Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.03703 | −0.733289 | −0.366645 | − | 0.930361i | \(-0.619493\pi\) | ||||
−0.366645 | + | 0.930361i | \(0.619493\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.924574 | −0.462287 | ||||||||
\(5\) | −1.10504 | −0.494188 | −0.247094 | − | 0.968992i | \(-0.579476\pi\) | ||||
−0.247094 | + | 0.968992i | \(0.579476\pi\) | |||||||
\(6\) | 1.03703 | 0.423365 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.03286 | 1.07228 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.14595 | 0.362382 | ||||||||
\(11\) | −3.63449 | −1.09584 | −0.547920 | − | 0.836531i | \(-0.684580\pi\) | ||||
−0.547920 | + | 0.836531i | \(0.684580\pi\) | |||||||
\(12\) | 0.924574 | 0.266901 | ||||||||
\(13\) | −3.11689 | −0.864468 | −0.432234 | − | 0.901761i | \(-0.642275\pi\) | ||||
−0.432234 | + | 0.901761i | \(0.642275\pi\) | |||||||
\(14\) | 1.03703 | 0.277157 | ||||||||
\(15\) | 1.10504 | 0.285319 | ||||||||
\(16\) | −1.29602 | −0.324004 | ||||||||
\(17\) | −0.947106 | −0.229707 | −0.114853 | − | 0.993382i | \(-0.536640\pi\) | ||||
−0.114853 | + | 0.993382i | \(0.536640\pi\) | |||||||
\(18\) | −1.03703 | −0.244430 | ||||||||
\(19\) | −5.88214 | −1.34946 | −0.674728 | − | 0.738067i | \(-0.735739\pi\) | ||||
−0.674728 | + | 0.738067i | \(0.735739\pi\) | |||||||
\(20\) | 1.02169 | 0.228457 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 3.76907 | 0.803568 | ||||||||
\(23\) | −4.48397 | −0.934972 | −0.467486 | − | 0.884000i | \(-0.654840\pi\) | ||||
−0.467486 | + | 0.884000i | \(0.654840\pi\) | |||||||
\(24\) | −3.03286 | −0.619081 | ||||||||
\(25\) | −3.77889 | −0.755779 | ||||||||
\(26\) | 3.23230 | 0.633905 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.924574 | 0.174728 | ||||||||
\(29\) | −0.208014 | −0.0386272 | −0.0193136 | − | 0.999813i | \(-0.506148\pi\) | ||||
−0.0193136 | + | 0.999813i | \(0.506148\pi\) | |||||||
\(30\) | −1.14595 | −0.209222 | ||||||||
\(31\) | −2.92063 | −0.524561 | −0.262281 | − | 0.964992i | \(-0.584475\pi\) | ||||
−0.262281 | + | 0.964992i | \(0.584475\pi\) | |||||||
\(32\) | −4.72172 | −0.834691 | ||||||||
\(33\) | 3.63449 | 0.632684 | ||||||||
\(34\) | 0.982175 | 0.168442 | ||||||||
\(35\) | 1.10504 | 0.186785 | ||||||||
\(36\) | −0.924574 | −0.154096 | ||||||||
\(37\) | 10.3878 | 1.70774 | 0.853870 | − | 0.520487i | \(-0.174249\pi\) | ||||
0.853870 | + | 0.520487i | \(0.174249\pi\) | |||||||
\(38\) | 6.09994 | 0.989541 | ||||||||
\(39\) | 3.11689 | 0.499101 | ||||||||
\(40\) | −3.35143 | −0.529907 | ||||||||
\(41\) | 4.40926 | 0.688610 | 0.344305 | − | 0.938858i | \(-0.388115\pi\) | ||||
0.344305 | + | 0.938858i | \(0.388115\pi\) | |||||||
\(42\) | −1.03703 | −0.160017 | ||||||||
\(43\) | −5.58070 | −0.851048 | −0.425524 | − | 0.904947i | \(-0.639910\pi\) | ||||
−0.425524 | + | 0.904947i | \(0.639910\pi\) | |||||||
\(44\) | 3.36036 | 0.506593 | ||||||||
\(45\) | −1.10504 | −0.164729 | ||||||||
\(46\) | 4.65000 | 0.685605 | ||||||||
\(47\) | −6.89665 | −1.00598 | −0.502990 | − | 0.864292i | \(-0.667767\pi\) | ||||
−0.502990 | + | 0.864292i | \(0.667767\pi\) | |||||||
\(48\) | 1.29602 | 0.187064 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.91882 | 0.554204 | ||||||||
\(51\) | 0.947106 | 0.132621 | ||||||||
\(52\) | 2.88179 | 0.399632 | ||||||||
\(53\) | 8.55990 | 1.17579 | 0.587896 | − | 0.808936i | \(-0.299956\pi\) | ||||
0.587896 | + | 0.808936i | \(0.299956\pi\) | |||||||
\(54\) | 1.03703 | 0.141122 | ||||||||
\(55\) | 4.01625 | 0.541551 | ||||||||
\(56\) | −3.03286 | −0.405283 | ||||||||
\(57\) | 5.88214 | 0.779109 | ||||||||
\(58\) | 0.215716 | 0.0283249 | ||||||||
\(59\) | −12.1039 | −1.57579 | −0.787895 | − | 0.615810i | \(-0.788829\pi\) | ||||
−0.787895 | + | 0.615810i | \(0.788829\pi\) | |||||||
\(60\) | −1.02169 | −0.131899 | ||||||||
\(61\) | −3.44450 | −0.441023 | −0.220512 | − | 0.975384i | \(-0.570773\pi\) | ||||
−0.220512 | + | 0.975384i | \(0.570773\pi\) | |||||||
\(62\) | 3.02878 | 0.384655 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 7.48859 | 0.936074 | ||||||||
\(65\) | 3.44427 | 0.427210 | ||||||||
\(66\) | −3.76907 | −0.463940 | ||||||||
\(67\) | −15.5558 | −1.90044 | −0.950220 | − | 0.311580i | \(-0.899142\pi\) | ||||
−0.950220 | + | 0.311580i | \(0.899142\pi\) | |||||||
\(68\) | 0.875670 | 0.106191 | ||||||||
\(69\) | 4.48397 | 0.539807 | ||||||||
\(70\) | −1.14595 | −0.136968 | ||||||||
\(71\) | −15.9734 | −1.89569 | −0.947844 | − | 0.318733i | \(-0.896743\pi\) | ||||
−0.947844 | + | 0.318733i | \(0.896743\pi\) | |||||||
\(72\) | 3.03286 | 0.357426 | ||||||||
\(73\) | −2.33818 | −0.273664 | −0.136832 | − | 0.990594i | \(-0.543692\pi\) | ||||
−0.136832 | + | 0.990594i | \(0.543692\pi\) | |||||||
\(74\) | −10.7724 | −1.25227 | ||||||||
\(75\) | 3.77889 | 0.436349 | ||||||||
\(76\) | 5.43847 | 0.623836 | ||||||||
\(77\) | 3.63449 | 0.414189 | ||||||||
\(78\) | −3.23230 | −0.365985 | ||||||||
\(79\) | −3.93588 | −0.442821 | −0.221410 | − | 0.975181i | \(-0.571066\pi\) | ||||
−0.221410 | + | 0.975181i | \(0.571066\pi\) | |||||||
\(80\) | 1.43215 | 0.160119 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.57252 | −0.504951 | ||||||||
\(83\) | −8.71714 | −0.956830 | −0.478415 | − | 0.878134i | \(-0.658789\pi\) | ||||
−0.478415 | + | 0.878134i | \(0.658789\pi\) | |||||||
\(84\) | −0.924574 | −0.100879 | ||||||||
\(85\) | 1.04659 | 0.113518 | ||||||||
\(86\) | 5.78733 | 0.624064 | ||||||||
\(87\) | 0.208014 | 0.0223014 | ||||||||
\(88\) | −11.0229 | −1.17505 | ||||||||
\(89\) | −4.31048 | −0.456910 | −0.228455 | − | 0.973554i | \(-0.573367\pi\) | ||||
−0.228455 | + | 0.973554i | \(0.573367\pi\) | |||||||
