429966\pi\) | |||||||
\(164\) | −0.844538 | −0.0659473 | ||||||||
\(165\) | −0.121790 | −0.00948137 | ||||||||
\(166\) | −9.76450 | −0.757872 | ||||||||
\(167\) | 21.0118 | 1.62594 | 0.812972 | − | 0.582303i | \(-0.197848\pi\) | ||||
0.812972 | + | 0.582303i | \(0.197848\pi\) | |||||||
\(168\) | 1.64448 | 0.126874 | ||||||||
\(169\) | −8.96007 | −0.689236 | ||||||||
\(170\) | −3.20519 | −0.245827 | ||||||||
\(171\) | −7.25787 | −0.555023 | ||||||||
\(172\) | −0.794251 | −0.0605611 | ||||||||
\(173\) | −10.1994 | −0.775448 | −0.387724 | − | 0.921776i | \(-0.626739\pi\) | ||||
−0.387724 | + | 0.921776i | \(0.626739\pi\) | |||||||
\(174\) | 2.13898 | 0.162156 | ||||||||
\(175\) | 0.457719 | 0.0346003 | ||||||||
\(176\) | 0.175086 | 0.0131976 | ||||||||
\(177\) | −6.27918 | −0.471972 | ||||||||
\(178\) | 23.5394 | 1.76435 | ||||||||
\(179\) | −7.80693 | −0.583517 | −0.291759 | − | 0.956492i | \(-0.594240\pi\) | ||||
−0.291759 | + | 0.956492i | \(0.594240\pi\) | |||||||
\(180\) | −0.571766 | −0.0426169 | ||||||||
\(181\) | 14.5974 | 1.08501 | 0.542507 | − | 0.840051i | \(-0.317475\pi\) | ||||
0.542507 | + | 0.840051i | \(0.317475\pi\) | |||||||
\(182\) | 1.47766 | 0.109532 | ||||||||
\(183\) | −4.50894 | −0.333311 | ||||||||
\(184\) | 10.6717 | 0.786727 | ||||||||
\(185\) | −21.8396 | −1.60568 | ||||||||
\(186\) | 1.84736 | 0.135455 | ||||||||
\(187\) | −0.0504547 | −0.00368961 | ||||||||
\(188\) | −0.476512 | −0.0347532 | ||||||||
\(189\) | 0.553664 | 0.0402731 | ||||||||
\(190\) | 23.2629 | 1.68767 | ||||||||
\(191\) | −14.0734 | −1.01832 | −0.509158 | − | 0.860673i | \(-0.670043\pi\) | ||||
−0.509158 | + | 0.860673i | \(0.670043\pi\) | |||||||
\(192\) | 8.70976 | 0.628573 | ||||||||
\(193\) | 4.68720 | 0.337392 | 0.168696 | − | 0.985668i | \(-0.446044\pi\) | ||||
0.168696 | + | 0.985668i | \(0.446044\pi\) | |||||||
\(194\) | 8.13481 | 0.584045 | ||||||||
\(195\) | −4.85175 | −0.347441 | ||||||||
\(196\) | 1.58547 | 0.113248 | ||||||||
\(197\) | −10.2314 | −0.728959 | −0.364480 | − | 0.931211i | \(-0.618753\pi\) | ||||
−0.364480 | + | 0.931211i | \(0.618753\pi\) | |||||||
\(198\) | 0.0669952 | 0.00476114 | ||||||||
\(199\) | −12.5828 | −0.891970 | −0.445985 | − | 0.895040i | \(-0.647147\pi\) | ||||
−0.445985 | + | 0.895040i | \(0.647147\pi\) | |||||||
\(200\) | 2.45548 | 0.173628 | ||||||||
\(201\) | −11.0415 | −0.778810 | ||||||||
\(202\) | 4.72285 | 0.332298 | ||||||||
\(203\) | −0.891890 | −0.0625984 | ||||||||
\(204\) | −0.236868 | −0.0165841 | ||||||||
\(205\) | 8.60645 | 0.601100 | ||||||||
\(206\) | −9.80365 | −0.683052 | ||||||||
\(207\) | 3.59294 | 0.249727 | ||||||||
\(208\) | 6.97487 | 0.483620 | ||||||||
\(209\) | 0.366194 | 0.0253301 | ||||||||
\(210\) | −1.77460 | −0.122459 | ||||||||
\(211\) | −1.89126 | −0.130200 | −0.0651000 | − | 0.997879i | \(-0.520737\pi\) | ||||
−0.0651000 | + | 0.997879i | \(0.520737\pi\) | |||||||
\(212\) | −3.07964 | −0.211510 | ||||||||
\(213\) | −9.22355 | −0.631987 | ||||||||
\(214\) | 4.12412 | 0.281919 | ||||||||
\(215\) | 8.09399 | 0.552005 | ||||||||
\(216\) | 2.97018 | 0.202095 | ||||||||
\(217\) | −0.770291 | −0.0522907 | ||||||||
\(218\) | −0.332071 | −0.0224907 | ||||||||
\(219\) | −4.15599 | −0.280836 | ||||||||
\(220\) | 0.0288483 | 0.00194495 | ||||||||
\(221\) | −2.00996 | −0.135204 | ||||||||
\(222\) | 12.0137 | 0.806304 | ||||||||
\(223\) | −18.6700 | −1.25023 | −0.625117 | − | 0.780531i | \(-0.714949\pi\) | ||||
−0.625117 | + | 0.780531i | \(0.714949\pi\) | |||||||
\(224\) | −0.737803 | −0.0492965 | ||||||||
\(225\) | 0.826709 | 0.0551139 | ||||||||
\(226\) | −24.1800 | −1.60843 | ||||||||
\(227\) | 22.5269 | 1.49517 | 0.747583 | − | 0.664169i | \(-0.231214\pi\) | ||||
0.747583 | + | 0.664169i | \(0.231214\pi\) | |||||||
\(228\) | 1.71916 | 0.113854 | ||||||||
\(229\) | 11.0212 | 0.728299 | 0.364150 | − | 0.931340i | \(-0.381360\pi\) | ||||
0.364150 | + | 0.931340i | \(0.381360\pi\) | |||||||
\(230\) | −11.5161 | −0.759347 | ||||||||
\(231\) | −0.0279349 | −0.00183798 | ||||||||
\(232\) | −4.78462 | −0.314126 | ||||||||
\(233\) | 3.14050 | 0.205741 | 0.102870 | − | 0.994695i | \(-0.467197\pi\) | ||||
0.102870 | + | 0.994695i | \(0.467197\pi\) | |||||||
\(234\) | 2.66888 | 0.174470 | ||||||||
\(235\) | 4.85600 | 0.316771 | ||||||||
\(236\) | 1.48734 | 0.0968175 | ||||||||
\(237\) | −4.22154 | −0.274219 | ||||||||
\(238\) | −0.735171 | −0.0476541 | ||||||||
\(239\) | 7.60926 | 0.492202 | 0.246101 | − | 0.969244i | \(-0.420851\pi\) | ||||
0.246101 | + | 0.969244i | \(0.420851\pi\) | |||||||
\(240\) | −8.37647 | −0.540699 | ||||||||
\(241\) | −3.97950 | −0.256342 | −0.128171 | − | 0.991752i | \(-0.540911\pi\) | ||||
−0.128171 | + | 0.991752i | \(0.540911\pi\) | |||||||
\(242\) | 14.6027 | 0.938700 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.06803 | 0.0683733 | ||||||||
\(245\) | −16.1571 | −1.03224 | ||||||||
\(246\) | −4.73429 | −0.301847 | ||||||||
\(247\) | 14.5880 | 0.928213 | ||||||||
\(248\) | −4.13229 | −0.262401 | ||||||||
\(249\) | 7.35373 | 0.466024 | ||||||||
\(250\) | 13.3762 | 0.845985 | ||||||||
\(251\) | 4.51023 | 0.284683 | 0.142342 | − | 0.989818i | \(-0.454537\pi\) | ||||
0.142342 | + | 0.989818i | \(0.454537\pi\) | |||||||
\(252\) | −0.131145 | −0.00826138 | ||||||||
\(253\) | −0.181281 | −0.0113970 | ||||||||
\(254\) | 17.7101 | 1.11123 | ||||||||
\(255\) | 2.41386 | 0.151162 | ||||||||
\(256\) | −5.60195 | −0.350122 | ||||||||
\(257\) | 1.07844 | 0.0672713 | 0.0336357 | − | 0.999434i | \(-0.489291\pi\) | ||||
0.0336357 | + | 0.999434i | \(0.489291\pi\) | |||||||
\(258\) | −4.45239 | −0.277194 | ||||||||
\(259\) | −5.00933 | −0.311264 | ||||||||
\(260\) | 1.14923 | 0.0712719 | ||||||||
\(261\) | −1.61089 | −0.0997114 | ||||||||
\(262\) | −2.35756 | −0.145651 | ||||||||
\(263\) | 29.7028 | 1.83155 | 0.915776 | − | 0.401689i | \(-0.131577\pi\) | ||||
0.915776 | + | 0.401689i | \(0.131577\pi\) | |||||||
\(264\) | −0.149860 | −0.00922322 | ||||||||
