Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.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: | \(32.1158316930\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.49586 | −0.863637 | −0.431819 | − | 0.901960i | \(-0.642128\pi\) | ||||
−0.431819 | + | 0.901960i | \(0.642128\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.62778 | 1.62239 | 0.811196 | − | 0.584775i | \(-0.198817\pi\) | ||||
0.811196 | + | 0.584775i | \(0.198817\pi\) | |||||||
\(6\) | −1.49586 | −0.610684 | ||||||||
\(7\) | −1.50310 | −0.568117 | −0.284059 | − | 0.958807i | \(-0.591681\pi\) | ||||
−0.284059 | + | 0.958807i | \(0.591681\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.762393 | −0.254131 | ||||||||
\(10\) | 3.62778 | 1.14720 | ||||||||
\(11\) | −3.49664 | −1.05428 | −0.527138 | − | 0.849780i | \(-0.676735\pi\) | ||||
−0.527138 | + | 0.849780i | \(0.676735\pi\) | |||||||
\(12\) | −1.49586 | −0.431819 | ||||||||
\(13\) | 2.70243 | 0.749518 | 0.374759 | − | 0.927122i | \(-0.377725\pi\) | ||||
0.374759 | + | 0.927122i | \(0.377725\pi\) | |||||||
\(14\) | −1.50310 | −0.401720 | ||||||||
\(15\) | −5.42666 | −1.40116 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.55648 | −1.10511 | −0.552554 | − | 0.833477i | \(-0.686347\pi\) | ||||
−0.552554 | + | 0.833477i | \(0.686347\pi\) | |||||||
\(18\) | −0.762393 | −0.179698 | ||||||||
\(19\) | −4.73207 | −1.08561 | −0.542805 | − | 0.839859i | \(-0.682638\pi\) | ||||
−0.542805 | + | 0.839859i | \(0.682638\pi\) | |||||||
\(20\) | 3.62778 | 0.811196 | ||||||||
\(21\) | 2.24843 | 0.490647 | ||||||||
\(22\) | −3.49664 | −0.745486 | ||||||||
\(23\) | −6.90130 | −1.43902 | −0.719511 | − | 0.694482i | \(-0.755634\pi\) | ||||
−0.719511 | + | 0.694482i | \(0.755634\pi\) | |||||||
\(24\) | −1.49586 | −0.305342 | ||||||||
\(25\) | 8.16077 | 1.63215 | ||||||||
\(26\) | 2.70243 | 0.529989 | ||||||||
\(27\) | 5.62803 | 1.08311 | ||||||||
\(28\) | −1.50310 | −0.284059 | ||||||||
\(29\) | 9.73743 | 1.80820 | 0.904098 | − | 0.427326i | \(-0.140544\pi\) | ||||
0.904098 | + | 0.427326i | \(0.140544\pi\) | |||||||
\(30\) | −5.42666 | −0.990768 | ||||||||
\(31\) | 9.42235 | 1.69230 | 0.846152 | − | 0.532941i | \(-0.178913\pi\) | ||||
0.846152 | + | 0.532941i | \(0.178913\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.23049 | 0.910512 | ||||||||
\(34\) | −4.55648 | −0.781429 | ||||||||
\(35\) | −5.45290 | −0.921709 | ||||||||
\(36\) | −0.762393 | −0.127065 | ||||||||
\(37\) | −5.74459 | −0.944405 | −0.472203 | − | 0.881490i | \(-0.656541\pi\) | ||||
−0.472203 | + | 0.881490i | \(0.656541\pi\) | |||||||
\(38\) | −4.73207 | −0.767642 | ||||||||
\(39\) | −4.04246 | −0.647312 | ||||||||
\(40\) | 3.62778 | 0.573602 | ||||||||
\(41\) | −11.9608 | −1.86796 | −0.933979 | − | 0.357328i | \(-0.883688\pi\) | ||||
−0.933979 | + | 0.357328i | \(0.883688\pi\) | |||||||
\(42\) | 2.24843 | 0.346940 | ||||||||
\(43\) | −10.7989 | −1.64681 | −0.823405 | − | 0.567454i | \(-0.807929\pi\) | ||||
−0.823405 | + | 0.567454i | \(0.807929\pi\) | |||||||
\(44\) | −3.49664 | −0.527138 | ||||||||
\(45\) | −2.76579 | −0.412300 | ||||||||
\(46\) | −6.90130 | −1.01754 | ||||||||
\(47\) | −5.41035 | −0.789180 | −0.394590 | − | 0.918857i | \(-0.629113\pi\) | ||||
−0.394590 | + | 0.918857i | \(0.629113\pi\) | |||||||
\(48\) | −1.49586 | −0.215909 | ||||||||
\(49\) | −4.74070 | −0.677243 | ||||||||
\(50\) | 8.16077 | 1.15411 | ||||||||
\(51\) | 6.81587 | 0.954412 | ||||||||
\(52\) | 2.70243 | 0.374759 | ||||||||
\(53\) | −9.69149 | −1.33123 | −0.665614 | − | 0.746296i | \(-0.731830\pi\) | ||||
−0.665614 | + | 0.746296i | \(0.731830\pi\) | |||||||
\(54\) | 5.62803 | 0.765877 | ||||||||
\(55\) | −12.6850 | −1.71045 | ||||||||
\(56\) | −1.50310 | −0.200860 | ||||||||
\(57\) | 7.07852 | 0.937573 | ||||||||
\(58\) | 9.73743 | 1.27859 | ||||||||
\(59\) | −5.55792 | −0.723580 | −0.361790 | − | 0.932260i | \(-0.617834\pi\) | ||||
−0.361790 | + | 0.932260i | \(0.617834\pi\) | |||||||
\(60\) | −5.42666 | −0.700579 | ||||||||
\(61\) | 11.2266 | 1.43742 | 0.718710 | − | 0.695310i | \(-0.244733\pi\) | ||||
0.718710 | + | 0.695310i | \(0.244733\pi\) | |||||||
\(62\) | 9.42235 | 1.19664 | ||||||||
\(63\) | 1.14595 | 0.144376 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.80380 | 1.21601 | ||||||||
\(66\) | 5.23049 | 0.643829 | ||||||||
\(67\) | −12.1387 | −1.48298 | −0.741491 | − | 0.670963i | \(-0.765881\pi\) | ||||
−0.741491 | + | 0.670963i | \(0.765881\pi\) | |||||||
\(68\) | −4.55648 | −0.552554 | ||||||||
\(69\) | 10.3234 | 1.24279 | ||||||||
\(70\) | −5.45290 | −0.651746 | ||||||||
\(71\) | 10.9179 | 1.29572 | 0.647860 | − | 0.761759i | \(-0.275664\pi\) | ||||
0.647860 | + | 0.761759i | \(0.275664\pi\) | |||||||
\(72\) | −0.762393 | −0.0898488 | ||||||||
\(73\) | −15.2619 | −1.78627 | −0.893135 | − | 0.449788i | \(-0.851499\pi\) | ||||
−0.893135 | + | 0.449788i | \(0.851499\pi\) | |||||||
\(74\) | −5.74459 | −0.667795 | ||||||||
\(75\) | −12.2074 | −1.40959 | ||||||||
\(76\) | −4.73207 | −0.542805 | ||||||||
\(77\) | 5.25579 | 0.598952 | ||||||||
\(78\) | −4.04246 | −0.457719 | ||||||||
\(79\) | 3.43435 | 0.386395 | 0.193197 | − | 0.981160i | \(-0.438114\pi\) | ||||
0.193197 | + | 0.981160i | \(0.438114\pi\) | |||||||
\(80\) | 3.62778 | 0.405598 | ||||||||
\(81\) | −6.13158 | −0.681287 | ||||||||
\(82\) | −11.9608 | −1.32085 | ||||||||
\(83\) | 6.27372 | 0.688631 | 0.344315 | − | 0.938854i | \(-0.388111\pi\) | ||||
0.344315 | + | 0.938854i | \(0.388111\pi\) | |||||||
\(84\) | 2.24843 | 0.245324 | ||||||||
\(85\) | −16.5299 | −1.79292 | ||||||||
\(86\) | −10.7989 | −1.16447 | ||||||||
\(87\) | −14.5659 | −1.56162 | ||||||||
\(88\) | −3.49664 | −0.372743 | ||||||||
\(89\) | 1.43060 | 0.151643 | 0.0758215 | − | 0.997121i | \(-0.475842\pi\) | ||||
0.0758215 | + | 0.997121i | \(0.475842\pi\) | |||||||
\(90\) | −2.76579 | −0.291540 | ||||||||
\(91\) | −4.06201 | −0.425814 | ||||||||
\(92\) | −6.90130 | −0.719511 | ||||||||
\(93\) | −14.0946 | −1.46154 | ||||||||
\(94\) | −5.41035 | −0.558035 | ||||||||
\(95\) | −17.1669 | −1.76128 | ||||||||
\(96\) | −1.49586 | −0.152671 | ||||||||
\(97\) | 11.2812 | 1.14543 | 0.572717 | − | 0.819753i | \(-0.305889\pi\) | ||||
0.572717 | + | 0.819753i | \(0.305889\pi\) | |||||||
\(98\) | −4.74070 | −0.478883 | ||||||||
\(99\) | 2.66581 | 0.267924 | ||||||||
\(100\) | 8.16077 | 0.816077 | ||||||||
\(101\) | 10.2606 | 1.02097 | 0.510485 | − | 0.859887i | \(-0.329466\pi\) | ||||
0.510485 | + | 0.859887i | \(0.329466\pi\) | |||||||
\(102\) | 6.81587 | 0.674871 | ||||||||
\(103\) | −9.36610 | −0.922869 | −0.461435 | − | 0.887174i | \(-0.652665\pi\) | ||||
−0.461435 | + | 0.887174i | \(0.652665\pi\) | |||||||
\(104\) | 2.70243 | 0.264995 | ||||||||
\(105\) | 8.15680 | 0.796022 | ||||||||
\(106\) | −9.69149 | −0.941321 | ||||||||
\(107\) | 6.92796 | 0.669751 | 0.334875 | − | 0.942262i | \(-0.391306\pi\) | ||||
0.334875 | + | 0.942262i | \(0.391306\pi\) | |||||||
\(108\) | 5.62803 | 0.541557 | ||||||||
\(109\) | −7.39654 | −0.708460 | −0.354230 | − | 0.935158i | \(-0.615257\pi\) | ||||
−0.354230 | + | 0.935158i | \(0.615257\pi\) | |||||||