\(90\) | 1.14595 | 0.120794 | ||||||||
\(91\) | 3.11689 | 0.326738 | ||||||||
\(92\) | 4.14576 | 0.432226 | ||||||||
\(93\) | 2.92063 | 0.302856 | ||||||||
\(94\) | 7.15202 | 0.737674 | ||||||||
\(95\) | 6.49999 | 0.666884 | ||||||||
\(96\) | 4.72172 | 0.481909 | ||||||||
\(97\) | 1.19390 | 0.121222 | 0.0606111 | − | 0.998161i | \(-0.480695\pi\) | ||||
0.0606111 | + | 0.998161i | \(0.480695\pi\) | |||||||
\(98\) | −1.03703 | −0.104756 | ||||||||
\(99\) | −3.63449 | −0.365280 | ||||||||
\(100\) | 3.49387 | 0.349387 | ||||||||
\(101\) | −18.9910 | −1.88968 | −0.944838 | − | 0.327539i | \(-0.893781\pi\) | ||||
−0.944838 | + | 0.327539i | \(0.893781\pi\) | |||||||
\(102\) | −0.982175 | −0.0972498 | ||||||||
\(103\) | −2.36424 | −0.232955 | −0.116478 | − | 0.993193i | \(-0.537160\pi\) | ||||
−0.116478 | + | 0.993193i | \(0.537160\pi\) | |||||||
\(104\) | −9.45309 | −0.926952 | ||||||||
\(105\) | −1.10504 | −0.107841 | ||||||||
\(106\) | −8.87685 | −0.862196 | ||||||||
\(107\) | 3.22132 | 0.311417 | 0.155708 | − | 0.987803i | \(-0.450234\pi\) | ||||
0.155708 | + | 0.987803i | \(0.450234\pi\) | |||||||
\(108\) | 0.924574 | 0.0889672 | ||||||||
\(109\) | −0.529736 | −0.0507395 | −0.0253698 | − | 0.999678i | \(-0.508076\pi\) | ||||
−0.0253698 | + | 0.999678i | \(0.508076\pi\) | |||||||
\(110\) | −4.16496 | −0.397113 | ||||||||
\(111\) | −10.3878 | −0.985964 | ||||||||
\(112\) | 1.29602 | 0.122462 | ||||||||
\(113\) | 1.76974 | 0.166484 | 0.0832418 | − | 0.996529i | \(-0.473473\pi\) | ||||
0.0832418 | + | 0.996529i | \(0.473473\pi\) | |||||||
\(114\) | −6.09994 | −0.571312 | ||||||||
\(115\) | 4.95495 | 0.462052 | ||||||||
\(116\) | 0.192324 | 0.0178568 | ||||||||
\(117\) | −3.11689 | −0.288156 | ||||||||
\(118\) | 12.5520 | 1.15551 | ||||||||
\(119\) | 0.947106 | 0.0868211 | ||||||||
\(120\) | 3.35143 | 0.305942 | ||||||||
\(121\) | 2.20953 | 0.200867 | ||||||||
\(122\) | 3.57204 | 0.323398 | ||||||||
\(123\) | −4.40926 | −0.397569 | ||||||||
\(124\) | 2.70034 | 0.242498 | ||||||||
\(125\) | 9.70100 | 0.867684 | ||||||||
\(126\) | 1.03703 | 0.0923858 | ||||||||
\(127\) | −1.32367 | −0.117456 | −0.0587282 | − | 0.998274i | \(-0.518705\pi\) | ||||
−0.0587282 | + | 0.998274i | \(0.518705\pi\) | |||||||
\(128\) | 1.67758 | 0.148278 | ||||||||
\(129\) | 5.58070 | 0.491353 | ||||||||
\(130\) | −3.57181 | −0.313268 | ||||||||
\(131\) | −0.795161 | −0.0694735 | −0.0347368 | − | 0.999396i | \(-0.511059\pi\) | ||||
−0.0347368 | + | 0.999396i | \(0.511059\pi\) | |||||||
\(132\) | −3.36036 | −0.292481 | ||||||||
\(133\) | 5.88214 | 0.510046 | ||||||||
\(134\) | 16.1318 | 1.39357 | ||||||||
\(135\) | 1.10504 | 0.0951065 | ||||||||
\(136\) | −2.87244 | −0.246310 | ||||||||
\(137\) | −15.2335 | −1.30148 | −0.650742 | − | 0.759299i | \(-0.725542\pi\) | ||||
−0.650742 | + | 0.759299i | \(0.725542\pi\) | |||||||
\(138\) | −4.65000 | −0.395834 | ||||||||
\(139\) | 18.7326 | 1.58888 | 0.794441 | − | 0.607342i | \(-0.207764\pi\) | ||||
0.794441 | + | 0.607342i | \(0.207764\pi\) | |||||||
\(140\) | −1.02169 | −0.0863484 | ||||||||
\(141\) | 6.89665 | 0.580803 | ||||||||
\(142\) | 16.5648 | 1.39009 | ||||||||
\(143\) | 11.3283 | 0.947320 | ||||||||
\(144\) | −1.29602 | −0.108001 | ||||||||
\(145\) | 0.229863 | 0.0190891 | ||||||||
\(146\) | 2.42476 | 0.200675 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −9.60427 | −0.789466 | ||||||||
\(149\) | 5.93727 | 0.486400 | 0.243200 | − | 0.969976i | \(-0.421803\pi\) | ||||
0.243200 | + | 0.969976i | \(0.421803\pi\) | |||||||
\(150\) | −3.91882 | −0.319970 | ||||||||
\(151\) | −7.85858 | −0.639522 | −0.319761 | − | 0.947498i | \(-0.603603\pi\) | ||||
−0.319761 | + | 0.947498i | \(0.603603\pi\) | |||||||
\(152\) | −17.8397 | −1.44699 | ||||||||
\(153\) | −0.947106 | −0.0765690 | ||||||||
\(154\) | −3.76907 | −0.303720 | ||||||||
\(155\) | 3.22741 | 0.259232 | ||||||||
\(156\) | −2.88179 | −0.230728 | ||||||||
\(157\) | 6.21046 | 0.495649 | 0.247824 | − | 0.968805i | \(-0.420284\pi\) | ||||
0.247824 | + | 0.968805i | \(0.420284\pi\) | |||||||
\(158\) | 4.08161 | 0.324716 | ||||||||
\(159\) | −8.55990 | −0.678844 | ||||||||
\(160\) | 5.21768 | 0.412494 | ||||||||
\(161\) | 4.48397 | 0.353386 | ||||||||
\(162\) | −1.03703 | −0.0814766 | ||||||||
\(163\) | 19.4849 | 1.52618 | 0.763089 | − | 0.646293i | \(-0.223682\pi\) | ||||
0.763089 | + | 0.646293i | \(0.223682\pi\) | |||||||
\(164\) | −4.07668 | −0.318336 | ||||||||
\(165\) | −4.01625 | −0.312665 | ||||||||
\(166\) | 9.03991 | 0.701633 | ||||||||
\(167\) | 1.48211 | 0.114689 | 0.0573445 | − | 0.998354i | \(-0.481737\pi\) | ||||
0.0573445 | + | 0.998354i | \(0.481737\pi\) | |||||||
\(168\) | 3.03286 | 0.233991 | ||||||||
\(169\) | −3.28503 | −0.252694 | ||||||||
\(170\) | −1.08534 | −0.0832418 | ||||||||
\(171\) | −5.88214 | −0.449819 | ||||||||
\(172\) | 5.15977 | 0.393428 | ||||||||
\(173\) | −11.0374 | −0.839159 | −0.419579 | − | 0.907719i | \(-0.637822\pi\) | ||||
−0.419579 | + | 0.907719i | \(0.637822\pi\) | |||||||
\(174\) | −0.215716 | −0.0163534 | ||||||||
\(175\) | 3.77889 | 0.285657 | ||||||||
\(176\) | 4.71036 | 0.355057 | ||||||||
\(177\) | 12.1039 | 0.909783 | ||||||||
\(178\) | 4.47009 | 0.335047 | ||||||||
\(179\) | 21.9314 | 1.63923 | 0.819615 | − | 0.572914i | \(-0.194187\pi\) | ||||
0.819615 | + | 0.572914i | \(0.194187\pi\) | |||||||
\(180\) | 1.02169 | 0.0761522 | ||||||||
\(181\) | 3.88994 | 0.289137 | 0.144568 | − | 0.989495i | \(-0.453821\pi\) | ||||
0.144568 | + | 0.989495i | \(0.453821\pi\) | |||||||
\(182\) | −3.23230 | −0.239594 | ||||||||
\(183\) | 3.44450 | 0.254625 | ||||||||
\(184\) | −13.5993 | −1.00255 | ||||||||