\(265\) | 31.3837 | 1.92789 | ||||||||
\(266\) | 5.33578 | 0.327157 | ||||||||
\(267\) | −17.7277 | −1.08492 | ||||||||
\(268\) | 2.61539 | 0.159760 | ||||||||
\(269\) | 18.9128 | 1.15313 | 0.576567 | − | 0.817050i | \(-0.304392\pi\) | ||||
0.576567 | + | 0.817050i | \(0.304392\pi\) | |||||||
\(270\) | −3.20519 | −0.195062 | ||||||||
\(271\) | 14.2519 | 0.865740 | 0.432870 | − | 0.901456i | \(-0.357501\pi\) | ||||
0.432870 | + | 0.901456i | \(0.357501\pi\) | |||||||
\(272\) | −3.47016 | −0.210409 | ||||||||
\(273\) | −1.11284 | −0.0673522 | ||||||||
\(274\) | −4.08684 | −0.246895 | ||||||||
\(275\) | −0.0417114 | −0.00251529 | ||||||||
\(276\) | −0.851054 | −0.0512274 | ||||||||
\(277\) | −7.32097 | −0.439874 | −0.219937 | − | 0.975514i | \(-0.570585\pi\) | ||||
−0.219937 | + | 0.975514i | \(0.570585\pi\) | |||||||
\(278\) | 12.2001 | 0.731716 | ||||||||
\(279\) | −1.39126 | −0.0832926 | ||||||||
\(280\) | 3.96954 | 0.237226 | ||||||||
\(281\) | 19.5759 | 1.16780 | 0.583901 | − | 0.811825i | \(-0.301526\pi\) | ||||
0.583901 | + | 0.811825i | \(0.301526\pi\) | |||||||
\(282\) | −2.67122 | −0.159069 | ||||||||
\(283\) | 0.112031 | 0.00665953 | 0.00332976 | − | 0.999994i | \(-0.498940\pi\) | ||||
0.00332976 | + | 0.999994i | \(0.498940\pi\) | |||||||
\(284\) | 2.18477 | 0.129642 | ||||||||
\(285\) | −17.5195 | −1.03776 | ||||||||
\(286\) | −0.134658 | −0.00796247 | ||||||||
\(287\) | 1.97405 | 0.116525 | ||||||||
\(288\) | −1.33258 | −0.0785232 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 5.16320 | 0.303194 | ||||||||
\(291\) | −6.12639 | −0.359136 | ||||||||
\(292\) | 0.984423 | 0.0576090 | ||||||||
\(293\) | −8.15206 | −0.476248 | −0.238124 | − | 0.971235i | \(-0.576533\pi\) | ||||
−0.238124 | + | 0.971235i | \(0.576533\pi\) | |||||||
\(294\) | 8.88777 | 0.518345 | ||||||||
\(295\) | −15.1571 | −0.882478 | ||||||||
\(296\) | −26.8730 | −1.56196 | ||||||||
\(297\) | −0.0504547 | −0.00292768 | ||||||||
\(298\) | 10.7709 | 0.623943 | ||||||||
\(299\) | −7.22166 | −0.417639 | ||||||||
\(300\) | −0.195821 | −0.0113057 | ||||||||
\(301\) | 1.85651 | 0.107007 | ||||||||
\(302\) | 5.11235 | 0.294183 | ||||||||
\(303\) | −3.55682 | −0.204334 | ||||||||
\(304\) | 25.1859 | 1.44451 | ||||||||
\(305\) | −10.8840 | −0.623213 | ||||||||
\(306\) | −1.32783 | −0.0759070 | ||||||||
\(307\) | −18.0295 | −1.02900 | −0.514498 | − | 0.857492i | \(-0.672022\pi\) | ||||
−0.514498 | + | 0.857492i | \(0.672022\pi\) | |||||||
\(308\) | 0.00661690 | 0.000377033 0 | ||||||||
\(309\) | 7.38321 | 0.420016 | ||||||||
\(310\) | 4.45926 | 0.253269 | ||||||||
\(311\) | −13.7148 | −0.777692 | −0.388846 | − | 0.921303i | \(-0.627126\pi\) | ||||
−0.388846 | + | 0.921303i | \(0.627126\pi\) | |||||||
\(312\) | −5.96993 | −0.337981 | ||||||||
\(313\) | −8.18923 | −0.462883 | −0.231441 | − | 0.972849i | \(-0.574344\pi\) | ||||
−0.231441 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(314\) | 1.32783 | 0.0749338 | ||||||||
\(315\) | 1.33647 | 0.0753013 | ||||||||
\(316\) | 0.999949 | 0.0562516 | ||||||||
\(317\) | −18.6053 | −1.04498 | −0.522489 | − | 0.852646i | \(-0.674997\pi\) | ||||
−0.522489 | + | 0.852646i | \(0.674997\pi\) | |||||||
\(318\) | −17.2637 | −0.968103 | ||||||||
\(319\) | 0.0812768 | 0.00455063 | ||||||||
\(320\) | 21.0241 | 1.17528 | ||||||||
\(321\) | −3.10591 | −0.173355 | ||||||||
\(322\) | −2.64143 | −0.147201 | ||||||||
\(323\) | −7.25787 | −0.403839 | ||||||||
\(324\) | −0.236868 | −0.0131593 | ||||||||
\(325\) | −1.66165 | −0.0921717 | ||||||||
\(326\) | −7.39968 | −0.409830 | ||||||||
\(327\) | 0.250085 | 0.0138298 | ||||||||
\(328\) | 10.5900 | 0.584734 | ||||||||
\(329\) | 1.11382 | 0.0614066 | ||||||||
\(330\) | 0.161717 | 0.00890223 | ||||||||
\(331\) | 20.9839 | 1.15338 | 0.576689 | − | 0.816964i | \(-0.304344\pi\) | ||||
0.576689 | + | 0.816964i | \(0.304344\pi\) | |||||||
\(332\) | −1.74187 | −0.0955973 | ||||||||
\(333\) | −9.04760 | −0.495805 | ||||||||
\(334\) | −27.9001 | −1.52663 | ||||||||
\(335\) | −26.6527 | −1.45619 | ||||||||
\(336\) | −1.92130 | −0.104816 | ||||||||
\(337\) | 25.5881 | 1.39387 | 0.696935 | − | 0.717134i | \(-0.254546\pi\) | ||||
0.696935 | + | 0.717134i | \(0.254546\pi\) | |||||||
\(338\) | 11.8975 | 0.647136 | ||||||||
\(339\) | 18.2101 | 0.989039 | ||||||||
\(340\) | −0.571766 | −0.0310084 | ||||||||
\(341\) | 0.0701956 | 0.00380131 | ||||||||
\(342\) | 9.63722 | 0.521121 | ||||||||
\(343\) | −7.58157 | −0.409366 | ||||||||
\(344\) | 9.95941 | 0.536976 | ||||||||
\(345\) | 8.67285 | 0.466931 | ||||||||
\(346\) | 13.5431 | 0.728081 | ||||||||
\(347\) | −12.6841 | −0.680919 | −0.340459 | − | 0.940259i | \(-0.610583\pi\) | ||||
−0.340459 | + | 0.940259i | \(0.610583\pi\) | |||||||
\(348\) | 0.381568 | 0.0204542 | ||||||||
\(349\) | −34.5027 | −1.84689 | −0.923444 | − | 0.383733i | \(-0.874638\pi\) | ||||
−0.923444 | + | 0.383733i | \(0.874638\pi\) | |||||||
\(350\) | −0.607773 | −0.0324868 | ||||||||
\(351\) | −2.00996 | −0.107284 | ||||||||
\(352\) | 0.0672351 | 0.00358364 | ||||||||
\(353\) | 24.0289 | 1.27893 | 0.639466 | − | 0.768820i | \(-0.279156\pi\) | ||||
0.639466 | + | 0.768820i | \(0.279156\pi\) | |||||||
\(354\) | 8.33768 | 0.443143 | ||||||||
\(355\) | −22.2643 | −1.18167 | ||||||||
\(356\) | 4.19913 | 0.222553 | ||||||||
\(357\) | 0.553664 | 0.0293030 | ||||||||
\(358\) | 10.3663 | 0.547874 | ||||||||
\(359\) | −20.9975 | −1.10820 | −0.554102 | − | 0.832449i | \(-0.686938\pi\) | ||||
−0.554102 | + | 0.832449i | \(0.686938\pi\) | |||||||
\(360\) | 7.16959 | 0.377871 | ||||||||
\(361\) | 33.6767 | 1.77246 | ||||||||
\(362\) | −19.3828 | −1.01874 | ||||||||
\(363\) | −10.9975 | −0.577217 | ||||||||
\(364\) | 0.263596 | 0.0138162 | ||||||||
\(365\) | −10.0320 | −0.525098 | ||||||||
\(366\) | 5.98711 | 0.312951 | ||||||||
\(367\) | −2.09038 | −0.109117 | −0.0545584 | − | 0.998511i | \(-0.517375\pi\) | ||||
−0.0545584 | + | 0.998511i | \(0.517375\pi\) | |||||||