\(110\) | −12.6850 | −1.20947 | ||||||||
\(111\) | 8.59312 | 0.815623 | ||||||||
\(112\) | −1.50310 | −0.142029 | ||||||||
\(113\) | 19.3027 | 1.81584 | 0.907921 | − | 0.419142i | \(-0.137669\pi\) | ||||
0.907921 | + | 0.419142i | \(0.137669\pi\) | |||||||
\(114\) | 7.07852 | 0.662964 | ||||||||
\(115\) | −25.0364 | −2.33466 | ||||||||
\(116\) | 9.73743 | 0.904098 | ||||||||
\(117\) | −2.06031 | −0.190476 | ||||||||
\(118\) | −5.55792 | −0.511648 | ||||||||
\(119\) | 6.84883 | 0.627831 | ||||||||
\(120\) | −5.42666 | −0.495384 | ||||||||
\(121\) | 1.22647 | 0.111497 | ||||||||
\(122\) | 11.2266 | 1.01641 | ||||||||
\(123\) | 17.8917 | 1.61324 | ||||||||
\(124\) | 9.42235 | 0.846152 | ||||||||
\(125\) | 11.4666 | 1.02560 | ||||||||
\(126\) | 1.14595 | 0.102089 | ||||||||
\(127\) | −7.60958 | −0.675241 | −0.337621 | − | 0.941282i | \(-0.609622\pi\) | ||||
−0.337621 | + | 0.941282i | \(0.609622\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 16.1536 | 1.42225 | ||||||||
\(130\) | 9.80380 | 0.859850 | ||||||||
\(131\) | −20.8788 | −1.82419 | −0.912097 | − | 0.409975i | \(-0.865537\pi\) | ||||
−0.912097 | + | 0.409975i | \(0.865537\pi\) | |||||||
\(132\) | 5.23049 | 0.455256 | ||||||||
\(133\) | 7.11275 | 0.616754 | ||||||||
\(134\) | −12.1387 | −1.04863 | ||||||||
\(135\) | 20.4172 | 1.75723 | ||||||||
\(136\) | −4.55648 | −0.390715 | ||||||||
\(137\) | 4.99729 | 0.426947 | 0.213474 | − | 0.976949i | \(-0.431522\pi\) | ||||
0.213474 | + | 0.976949i | \(0.431522\pi\) | |||||||
\(138\) | 10.3234 | 0.878787 | ||||||||
\(139\) | 18.0601 | 1.53183 | 0.765917 | − | 0.642939i | \(-0.222285\pi\) | ||||
0.765917 | + | 0.642939i | \(0.222285\pi\) | |||||||
\(140\) | −5.45290 | −0.460854 | ||||||||
\(141\) | 8.09314 | 0.681566 | ||||||||
\(142\) | 10.9179 | 0.916213 | ||||||||
\(143\) | −9.44940 | −0.790199 | ||||||||
\(144\) | −0.762393 | −0.0635327 | ||||||||
\(145\) | 35.3252 | 2.93360 | ||||||||
\(146\) | −15.2619 | −1.26308 | ||||||||
\(147\) | 7.09144 | 0.584892 | ||||||||
\(148\) | −5.74459 | −0.472203 | ||||||||
\(149\) | 2.22612 | 0.182371 | 0.0911855 | − | 0.995834i | \(-0.470934\pi\) | ||||
0.0911855 | + | 0.995834i | \(0.470934\pi\) | |||||||
\(150\) | −12.2074 | −0.996729 | ||||||||
\(151\) | −14.1180 | −1.14891 | −0.574455 | − | 0.818536i | \(-0.694786\pi\) | ||||
−0.574455 | + | 0.818536i | \(0.694786\pi\) | |||||||
\(152\) | −4.73207 | −0.383821 | ||||||||
\(153\) | 3.47382 | 0.280842 | ||||||||
\(154\) | 5.25579 | 0.423523 | ||||||||
\(155\) | 34.1822 | 2.74558 | ||||||||
\(156\) | −4.04246 | −0.323656 | ||||||||
\(157\) | 4.67349 | 0.372985 | 0.186492 | − | 0.982456i | \(-0.440288\pi\) | ||||
0.186492 | + | 0.982456i | \(0.440288\pi\) | |||||||
\(158\) | 3.43435 | 0.273222 | ||||||||
\(159\) | 14.4971 | 1.14970 | ||||||||
\(160\) | 3.62778 | 0.286801 | ||||||||
\(161\) | 10.3733 | 0.817533 | ||||||||
\(162\) | −6.13158 | −0.481742 | ||||||||
\(163\) | −20.9106 | −1.63785 | −0.818923 | − | 0.573903i | \(-0.805429\pi\) | ||||
−0.818923 | + | 0.573903i | \(0.805429\pi\) | |||||||
\(164\) | −11.9608 | −0.933979 | ||||||||
\(165\) | 18.9751 | 1.47721 | ||||||||
\(166\) | 6.27372 | 0.486935 | ||||||||
\(167\) | −8.91764 | −0.690067 | −0.345034 | − | 0.938590i | \(-0.612133\pi\) | ||||
−0.345034 | + | 0.938590i | \(0.612133\pi\) | |||||||
\(168\) | 2.24843 | 0.173470 | ||||||||
\(169\) | −5.69689 | −0.438222 | ||||||||
\(170\) | −16.5299 | −1.26778 | ||||||||
\(171\) | 3.60769 | 0.275887 | ||||||||
\(172\) | −10.7989 | −0.823405 | ||||||||
\(173\) | 12.6495 | 0.961723 | 0.480862 | − | 0.876797i | \(-0.340324\pi\) | ||||
0.480862 | + | 0.876797i | \(0.340324\pi\) | |||||||
\(174\) | −14.5659 | −1.10424 | ||||||||
\(175\) | −12.2664 | −0.927254 | ||||||||
\(176\) | −3.49664 | −0.263569 | ||||||||
\(177\) | 8.31390 | 0.624911 | ||||||||
\(178\) | 1.43060 | 0.107228 | ||||||||
\(179\) | −16.5914 | −1.24010 | −0.620050 | − | 0.784562i | \(-0.712888\pi\) | ||||
−0.620050 | + | 0.784562i | \(0.712888\pi\) | |||||||
\(180\) | −2.76579 | −0.206150 | ||||||||
\(181\) | −2.31522 | −0.172089 | −0.0860444 | − | 0.996291i | \(-0.527423\pi\) | ||||
−0.0860444 | + | 0.996291i | \(0.527423\pi\) | |||||||
\(182\) | −4.06201 | −0.301096 | ||||||||
\(183\) | −16.7935 | −1.24141 | ||||||||
\(184\) | −6.90130 | −0.508771 | ||||||||
\(185\) | −20.8401 | −1.53219 | ||||||||
\(186\) | −14.0946 | −1.03346 | ||||||||
\(187\) | 15.9323 | 1.16509 | ||||||||
\(188\) | −5.41035 | −0.394590 | ||||||||
\(189\) | −8.45947 | −0.615336 | ||||||||
\(190\) | −17.1669 | −1.24542 | ||||||||
\(191\) | −11.7056 | −0.846989 | −0.423495 | − | 0.905899i | \(-0.639197\pi\) | ||||
−0.423495 | + | 0.905899i | \(0.639197\pi\) | |||||||
\(192\) | −1.49586 | −0.107955 | ||||||||
\(193\) | −12.0489 | −0.867300 | −0.433650 | − | 0.901081i | \(-0.642775\pi\) | ||||
−0.433650 | + | 0.901081i | \(0.642775\pi\) | |||||||
\(194\) | 11.2812 | 0.809945 | ||||||||
\(195\) | −14.6651 | −1.05019 | ||||||||
\(196\) | −4.74070 | −0.338621 | ||||||||
\(197\) | −17.2450 | −1.22865 | −0.614327 | − | 0.789052i | \(-0.710572\pi\) | ||||
−0.614327 | + | 0.789052i | \(0.710572\pi\) | |||||||
\(198\) | 2.66581 | 0.189451 | ||||||||
\(199\) | 4.09423 | 0.290233 | 0.145116 | − | 0.989415i | \(-0.453644\pi\) | ||||
0.145116 | + | 0.989415i | \(0.453644\pi\) | |||||||
\(200\) | 8.16077 | 0.577053 | ||||||||
\(201\) | 18.1579 | 1.28076 | ||||||||
\(202\) | 10.2606 | 0.721934 | ||||||||
\(203\) | −14.6363 | −1.02727 | ||||||||
\(204\) | 6.81587 | 0.477206 | ||||||||
\(205\) | −43.3910 | −3.03056 | ||||||||
\(206\) | −9.36610 | −0.652567 | ||||||||
\(207\) | 5.26150 | 0.365700 | ||||||||
\(208\) | 2.70243 | 0.187380 | ||||||||
\(209\) | 16.5463 | 1.14453 | ||||||||
\(210\) | 8.15680 | 0.562872 | ||||||||
\(211\) | −1.59128 | −0.109548 | −0.0547740 | − | 0.998499i | \(-0.517444\pi\) | ||||
−0.0547740 | + | 0.998499i | \(0.517444\pi\) | |||||||
\(212\) | −9.69149 | −0.665614 | ||||||||
\(213\) | −16.3317 | −1.11903 | ||||||||
\(214\) | 6.92796 | 0.473585 | ||||||||
\(215\) | −39.1759 | −2.67177 | ||||||||
\(216\) | 5.62803 | 0.382939 | ||||||||
\(217\) | −14.1627 | −0.961427 | ||||||||
\(218\) | −7.39654 | −0.500957 | ||||||||
\(219\) | 22.8297 | 1.54269 | ||||||||
\(220\) | −12.6850 | −0.855224 | ||||||||
\(221\) | −12.3135 | −0.828299 | ||||||||
\(222\) | 8.59312 | 0.576733 | ||||||||
\(223\) | 18.5568 | 1.24266 | 0.621329 | − | 0.783550i | \(-0.286593\pi\) | ||||
0.621329 | + | 0.783550i | \(0.286593\pi\) | |||||||
\(224\) | −1.50310 | −0.100430 | ||||||||
\(225\) | −6.22171 | −0.414780 | ||||||||
\(226\) | 19.3027 | 1.28399 | ||||||||
\(227\) | −3.04139 | −0.201864 | −0.100932 | − | 0.994893i | \(-0.532182\pi\) | ||||
−0.100932 | + | 0.994893i | \(0.532182\pi\) | |||||||
\(228\) | 7.07852 | 0.468787 | ||||||||
\(229\) | 6.50956 | 0.430164 | 0.215082 | − | 0.976596i | \(-0.430998\pi\) | ||||
0.215082 | + | 0.976596i | \(0.430998\pi\) | |||||||
\(230\) | −25.0364 | −1.65085 | ||||||||
\(231\) | −7.86194 | −0.517277 | ||||||||
\(232\) | 9.73743 | 0.639294 | ||||||||
\(233\) | −3.98723 | −0.261212 | −0.130606 | − | 0.991434i | \(-0.541692\pi\) | ||||