\(185\) | −11.4789 | −0.843944 | ||||||||
\(186\) | −3.02878 | −0.222081 | ||||||||
\(187\) | 3.44225 | 0.251722 | ||||||||
\(188\) | 6.37646 | 0.465051 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −6.74066 | −0.489019 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | −7.48859 | −0.540442 | ||||||||
\(193\) | 16.6386 | 1.19767 | 0.598835 | − | 0.800872i | \(-0.295630\pi\) | ||||
0.598835 | + | 0.800872i | \(0.295630\pi\) | |||||||
\(194\) | −1.23811 | −0.0888909 | ||||||||
\(195\) | −3.44427 | −0.246650 | ||||||||
\(196\) | −0.924574 | −0.0660410 | ||||||||
\(197\) | −16.6427 | −1.18574 | −0.592870 | − | 0.805298i | \(-0.702005\pi\) | ||||
−0.592870 | + | 0.805298i | \(0.702005\pi\) | |||||||
\(198\) | 3.76907 | 0.267856 | ||||||||
\(199\) | −17.0296 | −1.20720 | −0.603599 | − | 0.797288i | \(-0.706267\pi\) | ||||
−0.603599 | + | 0.797288i | \(0.706267\pi\) | |||||||
\(200\) | −11.4609 | −0.810406 | ||||||||
\(201\) | 15.5558 | 1.09722 | ||||||||
\(202\) | 19.6942 | 1.38568 | ||||||||
\(203\) | 0.208014 | 0.0145997 | ||||||||
\(204\) | −0.875670 | −0.0613091 | ||||||||
\(205\) | −4.87239 | −0.340303 | ||||||||
\(206\) | 2.45178 | 0.170824 | ||||||||
\(207\) | −4.48397 | −0.311657 | ||||||||
\(208\) | 4.03953 | 0.280091 | ||||||||
\(209\) | 21.3786 | 1.47879 | ||||||||
\(210\) | 1.14595 | 0.0790783 | ||||||||
\(211\) | 21.3817 | 1.47197 | 0.735987 | − | 0.676996i | \(-0.236718\pi\) | ||||
0.735987 | + | 0.676996i | \(0.236718\pi\) | |||||||
\(212\) | −7.91426 | −0.543554 | ||||||||
\(213\) | 15.9734 | 1.09448 | ||||||||
\(214\) | −3.34060 | −0.228359 | ||||||||
\(215\) | 6.16688 | 0.420577 | ||||||||
\(216\) | −3.03286 | −0.206360 | ||||||||
\(217\) | 2.92063 | 0.198266 | ||||||||
\(218\) | 0.549351 | 0.0372067 | ||||||||
\(219\) | 2.33818 | 0.158000 | ||||||||
\(220\) | −3.71332 | −0.250352 | ||||||||
\(221\) | 2.95202 | 0.198574 | ||||||||
\(222\) | 10.7724 | 0.722997 | ||||||||
\(223\) | −5.93620 | −0.397517 | −0.198759 | − | 0.980048i | \(-0.563691\pi\) | ||||
−0.198759 | + | 0.980048i | \(0.563691\pi\) | |||||||
\(224\) | 4.72172 | 0.315483 | ||||||||
\(225\) | −3.77889 | −0.251926 | ||||||||
\(226\) | −1.83527 | −0.122081 | ||||||||
\(227\) | 7.49099 | 0.497195 | 0.248597 | − | 0.968607i | \(-0.420030\pi\) | ||||
0.248597 | + | 0.968607i | \(0.420030\pi\) | |||||||
\(228\) | −5.43847 | −0.360172 | ||||||||
\(229\) | 29.2528 | 1.93308 | 0.966540 | − | 0.256515i | \(-0.0825745\pi\) | ||||
0.966540 | + | 0.256515i | \(0.0825745\pi\) | |||||||
\(230\) | −5.13842 | −0.338818 | ||||||||
\(231\) | −3.63449 | −0.239132 | ||||||||
\(232\) | −0.630878 | −0.0414191 | ||||||||
\(233\) | −11.1443 | −0.730084 | −0.365042 | − | 0.930991i | \(-0.618945\pi\) | ||||
−0.365042 | + | 0.930991i | \(0.618945\pi\) | |||||||
\(234\) | 3.23230 | 0.211302 | ||||||||
\(235\) | 7.62106 | 0.497143 | ||||||||
\(236\) | 11.1909 | 0.728467 | ||||||||
\(237\) | 3.93588 | 0.255663 | ||||||||
\(238\) | −0.982175 | −0.0636650 | ||||||||
\(239\) | 28.7312 | 1.85847 | 0.929235 | − | 0.369490i | \(-0.120468\pi\) | ||||
0.929235 | + | 0.369490i | \(0.120468\pi\) | |||||||
\(240\) | −1.43215 | −0.0924446 | ||||||||
\(241\) | 20.8421 | 1.34255 | 0.671277 | − | 0.741206i | \(-0.265746\pi\) | ||||
0.671277 | + | 0.741206i | \(0.265746\pi\) | |||||||
\(242\) | −2.29135 | −0.147293 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.18470 | 0.203879 | ||||||||
\(245\) | −1.10504 | −0.0705982 | ||||||||
\(246\) | 4.57252 | 0.291533 | ||||||||
\(247\) | 18.3340 | 1.16656 | ||||||||
\(248\) | −8.85789 | −0.562476 | ||||||||
\(249\) | 8.71714 | 0.552426 | ||||||||
\(250\) | −10.0602 | −0.636263 | ||||||||
\(251\) | −1.85083 | −0.116823 | −0.0584116 | − | 0.998293i | \(-0.518604\pi\) | ||||
−0.0584116 | + | 0.998293i | \(0.518604\pi\) | |||||||
\(252\) | 0.924574 | 0.0582427 | ||||||||
\(253\) | 16.2970 | 1.02458 | ||||||||
\(254\) | 1.37268 | 0.0861295 | ||||||||
\(255\) | −1.04659 | −0.0655399 | ||||||||
\(256\) | −16.7169 | −1.04480 | ||||||||
\(257\) | −27.7137 | −1.72873 | −0.864366 | − | 0.502864i | \(-0.832280\pi\) | ||||
−0.864366 | + | 0.502864i | \(0.832280\pi\) | |||||||
\(258\) | −5.78733 | −0.360304 | ||||||||
\(259\) | −10.3878 | −0.645465 | ||||||||
\(260\) | −3.18449 | −0.197493 | ||||||||
\(261\) | −0.208014 | −0.0128757 | ||||||||
\(262\) | 0.824604 | 0.0509442 | ||||||||
\(263\) | 12.8633 | 0.793186 | 0.396593 | − | 0.917995i | \(-0.370192\pi\) | ||||
0.396593 | + | 0.917995i | \(0.370192\pi\) | |||||||
\(264\) | 11.0229 | 0.678414 | ||||||||
\(265\) | −9.45901 | −0.581062 | ||||||||
\(266\) | −6.09994 | −0.374011 | ||||||||
\(267\) | 4.31048 | 0.263797 | ||||||||
\(268\) | 14.3825 | 0.878549 | ||||||||
\(269\) | −25.0295 | −1.52607 | −0.763037 | − | 0.646355i | \(-0.776292\pi\) | ||||
−0.763037 | + | 0.646355i | \(0.776292\pi\) | |||||||
\(270\) | −1.14595 | −0.0697405 | ||||||||
\(271\) | 21.1717 | 1.28609 | 0.643045 | − | 0.765829i | \(-0.277671\pi\) | ||||
0.643045 | + | 0.765829i | \(0.277671\pi\) | |||||||
\(272\) | 1.22746 | 0.0744259 | ||||||||
\(273\) | −3.11689 | −0.188642 | ||||||||
\(274\) | 15.7975 | 0.954364 | ||||||||
\(275\) | 13.7344 | 0.828213 | ||||||||
\(276\) | −4.14576 | −0.249546 | ||||||||
\(277\) | −8.31613 | −0.499668 | −0.249834 | − | 0.968289i | \(-0.580376\pi\) | ||||
−0.249834 | + | 0.968289i | \(0.580376\pi\) | |||||||
\(278\) | −19.4263 | −1.16511 | ||||||||
\(279\) | −2.92063 | −0.174854 | ||||||||
\(280\) | 3.35143 | 0.200286 | ||||||||
\(281\) | 7.02617 | 0.419146 | 0.209573 | − | 0.977793i | \(-0.432793\pi\) | ||||
0.209573 | + | 0.977793i | \(0.432793\pi\) | |||||||
\(282\) | −7.15202 | −0.425896 | ||||||||