\(368\) | −12.4681 | −0.649943 | ||||||||
\(369\) | 3.56543 | 0.185609 | ||||||||
\(370\) | 28.9993 | 1.50760 | ||||||||
\(371\) | 7.19845 | 0.373725 | ||||||||
\(372\) | 0.329545 | 0.0170861 | ||||||||
\(373\) | −33.2812 | −1.72324 | −0.861619 | − | 0.507556i | \(-0.830549\pi\) | ||||
−0.861619 | + | 0.507556i | \(0.830549\pi\) | |||||||
\(374\) | 0.0669952 | 0.00346424 | ||||||||
\(375\) | −10.0737 | −0.520205 | ||||||||
\(376\) | 5.97517 | 0.308146 | ||||||||
\(377\) | 3.23781 | 0.166756 | ||||||||
\(378\) | −0.735171 | −0.0378131 | ||||||||
\(379\) | 34.7450 | 1.78473 | 0.892364 | − | 0.451315i | \(-0.149045\pi\) | ||||
0.892364 | + | 0.451315i | \(0.149045\pi\) | |||||||
\(380\) | 4.14981 | 0.212881 | ||||||||
\(381\) | −13.3376 | −0.683307 | ||||||||
\(382\) | 18.6871 | 0.956115 | ||||||||
\(383\) | 11.4728 | 0.586231 | 0.293115 | − | 0.956077i | \(-0.405308\pi\) | ||||
0.293115 | + | 0.956077i | \(0.405308\pi\) | |||||||
\(384\) | −8.89991 | −0.454172 | ||||||||
\(385\) | −0.0674310 | −0.00343660 | ||||||||
\(386\) | −6.22380 | −0.316783 | ||||||||
\(387\) | 3.35313 | 0.170449 | ||||||||
\(388\) | 1.45115 | 0.0736709 | ||||||||
\(389\) | −0.557480 | −0.0282654 | −0.0141327 | − | 0.999900i | \(-0.504499\pi\) | ||||
−0.0141327 | + | 0.999900i | \(0.504499\pi\) | |||||||
\(390\) | 6.44230 | 0.326218 | ||||||||
\(391\) | 3.59294 | 0.181703 | ||||||||
\(392\) | −19.8808 | −1.00413 | ||||||||
\(393\) | 1.77550 | 0.0895621 | ||||||||
\(394\) | 13.5856 | 0.684432 | ||||||||
\(395\) | −10.1902 | −0.512725 | ||||||||
\(396\) | 0.0119511 | 0.000600566 0 | ||||||||
\(397\) | 21.3771 | 1.07289 | 0.536443 | − | 0.843936i | \(-0.319767\pi\) | ||||
0.536443 | + | 0.843936i | \(0.319767\pi\) | |||||||
\(398\) | 16.7078 | 0.837487 | ||||||||
\(399\) | −4.01842 | −0.201173 | ||||||||
\(400\) | −2.86881 | −0.143441 | ||||||||
\(401\) | −32.6546 | −1.63070 | −0.815348 | − | 0.578972i | \(-0.803454\pi\) | ||||
−0.815348 | + | 0.578972i | \(0.803454\pi\) | |||||||
\(402\) | 14.6613 | 0.731238 | ||||||||
\(403\) | 2.79637 | 0.139297 | ||||||||
\(404\) | 0.842497 | 0.0419158 | ||||||||
\(405\) | 2.41386 | 0.119946 | ||||||||
\(406\) | 1.18428 | 0.0587747 | ||||||||
\(407\) | 0.456494 | 0.0226276 | ||||||||
\(408\) | 2.97018 | 0.147046 | ||||||||
\(409\) | 25.8625 | 1.27882 | 0.639408 | − | 0.768867i | \(-0.279179\pi\) | ||||
0.639408 | + | 0.768867i | \(0.279179\pi\) | |||||||
\(410\) | −11.4279 | −0.564383 | ||||||||
\(411\) | 3.07784 | 0.151819 | ||||||||
\(412\) | −1.74885 | −0.0861596 | ||||||||
\(413\) | −3.47656 | −0.171070 | ||||||||
\(414\) | −4.77081 | −0.234473 | ||||||||
\(415\) | 17.7509 | 0.871355 | ||||||||
\(416\) | 2.67843 | 0.131321 | ||||||||
\(417\) | −9.18804 | −0.449940 | ||||||||
\(418\) | −0.486243 | −0.0237829 | ||||||||
\(419\) | −33.9823 | −1.66014 | −0.830071 | − | 0.557658i | \(-0.811700\pi\) | ||||
−0.830071 | + | 0.557658i | \(0.811700\pi\) | |||||||
\(420\) | −0.316566 | −0.0154469 | ||||||||
\(421\) | −4.14710 | −0.202117 | −0.101059 | − | 0.994880i | \(-0.532223\pi\) | ||||
−0.101059 | + | 0.994880i | \(0.532223\pi\) | |||||||
\(422\) | 2.51128 | 0.122247 | ||||||||
\(423\) | 2.01172 | 0.0978131 | ||||||||
\(424\) | 38.6167 | 1.87539 | ||||||||
\(425\) | 0.826709 | 0.0401013 | ||||||||
\(426\) | 12.2473 | 0.593384 | ||||||||
\(427\) | −2.49644 | −0.120811 | ||||||||
\(428\) | 0.735692 | 0.0355610 | ||||||||
\(429\) | 0.101412 | 0.00489621 | ||||||||
\(430\) | −10.7474 | −0.518288 | ||||||||
\(431\) | −0.673825 | −0.0324570 | −0.0162285 | − | 0.999868i | \(-0.505166\pi\) | ||||
−0.0162285 | + | 0.999868i | \(0.505166\pi\) | |||||||
\(432\) | −3.47016 | −0.166958 | ||||||||
\(433\) | 22.5517 | 1.08376 | 0.541882 | − | 0.840455i | \(-0.317712\pi\) | ||||
0.541882 | + | 0.840455i | \(0.317712\pi\) | |||||||
\(434\) | 1.02281 | 0.0490967 | ||||||||
\(435\) | −3.88845 | −0.186437 | ||||||||
\(436\) | −0.0592373 | −0.00283695 | ||||||||
\(437\) | −26.0771 | −1.24744 | ||||||||
\(438\) | 5.51845 | 0.263682 | ||||||||
\(439\) | −31.0179 | −1.48040 | −0.740202 | − | 0.672384i | \(-0.765270\pi\) | ||||
−0.740202 | + | 0.672384i | \(0.765270\pi\) | |||||||
\(440\) | −0.361740 | −0.0172453 | ||||||||
\(441\) | −6.69346 | −0.318736 | ||||||||
\(442\) | 2.66888 | 0.126946 | ||||||||
\(443\) | 7.70043 | 0.365859 | 0.182929 | − | 0.983126i | \(-0.441442\pi\) | ||||
0.182929 | + | 0.983126i | \(0.441442\pi\) | |||||||
\(444\) | 2.14309 | 0.101706 | ||||||||
\(445\) | −42.7921 | −2.02854 | ||||||||
\(446\) | 24.7905 | 1.17387 | ||||||||
\(447\) | −8.11168 | −0.383669 | ||||||||
\(448\) | 4.82228 | 0.227831 | ||||||||
\(449\) | −24.2973 | −1.14666 | −0.573330 | − | 0.819325i | \(-0.694349\pi\) | ||||
−0.573330 | + | 0.819325i | \(0.694349\pi\) | |||||||
\(450\) | −1.09773 | −0.0517474 | ||||||||
\(451\) | −0.179893 | −0.00847082 | ||||||||
\(452\) | −4.31340 | −0.202885 | ||||||||
\(453\) | −3.85015 | −0.180896 | ||||||||
\(454\) | −29.9119 | −1.40384 | ||||||||
\(455\) | −2.68624 | −0.125933 | ||||||||
\(456\) | −21.5572 | −1.00951 | ||||||||
\(457\) | 15.6393 | 0.731576 | 0.365788 | − | 0.930698i | \(-0.380799\pi\) | ||||
0.365788 | + | 0.930698i | \(0.380799\pi\) | |||||||
\(458\) | −14.6342 | −0.683813 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −2.05432 | −0.0957833 | ||||||||
\(461\) | 4.58418 | 0.213506 | 0.106753 | − | 0.994286i | \(-0.465955\pi\) | ||||
0.106753 | + | 0.994286i | \(0.465955\pi\) | |||||||
\(462\) | 0.0370928 | 0.00172571 | ||||||||
\(463\) | 3.22679 | 0.149962 | 0.0749809 | − | 0.997185i | \(-0.476110\pi\) | ||||
0.0749809 | + | 0.997185i | \(0.476110\pi\) | |||||||
\(464\) | 5.59003 | 0.259511 | ||||||||
\(465\) | −3.35831 | −0.155738 | ||||||||
\(466\) | −4.17005 | −0.193174 | ||||||||
\(467\) | 23.6430 | 1.09407 | 0.547034 | − | 0.837110i | \(-0.315757\pi\) | ||||
0.547034 | + | 0.837110i | \(0.315757\pi\) | |||||||
\(468\) | 0.476095 | 0.0220075 | ||||||||