−0.130606 | + | 0.991434i | \(0.541692\pi\) | |||||||
\(234\) | −2.06031 | −0.134687 | ||||||||
\(235\) | −19.6275 | −1.28036 | ||||||||
\(236\) | −5.55792 | −0.361790 | ||||||||
\(237\) | −5.13732 | −0.333705 | ||||||||
\(238\) | 6.84883 | 0.443944 | ||||||||
\(239\) | 7.69185 | 0.497544 | 0.248772 | − | 0.968562i | \(-0.419973\pi\) | ||||
0.248772 | + | 0.968562i | \(0.419973\pi\) | |||||||
\(240\) | −5.42666 | −0.350289 | ||||||||
\(241\) | 26.7382 | 1.72236 | 0.861181 | − | 0.508298i | \(-0.169725\pi\) | ||||
0.861181 | + | 0.508298i | \(0.169725\pi\) | |||||||
\(242\) | 1.22647 | 0.0788405 | ||||||||
\(243\) | −7.71207 | −0.494730 | ||||||||
\(244\) | 11.2266 | 0.718710 | ||||||||
\(245\) | −17.1982 | −1.09875 | ||||||||
\(246\) | 17.8917 | 1.14073 | ||||||||
\(247\) | −12.7881 | −0.813685 | ||||||||
\(248\) | 9.42235 | 0.598320 | ||||||||
\(249\) | −9.38463 | −0.594727 | ||||||||
\(250\) | 11.4666 | 0.725208 | ||||||||
\(251\) | 6.31167 | 0.398389 | 0.199195 | − | 0.979960i | \(-0.436167\pi\) | ||||
0.199195 | + | 0.979960i | \(0.436167\pi\) | |||||||
\(252\) | 1.14595 | 0.0721881 | ||||||||
\(253\) | 24.1314 | 1.51713 | ||||||||
\(254\) | −7.60958 | −0.477468 | ||||||||
\(255\) | 24.7264 | 1.54843 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.7701 | −0.734196 | −0.367098 | − | 0.930182i | \(-0.619649\pi\) | ||||
−0.367098 | + | 0.930182i | \(0.619649\pi\) | |||||||
\(258\) | 16.1536 | 1.00568 | ||||||||
\(259\) | 8.63468 | 0.536533 | ||||||||
\(260\) | 9.80380 | 0.608006 | ||||||||
\(261\) | −7.42375 | −0.459518 | ||||||||
\(262\) | −20.8788 | −1.28990 | ||||||||
\(263\) | 14.7343 | 0.908555 | 0.454278 | − | 0.890860i | \(-0.349897\pi\) | ||||
0.454278 | + | 0.890860i | \(0.349897\pi\) | |||||||
\(264\) | 5.23049 | 0.321914 | ||||||||
\(265\) | −35.1586 | −2.15977 | ||||||||
\(266\) | 7.11275 | 0.436111 | ||||||||
\(267\) | −2.13998 | −0.130964 | ||||||||
\(268\) | −12.1387 | −0.741491 | ||||||||
\(269\) | −17.4625 | −1.06471 | −0.532353 | − | 0.846522i | \(-0.678692\pi\) | ||||
−0.532353 | + | 0.846522i | \(0.678692\pi\) | |||||||
\(270\) | 20.4172 | 1.24255 | ||||||||
\(271\) | −16.2335 | −0.986117 | −0.493059 | − | 0.869996i | \(-0.664121\pi\) | ||||
−0.493059 | + | 0.869996i | \(0.664121\pi\) | |||||||
\(272\) | −4.55648 | −0.276277 | ||||||||
\(273\) | 6.07621 | 0.367749 | ||||||||
\(274\) | 4.99729 | 0.301897 | ||||||||
\(275\) | −28.5352 | −1.72074 | ||||||||
\(276\) | 10.3234 | 0.621396 | ||||||||
\(277\) | 17.6711 | 1.06175 | 0.530875 | − | 0.847450i | \(-0.321863\pi\) | ||||
0.530875 | + | 0.847450i | \(0.321863\pi\) | |||||||
\(278\) | 18.0601 | 1.08317 | ||||||||
\(279\) | −7.18353 | −0.430067 | ||||||||
\(280\) | −5.45290 | −0.325873 | ||||||||
\(281\) | 11.5639 | 0.689845 | 0.344922 | − | 0.938631i | \(-0.387905\pi\) | ||||
0.344922 | + | 0.938631i | \(0.387905\pi\) | |||||||
\(282\) | 8.09314 | 0.481940 | ||||||||
\(283\) | −5.54353 | −0.329529 | −0.164764 | − | 0.986333i | \(-0.552686\pi\) | ||||
−0.164764 | + | 0.986333i | \(0.552686\pi\) | |||||||
\(284\) | 10.9179 | 0.647860 | ||||||||
\(285\) | 25.6793 | 1.52111 | ||||||||
\(286\) | −9.44940 | −0.558755 | ||||||||
\(287\) | 17.9782 | 1.06122 | ||||||||
\(288\) | −0.762393 | −0.0449244 | ||||||||
\(289\) | 3.76148 | 0.221264 | ||||||||
\(290\) | 35.3252 | 2.07437 | ||||||||
\(291\) | −16.8752 | −0.989240 | ||||||||
\(292\) | −15.2619 | −0.893135 | ||||||||
\(293\) | −26.7201 | −1.56100 | −0.780502 | − | 0.625154i | \(-0.785036\pi\) | ||||
−0.780502 | + | 0.625154i | \(0.785036\pi\) | |||||||
\(294\) | 7.09144 | 0.413581 | ||||||||
\(295\) | −20.1629 | −1.17393 | ||||||||
\(296\) | −5.74459 | −0.333898 | ||||||||
\(297\) | −19.6792 | −1.14190 | ||||||||
\(298\) | 2.22612 | 0.128956 | ||||||||
\(299\) | −18.6503 | −1.07857 | ||||||||
\(300\) | −12.2074 | −0.704794 | ||||||||
\(301\) | 16.2317 | 0.935582 | ||||||||
\(302\) | −14.1180 | −0.812402 | ||||||||
\(303\) | −15.3485 | −0.881747 | ||||||||
\(304\) | −4.73207 | −0.271403 | ||||||||
\(305\) | 40.7277 | 2.33206 | ||||||||
\(306\) | 3.47382 | 0.198585 | ||||||||
\(307\) | 2.42093 | 0.138170 | 0.0690848 | − | 0.997611i | \(-0.477992\pi\) | ||||
0.0690848 | + | 0.997611i | \(0.477992\pi\) | |||||||
\(308\) | 5.25579 | 0.299476 | ||||||||
\(309\) | 14.0104 | 0.797024 | ||||||||
\(310\) | 34.1822 | 1.94142 | ||||||||
\(311\) | 26.0257 | 1.47578 | 0.737891 | − | 0.674920i | \(-0.235822\pi\) | ||||
0.737891 | + | 0.674920i | \(0.235822\pi\) | |||||||
\(312\) | −4.04246 | −0.228859 | ||||||||
\(313\) | −2.18509 | −0.123509 | −0.0617544 | − | 0.998091i | \(-0.519670\pi\) | ||||
−0.0617544 | + | 0.998091i | \(0.519670\pi\) | |||||||
\(314\) | 4.67349 | 0.263740 | ||||||||
\(315\) | 4.15725 | 0.234235 | ||||||||
\(316\) | 3.43435 | 0.193197 | ||||||||
\(317\) | 28.6549 | 1.60942 | 0.804711 | − | 0.593667i | \(-0.202320\pi\) | ||||
0.804711 | + | 0.593667i | \(0.202320\pi\) | |||||||
\(318\) | 14.4971 | 0.812960 | ||||||||
\(319\) | −34.0483 | −1.90634 | ||||||||
\(320\) | 3.62778 | 0.202799 | ||||||||
\(321\) | −10.3633 | −0.578422 | ||||||||
\(322\) | 10.3733 | 0.578083 | ||||||||
\(323\) | 21.5615 | 1.19972 | ||||||||
\(324\) | −6.13158 | −0.340643 | ||||||||
\(325\) | 22.0539 | 1.22333 | ||||||||
\(326\) | −20.9106 | −1.15813 | ||||||||
\(327\) | 11.0642 | 0.611852 | ||||||||
\(328\) | −11.9608 | −0.660423 | ||||||||
\(329\) | 8.13228 | 0.448347 | ||||||||
\(330\) | 18.9751 | 1.04454 | ||||||||
\(331\) | −19.2549 | −1.05834 | −0.529171 | − | 0.848515i | \(-0.677497\pi\) | ||||
−0.529171 | + | 0.848515i | \(0.677497\pi\) | |||||||
\(332\) | 6.27372 | 0.344315 | ||||||||
\(333\) | 4.37963 | 0.240003 | ||||||||
\(334\) | −8.91764 | −0.487951 | ||||||||
\(335\) | −44.0366 | −2.40598 | ||||||||
\(336\) | 2.24843 | 0.122662 | ||||||||
\(337\) | 13.2036 | 0.719246 | 0.359623 | − | 0.933098i | \(-0.382905\pi\) | ||||
0.359623 | + | 0.933098i | \(0.382905\pi\) | |||||||
\(338\) | −5.69689 | −0.309870 | ||||||||
\(339\) | −28.8741 | −1.56823 | ||||||||
\(340\) | −16.5299 | −0.896459 | ||||||||
\(341\) | −32.9465 | −1.78416 | ||||||||
\(342\) | 3.60769 | 0.195082 | ||||||||
\(343\) | 17.6474 | 0.952871 | ||||||||
\(344\) | −10.7989 | −0.582236 | ||||||||
\(345\) | 37.4510 | 2.01629 | ||||||||
\(346\) | 12.6495 | 0.680041 | ||||||||
\(347\) | −11.0019 | −0.590613 | −0.295306 | − | 0.955403i | \(-0.595422\pi\) | ||||
−0.295306 | + | 0.955403i | \(0.595422\pi\) | |||||||
\(348\) | −14.5659 | −0.780812 | ||||||||
\(349\) | −12.1730 | −0.651607 | −0.325803 | − | 0.945438i | \(-0.605635\pi\) | ||||
−0.325803 | + | 0.945438i | \(0.605635\pi\) | |||||||
\(350\) | −12.2664 | −0.655668 | ||||||||
\(351\) | 15.2093 | 0.811814 | ||||||||
\(352\) | −3.49664 | −0.186371 | ||||||||
\(353\) | 22.3049 | 1.18717 | 0.593586 | − | 0.804770i | \(-0.297712\pi\) | ||||
0.593586 | + | 0.804770i | \(0.297712\pi\) | |||||||
\(354\) | 8.31390 | 0.441879 | ||||||||
\(355\) | 39.6078 | 2.10217 | ||||||||
\(356\) | 1.43060 | 0.0758215 | ||||||||
\(357\) | −10.2449 | −0.542218 | ||||||||
\(358\) | −16.5914 | −0.876883 | ||||||||
\(359\) | 9.94994 | 0.525138 | 0.262569 | − | 0.964913i | \(-0.415430\pi\) | ||||