\(283\) | −12.8768 | −0.765445 | −0.382722 | − | 0.923863i | \(-0.625013\pi\) | ||||
−0.382722 | + | 0.923863i | \(0.625013\pi\) | |||||||
\(284\) | 14.7686 | 0.876352 | ||||||||
\(285\) | −6.49999 | −0.385026 | ||||||||
\(286\) | −11.7478 | −0.694659 | ||||||||
\(287\) | −4.40926 | −0.260270 | ||||||||
\(288\) | −4.72172 | −0.278230 | ||||||||
\(289\) | −16.1030 | −0.947235 | ||||||||
\(290\) | −0.238374 | −0.0139978 | ||||||||
\(291\) | −1.19390 | −0.0699877 | ||||||||
\(292\) | 2.16182 | 0.126511 | ||||||||
\(293\) | −1.60819 | −0.0939513 | −0.0469757 | − | 0.998896i | \(-0.514958\pi\) | ||||
−0.0469757 | + | 0.998896i | \(0.514958\pi\) | |||||||
\(294\) | 1.03703 | 0.0604807 | ||||||||
\(295\) | 13.3752 | 0.778736 | ||||||||
\(296\) | 31.5047 | 1.83117 | ||||||||
\(297\) | 3.63449 | 0.210895 | ||||||||
\(298\) | −6.15711 | −0.356672 | ||||||||
\(299\) | 13.9760 | 0.808254 | ||||||||
\(300\) | −3.49387 | −0.201718 | ||||||||
\(301\) | 5.58070 | 0.321666 | ||||||||
\(302\) | 8.14956 | 0.468955 | ||||||||
\(303\) | 18.9910 | 1.09100 | ||||||||
\(304\) | 7.62335 | 0.437229 | ||||||||
\(305\) | 3.80630 | 0.217948 | ||||||||
\(306\) | 0.982175 | 0.0561472 | ||||||||
\(307\) | 13.6333 | 0.778091 | 0.389045 | − | 0.921219i | \(-0.372805\pi\) | ||||
0.389045 | + | 0.921219i | \(0.372805\pi\) | |||||||
\(308\) | −3.36036 | −0.191474 | ||||||||
\(309\) | 2.36424 | 0.134497 | ||||||||
\(310\) | −3.34691 | −0.190092 | ||||||||
\(311\) | −21.1376 | −1.19861 | −0.599303 | − | 0.800522i | \(-0.704555\pi\) | ||||
−0.599303 | + | 0.800522i | \(0.704555\pi\) | |||||||
\(312\) | 9.45309 | 0.535176 | ||||||||
\(313\) | 21.6650 | 1.22458 | 0.612290 | − | 0.790633i | \(-0.290249\pi\) | ||||
0.612290 | + | 0.790633i | \(0.290249\pi\) | |||||||
\(314\) | −6.44042 | −0.363454 | ||||||||
\(315\) | 1.10504 | 0.0622618 | ||||||||
\(316\) | 3.63901 | 0.204710 | ||||||||
\(317\) | −4.02993 | −0.226343 | −0.113172 | − | 0.993575i | \(-0.536101\pi\) | ||||
−0.113172 | + | 0.993575i | \(0.536101\pi\) | |||||||
\(318\) | 8.87685 | 0.497789 | ||||||||
\(319\) | 0.756025 | 0.0423292 | ||||||||
\(320\) | −8.27517 | −0.462596 | ||||||||
\(321\) | −3.22132 | −0.179797 | ||||||||
\(322\) | −4.65000 | −0.259134 | ||||||||
\(323\) | 5.57101 | 0.309979 | ||||||||
\(324\) | −0.924574 | −0.0513652 | ||||||||
\(325\) | 11.7784 | 0.653347 | ||||||||
\(326\) | −20.2064 | −1.11913 | ||||||||
\(327\) | 0.529736 | 0.0292945 | ||||||||
\(328\) | 13.3727 | 0.738383 | ||||||||
\(329\) | 6.89665 | 0.380225 | ||||||||
\(330\) | 4.16496 | 0.229274 | ||||||||
\(331\) | 32.3774 | 1.77962 | 0.889810 | − | 0.456330i | \(-0.150836\pi\) | ||||
0.889810 | + | 0.456330i | \(0.150836\pi\) | |||||||
\(332\) | 8.05964 | 0.442330 | ||||||||
\(333\) | 10.3878 | 0.569247 | ||||||||
\(334\) | −1.53699 | −0.0841002 | ||||||||
\(335\) | 17.1897 | 0.939174 | ||||||||
\(336\) | −1.29602 | −0.0707034 | ||||||||
\(337\) | 6.16555 | 0.335859 | 0.167930 | − | 0.985799i | \(-0.446292\pi\) | ||||
0.167930 | + | 0.985799i | \(0.446292\pi\) | |||||||
\(338\) | 3.40666 | 0.185298 | ||||||||
\(339\) | −1.76974 | −0.0961193 | ||||||||
\(340\) | −0.967648 | −0.0524781 | ||||||||
\(341\) | 10.6150 | 0.574836 | ||||||||
\(342\) | 6.09994 | 0.329847 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −16.9255 | −0.912561 | ||||||||
\(345\) | −4.95495 | −0.266766 | ||||||||
\(346\) | 11.4461 | 0.615346 | ||||||||
\(347\) | 11.9209 | 0.639949 | 0.319975 | − | 0.947426i | \(-0.396326\pi\) | ||||
0.319975 | + | 0.947426i | \(0.396326\pi\) | |||||||
\(348\) | −0.192324 | −0.0103097 | ||||||||
\(349\) | −19.5567 | −1.04684 | −0.523422 | − | 0.852073i | \(-0.675345\pi\) | ||||
−0.523422 | + | 0.852073i | \(0.675345\pi\) | |||||||
\(350\) | −3.91882 | −0.209470 | ||||||||
\(351\) | 3.11689 | 0.166367 | ||||||||
\(352\) | 17.1611 | 0.914688 | ||||||||
\(353\) | 10.6088 | 0.564651 | 0.282326 | − | 0.959319i | \(-0.408894\pi\) | ||||
0.282326 | + | 0.959319i | \(0.408894\pi\) | |||||||
\(354\) | −12.5520 | −0.667134 | ||||||||
\(355\) | 17.6512 | 0.936826 | ||||||||
\(356\) | 3.98536 | 0.211224 | ||||||||
\(357\) | −0.947106 | −0.0501262 | ||||||||
\(358\) | −22.7435 | −1.20203 | ||||||||
\(359\) | −17.3249 | −0.914374 | −0.457187 | − | 0.889371i | \(-0.651143\pi\) | ||||
−0.457187 | + | 0.889371i | \(0.651143\pi\) | |||||||
\(360\) | −3.35143 | −0.176636 | ||||||||
\(361\) | 15.5996 | 0.821031 | ||||||||
\(362\) | −4.03397 | −0.212021 | ||||||||
\(363\) | −2.20953 | −0.115970 | ||||||||
\(364\) | −2.88179 | −0.151047 | ||||||||
\(365\) | 2.58378 | 0.135241 | ||||||||
\(366\) | −3.57204 | −0.186714 | ||||||||
\(367\) | −16.3946 | −0.855790 | −0.427895 | − | 0.903828i | \(-0.640745\pi\) | ||||
−0.427895 | + | 0.903828i | \(0.640745\pi\) | |||||||
\(368\) | 5.81129 | 0.302935 | ||||||||
\(369\) | 4.40926 | 0.229537 | ||||||||
\(370\) | 11.9039 | 0.618855 | ||||||||
\(371\) | −8.55990 | −0.444408 | ||||||||
\(372\) | −2.70034 | −0.140006 | ||||||||
\(373\) | −14.8397 | −0.768371 | −0.384185 | − | 0.923256i | \(-0.625518\pi\) | ||||
−0.384185 | + | 0.923256i | \(0.625518\pi\) | |||||||
\(374\) | −3.56971 | −0.184585 | ||||||||
\(375\) | −9.70100 | −0.500958 | ||||||||
\(376\) | −20.9166 | −1.07869 | ||||||||
\(377\) | 0.648355 | 0.0333920 | ||||||||
\(378\) | −1.03703 | −0.0533389 | ||||||||
\(379\) | 4.27019 | 0.219345 | 0.109672 | − | 0.993968i | \(-0.465020\pi\) | ||||
0.109672 | + | 0.993968i | \(0.465020\pi\) | |||||||
\(380\) | −6.00972 | −0.308292 | ||||||||
\(381\) | 1.32367 | 0.0678135 | ||||||||
\(382\) | −1.03703 | −0.0530589 | ||||||||
\(383\) | −3.24085 | −0.165600 | −0.0827999 | − | 0.996566i | \(-0.526386\pi\) | ||||