\(469\) | −6.11330 | −0.282286 | ||||||||
\(470\) | −6.44794 | −0.297422 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | −18.6503 | −0.858450 | ||||||||
\(473\) | −0.169181 | −0.00777897 | ||||||||
\(474\) | 5.60549 | 0.257469 | ||||||||
\(475\) | −6.00015 | −0.275306 | ||||||||
\(476\) | −0.131145 | −0.00601104 | ||||||||
\(477\) | 13.0015 | 0.595297 | ||||||||
\(478\) | −10.1038 | −0.462137 | ||||||||
\(479\) | 13.0903 | 0.598112 | 0.299056 | − | 0.954236i | \(-0.403328\pi\) | ||||
0.299056 | + | 0.954236i | \(0.403328\pi\) | |||||||
\(480\) | −3.21667 | −0.146820 | ||||||||
\(481\) | 18.1853 | 0.829177 | ||||||||
\(482\) | 5.28409 | 0.240684 | ||||||||
\(483\) | 1.98928 | 0.0905154 | ||||||||
\(484\) | 2.60495 | 0.118407 | ||||||||
\(485\) | −14.7882 | −0.671500 | ||||||||
\(486\) | −1.32783 | −0.0602316 | ||||||||
\(487\) | 20.3524 | 0.922256 | 0.461128 | − | 0.887334i | \(-0.347445\pi\) | ||||
0.461128 | + | 0.887334i | \(0.347445\pi\) | |||||||
\(488\) | −13.3924 | −0.606244 | ||||||||
\(489\) | 5.57276 | 0.252009 | ||||||||
\(490\) | 21.4538 | 0.969184 | ||||||||
\(491\) | −19.5929 | −0.884215 | −0.442107 | − | 0.896962i | \(-0.645769\pi\) | ||||
−0.442107 | + | 0.896962i | \(0.645769\pi\) | |||||||
\(492\) | −0.844538 | −0.0380747 | ||||||||
\(493\) | −1.61089 | −0.0725507 | ||||||||
\(494\) | −19.3704 | −0.871515 | ||||||||
\(495\) | −0.121790 | −0.00547407 | ||||||||
\(496\) | 4.82789 | 0.216779 | ||||||||
\(497\) | −5.10675 | −0.229069 | ||||||||
\(498\) | −9.76450 | −0.437558 | ||||||||
\(499\) | −5.37507 | −0.240621 | −0.120311 | − | 0.992736i | \(-0.538389\pi\) | ||||
−0.120311 | + | 0.992736i | \(0.538389\pi\) | |||||||
\(500\) | 2.38615 | 0.106712 | ||||||||
\(501\) | 21.0118 | 0.938739 | ||||||||
\(502\) | −5.98882 | −0.267294 | ||||||||
\(503\) | −26.9146 | −1.20006 | −0.600031 | − | 0.799976i | \(-0.704845\pi\) | ||||
−0.600031 | + | 0.799976i | \(0.704845\pi\) | |||||||
\(504\) | 1.64448 | 0.0732510 | ||||||||
\(505\) | −8.58565 | −0.382056 | ||||||||
\(506\) | 0.240710 | 0.0107009 | ||||||||
\(507\) | −8.96007 | −0.397931 | ||||||||
\(508\) | 3.15926 | 0.140169 | ||||||||
\(509\) | −27.1299 | −1.20251 | −0.601256 | − | 0.799057i | \(-0.705333\pi\) | ||||
−0.601256 | + | 0.799057i | \(0.705333\pi\) | |||||||
\(510\) | −3.20519 | −0.141928 | ||||||||
\(511\) | −2.30102 | −0.101791 | ||||||||
\(512\) | 25.2383 | 1.11538 | ||||||||
\(513\) | −7.25787 | −0.320443 | ||||||||
\(514\) | −1.43199 | −0.0631622 | ||||||||
\(515\) | 17.8220 | 0.785332 | ||||||||
\(516\) | −0.794251 | −0.0349649 | ||||||||
\(517\) | −0.101501 | −0.00446399 | ||||||||
\(518\) | 6.65153 | 0.292252 | ||||||||
\(519\) | −10.1994 | −0.447705 | ||||||||
\(520\) | −14.4106 | −0.631945 | ||||||||
\(521\) | −31.1032 | −1.36266 | −0.681329 | − | 0.731977i | \(-0.738598\pi\) | ||||
−0.681329 | + | 0.731977i | \(0.738598\pi\) | |||||||
\(522\) | 2.13898 | 0.0936208 | ||||||||
\(523\) | −27.5421 | −1.20433 | −0.602166 | − | 0.798371i | \(-0.705696\pi\) | ||||
−0.602166 | + | 0.798371i | \(0.705696\pi\) | |||||||
\(524\) | −0.420559 | −0.0183722 | ||||||||
\(525\) | 0.457719 | 0.0199765 | ||||||||
\(526\) | −39.4402 | −1.71968 | ||||||||
\(527\) | −1.39126 | −0.0606043 | ||||||||
\(528\) | 0.175086 | 0.00761963 | ||||||||
\(529\) | −10.0908 | −0.438729 | ||||||||
\(530\) | −41.6722 | −1.81013 | ||||||||
\(531\) | −6.27918 | −0.272493 | ||||||||
\(532\) | 0.951836 | 0.0412673 | ||||||||
\(533\) | −7.16636 | −0.310410 | ||||||||
\(534\) | 23.5394 | 1.01865 | ||||||||
\(535\) | −7.49723 | −0.324133 | ||||||||
\(536\) | −32.7953 | −1.41654 | ||||||||
\(537\) | −7.80693 | −0.336894 | ||||||||
\(538\) | −25.1130 | −1.08270 | ||||||||
\(539\) | 0.337716 | 0.0145465 | ||||||||
\(540\) | −0.571766 | −0.0246049 | ||||||||
\(541\) | 18.5985 | 0.799612 | 0.399806 | − | 0.916600i | \(-0.369077\pi\) | ||||
0.399806 | + | 0.916600i | \(0.369077\pi\) | |||||||
\(542\) | −18.9241 | −0.812859 | ||||||||
\(543\) | 14.5974 | 0.626433 | ||||||||
\(544\) | −1.33258 | −0.0571340 | ||||||||
\(545\) | 0.603671 | 0.0258584 | ||||||||
\(546\) | 1.47766 | 0.0632381 | ||||||||
\(547\) | 45.5835 | 1.94901 | 0.974505 | − | 0.224366i | \(-0.0720313\pi\) | ||||
0.974505 | + | 0.224366i | \(0.0720313\pi\) | |||||||
\(548\) | −0.729042 | −0.0311431 | ||||||||
\(549\) | −4.50894 | −0.192437 | ||||||||
\(550\) | 0.0553856 | 0.00236165 | ||||||||
\(551\) | 11.6916 | 0.498079 | ||||||||
\(552\) | 10.6717 | 0.454217 | ||||||||
\(553\) | −2.33732 | −0.0993928 | ||||||||
\(554\) | 9.72099 | 0.413005 | ||||||||
\(555\) | −21.8396 | −0.927040 | ||||||||
\(556\) | 2.17635 | 0.0922980 | ||||||||
\(557\) | −2.43056 | −0.102986 | −0.0514931 | − | 0.998673i | \(-0.516398\pi\) | ||||
−0.0514931 | + | 0.998673i | \(0.516398\pi\) | |||||||
\(558\) | 1.84736 | 0.0782049 | ||||||||
\(559\) | −6.73965 | −0.285057 | ||||||||
\(560\) | −4.63775 | −0.195981 | ||||||||
\(561\) | −0.0504547 | −0.00213020 | ||||||||
\(562\) | −25.9935 | −1.09647 | ||||||||
\(563\) | 10.5339 | 0.443952 | 0.221976 | − | 0.975052i | \(-0.428749\pi\) | ||||
0.221976 | + | 0.975052i | \(0.428749\pi\) | |||||||
\(564\) | −0.476512 | −0.0200648 | ||||||||
\(565\) | 43.9567 | 1.84927 | ||||||||
\(566\) | −0.148758 | −0.00625275 | ||||||||
\(567\) | 0.553664 | 0.0232517 | ||||||||
\(568\) | −27.3956 | −1.14949 | ||||||||
\(569\) | −18.4295 | −0.772605 | −0.386303 | − | 0.922372i | \(-0.626248\pi\) | ||||
−0.386303 | + | 0.922372i | \(0.626248\pi\) | |||||||
\(570\) | 23.2629 | 0.974374 | ||||||||
\(571\) | −27.2558 | −1.14062 | −0.570311 | − | 0.821429i | \(-0.693177\pi\) | ||||
−0.570311 | + | 0.821429i | \(0.693177\pi\) | |||||||
\(572\) | −0.0240212 | −0.00100438 | ||||||||
\(573\) | −14.0734 | −0.587925 | ||||||||
\(574\) | −2.62120 | −0.109407 | ||||||||
\(575\) | 2.97032 | 0.123871 | ||||||||
\(576\) | 8.70976 | 0.362907 | ||||||||
\(577\) | −16.6908 | −0.694849 | −0.347424 | − | 0.937708i | \(-0.612944\pi\) | ||||