0.262569 | + | 0.964913i | \(0.415430\pi\) | |||||||
\(360\) | −2.76579 | −0.145770 | ||||||||
\(361\) | 3.39244 | 0.178550 | ||||||||
\(362\) | −2.31522 | −0.121685 | ||||||||
\(363\) | −1.83463 | −0.0962933 | ||||||||
\(364\) | −4.06201 | −0.212907 | ||||||||
\(365\) | −55.3668 | −2.89803 | ||||||||
\(366\) | −16.7935 | −0.877809 | ||||||||
\(367\) | 21.2306 | 1.10823 | 0.554115 | − | 0.832440i | \(-0.313057\pi\) | ||||
0.554115 | + | 0.832440i | \(0.313057\pi\) | |||||||
\(368\) | −6.90130 | −0.359755 | ||||||||
\(369\) | 9.11880 | 0.474706 | ||||||||
\(370\) | −20.8401 | −1.08343 | ||||||||
\(371\) | 14.5673 | 0.756294 | ||||||||
\(372\) | −14.0946 | −0.730768 | ||||||||
\(373\) | 17.8721 | 0.925380 | 0.462690 | − | 0.886520i | \(-0.346884\pi\) | ||||
0.462690 | + | 0.886520i | \(0.346884\pi\) | |||||||
\(374\) | 15.9323 | 0.823842 | ||||||||
\(375\) | −17.1524 | −0.885746 | ||||||||
\(376\) | −5.41035 | −0.279017 | ||||||||
\(377\) | 26.3147 | 1.35528 | ||||||||
\(378\) | −8.45947 | −0.435108 | ||||||||
\(379\) | 20.5879 | 1.05753 | 0.528764 | − | 0.848769i | \(-0.322656\pi\) | ||||
0.528764 | + | 0.848769i | \(0.322656\pi\) | |||||||
\(380\) | −17.1669 | −0.880642 | ||||||||
\(381\) | 11.3829 | 0.583163 | ||||||||
\(382\) | −11.7056 | −0.598912 | ||||||||
\(383\) | −28.5254 | −1.45758 | −0.728789 | − | 0.684739i | \(-0.759916\pi\) | ||||
−0.728789 | + | 0.684739i | \(0.759916\pi\) | |||||||
\(384\) | −1.49586 | −0.0763355 | ||||||||
\(385\) | 19.0668 | 0.971735 | ||||||||
\(386\) | −12.0489 | −0.613274 | ||||||||
\(387\) | 8.23297 | 0.418506 | ||||||||
\(388\) | 11.2812 | 0.572717 | ||||||||
\(389\) | −17.2629 | −0.875261 | −0.437631 | − | 0.899155i | \(-0.644182\pi\) | ||||
−0.437631 | + | 0.899155i | \(0.644182\pi\) | |||||||
\(390\) | −14.6651 | −0.742598 | ||||||||
\(391\) | 31.4456 | 1.59027 | ||||||||
\(392\) | −4.74070 | −0.239441 | ||||||||
\(393\) | 31.2319 | 1.57544 | ||||||||
\(394\) | −17.2450 | −0.868789 | ||||||||
\(395\) | 12.4591 | 0.626884 | ||||||||
\(396\) | 2.66581 | 0.133962 | ||||||||
\(397\) | −33.6567 | −1.68918 | −0.844591 | − | 0.535411i | \(-0.820157\pi\) | ||||
−0.844591 | + | 0.535411i | \(0.820157\pi\) | |||||||
\(398\) | 4.09423 | 0.205225 | ||||||||
\(399\) | −10.6397 | −0.532652 | ||||||||
\(400\) | 8.16077 | 0.408038 | ||||||||
\(401\) | −21.0584 | −1.05161 | −0.525803 | − | 0.850607i | \(-0.676235\pi\) | ||||
−0.525803 | + | 0.850607i | \(0.676235\pi\) | |||||||
\(402\) | 18.1579 | 0.905633 | ||||||||
\(403\) | 25.4632 | 1.26841 | ||||||||
\(404\) | 10.2606 | 0.510485 | ||||||||
\(405\) | −22.2440 | −1.10531 | ||||||||
\(406\) | −14.6363 | −0.726388 | ||||||||
\(407\) | 20.0868 | 0.995663 | ||||||||
\(408\) | 6.81587 | 0.337436 | ||||||||
\(409\) | −14.8304 | −0.733318 | −0.366659 | − | 0.930355i | \(-0.619498\pi\) | ||||
−0.366659 | + | 0.930355i | \(0.619498\pi\) | |||||||
\(410\) | −43.3910 | −2.14293 | ||||||||
\(411\) | −7.47526 | −0.368728 | ||||||||
\(412\) | −9.36610 | −0.461435 | ||||||||
\(413\) | 8.35410 | 0.411078 | ||||||||
\(414\) | 5.26150 | 0.258589 | ||||||||
\(415\) | 22.7597 | 1.11723 | ||||||||
\(416\) | 2.70243 | 0.132497 | ||||||||
\(417\) | −27.0154 | −1.32295 | ||||||||
\(418\) | 16.5463 | 0.809307 | ||||||||
\(419\) | 11.9369 | 0.583157 | 0.291579 | − | 0.956547i | \(-0.405819\pi\) | ||||
0.291579 | + | 0.956547i | \(0.405819\pi\) | |||||||
\(420\) | 8.15680 | 0.398011 | ||||||||
\(421\) | −26.9131 | −1.31167 | −0.655833 | − | 0.754906i | \(-0.727683\pi\) | ||||
−0.655833 | + | 0.754906i | \(0.727683\pi\) | |||||||
\(422\) | −1.59128 | −0.0774622 | ||||||||
\(423\) | 4.12481 | 0.200555 | ||||||||
\(424\) | −9.69149 | −0.470661 | ||||||||
\(425\) | −37.1843 | −1.80371 | ||||||||
\(426\) | −16.3317 | −0.791276 | ||||||||
\(427\) | −16.8747 | −0.816624 | ||||||||
\(428\) | 6.92796 | 0.334875 | ||||||||
\(429\) | 14.1350 | 0.682445 | ||||||||
\(430\) | −39.1759 | −1.88923 | ||||||||
\(431\) | 8.13486 | 0.391842 | 0.195921 | − | 0.980620i | \(-0.437230\pi\) | ||||
0.195921 | + | 0.980620i | \(0.437230\pi\) | |||||||
\(432\) | 5.62803 | 0.270779 | ||||||||
\(433\) | 5.64742 | 0.271398 | 0.135699 | − | 0.990750i | \(-0.456672\pi\) | ||||
0.135699 | + | 0.990750i | \(0.456672\pi\) | |||||||
\(434\) | −14.1627 | −0.679832 | ||||||||
\(435\) | −52.8417 | −2.53357 | ||||||||
\(436\) | −7.39654 | −0.354230 | ||||||||
\(437\) | 32.6574 | 1.56222 | ||||||||
\(438\) | 22.8297 | 1.09085 | ||||||||
\(439\) | 12.9933 | 0.620136 | 0.310068 | − | 0.950714i | \(-0.399648\pi\) | ||||
0.310068 | + | 0.950714i | \(0.399648\pi\) | |||||||
\(440\) | −12.6850 | −0.604735 | ||||||||
\(441\) | 3.61427 | 0.172108 | ||||||||
\(442\) | −12.3135 | −0.585696 | ||||||||
\(443\) | 5.55165 | 0.263767 | 0.131883 | − | 0.991265i | \(-0.457898\pi\) | ||||
0.131883 | + | 0.991265i | \(0.457898\pi\) | |||||||
\(444\) | 8.59312 | 0.407812 | ||||||||
\(445\) | 5.18988 | 0.246024 | ||||||||
\(446\) | 18.5568 | 0.878692 | ||||||||
\(447\) | −3.32998 | −0.157502 | ||||||||
\(448\) | −1.50310 | −0.0710147 | ||||||||
\(449\) | −12.9881 | −0.612945 | −0.306472 | − | 0.951880i | \(-0.599149\pi\) | ||||
−0.306472 | + | 0.951880i | \(0.599149\pi\) | |||||||
\(450\) | −6.22171 | −0.293294 | ||||||||
\(451\) | 41.8225 | 1.96934 | ||||||||
\(452\) | 19.3027 | 0.907921 | ||||||||
\(453\) | 21.1187 | 0.992241 | ||||||||
\(454\) | −3.04139 | −0.142739 | ||||||||
\(455\) | −14.7361 | −0.690837 | ||||||||
\(456\) | 7.07852 | 0.331482 | ||||||||
\(457\) | −2.34198 | −0.109553 | −0.0547765 | − | 0.998499i | \(-0.517445\pi\) | ||||
−0.0547765 | + | 0.998499i | \(0.517445\pi\) | |||||||
\(458\) | 6.50956 | 0.304172 | ||||||||
\(459\) | −25.6440 | −1.19696 | ||||||||
\(460\) | −25.0364 | −1.16733 | ||||||||
\(461\) | 28.0100 | 1.30456 | 0.652278 | − | 0.757979i | \(-0.273813\pi\) | ||||
0.652278 | + | 0.757979i | \(0.273813\pi\) | |||||||
\(462\) | −7.86194 | −0.365770 | ||||||||
\(463\) | 24.0740 | 1.11881 | 0.559407 | − | 0.828893i | \(-0.311029\pi\) | ||||
0.559407 | + | 0.828893i | \(0.311029\pi\) | |||||||
\(464\) | 9.73743 | 0.452049 | ||||||||
\(465\) | −51.1319 | −2.37118 | ||||||||
\(466\) | −3.98723 | −0.184705 | ||||||||
\(467\) | 8.58512 | 0.397272 | 0.198636 | − | 0.980073i | \(-0.436349\pi\) | ||||
0.198636 | + | 0.980073i | \(0.436349\pi\) | |||||||
\(468\) | −2.06031 | −0.0952379 | ||||||||
\(469\) | 18.2457 | 0.842508 | ||||||||
\(470\) | −19.6275 | −0.905351 | ||||||||
\(471\) | −6.99090 | −0.322124 | ||||||||
\(472\) | −5.55792 | −0.255824 | ||||||||
\(473\) | 37.7597 | 1.73619 | ||||||||
\(474\) | −5.13732 | −0.235965 | ||||||||
\(475\) | −38.6173 | −1.77188 | ||||||||
\(476\) | 6.84883 | 0.313916 | ||||||||
\(477\) | 7.38872 | 0.338306 | ||||||||
\(478\) | 7.69185 | 0.351817 | ||||||||
\(479\) | 31.3404 | 1.43198 | 0.715991 | − | 0.698110i | \(-0.245975\pi\) | ||||
0.715991 | + | 0.698110i | \(0.245975\pi\) | |||||||
\(480\) | −5.42666 | −0.247692 | ||||||||
\(481\) | −15.5243 | −0.707849 | ||||||||
\(482\) | 26.7382 | 1.21789 | ||||||||
\(483\) | −15.5171 | −0.706052 | ||||||||
\(484\) | 1.22647 | 0.0557487 | ||||||||
\(485\) | 40.9258 | 1.85834 | ||||||||