−0.0827999 | + | 0.996566i | \(0.526386\pi\) | |||||||
\(384\) | −1.67758 | −0.0856084 | ||||||||
\(385\) | −4.01625 | −0.204687 | ||||||||
\(386\) | −17.2547 | −0.878239 | ||||||||
\(387\) | −5.58070 | −0.283683 | ||||||||
\(388\) | −1.10385 | −0.0560394 | ||||||||
\(389\) | 6.13044 | 0.310825 | 0.155413 | − | 0.987850i | \(-0.450329\pi\) | ||||
0.155413 | + | 0.987850i | \(0.450329\pi\) | |||||||
\(390\) | 3.57181 | 0.180866 | ||||||||
\(391\) | 4.24680 | 0.214770 | ||||||||
\(392\) | 3.03286 | 0.153183 | ||||||||
\(393\) | 0.795161 | 0.0401106 | ||||||||
\(394\) | 17.2589 | 0.869490 | ||||||||
\(395\) | 4.34929 | 0.218837 | ||||||||
\(396\) | 3.36036 | 0.168864 | ||||||||
\(397\) | 15.5375 | 0.779803 | 0.389901 | − | 0.920857i | \(-0.372509\pi\) | ||||
0.389901 | + | 0.920857i | \(0.372509\pi\) | |||||||
\(398\) | 17.6602 | 0.885226 | ||||||||
\(399\) | −5.88214 | −0.294475 | ||||||||
\(400\) | 4.89750 | 0.244875 | ||||||||
\(401\) | −18.2847 | −0.913096 | −0.456548 | − | 0.889699i | \(-0.650914\pi\) | ||||
−0.456548 | + | 0.889699i | \(0.650914\pi\) | |||||||
\(402\) | −16.1318 | −0.804579 | ||||||||
\(403\) | 9.10328 | 0.453467 | ||||||||
\(404\) | 17.5586 | 0.873572 | ||||||||
\(405\) | −1.10504 | −0.0549097 | ||||||||
\(406\) | −0.215716 | −0.0107058 | ||||||||
\(407\) | −37.7543 | −1.87141 | ||||||||
\(408\) | 2.87244 | 0.142207 | ||||||||
\(409\) | −12.4054 | −0.613408 | −0.306704 | − | 0.951805i | \(-0.599226\pi\) | ||||
−0.306704 | + | 0.951805i | \(0.599226\pi\) | |||||||
\(410\) | 5.05281 | 0.249540 | ||||||||
\(411\) | 15.2335 | 0.751412 | ||||||||
\(412\) | 2.18591 | 0.107692 | ||||||||
\(413\) | 12.1039 | 0.595593 | ||||||||
\(414\) | 4.65000 | 0.228535 | ||||||||
\(415\) | 9.63276 | 0.472854 | ||||||||
\(416\) | 14.7171 | 0.721564 | ||||||||
\(417\) | −18.7326 | −0.917341 | ||||||||
\(418\) | −22.1702 | −1.08438 | ||||||||
\(419\) | −23.4003 | −1.14318 | −0.571589 | − | 0.820540i | \(-0.693673\pi\) | ||||
−0.571589 | + | 0.820540i | \(0.693673\pi\) | |||||||
\(420\) | 1.02169 | 0.0498533 | ||||||||
\(421\) | −28.1342 | −1.37118 | −0.685589 | − | 0.727989i | \(-0.740455\pi\) | ||||
−0.685589 | + | 0.727989i | \(0.740455\pi\) | |||||||
\(422\) | −22.1734 | −1.07938 | ||||||||
\(423\) | −6.89665 | −0.335327 | ||||||||
\(424\) | 25.9610 | 1.26078 | ||||||||
\(425\) | 3.57901 | 0.173608 | ||||||||
\(426\) | −16.5648 | −0.802568 | ||||||||
\(427\) | 3.44450 | 0.166691 | ||||||||
\(428\) | −2.97835 | −0.143964 | ||||||||
\(429\) | −11.3283 | −0.546935 | ||||||||
\(430\) | −6.39522 | −0.308405 | ||||||||
\(431\) | −15.9764 | −0.769556 | −0.384778 | − | 0.923009i | \(-0.625722\pi\) | ||||
−0.384778 | + | 0.923009i | \(0.625722\pi\) | |||||||
\(432\) | 1.29602 | 0.0623546 | ||||||||
\(433\) | 6.10886 | 0.293573 | 0.146786 | − | 0.989168i | \(-0.453107\pi\) | ||||
0.146786 | + | 0.989168i | \(0.453107\pi\) | |||||||
\(434\) | −3.02878 | −0.145386 | ||||||||
\(435\) | −0.229863 | −0.0110211 | ||||||||
\(436\) | 0.489780 | 0.0234562 | ||||||||
\(437\) | 26.3753 | 1.26170 | ||||||||
\(438\) | −2.42476 | −0.115860 | ||||||||
\(439\) | −27.1465 | −1.29563 | −0.647815 | − | 0.761798i | \(-0.724317\pi\) | ||||
−0.647815 | + | 0.761798i | \(0.724317\pi\) | |||||||
\(440\) | 12.1807 | 0.580694 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −3.06133 | −0.145612 | ||||||||
\(443\) | −0.710893 | −0.0337755 | −0.0168878 | − | 0.999857i | \(-0.505376\pi\) | ||||
−0.0168878 | + | 0.999857i | \(0.505376\pi\) | |||||||
\(444\) | 9.60427 | 0.455798 | ||||||||
\(445\) | 4.76325 | 0.225800 | ||||||||
\(446\) | 6.15600 | 0.291495 | ||||||||
\(447\) | −5.93727 | −0.280823 | ||||||||
\(448\) | −7.48859 | −0.353803 | ||||||||
\(449\) | 8.87985 | 0.419066 | 0.209533 | − | 0.977802i | \(-0.432806\pi\) | ||||
0.209533 | + | 0.977802i | \(0.432806\pi\) | |||||||
\(450\) | 3.91882 | 0.184735 | ||||||||
\(451\) | −16.0254 | −0.754607 | ||||||||
\(452\) | −1.63626 | −0.0769632 | ||||||||
\(453\) | 7.85858 | 0.369228 | ||||||||
\(454\) | −7.76836 | −0.364587 | ||||||||
\(455\) | −3.44427 | −0.161470 | ||||||||
\(456\) | 17.8397 | 0.835422 | ||||||||
\(457\) | 12.0478 | 0.563571 | 0.281785 | − | 0.959477i | \(-0.409073\pi\) | ||||
0.281785 | + | 0.959477i | \(0.409073\pi\) | |||||||
\(458\) | −30.3360 | −1.41751 | ||||||||
\(459\) | 0.947106 | 0.0442071 | ||||||||
\(460\) | −4.58122 | −0.213601 | ||||||||
\(461\) | 26.5290 | 1.23558 | 0.617790 | − | 0.786343i | \(-0.288028\pi\) | ||||
0.617790 | + | 0.786343i | \(0.288028\pi\) | |||||||
\(462\) | 3.76907 | 0.175353 | ||||||||
\(463\) | 16.2694 | 0.756102 | 0.378051 | − | 0.925785i | \(-0.376594\pi\) | ||||
0.378051 | + | 0.925785i | \(0.376594\pi\) | |||||||
\(464\) | 0.269589 | 0.0125154 | ||||||||
\(465\) | −3.22741 | −0.149668 | ||||||||
\(466\) | 11.5569 | 0.535363 | ||||||||
\(467\) | −11.6417 | −0.538713 | −0.269356 | − | 0.963041i | \(-0.586811\pi\) | ||||
−0.269356 | + | 0.963041i | \(0.586811\pi\) | |||||||
\(468\) | 2.88179 | 0.133211 | ||||||||
\(469\) | 15.5558 | 0.718299 | ||||||||
\(470\) | −7.90325 | −0.364550 | ||||||||
\(471\) | −6.21046 | −0.286163 | ||||||||
\(472\) | −36.7094 | −1.68969 | ||||||||
\(473\) | 20.2830 | 0.932613 | ||||||||
\(474\) | −4.08161 | −0.187475 | ||||||||
\(475\) | 22.2280 | 1.01989 | ||||||||
\(476\) | −0.875670 | −0.0401363 | ||||||||
\(477\) | 8.55990 | 0.391931 | ||||||||
\(478\) | −29.7951 | −1.36280 | ||||||||
\(479\) | −13.9042 | −0.635298 | −0.317649 | − | 0.948208i | \(-0.602893\pi\) | ||||
−0.317649 | + | 0.948208i | \(0.602893\pi\) | |||||||
\(480\) | −5.21768 | −0.238153 | ||||||||
\(481\) | −32.3775 | −1.47629 | ||||||||
\(482\) | −21.6138 | −0.984481 | ||||||||