−0.347424 | + | 0.937708i | \(0.612944\pi\) | |||||||
\(578\) | −1.32783 | −0.0552304 | ||||||||
\(579\) | 4.68720 | 0.194793 | ||||||||
\(580\) | 0.921051 | 0.0382445 | ||||||||
\(581\) | 4.07149 | 0.168914 | ||||||||
\(582\) | 8.13481 | 0.337199 | ||||||||
\(583\) | −0.655985 | −0.0271681 | ||||||||
\(584\) | −12.3441 | −0.510801 | ||||||||
\(585\) | −4.85175 | −0.200595 | ||||||||
\(586\) | 10.8245 | 0.447158 | ||||||||
\(587\) | 37.8588 | 1.56260 | 0.781299 | − | 0.624157i | \(-0.214557\pi\) | ||||
0.781299 | + | 0.624157i | \(0.214557\pi\) | |||||||
\(588\) | 1.58547 | 0.0653836 | ||||||||
\(589\) | 10.0976 | 0.416064 | ||||||||
\(590\) | 20.1260 | 0.828574 | ||||||||
\(591\) | −10.2314 | −0.420865 | ||||||||
\(592\) | 31.3966 | 1.29039 | ||||||||
\(593\) | −22.5803 | −0.927260 | −0.463630 | − | 0.886029i | \(-0.653453\pi\) | ||||
−0.463630 | + | 0.886029i | \(0.653453\pi\) | |||||||
\(594\) | 0.0669952 | 0.00274885 | ||||||||
\(595\) | 1.33647 | 0.0547897 | ||||||||
\(596\) | 1.92140 | 0.0787036 | ||||||||
\(597\) | −12.5828 | −0.514979 | ||||||||
\(598\) | 9.58913 | 0.392129 | ||||||||
\(599\) | −26.2397 | −1.07213 | −0.536063 | − | 0.844178i | \(-0.680089\pi\) | ||||
−0.536063 | + | 0.844178i | \(0.680089\pi\) | |||||||
\(600\) | 2.45548 | 0.100244 | ||||||||
\(601\) | −35.6016 | −1.45222 | −0.726109 | − | 0.687580i | \(-0.758673\pi\) | ||||
−0.726109 | + | 0.687580i | \(0.758673\pi\) | |||||||
\(602\) | −2.46513 | −0.100471 | ||||||||
\(603\) | −11.0415 | −0.449646 | ||||||||
\(604\) | 0.911979 | 0.0371079 | ||||||||
\(605\) | −26.5463 | −1.07926 | ||||||||
\(606\) | 4.72285 | 0.191853 | ||||||||
\(607\) | 33.0431 | 1.34118 | 0.670588 | − | 0.741830i | \(-0.266042\pi\) | ||||
0.670588 | + | 0.741830i | \(0.266042\pi\) | |||||||
\(608\) | 9.67171 | 0.392240 | ||||||||
\(609\) | −0.891890 | −0.0361412 | ||||||||
\(610\) | 14.4520 | 0.585146 | ||||||||
\(611\) | −4.04347 | −0.163581 | ||||||||
\(612\) | −0.236868 | −0.00957483 | ||||||||
\(613\) | 10.1310 | 0.409188 | 0.204594 | − | 0.978847i | \(-0.434413\pi\) | ||||
0.204594 | + | 0.978847i | \(0.434413\pi\) | |||||||
\(614\) | 23.9400 | 0.966142 | ||||||||
\(615\) | 8.60645 | 0.347045 | ||||||||
\(616\) | −0.0829718 | −0.00334303 | ||||||||
\(617\) | 20.2283 | 0.814362 | 0.407181 | − | 0.913348i | \(-0.366512\pi\) | ||||
0.407181 | + | 0.913348i | \(0.366512\pi\) | |||||||
\(618\) | −9.80365 | −0.394361 | ||||||||
\(619\) | −3.68516 | −0.148119 | −0.0740596 | − | 0.997254i | \(-0.523595\pi\) | ||||
−0.0740596 | + | 0.997254i | \(0.523595\pi\) | |||||||
\(620\) | 0.795476 | 0.0319471 | ||||||||
\(621\) | 3.59294 | 0.144180 | ||||||||
\(622\) | 18.2109 | 0.730189 | ||||||||
\(623\) | −9.81518 | −0.393237 | ||||||||
\(624\) | 6.97487 | 0.279218 | ||||||||
\(625\) | −28.4501 | −1.13800 | ||||||||
\(626\) | 10.8739 | 0.434609 | ||||||||
\(627\) | 0.366194 | 0.0146244 | ||||||||
\(628\) | 0.236868 | 0.00945207 | ||||||||
\(629\) | −9.04760 | −0.360751 | ||||||||
\(630\) | −1.77460 | −0.0707017 | ||||||||
\(631\) | 45.1375 | 1.79689 | 0.898447 | − | 0.439082i | \(-0.144696\pi\) | ||||
0.898447 | + | 0.439082i | \(0.144696\pi\) | |||||||
\(632\) | −12.5387 | −0.498764 | ||||||||
\(633\) | −1.89126 | −0.0751710 | ||||||||
\(634\) | 24.7047 | 0.981149 | ||||||||
\(635\) | −32.1951 | −1.27762 | ||||||||
\(636\) | −3.07964 | −0.122116 | ||||||||
\(637\) | 13.4536 | 0.533049 | ||||||||
\(638\) | −0.107922 | −0.00427266 | ||||||||
\(639\) | −9.22355 | −0.364878 | ||||||||
\(640\) | −21.4831 | −0.849195 | ||||||||
\(641\) | −33.3272 | −1.31634 | −0.658172 | − | 0.752868i | \(-0.728670\pi\) | ||||
−0.658172 | + | 0.752868i | \(0.728670\pi\) | |||||||
\(642\) | 4.12412 | 0.162766 | ||||||||
\(643\) | 24.6751 | 0.973092 | 0.486546 | − | 0.873655i | \(-0.338257\pi\) | ||||
0.486546 | + | 0.873655i | \(0.338257\pi\) | |||||||
\(644\) | −0.471198 | −0.0185678 | ||||||||
\(645\) | 8.09399 | 0.318700 | ||||||||
\(646\) | 9.63722 | 0.379171 | ||||||||
\(647\) | −42.1781 | −1.65819 | −0.829096 | − | 0.559107i | \(-0.811144\pi\) | ||||
−0.829096 | + | 0.559107i | \(0.811144\pi\) | |||||||
\(648\) | 2.97018 | 0.116680 | ||||||||
\(649\) | 0.316814 | 0.0124360 | ||||||||
\(650\) | 2.20639 | 0.0865417 | ||||||||
\(651\) | −0.770291 | −0.0301901 | ||||||||
\(652\) | −1.32001 | −0.0516956 | ||||||||
\(653\) | 17.0706 | 0.668023 | 0.334012 | − | 0.942569i | \(-0.391598\pi\) | ||||
0.334012 | + | 0.942569i | \(0.391598\pi\) | |||||||
\(654\) | −0.332071 | −0.0129850 | ||||||||
\(655\) | 4.28580 | 0.167460 | ||||||||
\(656\) | −12.3726 | −0.483069 | ||||||||
\(657\) | −4.15599 | −0.162141 | ||||||||
\(658\) | −1.47896 | −0.0576558 | ||||||||
\(659\) | −0.174435 | −0.00679504 | −0.00339752 | − | 0.999994i | \(-0.501081\pi\) | ||||
−0.00339752 | + | 0.999994i | \(0.501081\pi\) | |||||||
\(660\) | 0.0288483 | 0.00112292 | ||||||||
\(661\) | −2.61970 | −0.101894 | −0.0509472 | − | 0.998701i | \(-0.516224\pi\) | ||||
−0.0509472 | + | 0.998701i | \(0.516224\pi\) | |||||||
\(662\) | −27.8630 | −1.08293 | ||||||||
\(663\) | −2.00996 | −0.0780602 | ||||||||
\(664\) | 21.8419 | 0.847630 | ||||||||
\(665\) | −9.69989 | −0.376146 | ||||||||
\(666\) | 12.0137 | 0.465520 | ||||||||
\(667\) | −5.78782 | −0.224105 | ||||||||
\(668\) | −4.97704 | −0.192567 | ||||||||
\(669\) | −18.6700 | −0.721823 | ||||||||
\(670\) | 35.3902 | 1.36724 | ||||||||
\(671\) | 0.227497 | 0.00878244 | ||||||||
\(672\) | −0.737803 | −0.0284614 | ||||||||
\(673\) | −35.6965 | −1.37600 | −0.687999 | − | 0.725712i | \(-0.741511\pi\) | ||||
−0.687999 | + | 0.725712i | \(0.741511\pi\) | |||||||
\(674\) | −33.9766 | −1.30873 | ||||||||
\(675\) | 0.826709 | 0.0318201 | ||||||||
\(676\) | 2.12236 | 0.0816291 | ||||||||
\(677\) | 39.6539 | 1.52402 | 0.762011 | − | 0.647564i | \(-0.224212\pi\) | ||||
0.762011 | + | 0.647564i | \(0.224212\pi\) | |||||||
\(678\) | −24.1800 | −0.928626 | ||||||||