\(486\) | −7.71207 | −0.349827 | ||||||||
\(487\) | −31.7625 | −1.43929 | −0.719647 | − | 0.694340i | \(-0.755697\pi\) | ||||
−0.719647 | + | 0.694340i | \(0.755697\pi\) | |||||||
\(488\) | 11.2266 | 0.508205 | ||||||||
\(489\) | 31.2794 | 1.41451 | ||||||||
\(490\) | −17.1982 | −0.776935 | ||||||||
\(491\) | −11.7168 | −0.528771 | −0.264386 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264386 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(492\) | 17.8917 | 0.806619 | ||||||||
\(493\) | −44.3684 | −1.99825 | ||||||||
\(494\) | −12.7881 | −0.575362 | ||||||||
\(495\) | 9.67097 | 0.434678 | ||||||||
\(496\) | 9.42235 | 0.423076 | ||||||||
\(497\) | −16.4107 | −0.736122 | ||||||||
\(498\) | −9.38463 | −0.420536 | ||||||||
\(499\) | 3.23553 | 0.144842 | 0.0724210 | − | 0.997374i | \(-0.476927\pi\) | ||||
0.0724210 | + | 0.997374i | \(0.476927\pi\) | |||||||
\(500\) | 11.4666 | 0.512800 | ||||||||
\(501\) | 13.3396 | 0.595968 | ||||||||
\(502\) | 6.31167 | 0.281704 | ||||||||
\(503\) | 34.5273 | 1.53949 | 0.769747 | − | 0.638349i | \(-0.220382\pi\) | ||||
0.769747 | + | 0.638349i | \(0.220382\pi\) | |||||||
\(504\) | 1.14595 | 0.0510447 | ||||||||
\(505\) | 37.2232 | 1.65641 | ||||||||
\(506\) | 24.1314 | 1.07277 | ||||||||
\(507\) | 8.52177 | 0.378465 | ||||||||
\(508\) | −7.60958 | −0.337621 | ||||||||
\(509\) | 8.43618 | 0.373927 | 0.186964 | − | 0.982367i | \(-0.440135\pi\) | ||||
0.186964 | + | 0.982367i | \(0.440135\pi\) | |||||||
\(510\) | 24.7264 | 1.09491 | ||||||||
\(511\) | 22.9401 | 1.01481 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −26.6322 | −1.17584 | ||||||||
\(514\) | −11.7701 | −0.519155 | ||||||||
\(515\) | −33.9781 | −1.49725 | ||||||||
\(516\) | 16.1536 | 0.711124 | ||||||||
\(517\) | 18.9180 | 0.832014 | ||||||||
\(518\) | 8.63468 | 0.379386 | ||||||||
\(519\) | −18.9219 | −0.830580 | ||||||||
\(520\) | 9.80380 | 0.429925 | ||||||||
\(521\) | 13.1006 | 0.573948 | 0.286974 | − | 0.957938i | \(-0.407351\pi\) | ||||
0.286974 | + | 0.957938i | \(0.407351\pi\) | |||||||
\(522\) | −7.42375 | −0.324929 | ||||||||
\(523\) | −35.7014 | −1.56112 | −0.780558 | − | 0.625084i | \(-0.785065\pi\) | ||||
−0.780558 | + | 0.625084i | \(0.785065\pi\) | |||||||
\(524\) | −20.8788 | −0.912097 | ||||||||
\(525\) | 18.3489 | 0.800811 | ||||||||
\(526\) | 14.7343 | 0.642446 | ||||||||
\(527\) | −42.9327 | −1.87018 | ||||||||
\(528\) | 5.23049 | 0.227628 | ||||||||
\(529\) | 24.6280 | 1.07078 | ||||||||
\(530\) | −35.1586 | −1.52719 | ||||||||
\(531\) | 4.23732 | 0.183884 | ||||||||
\(532\) | 7.11275 | 0.308377 | ||||||||
\(533\) | −32.3231 | −1.40007 | ||||||||
\(534\) | −2.13998 | −0.0926059 | ||||||||
\(535\) | 25.1331 | 1.08660 | ||||||||
\(536\) | −12.1387 | −0.524313 | ||||||||
\(537\) | 24.8185 | 1.07100 | ||||||||
\(538\) | −17.4625 | −0.752861 | ||||||||
\(539\) | 16.5765 | 0.714001 | ||||||||
\(540\) | 20.4172 | 0.878617 | ||||||||
\(541\) | −6.97435 | −0.299851 | −0.149925 | − | 0.988697i | \(-0.547903\pi\) | ||||
−0.149925 | + | 0.988697i | \(0.547903\pi\) | |||||||
\(542\) | −16.2335 | −0.697290 | ||||||||
\(543\) | 3.46325 | 0.148622 | ||||||||
\(544\) | −4.55648 | −0.195357 | ||||||||
\(545\) | −26.8330 | −1.14940 | ||||||||
\(546\) | 6.07621 | 0.260038 | ||||||||
\(547\) | 2.06812 | 0.0884263 | 0.0442132 | − | 0.999022i | \(-0.485922\pi\) | ||||
0.0442132 | + | 0.999022i | \(0.485922\pi\) | |||||||
\(548\) | 4.99729 | 0.213474 | ||||||||
\(549\) | −8.55909 | −0.365293 | ||||||||
\(550\) | −28.5352 | −1.21675 | ||||||||
\(551\) | −46.0782 | −1.96300 | ||||||||
\(552\) | 10.3234 | 0.439393 | ||||||||
\(553\) | −5.16217 | −0.219518 | ||||||||
\(554\) | 17.6711 | 0.750771 | ||||||||
\(555\) | 31.1739 | 1.32326 | ||||||||
\(556\) | 18.0601 | 0.765917 | ||||||||
\(557\) | −17.7347 | −0.751443 | −0.375721 | − | 0.926733i | \(-0.622605\pi\) | ||||
−0.375721 | + | 0.926733i | \(0.622605\pi\) | |||||||
\(558\) | −7.18353 | −0.304103 | ||||||||
\(559\) | −29.1831 | −1.23431 | ||||||||
\(560\) | −5.45290 | −0.230427 | ||||||||
\(561\) | −23.8326 | −1.00621 | ||||||||
\(562\) | 11.5639 | 0.487794 | ||||||||
\(563\) | 30.3753 | 1.28017 | 0.640083 | − | 0.768306i | \(-0.278900\pi\) | ||||
0.640083 | + | 0.768306i | \(0.278900\pi\) | |||||||
\(564\) | 8.09314 | 0.340783 | ||||||||
\(565\) | 70.0257 | 2.94601 | ||||||||
\(566\) | −5.54353 | −0.233012 | ||||||||
\(567\) | 9.21636 | 0.387051 | ||||||||
\(568\) | 10.9179 | 0.458107 | ||||||||
\(569\) | −20.3967 | −0.855073 | −0.427537 | − | 0.903998i | \(-0.640619\pi\) | ||||
−0.427537 | + | 0.903998i | \(0.640619\pi\) | |||||||
\(570\) | 25.6793 | 1.07559 | ||||||||
\(571\) | 18.2569 | 0.764027 | 0.382014 | − | 0.924157i | \(-0.375231\pi\) | ||||
0.382014 | + | 0.924157i | \(0.375231\pi\) | |||||||
\(572\) | −9.44940 | −0.395099 | ||||||||
\(573\) | 17.5100 | 0.731492 | ||||||||
\(574\) | 17.9782 | 0.750395 | ||||||||
\(575\) | −56.3199 | −2.34870 | ||||||||
\(576\) | −0.762393 | −0.0317664 | ||||||||
\(577\) | 38.2990 | 1.59441 | 0.797203 | − | 0.603711i | \(-0.206312\pi\) | ||||
0.797203 | + | 0.603711i | \(0.206312\pi\) | |||||||
\(578\) | 3.76148 | 0.156457 | ||||||||
\(579\) | 18.0235 | 0.749032 | ||||||||
\(580\) | 35.3252 | 1.46680 | ||||||||
\(581\) | −9.43002 | −0.391223 | ||||||||
\(582\) | −16.8752 | −0.699498 | ||||||||
\(583\) | 33.8876 | 1.40348 | ||||||||
\(584\) | −15.2619 | −0.631542 | ||||||||
\(585\) | −7.47434 | −0.309026 | ||||||||
\(586\) | −26.7201 | −1.10380 | ||||||||
\(587\) | −3.26606 | −0.134805 | −0.0674023 | − | 0.997726i | \(-0.521471\pi\) | ||||
−0.0674023 | + | 0.997726i | \(0.521471\pi\) | |||||||
\(588\) | 7.09144 | 0.292446 | ||||||||
\(589\) | −44.5872 | −1.83718 | ||||||||
\(590\) | −20.1629 | −0.830094 | ||||||||
\(591\) | 25.7961 | 1.06111 | ||||||||
\(592\) | −5.74459 | −0.236101 | ||||||||
\(593\) | −28.4117 | −1.16673 | −0.583365 | − | 0.812210i | \(-0.698264\pi\) | ||||
−0.583365 | + | 0.812210i | \(0.698264\pi\) | |||||||
\(594\) | −19.6792 | −0.807446 | ||||||||
\(595\) | 24.8460 | 1.01859 | ||||||||
\(596\) | 2.22612 | 0.0911855 | ||||||||
\(597\) | −6.12442 | −0.250656 | ||||||||
\(598\) | −18.6503 | −0.762666 | ||||||||
\(599\) | 37.2628 | 1.52252 | 0.761259 | − | 0.648448i | \(-0.224581\pi\) | ||||
0.761259 | + | 0.648448i | \(0.224581\pi\) | |||||||
\(600\) | −12.2074 | −0.498365 | ||||||||
\(601\) | 20.3225 | 0.828970 | 0.414485 | − | 0.910056i | \(-0.363962\pi\) | ||||
0.414485 | + | 0.910056i | \(0.363962\pi\) | |||||||
\(602\) | 16.2317 | 0.661556 | ||||||||
\(603\) | 9.25448 | 0.376871 | ||||||||
\(604\) | −14.1180 | −0.574455 | ||||||||
\(605\) | 4.44936 | 0.180892 | ||||||||
\(606\) | −15.3485 | −0.623489 | ||||||||
\(607\) | −13.7892 | −0.559685 | −0.279842 | − | 0.960046i | \(-0.590282\pi\) | ||||
−0.279842 | + | 0.960046i | \(0.590282\pi\) | |||||||
\(608\) | −4.73207 | −0.191911 | ||||||||
\(609\) | 21.8939 | 0.887186 | ||||||||
\(610\) | 40.7277 | 1.64901 | ||||||||
\(611\) | −14.6211 | −0.591505 | ||||||||
\(612\) | 3.47382 | 0.140421 | ||||||||
\(613\) | −15.3938 | −0.621751 | −0.310876 | − | 0.950451i | \(-0.600622\pi\) | ||||