\(483\) | −4.48397 | −0.204028 | ||||||||
\(484\) | −2.04288 | −0.0928580 | ||||||||
\(485\) | −1.31930 | −0.0599065 | ||||||||
\(486\) | 1.03703 | 0.0470405 | ||||||||
\(487\) | 20.0714 | 0.909521 | 0.454760 | − | 0.890614i | \(-0.349725\pi\) | ||||
0.454760 | + | 0.890614i | \(0.349725\pi\) | |||||||
\(488\) | −10.4467 | −0.472900 | ||||||||
\(489\) | −19.4849 | −0.881139 | ||||||||
\(490\) | 1.14595 | 0.0517689 | ||||||||
\(491\) | −25.7718 | −1.16306 | −0.581532 | − | 0.813524i | \(-0.697546\pi\) | ||||
−0.581532 | + | 0.813524i | \(0.697546\pi\) | |||||||
\(492\) | 4.07668 | 0.183791 | ||||||||
\(493\) | 0.197011 | 0.00887294 | ||||||||
\(494\) | −19.0128 | −0.855427 | ||||||||
\(495\) | 4.01625 | 0.180517 | ||||||||
\(496\) | 3.78519 | 0.169960 | ||||||||
\(497\) | 15.9734 | 0.716503 | ||||||||
\(498\) | −9.03991 | −0.405088 | ||||||||
\(499\) | −10.1009 | −0.452179 | −0.226089 | − | 0.974107i | \(-0.572594\pi\) | ||||
−0.226089 | + | 0.974107i | \(0.572594\pi\) | |||||||
\(500\) | −8.96929 | −0.401119 | ||||||||
\(501\) | −1.48211 | −0.0662157 | ||||||||
\(502\) | 1.91936 | 0.0856652 | ||||||||
\(503\) | −36.5060 | −1.62772 | −0.813861 | − | 0.581060i | \(-0.802638\pi\) | ||||
−0.813861 | + | 0.581060i | \(0.802638\pi\) | |||||||
\(504\) | −3.03286 | −0.135094 | ||||||||
\(505\) | 20.9858 | 0.933854 | ||||||||
\(506\) | −16.9004 | −0.751314 | ||||||||
\(507\) | 3.28503 | 0.145893 | ||||||||
\(508\) | 1.22383 | 0.0542986 | ||||||||
\(509\) | 27.7174 | 1.22855 | 0.614275 | − | 0.789092i | \(-0.289448\pi\) | ||||
0.614275 | + | 0.789092i | \(0.289448\pi\) | |||||||
\(510\) | 1.08534 | 0.0480597 | ||||||||
\(511\) | 2.33818 | 0.103435 | ||||||||
\(512\) | 13.9807 | 0.617866 | ||||||||
\(513\) | 5.88214 | 0.259703 | ||||||||
\(514\) | 28.7398 | 1.26766 | ||||||||
\(515\) | 2.61257 | 0.115124 | ||||||||
\(516\) | −5.15977 | −0.227146 | ||||||||
\(517\) | 25.0658 | 1.10239 | ||||||||
\(518\) | 10.7724 | 0.473312 | ||||||||
\(519\) | 11.0374 | 0.484489 | ||||||||
\(520\) | 10.4460 | 0.458088 | ||||||||
\(521\) | 32.4414 | 1.42128 | 0.710641 | − | 0.703554i | \(-0.248405\pi\) | ||||
0.710641 | + | 0.703554i | \(0.248405\pi\) | |||||||
\(522\) | 0.215716 | 0.00944164 | ||||||||
\(523\) | 8.70652 | 0.380709 | 0.190355 | − | 0.981715i | \(-0.439036\pi\) | ||||
0.190355 | + | 0.981715i | \(0.439036\pi\) | |||||||
\(524\) | 0.735185 | 0.0321167 | ||||||||
\(525\) | −3.77889 | −0.164924 | ||||||||
\(526\) | −13.3396 | −0.581635 | ||||||||
\(527\) | 2.76615 | 0.120495 | ||||||||
\(528\) | −4.71036 | −0.204992 | ||||||||
\(529\) | −2.89401 | −0.125827 | ||||||||
\(530\) | 9.80925 | 0.426087 | ||||||||
\(531\) | −12.1039 | −0.525263 | ||||||||
\(532\) | −5.43847 | −0.235788 | ||||||||
\(533\) | −13.7432 | −0.595282 | ||||||||
\(534\) | −4.47009 | −0.193440 | ||||||||
\(535\) | −3.55968 | −0.153898 | ||||||||
\(536\) | −47.1785 | −2.03780 | ||||||||
\(537\) | −21.9314 | −0.946410 | ||||||||
\(538\) | 25.9562 | 1.11905 | ||||||||
\(539\) | −3.63449 | −0.156549 | ||||||||
\(540\) | −1.02169 | −0.0439665 | ||||||||
\(541\) | 27.5515 | 1.18453 | 0.592265 | − | 0.805743i | \(-0.298234\pi\) | ||||
0.592265 | + | 0.805743i | \(0.298234\pi\) | |||||||
\(542\) | −21.9556 | −0.943075 | ||||||||
\(543\) | −3.88994 | −0.166933 | ||||||||
\(544\) | 4.47197 | 0.191734 | ||||||||
\(545\) | 0.585378 | 0.0250748 | ||||||||
\(546\) | 3.23230 | 0.138329 | ||||||||
\(547\) | 26.9337 | 1.15160 | 0.575801 | − | 0.817590i | \(-0.304690\pi\) | ||||
0.575801 | + | 0.817590i | \(0.304690\pi\) | |||||||
\(548\) | 14.0845 | 0.601659 | ||||||||
\(549\) | −3.44450 | −0.147008 | ||||||||
\(550\) | −14.2429 | −0.607319 | ||||||||
\(551\) | 1.22357 | 0.0521257 | ||||||||
\(552\) | 13.5993 | 0.578823 | ||||||||
\(553\) | 3.93588 | 0.167371 | ||||||||
\(554\) | 8.62406 | 0.366401 | ||||||||
\(555\) | 11.4789 | 0.487251 | ||||||||
\(556\) | −17.3197 | −0.734519 | ||||||||
\(557\) | −34.4089 | −1.45795 | −0.728975 | − | 0.684540i | \(-0.760003\pi\) | ||||
−0.728975 | + | 0.684540i | \(0.760003\pi\) | |||||||
\(558\) | 3.02878 | 0.128218 | ||||||||
\(559\) | 17.3944 | 0.735704 | ||||||||
\(560\) | −1.43215 | −0.0605192 | ||||||||
\(561\) | −3.44225 | −0.145332 | ||||||||
\(562\) | −7.28633 | −0.307355 | ||||||||
\(563\) | −11.5076 | −0.484986 | −0.242493 | − | 0.970153i | \(-0.577965\pi\) | ||||
−0.242493 | + | 0.970153i | \(0.577965\pi\) | |||||||
\(564\) | −6.37646 | −0.268498 | ||||||||
\(565\) | −1.95563 | −0.0822741 | ||||||||
\(566\) | 13.3536 | 0.561292 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −48.4450 | −2.03271 | ||||||||
\(569\) | −7.35747 | −0.308441 | −0.154221 | − | 0.988036i | \(-0.549287\pi\) | ||||
−0.154221 | + | 0.988036i | \(0.549287\pi\) | |||||||
\(570\) | 6.74066 | 0.282335 | ||||||||
\(571\) | −3.16207 | −0.132328 | −0.0661642 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661642 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(572\) | −10.4738 | −0.437933 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | 4.57252 | 0.190853 | ||||||||
\(575\) | 16.9444 | 0.706632 | ||||||||
\(576\) | 7.48859 | 0.312025 | ||||||||
\(577\) | 1.29342 | 0.0538459 | 0.0269229 | − | 0.999638i | \(-0.491429\pi\) | ||||
0.0269229 | + | 0.999638i | \(0.491429\pi\) | |||||||
\(578\) | 16.6992 | 0.694597 | ||||||||
\(579\) | −16.6386 | −0.691476 | ||||||||
\(580\) | −0.212525 | −0.00882463 | ||||||||
\(581\) | 8.71714 | 0.361648 | ||||||||
\(582\) | 1.23811 | 0.0513212 | ||||||||
\(583\) | −31.1109 | −1.28848 | ||||||||
\(584\) | −7.09139 | −0.293444 | ||||||||
\(585\) | 3.44427 | 0.142403 | ||||||||
\(586\) | 1.66773 | 0.0688935 | ||||||||