\(679\) | −3.39196 | −0.130172 | ||||||||
\(680\) | 7.16959 | 0.274941 | ||||||||
\(681\) | 22.5269 | 0.863234 | ||||||||
\(682\) | −0.0932078 | −0.00356911 | ||||||||
\(683\) | 29.0643 | 1.11212 | 0.556058 | − | 0.831144i | \(-0.312313\pi\) | ||||
0.556058 | + | 0.831144i | \(0.312313\pi\) | |||||||
\(684\) | 1.71916 | 0.0657337 | ||||||||
\(685\) | 7.42946 | 0.283865 | ||||||||
\(686\) | 10.0670 | 0.384361 | ||||||||
\(687\) | 11.0212 | 0.420484 | ||||||||
\(688\) | −11.6359 | −0.443615 | ||||||||
\(689\) | −26.1324 | −0.995565 | ||||||||
\(690\) | −11.5161 | −0.438409 | ||||||||
\(691\) | −16.0607 | −0.610979 | −0.305490 | − | 0.952195i | \(-0.598820\pi\) | ||||
−0.305490 | + | 0.952195i | \(0.598820\pi\) | |||||||
\(692\) | 2.41592 | 0.0918395 | ||||||||
\(693\) | −0.0279349 | −0.00106116 | ||||||||
\(694\) | 16.8423 | 0.639327 | ||||||||
\(695\) | −22.1786 | −0.841283 | ||||||||
\(696\) | −4.78462 | −0.181361 | ||||||||
\(697\) | 3.56543 | 0.135050 | ||||||||
\(698\) | 45.8137 | 1.73408 | ||||||||
\(699\) | 3.14050 | 0.118785 | ||||||||
\(700\) | −0.108419 | −0.00409786 | ||||||||
\(701\) | 34.7415 | 1.31217 | 0.656084 | − | 0.754688i | \(-0.272212\pi\) | ||||
0.656084 | + | 0.754688i | \(0.272212\pi\) | |||||||
\(702\) | 2.66888 | 0.100730 | ||||||||
\(703\) | 65.6663 | 2.47665 | ||||||||
\(704\) | −0.439448 | −0.0165623 | ||||||||
\(705\) | 4.85600 | 0.182888 | ||||||||
\(706\) | −31.9063 | −1.20081 | ||||||||
\(707\) | −1.96928 | −0.0740624 | ||||||||
\(708\) | 1.48734 | 0.0558976 | ||||||||
\(709\) | 18.3622 | 0.689608 | 0.344804 | − | 0.938675i | \(-0.387945\pi\) | ||||
0.344804 | + | 0.938675i | \(0.387945\pi\) | |||||||
\(710\) | 29.5633 | 1.10949 | ||||||||
\(711\) | −4.22154 | −0.158320 | ||||||||
\(712\) | −52.6545 | −1.97331 | ||||||||
\(713\) | −4.99872 | −0.187203 | ||||||||
\(714\) | −0.735171 | −0.0275131 | ||||||||
\(715\) | 0.244794 | 0.00915476 | ||||||||
\(716\) | 1.84921 | 0.0691084 | ||||||||
\(717\) | 7.60926 | 0.284173 | ||||||||
\(718\) | 27.8810 | 1.04051 | ||||||||
\(719\) | −18.2982 | −0.682407 | −0.341203 | − | 0.939989i | \(-0.610835\pi\) | ||||
−0.341203 | + | 0.939989i | \(0.610835\pi\) | |||||||
\(720\) | −8.37647 | −0.312172 | ||||||||
\(721\) | 4.08782 | 0.152238 | ||||||||
\(722\) | −44.7169 | −1.66419 | ||||||||
\(723\) | −3.97950 | −0.147999 | ||||||||
\(724\) | −3.45765 | −0.128503 | ||||||||
\(725\) | −1.33173 | −0.0494594 | ||||||||
\(726\) | 14.6027 | 0.541959 | ||||||||
\(727\) | −29.6981 | −1.10144 | −0.550721 | − | 0.834690i | \(-0.685647\pi\) | ||||
−0.550721 | + | 0.834690i | \(0.685647\pi\) | |||||||
\(728\) | −3.30534 | −0.122504 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.3208 | 0.493023 | ||||||||
\(731\) | 3.35313 | 0.124020 | ||||||||
\(732\) | 1.06803 | 0.0394754 | ||||||||
\(733\) | −29.9277 | −1.10541 | −0.552703 | − | 0.833378i | \(-0.686404\pi\) | ||||
−0.552703 | + | 0.833378i | \(0.686404\pi\) | |||||||
\(734\) | 2.77566 | 0.102452 | ||||||||
\(735\) | −16.1571 | −0.595962 | ||||||||
\(736\) | −4.78789 | −0.176484 | ||||||||
\(737\) | 0.557097 | 0.0205209 | ||||||||
\(738\) | −4.73429 | −0.174271 | ||||||||
\(739\) | 23.4106 | 0.861173 | 0.430586 | − | 0.902549i | \(-0.358307\pi\) | ||||
0.430586 | + | 0.902549i | \(0.358307\pi\) | |||||||
\(740\) | 5.17311 | 0.190167 | ||||||||
\(741\) | 14.5880 | 0.535904 | ||||||||
\(742\) | −9.55831 | −0.350897 | ||||||||
\(743\) | 46.9788 | 1.72348 | 0.861742 | − | 0.507347i | \(-0.169374\pi\) | ||||
0.861742 | + | 0.507347i | \(0.169374\pi\) | |||||||
\(744\) | −4.13229 | −0.151497 | ||||||||
\(745\) | −19.5804 | −0.717372 | ||||||||
\(746\) | 44.1918 | 1.61798 | ||||||||
\(747\) | 7.35373 | 0.269059 | ||||||||
\(748\) | 0.0119511 | 0.000436976 0 | ||||||||
\(749\) | −1.71963 | −0.0628339 | ||||||||
\(750\) | 13.3762 | 0.488430 | ||||||||
\(751\) | −30.6974 | −1.12016 | −0.560082 | − | 0.828437i | \(-0.689230\pi\) | ||||
−0.560082 | + | 0.828437i | \(0.689230\pi\) | |||||||
\(752\) | −6.98098 | −0.254570 | ||||||||
\(753\) | 4.51023 | 0.164362 | ||||||||
\(754\) | −4.29926 | −0.156570 | ||||||||
\(755\) | −9.29372 | −0.338233 | ||||||||
\(756\) | −0.131145 | −0.00476971 | ||||||||
\(757\) | 5.70179 | 0.207235 | 0.103617 | − | 0.994617i | \(-0.466958\pi\) | ||||
0.103617 | + | 0.994617i | \(0.466958\pi\) | |||||||
\(758\) | −46.1354 | −1.67571 | ||||||||
\(759\) | −0.181281 | −0.00658008 | ||||||||
\(760\) | −52.0360 | −1.88754 | ||||||||
\(761\) | −13.4666 | −0.488164 | −0.244082 | − | 0.969755i | \(-0.578487\pi\) | ||||
−0.244082 | + | 0.969755i | \(0.578487\pi\) | |||||||
\(762\) | 17.7101 | 0.641569 | ||||||||
\(763\) | 0.138463 | 0.00501271 | ||||||||
\(764\) | 3.33354 | 0.120603 | ||||||||
\(765\) | 2.41386 | 0.0872732 | ||||||||
\(766\) | −15.2339 | −0.550422 | ||||||||
\(767\) | 12.6209 | 0.455714 | ||||||||
\(768\) | −5.60195 | −0.202143 | ||||||||
\(769\) | 6.11274 | 0.220431 | 0.110216 | − | 0.993908i | \(-0.464846\pi\) | ||||
0.110216 | + | 0.993908i | \(0.464846\pi\) | |||||||
\(770\) | 0.0895368 | 0.00322668 | ||||||||
\(771\) | 1.07844 | 0.0388391 | ||||||||
\(772\) | −1.11025 | −0.0399587 | ||||||||
\(773\) | 14.1557 | 0.509147 | 0.254573 | − | 0.967053i | \(-0.418065\pi\) | ||||
0.254573 | + | 0.967053i | \(0.418065\pi\) | |||||||
\(774\) | −4.45239 | −0.160038 | ||||||||
\(775\) | −1.15017 | −0.0413153 | ||||||||
\(776\) | −18.1965 | −0.653216 | ||||||||
\(777\) | −5.00933 | −0.179709 | ||||||||
\(778\) | 0.740239 | 0.0265389 | ||||||||
\(779\) | −25.8774 | −0.927156 | ||||||||
\(780\) | 1.14923 | 0.0411489 | ||||||||
\(781\) | 0.465372 | 0.0166523 | ||||||||
\(782\) | −4.77081 | −0.170604 | ||||||||
\(783\) | −1.61089 | −0.0575684 | ||||||||
\(784\) | 23.2273 | 0.829548 | ||||||||
\(785\) | −2.41386 | −0.0861543 | ||||||||
\(786\) | −2.35756 | −0.0840914 | ||||||||
\(787\) | 4.45516 | 0.158809 | 0.0794047 | − | 0.996842i | \(-0.474698\pi\) | ||||
0.0794047 | + | 0.996842i | \(0.474698\pi\) | |||||||