−0.310876 | + | 0.950451i | \(0.600622\pi\) | |||||||
\(614\) | 2.42093 | 0.0977006 | ||||||||
\(615\) | 64.9070 | 2.61730 | ||||||||
\(616\) | 5.25579 | 0.211762 | ||||||||
\(617\) | −39.0794 | −1.57328 | −0.786639 | − | 0.617414i | \(-0.788181\pi\) | ||||
−0.786639 | + | 0.617414i | \(0.788181\pi\) | |||||||
\(618\) | 14.0104 | 0.563581 | ||||||||
\(619\) | 35.4401 | 1.42446 | 0.712229 | − | 0.701947i | \(-0.247686\pi\) | ||||
0.712229 | + | 0.701947i | \(0.247686\pi\) | |||||||
\(620\) | 34.1822 | 1.37279 | ||||||||
\(621\) | −38.8407 | −1.55862 | ||||||||
\(622\) | 26.0257 | 1.04354 | ||||||||
\(623\) | −2.15033 | −0.0861510 | ||||||||
\(624\) | −4.04246 | −0.161828 | ||||||||
\(625\) | 0.794261 | 0.0317704 | ||||||||
\(626\) | −2.18509 | −0.0873339 | ||||||||
\(627\) | −24.7510 | −0.988461 | ||||||||
\(628\) | 4.67349 | 0.186492 | ||||||||
\(629\) | 26.1751 | 1.04367 | ||||||||
\(630\) | 4.15725 | 0.165629 | ||||||||
\(631\) | −14.8991 | −0.593125 | −0.296563 | − | 0.955013i | \(-0.595840\pi\) | ||||
−0.296563 | + | 0.955013i | \(0.595840\pi\) | |||||||
\(632\) | 3.43435 | 0.136611 | ||||||||
\(633\) | 2.38033 | 0.0946098 | ||||||||
\(634\) | 28.6549 | 1.13803 | ||||||||
\(635\) | −27.6059 | −1.09551 | ||||||||
\(636\) | 14.4971 | 0.574849 | ||||||||
\(637\) | −12.8114 | −0.507606 | ||||||||
\(638\) | −34.0483 | −1.34798 | ||||||||
\(639\) | −8.32376 | −0.329283 | ||||||||
\(640\) | 3.62778 | 0.143400 | ||||||||
\(641\) | 36.3219 | 1.43463 | 0.717314 | − | 0.696750i | \(-0.245371\pi\) | ||||
0.717314 | + | 0.696750i | \(0.245371\pi\) | |||||||
\(642\) | −10.3633 | −0.409006 | ||||||||
\(643\) | −20.6587 | −0.814701 | −0.407350 | − | 0.913272i | \(-0.633547\pi\) | ||||
−0.407350 | + | 0.913272i | \(0.633547\pi\) | |||||||
\(644\) | 10.3733 | 0.408766 | ||||||||
\(645\) | 58.6017 | 2.30744 | ||||||||
\(646\) | 21.5615 | 0.848328 | ||||||||
\(647\) | −35.1471 | −1.38177 | −0.690887 | − | 0.722963i | \(-0.742780\pi\) | ||||
−0.690887 | + | 0.722963i | \(0.742780\pi\) | |||||||
\(648\) | −6.13158 | −0.240871 | ||||||||
\(649\) | 19.4340 | 0.762853 | ||||||||
\(650\) | 22.0539 | 0.865024 | ||||||||
\(651\) | 21.1855 | 0.830324 | ||||||||
\(652\) | −20.9106 | −0.818923 | ||||||||
\(653\) | 26.2863 | 1.02866 | 0.514331 | − | 0.857592i | \(-0.328040\pi\) | ||||
0.514331 | + | 0.857592i | \(0.328040\pi\) | |||||||
\(654\) | 11.0642 | 0.432645 | ||||||||
\(655\) | −75.7438 | −2.95955 | ||||||||
\(656\) | −11.9608 | −0.466990 | ||||||||
\(657\) | 11.6356 | 0.453947 | ||||||||
\(658\) | 8.13228 | 0.317029 | ||||||||
\(659\) | 5.99504 | 0.233534 | 0.116767 | − | 0.993159i | \(-0.462747\pi\) | ||||
0.116767 | + | 0.993159i | \(0.462747\pi\) | |||||||
\(660\) | 18.9751 | 0.738603 | ||||||||
\(661\) | −36.9297 | −1.43640 | −0.718199 | − | 0.695838i | \(-0.755033\pi\) | ||||
−0.718199 | + | 0.695838i | \(0.755033\pi\) | |||||||
\(662\) | −19.2549 | −0.748361 | ||||||||
\(663\) | 18.4194 | 0.715349 | ||||||||
\(664\) | 6.27372 | 0.243468 | ||||||||
\(665\) | 25.8035 | 1.00062 | ||||||||
\(666\) | 4.37963 | 0.169707 | ||||||||
\(667\) | −67.2010 | −2.60203 | ||||||||
\(668\) | −8.91764 | −0.345034 | ||||||||
\(669\) | −27.7585 | −1.07321 | ||||||||
\(670\) | −44.0366 | −1.70128 | ||||||||
\(671\) | −39.2554 | −1.51544 | ||||||||
\(672\) | 2.24843 | 0.0867350 | ||||||||
\(673\) | 16.4358 | 0.633555 | 0.316778 | − | 0.948500i | \(-0.397399\pi\) | ||||
0.316778 | + | 0.948500i | \(0.397399\pi\) | |||||||
\(674\) | 13.2036 | 0.508584 | ||||||||
\(675\) | 45.9290 | 1.76781 | ||||||||
\(676\) | −5.69689 | −0.219111 | ||||||||
\(677\) | −18.5996 | −0.714841 | −0.357421 | − | 0.933944i | \(-0.616344\pi\) | ||||
−0.357421 | + | 0.933944i | \(0.616344\pi\) | |||||||
\(678\) | −28.8741 | −1.10890 | ||||||||
\(679\) | −16.9568 | −0.650741 | ||||||||
\(680\) | −16.5299 | −0.633892 | ||||||||
\(681\) | 4.54950 | 0.174337 | ||||||||
\(682\) | −32.9465 | −1.26159 | ||||||||
\(683\) | −15.8606 | −0.606889 | −0.303444 | − | 0.952849i | \(-0.598137\pi\) | ||||
−0.303444 | + | 0.952849i | \(0.598137\pi\) | |||||||
\(684\) | 3.60769 | 0.137944 | ||||||||
\(685\) | 18.1291 | 0.692676 | ||||||||
\(686\) | 17.6474 | 0.673781 | ||||||||
\(687\) | −9.73741 | −0.371505 | ||||||||
\(688\) | −10.7989 | −0.411703 | ||||||||
\(689\) | −26.1905 | −0.997780 | ||||||||
\(690\) | 37.4510 | 1.42574 | ||||||||
\(691\) | 21.3595 | 0.812552 | 0.406276 | − | 0.913750i | \(-0.366827\pi\) | ||||
0.406276 | + | 0.913750i | \(0.366827\pi\) | |||||||
\(692\) | 12.6495 | 0.480862 | ||||||||
\(693\) | −4.00697 | −0.152212 | ||||||||
\(694\) | −11.0019 | −0.417626 | ||||||||
\(695\) | 65.5179 | 2.48524 | ||||||||
\(696\) | −14.5659 | −0.552118 | ||||||||
\(697\) | 54.4990 | 2.06430 | ||||||||
\(698\) | −12.1730 | −0.460756 | ||||||||
\(699\) | 5.96436 | 0.225593 | ||||||||
\(700\) | −12.2664 | −0.463627 | ||||||||
\(701\) | 7.81487 | 0.295163 | 0.147582 | − | 0.989050i | \(-0.452851\pi\) | ||||
0.147582 | + | 0.989050i | \(0.452851\pi\) | |||||||
\(702\) | 15.2093 | 0.574039 | ||||||||
\(703\) | 27.1838 | 1.02526 | ||||||||
\(704\) | −3.49664 | −0.131784 | ||||||||
\(705\) | 29.3601 | 1.10577 | ||||||||
\(706\) | 22.3049 | 0.839458 | ||||||||
\(707\) | −15.4227 | −0.580030 | ||||||||
\(708\) | 8.31390 | 0.312455 | ||||||||
\(709\) | 18.6148 | 0.699092 | 0.349546 | − | 0.936919i | \(-0.386336\pi\) | ||||
0.349546 | + | 0.936919i | \(0.386336\pi\) | |||||||
\(710\) | 39.6078 | 1.48646 | ||||||||
\(711\) | −2.61833 | −0.0981949 | ||||||||
\(712\) | 1.43060 | 0.0536139 | ||||||||
\(713\) | −65.0265 | −2.43526 | ||||||||
\(714\) | −10.2449 | −0.383406 | ||||||||
\(715\) | −34.2803 | −1.28201 | ||||||||
\(716\) | −16.5914 | −0.620050 | ||||||||
\(717\) | −11.5060 | −0.429698 | ||||||||
\(718\) | 9.94994 | 0.371328 | ||||||||
\(719\) | −28.8184 | −1.07474 | −0.537372 | − | 0.843345i | \(-0.680583\pi\) | ||||
−0.537372 | + | 0.843345i | \(0.680583\pi\) | |||||||
\(720\) | −2.76579 | −0.103075 | ||||||||
\(721\) | 14.0782 | 0.524298 | ||||||||
\(722\) | 3.39244 | 0.126254 | ||||||||
\(723\) | −39.9968 | −1.48750 | ||||||||
\(724\) | −2.31522 | −0.0860444 | ||||||||
\(725\) | 79.4649 | 2.95125 | ||||||||
\(726\) | −1.83463 | −0.0680896 | ||||||||
\(727\) | 42.9152 | 1.59164 | 0.795818 | − | 0.605536i | \(-0.207041\pi\) | ||||
0.795818 | + | 0.605536i | \(0.207041\pi\) | |||||||
\(728\) | −4.06201 | −0.150548 | ||||||||
\(729\) | 29.9309 | 1.10855 | ||||||||
\(730\) | −55.3668 | −2.04922 | ||||||||
\(731\) | 49.2048 | 1.81990 | ||||||||
\(732\) | −16.7935 | −0.620705 | ||||||||
\(733\) | −1.99756 | −0.0737816 | −0.0368908 | − | 0.999319i | \(-0.511745\pi\) | ||||
−0.0368908 | + | 0.999319i | \(0.511745\pi\) | |||||||
\(734\) | 21.2306 | 0.783637 | ||||||||
\(735\) | 25.7262 | 0.948924 | ||||||||
\(736\) | −6.90130 | −0.254385 | ||||||||
\(737\) | 42.4447 | 1.56347 | ||||||||
\(738\) | 9.11880 | 0.335668 | ||||||||
\(739\) | −11.4165 | −0.419964 | −0.209982 | − | 0.977705i | \(-0.567341\pi\) | ||||
−0.209982 | + | 0.977705i | \(0.567341\pi\) | |||||||
\(740\) | −20.8401 | −0.766097 | ||||||||
\(741\) | 19.1292 | 0.702728 | ||||||||