\(587\) | 11.8711 | 0.489973 | 0.244986 | − | 0.969527i | \(-0.421217\pi\) | ||||
0.244986 | + | 0.969527i | \(0.421217\pi\) | |||||||
\(588\) | 0.924574 | 0.0381288 | ||||||||
\(589\) | 17.1796 | 0.707872 | ||||||||
\(590\) | −13.8705 | −0.571039 | ||||||||
\(591\) | 16.6427 | 0.684587 | ||||||||
\(592\) | −13.4627 | −0.553314 | ||||||||
\(593\) | −25.9049 | −1.06379 | −0.531894 | − | 0.846811i | \(-0.678520\pi\) | ||||
−0.531894 | + | 0.846811i | \(0.678520\pi\) | |||||||
\(594\) | −3.76907 | −0.154647 | ||||||||
\(595\) | −1.04659 | −0.0429059 | ||||||||
\(596\) | −5.48944 | −0.224856 | ||||||||
\(597\) | 17.0296 | 0.696976 | ||||||||
\(598\) | −14.4935 | −0.592684 | ||||||||
\(599\) | 10.1528 | 0.414831 | 0.207416 | − | 0.978253i | \(-0.433495\pi\) | ||||
0.207416 | + | 0.978253i | \(0.433495\pi\) | |||||||
\(600\) | 11.4609 | 0.467888 | ||||||||
\(601\) | 42.6428 | 1.73943 | 0.869717 | − | 0.493550i | \(-0.164301\pi\) | ||||
0.869717 | + | 0.493550i | \(0.164301\pi\) | |||||||
\(602\) | −5.78733 | −0.235874 | ||||||||
\(603\) | −15.5558 | −0.633480 | ||||||||
\(604\) | 7.26583 | 0.295643 | ||||||||
\(605\) | −2.44162 | −0.0992658 | ||||||||
\(606\) | −19.6942 | −0.800022 | ||||||||
\(607\) | 8.63548 | 0.350503 | 0.175252 | − | 0.984524i | \(-0.443926\pi\) | ||||
0.175252 | + | 0.984524i | \(0.443926\pi\) | |||||||
\(608\) | 27.7738 | 1.12638 | ||||||||
\(609\) | −0.208014 | −0.00842915 | ||||||||
\(610\) | −3.94724 | −0.159819 | ||||||||
\(611\) | 21.4961 | 0.869638 | ||||||||
\(612\) | 0.875670 | 0.0353968 | ||||||||
\(613\) | −20.5553 | −0.830219 | −0.415109 | − | 0.909771i | \(-0.636257\pi\) | ||||
−0.415109 | + | 0.909771i | \(0.636257\pi\) | |||||||
\(614\) | −14.1381 | −0.570566 | ||||||||
\(615\) | 4.87239 | 0.196474 | ||||||||
\(616\) | 11.0229 | 0.444126 | ||||||||
\(617\) | −4.93511 | −0.198680 | −0.0993401 | − | 0.995054i | \(-0.531673\pi\) | ||||
−0.0993401 | + | 0.995054i | \(0.531673\pi\) | |||||||
\(618\) | −2.45178 | −0.0986251 | ||||||||
\(619\) | 20.5246 | 0.824952 | 0.412476 | − | 0.910968i | \(-0.364664\pi\) | ||||
0.412476 | + | 0.910968i | \(0.364664\pi\) | |||||||
\(620\) | −2.98398 | −0.119839 | ||||||||
\(621\) | 4.48397 | 0.179936 | ||||||||
\(622\) | 21.9203 | 0.878924 | ||||||||
\(623\) | 4.31048 | 0.172696 | ||||||||
\(624\) | −4.03953 | −0.161711 | ||||||||
\(625\) | 8.17449 | 0.326980 | ||||||||
\(626\) | −22.4672 | −0.897971 | ||||||||
\(627\) | −21.3786 | −0.853779 | ||||||||
\(628\) | −5.74203 | −0.229132 | ||||||||
\(629\) | −9.83833 | −0.392280 | ||||||||
\(630\) | −1.14595 | −0.0456559 | ||||||||
\(631\) | −7.49153 | −0.298233 | −0.149117 | − | 0.988820i | \(-0.547643\pi\) | ||||
−0.149117 | + | 0.988820i | \(0.547643\pi\) | |||||||
\(632\) | −11.9370 | −0.474828 | ||||||||
\(633\) | −21.3817 | −0.849845 | ||||||||
\(634\) | 4.17915 | 0.165975 | ||||||||
\(635\) | 1.46270 | 0.0580455 | ||||||||
\(636\) | 7.91426 | 0.313821 | ||||||||
\(637\) | −3.11689 | −0.123495 | ||||||||
\(638\) | −0.784018 | −0.0310396 | ||||||||
\(639\) | −15.9734 | −0.631896 | ||||||||
\(640\) | −1.85378 | −0.0732772 | ||||||||
\(641\) | −32.0169 | −1.26459 | −0.632295 | − | 0.774727i | \(-0.717887\pi\) | ||||
−0.632295 | + | 0.774727i | \(0.717887\pi\) | |||||||
\(642\) | 3.34060 | 0.131843 | ||||||||
\(643\) | 8.94738 | 0.352850 | 0.176425 | − | 0.984314i | \(-0.443547\pi\) | ||||
0.176425 | + | 0.984314i | \(0.443547\pi\) | |||||||
\(644\) | −4.14576 | −0.163366 | ||||||||
\(645\) | −6.16688 | −0.242821 | ||||||||
\(646\) | −5.77729 | −0.227305 | ||||||||
\(647\) | −35.5722 | −1.39849 | −0.699243 | − | 0.714884i | \(-0.746479\pi\) | ||||
−0.699243 | + | 0.714884i | \(0.746479\pi\) | |||||||
\(648\) | 3.03286 | 0.119142 | ||||||||
\(649\) | 43.9914 | 1.72681 | ||||||||
\(650\) | −12.2145 | −0.479092 | ||||||||
\(651\) | −2.92063 | −0.114469 | ||||||||
\(652\) | −18.0153 | −0.705532 | ||||||||
\(653\) | 18.8391 | 0.737231 | 0.368616 | − | 0.929582i | \(-0.379832\pi\) | ||||
0.368616 | + | 0.929582i | \(0.379832\pi\) | |||||||
\(654\) | −0.549351 | −0.0214813 | ||||||||
\(655\) | 0.878682 | 0.0343330 | ||||||||
\(656\) | −5.71447 | −0.223112 | ||||||||
\(657\) | −2.33818 | −0.0912212 | ||||||||
\(658\) | −7.15202 | −0.278815 | ||||||||
\(659\) | −1.61347 | −0.0628519 | −0.0314259 | − | 0.999506i | \(-0.510005\pi\) | ||||
−0.0314259 | + | 0.999506i | \(0.510005\pi\) | |||||||
\(660\) | 3.71332 | 0.144541 | ||||||||
\(661\) | −19.2672 | −0.749407 | −0.374703 | − | 0.927145i | \(-0.622255\pi\) | ||||
−0.374703 | + | 0.927145i | \(0.622255\pi\) | |||||||
\(662\) | −33.5762 | −1.30498 | ||||||||
\(663\) | −2.95202 | −0.114647 | ||||||||
\(664\) | −26.4379 | −1.02599 | ||||||||
\(665\) | −6.49999 | −0.252059 | ||||||||
\(666\) | −10.7724 | −0.417422 | ||||||||
\(667\) | 0.932728 | 0.0361154 | ||||||||
\(668\) | −1.37032 | −0.0530192 | ||||||||
\(669\) | 5.93620 | 0.229507 | ||||||||
\(670\) | −17.8262 | −0.688686 | ||||||||
\(671\) | 12.5190 | 0.483291 | ||||||||
\(672\) | −4.72172 | −0.182144 | ||||||||
\(673\) | 21.5656 | 0.831293 | 0.415646 | − | 0.909526i | \(-0.363555\pi\) | ||||
0.415646 | + | 0.909526i | \(0.363555\pi\) | |||||||
\(674\) | −6.39385 | −0.246282 | ||||||||
\(675\) | 3.77889 | 0.145450 | ||||||||
\(676\) | 3.03725 | 0.116817 | ||||||||
\(677\) | 29.6716 | 1.14037 | 0.570186 | − | 0.821516i | \(-0.306871\pi\) | ||||
0.570186 | + | 0.821516i | \(0.306871\pi\) | |||||||
\(678\) | 1.83527 | 0.0704833 | ||||||||
\(679\) | −1.19390 | −0.0458177 | ||||||||
\(680\) | 3.17416 | 0.121723 | ||||||||
\(681\) | −7.49099 | −0.287055 | ||||||||
\(682\) | −11.0081 | −0.421521 | ||||||||