\(788\) | 2.42350 | 0.0863336 | ||||||||
\(789\) | 29.7028 | 1.05745 | ||||||||
\(790\) | 13.5309 | 0.481406 | ||||||||
\(791\) | 10.0823 | 0.358485 | ||||||||
\(792\) | −0.149860 | −0.00532503 | ||||||||
\(793\) | 9.06278 | 0.321829 | ||||||||
\(794\) | −28.3852 | −1.00735 | ||||||||
\(795\) | 31.3837 | 1.11307 | ||||||||
\(796\) | 2.98046 | 0.105640 | ||||||||
\(797\) | −46.0812 | −1.63228 | −0.816140 | − | 0.577855i | \(-0.803890\pi\) | ||||
−0.816140 | + | 0.577855i | \(0.803890\pi\) | |||||||
\(798\) | 5.33578 | 0.188884 | ||||||||
\(799\) | 2.01172 | 0.0711695 | ||||||||
\(800\) | −1.10166 | −0.0389495 | ||||||||
\(801\) | −17.7277 | −0.626377 | ||||||||
\(802\) | 43.3598 | 1.53109 | ||||||||
\(803\) | 0.209689 | 0.00739978 | ||||||||
\(804\) | 2.61539 | 0.0922376 | ||||||||
\(805\) | 4.80184 | 0.169243 | ||||||||
\(806\) | −3.71311 | −0.130789 | ||||||||
\(807\) | 18.9128 | 0.665762 | ||||||||
\(808\) | −10.5644 | −0.371654 | ||||||||
\(809\) | 3.45973 | 0.121638 | 0.0608188 | − | 0.998149i | \(-0.480629\pi\) | ||||
0.0608188 | + | 0.998149i | \(0.480629\pi\) | |||||||
\(810\) | −3.20519 | −0.112619 | ||||||||
\(811\) | −8.12824 | −0.285421 | −0.142710 | − | 0.989764i | \(-0.545582\pi\) | ||||
−0.142710 | + | 0.989764i | \(0.545582\pi\) | |||||||
\(812\) | 0.211260 | 0.00741378 | ||||||||
\(813\) | 14.2519 | 0.499835 | ||||||||
\(814\) | −0.606146 | −0.0212454 | ||||||||
\(815\) | 13.4519 | 0.471198 | ||||||||
\(816\) | −3.47016 | −0.121480 | ||||||||
\(817\) | −24.3366 | −0.851430 | ||||||||
\(818\) | −34.3409 | −1.20070 | ||||||||
\(819\) | −1.11284 | −0.0388858 | ||||||||
\(820\) | −2.03859 | −0.0711908 | ||||||||
\(821\) | 6.17843 | 0.215629 | 0.107814 | − | 0.994171i | \(-0.465615\pi\) | ||||
0.107814 | + | 0.994171i | \(0.465615\pi\) | |||||||
\(822\) | −4.08684 | −0.142545 | ||||||||
\(823\) | −20.2690 | −0.706532 | −0.353266 | − | 0.935523i | \(-0.614929\pi\) | ||||
−0.353266 | + | 0.935523i | \(0.614929\pi\) | |||||||
\(824\) | 21.9295 | 0.763949 | ||||||||
\(825\) | −0.0417114 | −0.00145220 | ||||||||
\(826\) | 4.61627 | 0.160621 | ||||||||
\(827\) | 20.0180 | 0.696095 | 0.348047 | − | 0.937477i | \(-0.386845\pi\) | ||||
0.348047 | + | 0.937477i | \(0.386845\pi\) | |||||||
\(828\) | −0.851054 | −0.0295762 | ||||||||
\(829\) | 24.8638 | 0.863556 | 0.431778 | − | 0.901980i | \(-0.357886\pi\) | ||||
0.431778 | + | 0.901980i | \(0.357886\pi\) | |||||||
\(830\) | −23.5701 | −0.818131 | ||||||||
\(831\) | −7.32097 | −0.253961 | ||||||||
\(832\) | −17.5062 | −0.606919 | ||||||||
\(833\) | −6.69346 | −0.231915 | ||||||||
\(834\) | 12.2001 | 0.422457 | ||||||||
\(835\) | 50.7196 | 1.75522 | ||||||||
\(836\) | −0.0867396 | −0.00299995 | ||||||||
\(837\) | −1.39126 | −0.0480890 | ||||||||
\(838\) | 45.1226 | 1.55874 | ||||||||
\(839\) | −16.8215 | −0.580743 | −0.290372 | − | 0.956914i | \(-0.593779\pi\) | ||||
−0.290372 | + | 0.956914i | \(0.593779\pi\) | |||||||
\(840\) | 3.96954 | 0.136962 | ||||||||
\(841\) | −26.4050 | −0.910519 | ||||||||
\(842\) | 5.50664 | 0.189771 | ||||||||
\(843\) | 19.5759 | 0.674231 | ||||||||
\(844\) | 0.447980 | 0.0154201 | ||||||||
\(845\) | −21.6283 | −0.744038 | ||||||||
\(846\) | −2.67122 | −0.0918384 | ||||||||
\(847\) | −6.08889 | −0.209217 | ||||||||
\(848\) | −45.1172 | −1.54933 | ||||||||
\(849\) | 0.112031 | 0.00384488 | ||||||||
\(850\) | −1.09773 | −0.0376518 | ||||||||
\(851\) | −32.5075 | −1.11434 | ||||||||
\(852\) | 2.18477 | 0.0748489 | ||||||||
\(853\) | 33.7858 | 1.15680 | 0.578402 | − | 0.815752i | \(-0.303677\pi\) | ||||
0.578402 | + | 0.815752i | \(0.303677\pi\) | |||||||
\(854\) | 3.31485 | 0.113432 | ||||||||
\(855\) | −17.5195 | −0.599153 | ||||||||
\(856\) | −9.22512 | −0.315308 | ||||||||
\(857\) | 37.0981 | 1.26725 | 0.633623 | − | 0.773642i | \(-0.281567\pi\) | ||||
0.633623 | + | 0.773642i | \(0.281567\pi\) | |||||||
\(858\) | −0.134658 | −0.00459713 | ||||||||
\(859\) | 7.33435 | 0.250245 | 0.125122 | − | 0.992141i | \(-0.460068\pi\) | ||||
0.125122 | + | 0.992141i | \(0.460068\pi\) | |||||||
\(860\) | −1.91721 | −0.0653763 | ||||||||
\(861\) | 1.97405 | 0.0672755 | ||||||||
\(862\) | 0.894725 | 0.0304744 | ||||||||
\(863\) | −21.9356 | −0.746698 | −0.373349 | − | 0.927691i | \(-0.621791\pi\) | ||||
−0.373349 | + | 0.927691i | \(0.621791\pi\) | |||||||
\(864\) | −1.33258 | −0.0453354 | ||||||||
\(865\) | −24.6200 | −0.837104 | ||||||||
\(866\) | −29.9448 | −1.01757 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0.182457 | 0.00619301 | ||||||||
\(869\) | 0.212997 | 0.00722542 | ||||||||
\(870\) | 5.16320 | 0.175049 | ||||||||
\(871\) | 22.1930 | 0.751981 | ||||||||
\(872\) | 0.742799 | 0.0251543 | ||||||||
\(873\) | −6.12639 | −0.207347 | ||||||||
\(874\) | 34.6260 | 1.17124 | ||||||||
\(875\) | −5.57746 | −0.188553 | ||||||||
\(876\) | 0.984423 | 0.0332606 | ||||||||
\(877\) | −50.6130 | −1.70908 | −0.854540 | − | 0.519385i | \(-0.826161\pi\) | ||||
−0.854540 | + | 0.519385i | \(0.826161\pi\) | |||||||
\(878\) | 41.1865 | 1.38998 | ||||||||
\(879\) | −8.15206 | −0.274962 | ||||||||
\(880\) | 0.422632 | 0.0142469 | ||||||||
\(881\) | −18.0794 | −0.609112 | −0.304556 | − | 0.952494i | \(-0.598508\pi\) | ||||
−0.304556 | + | 0.952494i | \(0.598508\pi\) | |||||||
\(882\) | 8.88777 | 0.299267 | ||||||||
\(883\) | −32.9391 | −1.10849 | −0.554244 | − | 0.832354i | \(-0.686992\pi\) | ||||
−0.554244 | + | 0.832354i | \(0.686992\pi\) | |||||||
\(884\) | 0.476095 | 0.0160128 | ||||||||
\(885\) | −15.1571 | −0.509499 | ||||||||
\(886\) | −10.2249 | −0.343511 | ||||||||
\(887\) | −13.3264 | −0.447456 | −0.223728 | − | 0.974652i | \(-0.571823\pi\) | ||||
−0.223728 | + | 0.974652i | \(0.571823\pi\) | |||||||
\(888\) | −26.8730 | −0.901798 | ||||||||
\(889\) | −7.38456 | −0.247670 | ||||||||
\(890\) | 56.8207 | 1.90463 | ||||||||
\(891\) | −0.0504547 | −0.00169030 | ||||||||
\(892\) | 4.42232 | 0.148070 | ||||||||
\(893\) | −14.6008 | −0.488597 | ||||||||