\(742\) | 14.5673 | 0.534781 | ||||||||
\(743\) | 5.85467 | 0.214787 | 0.107393 | − | 0.994217i | \(-0.465750\pi\) | ||||
0.107393 | + | 0.994217i | \(0.465750\pi\) | |||||||
\(744\) | −14.0946 | −0.516731 | ||||||||
\(745\) | 8.07588 | 0.295877 | ||||||||
\(746\) | 17.8721 | 0.654342 | ||||||||
\(747\) | −4.78304 | −0.175002 | ||||||||
\(748\) | 15.9323 | 0.582544 | ||||||||
\(749\) | −10.4134 | −0.380497 | ||||||||
\(750\) | −17.1524 | −0.626317 | ||||||||
\(751\) | −8.16013 | −0.297767 | −0.148884 | − | 0.988855i | \(-0.547568\pi\) | ||||
−0.148884 | + | 0.988855i | \(0.547568\pi\) | |||||||
\(752\) | −5.41035 | −0.197295 | ||||||||
\(753\) | −9.44140 | −0.344064 | ||||||||
\(754\) | 26.3147 | 0.958324 | ||||||||
\(755\) | −51.2171 | −1.86398 | ||||||||
\(756\) | −8.45947 | −0.307668 | ||||||||
\(757\) | 9.09891 | 0.330706 | 0.165353 | − | 0.986234i | \(-0.447124\pi\) | ||||
0.165353 | + | 0.986234i | \(0.447124\pi\) | |||||||
\(758\) | 20.5879 | 0.747785 | ||||||||
\(759\) | −36.0972 | −1.31025 | ||||||||
\(760\) | −17.1669 | −0.622708 | ||||||||
\(761\) | 30.2631 | 1.09703 | 0.548517 | − | 0.836139i | \(-0.315192\pi\) | ||||
0.548517 | + | 0.836139i | \(0.315192\pi\) | |||||||
\(762\) | 11.3829 | 0.412359 | ||||||||
\(763\) | 11.1177 | 0.402488 | ||||||||
\(764\) | −11.7056 | −0.423495 | ||||||||
\(765\) | 12.6023 | 0.455636 | ||||||||
\(766\) | −28.5254 | −1.03066 | ||||||||
\(767\) | −15.0199 | −0.542336 | ||||||||
\(768\) | −1.49586 | −0.0539773 | ||||||||
\(769\) | −24.3360 | −0.877579 | −0.438790 | − | 0.898590i | \(-0.644593\pi\) | ||||
−0.438790 | + | 0.898590i | \(0.644593\pi\) | |||||||
\(770\) | 19.0668 | 0.687120 | ||||||||
\(771\) | 17.6064 | 0.634079 | ||||||||
\(772\) | −12.0489 | −0.433650 | ||||||||
\(773\) | 27.4969 | 0.988994 | 0.494497 | − | 0.869179i | \(-0.335352\pi\) | ||||
0.494497 | + | 0.869179i | \(0.335352\pi\) | |||||||
\(774\) | 8.23297 | 0.295928 | ||||||||
\(775\) | 76.8936 | 2.76210 | ||||||||
\(776\) | 11.2812 | 0.404972 | ||||||||
\(777\) | −12.9163 | −0.463370 | ||||||||
\(778\) | −17.2629 | −0.618903 | ||||||||
\(779\) | 56.5991 | 2.02787 | ||||||||
\(780\) | −14.6651 | −0.525096 | ||||||||
\(781\) | −38.1761 | −1.36605 | ||||||||
\(782\) | 31.4456 | 1.12449 | ||||||||
\(783\) | 54.8025 | 1.95848 | ||||||||
\(784\) | −4.74070 | −0.169311 | ||||||||
\(785\) | 16.9544 | 0.605127 | ||||||||
\(786\) | 31.2319 | 1.11400 | ||||||||
\(787\) | 29.9692 | 1.06829 | 0.534143 | − | 0.845394i | \(-0.320634\pi\) | ||||
0.534143 | + | 0.845394i | \(0.320634\pi\) | |||||||
\(788\) | −17.2450 | −0.614327 | ||||||||
\(789\) | −22.0405 | −0.784662 | ||||||||
\(790\) | 12.4591 | 0.443274 | ||||||||
\(791\) | −29.0138 | −1.03161 | ||||||||
\(792\) | 2.66581 | 0.0947254 | ||||||||
\(793\) | 30.3391 | 1.07737 | ||||||||
\(794\) | −33.6567 | −1.19443 | ||||||||
\(795\) | 52.5924 | 1.86526 | ||||||||
\(796\) | 4.09423 | 0.145116 | ||||||||
\(797\) | 31.7567 | 1.12488 | 0.562440 | − | 0.826838i | \(-0.309863\pi\) | ||||
0.562440 | + | 0.826838i | \(0.309863\pi\) | |||||||
\(798\) | −10.6397 | −0.376642 | ||||||||
\(799\) | 24.6521 | 0.872130 | ||||||||
\(800\) | 8.16077 | 0.288527 | ||||||||
\(801\) | −1.09068 | −0.0385372 | ||||||||
\(802\) | −21.0584 | −0.743597 | ||||||||
\(803\) | 53.3653 | 1.88322 | ||||||||
\(804\) | 18.1579 | 0.640379 | ||||||||
\(805\) | 37.6321 | 1.32636 | ||||||||
\(806\) | 25.4632 | 0.896903 | ||||||||
\(807\) | 26.1215 | 0.919520 | ||||||||
\(808\) | 10.2606 | 0.360967 | ||||||||
\(809\) | −2.23254 | −0.0784921 | −0.0392460 | − | 0.999230i | \(-0.512496\pi\) | ||||
−0.0392460 | + | 0.999230i | \(0.512496\pi\) | |||||||
\(810\) | −22.2440 | −0.781575 | ||||||||
\(811\) | 7.67771 | 0.269601 | 0.134800 | − | 0.990873i | \(-0.456961\pi\) | ||||
0.134800 | + | 0.990873i | \(0.456961\pi\) | |||||||
\(812\) | −14.6363 | −0.513634 | ||||||||
\(813\) | 24.2832 | 0.851647 | ||||||||
\(814\) | 20.0868 | 0.704040 | ||||||||
\(815\) | −75.8591 | −2.65723 | ||||||||
\(816\) | 6.81587 | 0.238603 | ||||||||
\(817\) | 51.1009 | 1.78779 | ||||||||
\(818\) | −14.8304 | −0.518534 | ||||||||
\(819\) | 3.09685 | 0.108213 | ||||||||
\(820\) | −43.3910 | −1.51528 | ||||||||
\(821\) | −7.52119 | −0.262491 | −0.131246 | − | 0.991350i | \(-0.541898\pi\) | ||||
−0.131246 | + | 0.991350i | \(0.541898\pi\) | |||||||
\(822\) | −7.47526 | −0.260730 | ||||||||
\(823\) | −38.2704 | −1.33402 | −0.667011 | − | 0.745048i | \(-0.732427\pi\) | ||||
−0.667011 | + | 0.745048i | \(0.732427\pi\) | |||||||
\(824\) | −9.36610 | −0.326283 | ||||||||
\(825\) | 42.6848 | 1.48609 | ||||||||
\(826\) | 8.35410 | 0.290676 | ||||||||
\(827\) | −2.52723 | −0.0878804 | −0.0439402 | − | 0.999034i | \(-0.513991\pi\) | ||||
−0.0439402 | + | 0.999034i | \(0.513991\pi\) | |||||||
\(828\) | 5.26150 | 0.182850 | ||||||||
\(829\) | −5.76684 | −0.200291 | −0.100145 | − | 0.994973i | \(-0.531931\pi\) | ||||
−0.100145 | + | 0.994973i | \(0.531931\pi\) | |||||||
\(830\) | 22.7597 | 0.790000 | ||||||||
\(831\) | −26.4335 | −0.916967 | ||||||||
\(832\) | 2.70243 | 0.0936898 | ||||||||
\(833\) | 21.6009 | 0.748426 | ||||||||
\(834\) | −27.0154 | −0.935467 | ||||||||
\(835\) | −32.3512 | −1.11956 | ||||||||
\(836\) | 16.5463 | 0.572266 | ||||||||
\(837\) | 53.0292 | 1.83296 | ||||||||
\(838\) | 11.9369 | 0.412355 | ||||||||
\(839\) | −9.20909 | −0.317933 | −0.158967 | − | 0.987284i | \(-0.550816\pi\) | ||||
−0.158967 | + | 0.987284i | \(0.550816\pi\) | |||||||
\(840\) | 8.15680 | 0.281436 | ||||||||
\(841\) | 65.8175 | 2.26957 | ||||||||
\(842\) | −26.9131 | −0.927488 | ||||||||
\(843\) | −17.2980 | −0.595775 | ||||||||
\(844\) | −1.59128 | −0.0547740 | ||||||||
\(845\) | −20.6671 | −0.710968 | ||||||||
\(846\) | 4.12481 | 0.141814 | ||||||||
\(847\) | −1.84350 | −0.0633436 | ||||||||
\(848\) | −9.69149 | −0.332807 | ||||||||
\(849\) | 8.29237 | 0.284593 | ||||||||
\(850\) | −37.1843 | −1.27541 | ||||||||
\(851\) | 39.6452 | 1.35902 | ||||||||
\(852\) | −16.3317 | −0.559516 | ||||||||
\(853\) | −25.1629 | −0.861562 | −0.430781 | − | 0.902457i | \(-0.641762\pi\) | ||||
−0.430781 | + | 0.902457i | \(0.641762\pi\) | |||||||
\(854\) | −16.8747 | −0.577440 | ||||||||
\(855\) | 13.0879 | 0.447597 | ||||||||
\(856\) | 6.92796 | 0.236793 | ||||||||
\(857\) | 40.8657 | 1.39594 | 0.697972 | − | 0.716125i | \(-0.254086\pi\) | ||||
0.697972 | + | 0.716125i | \(0.254086\pi\) | |||||||
\(858\) | 14.1350 | 0.482562 | ||||||||
\(859\) | 13.3540 | 0.455632 | 0.227816 | − | 0.973704i | \(-0.426841\pi\) | ||||
0.227816 | + | 0.973704i | \(0.426841\pi\) | |||||||
\(860\) | −39.1759 | −1.33589 | ||||||||
\(861\) | −26.8929 | −0.916509 | ||||||||
\(862\) | 8.13486 | 0.277074 | ||||||||
\(863\) | −34.3408 | −1.16898 | −0.584488 | − | 0.811403i | \(-0.698704\pi\) | ||||
−0.584488 | + | 0.811403i | \(0.698704\pi\) | |||||||
\(864\) | 5.62803 | 0.191469 | ||||||||
\(865\) | 45.8895 | 1.56029 | ||||||||
\(866\) | 5.64742 | 0.191907 | ||||||||
\(867\) | −5.62666 | −0.191092 | ||||||||
\(868\) | −14.1627 | −0.480714 | ||||||||
\(869\) | −12.0087 | −0.407367 | ||||||||
\(870\) | −52.8417 | −1.79150 | ||||||||
\(871\) | −32.8040 | −1.11152 | ||||||||
\(872\) | −7.39654 | −0.250478 | ||||||||
\(873\) | −8.60072 | −0.291090 | ||||||||
\(874\) | 32.6574 | 1.10465 | ||||||||
\(875\) | −17.2353 | −0.582661 | ||||||||
\(876\) | 22.8297 | 0.771345 | ||||||||
\(877\) | −44.9398 | −1.51751 | −0.758755 | − | 0.651376i | \(-0.774192\pi\) | ||||
−0.758755 | + | 0.651376i | \(0.774192\pi\) | |||||||
\(878\) | 12.9933 | 0.438503 | ||||||||
\(879\) | 39.9696 | 1.34814 | ||||||||
\(880\) | −12.6850 | −0.427612 | ||||||||
\(881\) | −35.1303 | −1.18357 | −0.591785 | − | 0.806096i | \(-0.701577\pi\) | ||||
−0.591785 | + | 0.806096i | \(0.701577\pi\) | |||||||
\(882\) | 3.61427 | 0.121699 | ||||||||
\(883\) | −13.8957 | −0.467628 | −0.233814 | − | 0.972281i | \(-0.575121\pi\) | ||||
−0.233814 | + | 0.972281i | \(0.575121\pi\) | |||||||
\(884\) | −12.3135 | −0.414149 | ||||||||
\(885\) | 30.1610 | 1.01385 | ||||||||
\(886\) | 5.55165 | 0.186511 | ||||||||
\(887\) | −29.6682 | −0.996162 | −0.498081 | − | 0.867130i | \(-0.665962\pi\) | ||||
−0.498081 | + | 0.867130i | \(0.665962\pi\) | |||||||
\(888\) | 8.59312 | 0.288366 | ||||||||
\(889\) | 11.4379 | 0.383616 | ||||||||
\(890\) | 5.18988 | 0.173965 | ||||||||
\(891\) | 21.4399 | 0.718264 | ||||||||
\(892\) | 18.5568 | 0.621329 | ||||||||
\(893\) | 25.6021 | 0.856742 | ||||||||
\(894\) | −3.32998 | −0.111371 | ||||||||
\(895\) | −60.1899 | −2.01193 | ||||||||
\(896\) | −1.50310 | −0.0502150 | ||||||||
\(897\) | 27.8982 | 0.931495 | ||||||||
\(898\) | −12.9881 | −0.433417 | ||||||||
\(899\) | 91.7495 | 3.06002 | ||||||||
\(900\) | −6.22171 | −0.207390 | ||||||||
\(901\) | 44.1591 | 1.47115 | ||||||||
\(902\) | 41.8225 | 1.39254 | ||||||||
\(903\) | −24.2805 | −0.808003 | ||||||||
\(904\) | 19.3027 | 0.641997 | ||||||||
\(905\) | −8.39909 | −0.279195 | ||||||||
\(906\) | 21.1187 | 0.701620 | ||||||||
\(907\) | 28.1012 | 0.933086 | 0.466543 | − | 0.884499i | \(-0.345499\pi\) | ||||
0.466543 | + | 0.884499i | \(0.345499\pi\) | |||||||
\(908\) | −3.04139 | −0.100932 | ||||||||
\(909\) | −7.82262 | −0.259460 | ||||||||
\(910\) | −14.7361 | −0.488496 | ||||||||
\(911\) | 0.978883 | 0.0324318 | 0.0162159 | − | 0.999869i | \(-0.494838\pi\) | ||||
0.0162159 | + | 0.999869i | \(0.494838\pi\) | |||||||
\(912\) | 7.07852 | 0.234393 | ||||||||
\(913\) | −21.9369 | −0.726007 | ||||||||
\(914\) | −2.34198 | −0.0774657 | ||||||||
\(915\) | −60.9230 | −2.01405 | ||||||||
\(916\) | 6.50956 | 0.215082 | ||||||||
\(917\) | 31.3829 | 1.03636 | ||||||||
\(918\) | −25.6440 | −0.846377 | ||||||||
\(919\) | 11.0676 | 0.365088 | 0.182544 | − | 0.983198i | \(-0.441567\pi\) | ||||
0.182544 | + | 0.983198i | \(0.441567\pi\) | |||||||
\(920\) | −25.0364 | −0.825425 | ||||||||
\(921\) | −3.62137 | −0.119328 | ||||||||
\(922\) | 28.0100 | 0.922461 | ||||||||
\(923\) | 29.5049 | 0.971166 | ||||||||
\(924\) | −7.86194 | −0.258639 | ||||||||
\(925\) | −46.8803 | −1.54141 | ||||||||
\(926\) | 24.0740 | 0.791121 | ||||||||
\(927\) | 7.14064 | 0.234530 | ||||||||
\(928\) | 9.73743 | 0.319647 | ||||||||
\(929\) | −31.6228 | −1.03751 | −0.518755 | − | 0.854923i | \(-0.673604\pi\) | ||||
−0.518755 | + | 0.854923i | \(0.673604\pi\) | |||||||
\(930\) | −51.1319 | −1.67668 | ||||||||
\(931\) | 22.4333 | 0.735222 | ||||||||
\(932\) | −3.98723 | −0.130606 | ||||||||
\(933\) | −38.9309 | −1.27454 | ||||||||
\(934\) | 8.58512 | 0.280914 | ||||||||
\(935\) | 57.7990 | 1.89023 | ||||||||
\(936\) | −2.06031 | −0.0673433 | ||||||||
\(937\) | 32.1481 | 1.05023 | 0.525116 | − | 0.851031i | \(-0.324022\pi\) | ||||
0.525116 | + | 0.851031i | \(0.324022\pi\) | |||||||
\(938\) | 18.2457 | 0.595743 | ||||||||
\(939\) | 3.26860 | 0.106667 | ||||||||
\(940\) | −19.6275 | −0.640180 | ||||||||
\(941\) | 15.9760 | 0.520803 | 0.260402 | − | 0.965500i | \(-0.416145\pi\) | ||||
0.260402 | + | 0.965500i | \(0.416145\pi\) | |||||||
\(942\) | −6.99090 | −0.227776 | ||||||||
\(943\) | 82.5449 | 2.68803 | ||||||||
\(944\) | −5.55792 | −0.180895 | ||||||||
\(945\) | −30.6891 | −0.998315 | ||||||||
\(946\) | 37.7597 | 1.22767 | ||||||||
\(947\) | 15.9632 | 0.518734 | 0.259367 | − | 0.965779i | \(-0.416486\pi\) | ||||
0.259367 | + | 0.965779i | \(0.416486\pi\) | |||||||
\(948\) | −5.13732 | −0.166852 | ||||||||
\(949\) | −41.2442 | −1.33884 | ||||||||
\(950\) | −38.6173 | −1.25291 | ||||||||
\(951\) | −42.8639 | −1.38996 | ||||||||
\(952\) | 6.84883 | 0.221972 | ||||||||
\(953\) | −33.4673 | −1.08411 | −0.542056 | − | 0.840342i | \(-0.682354\pi\) | ||||
−0.542056 | + | 0.840342i | \(0.682354\pi\) | |||||||
\(954\) | 7.38872 | 0.239219 | ||||||||
\(955\) | −42.4654 | −1.37415 | ||||||||
\(956\) | 7.69185 | 0.248772 | ||||||||
\(957\) | 50.9315 | 1.64638 | ||||||||
\(958\) | 31.3404 | 1.01256 | ||||||||
\(959\) | −7.51141 | −0.242556 | ||||||||
\(960\) | −5.42666 | −0.175145 | ||||||||
\(961\) | 57.7807 | 1.86389 | ||||||||
\(962\) | −15.5243 | −0.500525 | ||||||||
\(963\) | −5.28182 | −0.170204 | ||||||||
\(964\) | 26.7382 | 0.861181 | ||||||||
\(965\) | −43.7108 | −1.40710 | ||||||||
\(966\) | −15.5171 | −0.499254 | ||||||||
\(967\) | 33.4059 | 1.07426 | 0.537130 | − | 0.843499i | \(-0.319508\pi\) | ||||
0.537130 | + | 0.843499i | \(0.319508\pi\) | |||||||
\(968\) | 1.22647 | 0.0394203 | ||||||||
\(969\) | −32.2531 | −1.03612 | ||||||||
\(970\) | 40.9258 | 1.31405 | ||||||||
\(971\) | −39.6081 | −1.27109 | −0.635543 | − | 0.772066i | \(-0.719224\pi\) | ||||
−0.635543 | + | 0.772066i | \(0.719224\pi\) | |||||||
\(972\) | −7.71207 | −0.247365 | ||||||||
\(973\) | −27.1460 | −0.870262 | ||||||||
\(974\) | −31.7625 | −1.01774 | ||||||||
\(975\) | −32.9896 | −1.05651 | ||||||||
\(976\) | 11.2266 | 0.359355 | ||||||||
\(977\) | 58.5224 | 1.87230 | 0.936148 | − | 0.351605i | \(-0.114364\pi\) | ||||
0.936148 | + | 0.351605i | \(0.114364\pi\) | |||||||
\(978\) | 31.2794 | 1.00021 | ||||||||
\(979\) | −5.00228 | −0.159873 | ||||||||
\(980\) | −17.1982 | −0.549376 | ||||||||
\(981\) | 5.63907 | 0.180042 | ||||||||
\(982\) | −11.7168 | −0.373898 | ||||||||
\(983\) | 4.85826 | 0.154955 | 0.0774773 | − | 0.996994i | \(-0.475313\pi\) | ||||
0.0774773 | + | 0.996994i | \(0.475313\pi\) | |||||||
\(984\) | 17.8917 | 0.570366 | ||||||||
\(985\) | −62.5609 | −1.99336 | ||||||||
\(986\) | −44.3684 | −1.41298 | ||||||||
\(987\) | −12.1648 | −0.387209 | ||||||||
\(988\) | −12.7881 | −0.406842 | ||||||||
\(989\) | 74.5262 | 2.36980 | ||||||||
\(990\) | 9.67097 | 0.307363 | ||||||||
\(991\) | 10.2855 | 0.326729 | 0.163365 | − | 0.986566i | \(-0.447765\pi\) | ||||
0.163365 | + | 0.986566i | \(0.447765\pi\) | |||||||
\(992\) | 9.42235 | 0.299160 | ||||||||
\(993\) | 28.8026 | 0.914024 | ||||||||
\(994\) | −16.4107 | −0.520517 | ||||||||
\(995\) | 14.8530 | 0.470871 | ||||||||
\(996\) | −9.38463 | −0.297364 | ||||||||
\(997\) | 21.4121 | 0.678130 | 0.339065 | − | 0.940763i | \(-0.389889\pi\) | ||||
0.339065 | + | 0.940763i | \(0.389889\pi\) | |||||||
\(998\) | 3.23553 | 0.102419 | ||||||||
\(999\) | −32.3307 | −1.02290 |
(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 | 4022.2.a.c.1.12 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.c.1.12 | ✓ | 31 | 1.1 | even | 1 | trivial |