\(894\) | 10.7709 | 0.360234 | ||||||||
\(895\) | −18.8448 | −0.629913 | ||||||||
\(896\) | −4.92756 | −0.164618 | ||||||||
\(897\) | −7.22166 | −0.241124 | ||||||||
\(898\) | 32.2626 | 1.07662 | ||||||||
\(899\) | 2.24116 | 0.0747470 | ||||||||
\(900\) | −0.195821 | −0.00652737 | ||||||||
\(901\) | 13.0015 | 0.433142 | ||||||||
\(902\) | 0.238867 | 0.00795340 | ||||||||
\(903\) | 1.85651 | 0.0617807 | ||||||||
\(904\) | 54.0874 | 1.79892 | ||||||||
\(905\) | 35.2360 | 1.17128 | ||||||||
\(906\) | 5.11235 | 0.169846 | ||||||||
\(907\) | −14.4746 | −0.480621 | −0.240310 | − | 0.970696i | \(-0.577249\pi\) | ||||
−0.240310 | + | 0.970696i | \(0.577249\pi\) | |||||||
\(908\) | −5.33592 | −0.177079 | ||||||||
\(909\) | −3.55682 | −0.117972 | ||||||||
\(910\) | 3.56687 | 0.118240 | ||||||||
\(911\) | 9.49756 | 0.314668 | 0.157334 | − | 0.987545i | \(-0.449710\pi\) | ||||
0.157334 | + | 0.987545i | \(0.449710\pi\) | |||||||
\(912\) | 25.1859 | 0.833990 | ||||||||
\(913\) | −0.371030 | −0.0122793 | ||||||||
\(914\) | −20.7663 | −0.686890 | ||||||||
\(915\) | −10.8840 | −0.359812 | ||||||||
\(916\) | −2.61056 | −0.0862555 | ||||||||
\(917\) | 0.983030 | 0.0324625 | ||||||||
\(918\) | −1.32783 | −0.0438249 | ||||||||
\(919\) | −37.0773 | −1.22307 | −0.611534 | − | 0.791218i | \(-0.709447\pi\) | ||||
−0.611534 | + | 0.791218i | \(0.709447\pi\) | |||||||
\(920\) | 25.7599 | 0.849280 | ||||||||
\(921\) | −18.0295 | −0.594091 | ||||||||
\(922\) | −6.08701 | −0.200465 | ||||||||
\(923\) | 18.5389 | 0.610217 | ||||||||
\(924\) | 0.00661690 | 0.000217680 0 | ||||||||
\(925\) | −7.47973 | −0.245932 | ||||||||
\(926\) | −4.28463 | −0.140802 | ||||||||
\(927\) | 7.38321 | 0.242496 | ||||||||
\(928\) | 2.14664 | 0.0704669 | ||||||||
\(929\) | −35.1644 | −1.15371 | −0.576853 | − | 0.816848i | \(-0.695720\pi\) | ||||
−0.576853 | + | 0.816848i | \(0.695720\pi\) | |||||||
\(930\) | 4.45926 | 0.146225 | ||||||||
\(931\) | 48.5802 | 1.59215 | ||||||||
\(932\) | −0.743884 | −0.0243667 | ||||||||
\(933\) | −13.7148 | −0.449001 | ||||||||
\(934\) | −31.3939 | −1.02724 | ||||||||
\(935\) | −0.121790 | −0.00398297 | ||||||||
\(936\) | −5.96993 | −0.195133 | ||||||||
\(937\) | −8.33411 | −0.272263 | −0.136132 | − | 0.990691i | \(-0.543467\pi\) | ||||
−0.136132 | + | 0.990691i | \(0.543467\pi\) | |||||||
\(938\) | 8.11742 | 0.265043 | ||||||||
\(939\) | −8.18923 | −0.267245 | ||||||||
\(940\) | −1.15023 | −0.0375165 | ||||||||
\(941\) | 1.75364 | 0.0571669 | 0.0285835 | − | 0.999591i | \(-0.490900\pi\) | ||||
0.0285835 | + | 0.999591i | \(0.490900\pi\) | |||||||
\(942\) | 1.32783 | 0.0432630 | ||||||||
\(943\) | 12.8104 | 0.417164 | ||||||||
\(944\) | 21.7897 | 0.709196 | ||||||||
\(945\) | 1.33647 | 0.0434752 | ||||||||
\(946\) | 0.224644 | 0.00730381 | ||||||||
\(947\) | −18.2836 | −0.594139 | −0.297069 | − | 0.954856i | \(-0.596009\pi\) | ||||
−0.297069 | + | 0.954856i | \(0.596009\pi\) | |||||||
\(948\) | 0.999949 | 0.0324768 | ||||||||
\(949\) | 8.35337 | 0.271162 | ||||||||
\(950\) | 7.96718 | 0.258489 | ||||||||
\(951\) | −18.6053 | −0.603319 | ||||||||
\(952\) | 1.64448 | 0.0532979 | ||||||||
\(953\) | 7.55361 | 0.244685 | 0.122343 | − | 0.992488i | \(-0.460959\pi\) | ||||
0.122343 | + | 0.992488i | \(0.460959\pi\) | |||||||
\(954\) | −17.2637 | −0.558934 | ||||||||
\(955\) | −33.9712 | −1.09928 | ||||||||
\(956\) | −1.80239 | −0.0582935 | ||||||||
\(957\) | 0.0812768 | 0.00262731 | ||||||||
\(958\) | −17.3817 | −0.561578 | ||||||||
\(959\) | 1.70409 | 0.0550278 | ||||||||
\(960\) | 21.0241 | 0.678550 | ||||||||
\(961\) | −29.0644 | −0.937561 | ||||||||
\(962\) | −24.1469 | −0.778529 | ||||||||
\(963\) | −3.10591 | −0.100087 | ||||||||
\(964\) | 0.942616 | 0.0303596 | ||||||||
\(965\) | 11.3142 | 0.364218 | ||||||||
\(966\) | −2.64143 | −0.0849865 | ||||||||
\(967\) | 7.72662 | 0.248471 | 0.124236 | − | 0.992253i | \(-0.460352\pi\) | ||||
0.124236 | + | 0.992253i | \(0.460352\pi\) | |||||||
\(968\) | −32.6644 | −1.04987 | ||||||||
\(969\) | −7.25787 | −0.233156 | ||||||||
\(970\) | 19.6363 | 0.630483 | ||||||||
\(971\) | −7.39736 | −0.237393 | −0.118696 | − | 0.992931i | \(-0.537872\pi\) | ||||
−0.118696 | + | 0.992931i | \(0.537872\pi\) | |||||||
\(972\) | −0.236868 | −0.00759755 | ||||||||
\(973\) | −5.08708 | −0.163084 | ||||||||
\(974\) | −27.0246 | −0.865923 | ||||||||
\(975\) | −1.66165 | −0.0532154 | ||||||||
\(976\) | 15.6467 | 0.500840 | ||||||||
\(977\) | −40.6715 | −1.30120 | −0.650599 | − | 0.759421i | \(-0.725482\pi\) | ||||
−0.650599 | + | 0.759421i | \(0.725482\pi\) | |||||||
\(978\) | −7.39968 | −0.236616 | ||||||||
\(979\) | 0.894446 | 0.0285866 | ||||||||
\(980\) | 3.82709 | 0.122252 | ||||||||
\(981\) | 0.250085 | 0.00798461 | ||||||||
\(982\) | 26.0160 | 0.830204 | ||||||||
\(983\) | −11.4955 | −0.366649 | −0.183324 | − | 0.983052i | \(-0.558686\pi\) | ||||
−0.183324 | + | 0.983052i | \(0.558686\pi\) | |||||||
\(984\) | 10.5900 | 0.337596 | ||||||||
\(985\) | −24.6972 | −0.786919 | ||||||||
\(986\) | 2.13898 | 0.0681191 | ||||||||
\(987\) | 1.11382 | 0.0354531 | ||||||||
\(988\) | −3.45544 | −0.109932 | ||||||||
\(989\) | 12.0476 | 0.383092 | ||||||||
\(990\) | 0.161717 | 0.00513970 | ||||||||
\(991\) | 13.0319 | 0.413971 | 0.206986 | − | 0.978344i | \(-0.433635\pi\) | ||||
0.206986 | + | 0.978344i | \(0.433635\pi\) | |||||||
\(992\) | 1.85397 | 0.0588636 | ||||||||
\(993\) | 20.9839 | 0.665903 | ||||||||
\(994\) | 6.78089 | 0.215077 | ||||||||
\(995\) | −30.3731 | −0.962891 | ||||||||
\(996\) | −1.74187 | −0.0551931 | ||||||||
\(997\) | −57.2694 | −1.81374 | −0.906870 | − | 0.421411i | \(-0.861535\pi\) | ||||
−0.906870 | + | 0.421411i | \(0.861535\pi\) | |||||||
\(998\) | 7.13718 | 0.225924 | ||||||||
\(999\) | −9.04760 | −0.286253 |
(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.d.1.13 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.d.1.13 | ✓ | 40 | 1.1 | even | 1 | trivial |