\(683\) | 5.48534 | 0.209891 | 0.104945 | − | 0.994478i | \(-0.466533\pi\) | ||||
0.104945 | + | 0.994478i | \(0.466533\pi\) | |||||||
\(684\) | 5.43847 | 0.207945 | ||||||||
\(685\) | 16.8336 | 0.643177 | ||||||||
\(686\) | 1.03703 | 0.0395939 | ||||||||
\(687\) | −29.2528 | −1.11606 | ||||||||
\(688\) | 7.23267 | 0.275743 | ||||||||
\(689\) | −26.6802 | −1.01644 | ||||||||
\(690\) | 5.13842 | 0.195616 | ||||||||
\(691\) | −18.4418 | −0.701560 | −0.350780 | − | 0.936458i | \(-0.614084\pi\) | ||||
−0.350780 | + | 0.936458i | \(0.614084\pi\) | |||||||
\(692\) | 10.2049 | 0.387932 | ||||||||
\(693\) | 3.63449 | 0.138063 | ||||||||
\(694\) | −12.3623 | −0.469268 | ||||||||
\(695\) | −20.7003 | −0.785206 | ||||||||
\(696\) | 0.630878 | 0.0239134 | ||||||||
\(697\) | −4.17603 | −0.158179 | ||||||||
\(698\) | 20.2808 | 0.767640 | ||||||||
\(699\) | 11.1443 | 0.421514 | ||||||||
\(700\) | −3.49387 | −0.132056 | ||||||||
\(701\) | 5.75346 | 0.217305 | 0.108653 | − | 0.994080i | \(-0.465346\pi\) | ||||
0.108653 | + | 0.994080i | \(0.465346\pi\) | |||||||
\(702\) | −3.23230 | −0.121995 | ||||||||
\(703\) | −61.1024 | −2.30452 | ||||||||
\(704\) | −27.2172 | −1.02579 | ||||||||
\(705\) | −7.62106 | −0.287026 | ||||||||
\(706\) | −11.0017 | −0.414053 | ||||||||
\(707\) | 18.9910 | 0.714230 | ||||||||
\(708\) | −11.1909 | −0.420581 | ||||||||
\(709\) | 37.2116 | 1.39751 | 0.698755 | − | 0.715361i | \(-0.253738\pi\) | ||||
0.698755 | + | 0.715361i | \(0.253738\pi\) | |||||||
\(710\) | −18.3047 | −0.686964 | ||||||||
\(711\) | −3.93588 | −0.147607 | ||||||||
\(712\) | −13.0731 | −0.489936 | ||||||||
\(713\) | 13.0960 | 0.490450 | ||||||||
\(714\) | 0.982175 | 0.0367570 | ||||||||
\(715\) | −12.5182 | −0.468154 | ||||||||
\(716\) | −20.2772 | −0.757795 | ||||||||
\(717\) | −28.7312 | −1.07299 | ||||||||
\(718\) | 17.9664 | 0.670501 | ||||||||
\(719\) | −7.63506 | −0.284740 | −0.142370 | − | 0.989814i | \(-0.545472\pi\) | ||||
−0.142370 | + | 0.989814i | \(0.545472\pi\) | |||||||
\(720\) | 1.43215 | 0.0533729 | ||||||||
\(721\) | 2.36424 | 0.0880488 | ||||||||
\(722\) | −16.1772 | −0.602053 | ||||||||
\(723\) | −20.8421 | −0.775124 | ||||||||
\(724\) | −3.59654 | −0.133664 | ||||||||
\(725\) | 0.786062 | 0.0291936 | ||||||||
\(726\) | 2.29135 | 0.0850398 | ||||||||
\(727\) | 22.6101 | 0.838561 | 0.419280 | − | 0.907857i | \(-0.362282\pi\) | ||||
0.419280 | + | 0.907857i | \(0.362282\pi\) | |||||||
\(728\) | 9.45309 | 0.350355 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.67945 | −0.0991709 | ||||||||
\(731\) | 5.28551 | 0.195492 | ||||||||
\(732\) | −3.18470 | −0.117710 | ||||||||
\(733\) | −2.30605 | −0.0851760 | −0.0425880 | − | 0.999093i | \(-0.513560\pi\) | ||||
−0.0425880 | + | 0.999093i | \(0.513560\pi\) | |||||||
\(734\) | 17.0016 | 0.627541 | ||||||||
\(735\) | 1.10504 | 0.0407599 | ||||||||
\(736\) | 21.1721 | 0.780413 | ||||||||
\(737\) | 56.5373 | 2.08258 | ||||||||
\(738\) | −4.57252 | −0.168317 | ||||||||
\(739\) | 32.8528 | 1.20851 | 0.604256 | − | 0.796791i | \(-0.293471\pi\) | ||||
0.604256 | + | 0.796791i | \(0.293471\pi\) | |||||||
\(740\) | 10.6131 | 0.390144 | ||||||||
\(741\) | −18.3340 | −0.673515 | ||||||||
\(742\) | 8.87685 | 0.325879 | ||||||||
\(743\) | 39.8459 | 1.46180 | 0.730902 | − | 0.682483i | \(-0.239100\pi\) | ||||
0.730902 | + | 0.682483i | \(0.239100\pi\) | |||||||
\(744\) | 8.85789 | 0.324746 | ||||||||
\(745\) | −6.56090 | −0.240373 | ||||||||
\(746\) | 15.3892 | 0.563438 | ||||||||
\(747\) | −8.71714 | −0.318943 | ||||||||
\(748\) | −3.18261 | −0.116368 | ||||||||
\(749\) | −3.22132 | −0.117705 | ||||||||
\(750\) | 10.0602 | 0.367347 | ||||||||
\(751\) | 49.7512 | 1.81545 | 0.907724 | − | 0.419567i | \(-0.137818\pi\) | ||||
0.907724 | + | 0.419567i | \(0.137818\pi\) | |||||||
\(752\) | 8.93817 | 0.325941 | ||||||||
\(753\) | 1.85083 | 0.0674479 | ||||||||
\(754\) | −0.672362 | −0.0244860 | ||||||||
\(755\) | 8.68402 | 0.316044 | ||||||||
\(756\) | −0.924574 | −0.0336264 | ||||||||
\(757\) | −33.2413 | −1.20817 | −0.604087 | − | 0.796918i | \(-0.706462\pi\) | ||||
−0.604087 | + | 0.796918i | \(0.706462\pi\) | |||||||
\(758\) | −4.42831 | −0.160843 | ||||||||
\(759\) | −16.2970 | −0.591542 | ||||||||
\(760\) | 19.7136 | 0.715086 | ||||||||
\(761\) | −22.7486 | −0.824635 | −0.412317 | − | 0.911040i | \(-0.635281\pi\) | ||||
−0.412317 | + | 0.911040i | \(0.635281\pi\) | |||||||
\(762\) | −1.37268 | −0.0497269 | ||||||||
\(763\) | 0.529736 | 0.0191777 | ||||||||
\(764\) | −0.924574 | −0.0334499 | ||||||||
\(765\) | 1.04659 | 0.0378395 | ||||||||
\(766\) | 3.36085 | 0.121433 | ||||||||
\(767\) | 37.7264 | 1.36222 | ||||||||
\(768\) | 16.7169 | 0.603218 | ||||||||
\(769\) | −26.7163 | −0.963413 | −0.481706 | − | 0.876333i | \(-0.659983\pi\) | ||||
−0.481706 | + | 0.876333i | \(0.659983\pi\) | |||||||
\(770\) | 4.16496 | 0.150095 | ||||||||
\(771\) | 27.7137 | 0.998083 | ||||||||
\(772\) | −15.3836 | −0.553668 | ||||||||
\(773\) | 40.9745 | 1.47375 | 0.736875 | − | 0.676029i | \(-0.236301\pi\) | ||||
0.736875 | + | 0.676029i | \(0.236301\pi\) | |||||||
\(774\) | 5.78733 | 0.208021 | ||||||||
\(775\) | 11.0368 | 0.396452 | ||||||||
\(776\) | 3.62094 | 0.129984 | ||||||||
\(777\) | 10.3878 | 0.372659 | ||||||||
\(778\) | −6.35743 | −0.227925 | ||||||||
\(779\) | −25.9359 | −0.929249 | ||||||||
\(780\) | 3.18449 | 0.114023 | ||||||||
\(781\) | 58.0550 | 2.07737 | ||||||||
\(782\) | −4.40404 | −0.157488 | ||||||||
\(783\) | 0.208014 | 0.00743381 | ||||||||
\(784\) | −1.29602 | −0.0462863 | ||||||||
\(785\) | −6.86279 | −0.244944 | ||||||||
\(786\) | −0.824604 | −0.0294126 | ||||||||
\(787\) | −37.0708 | −1.32143 | −0.660715 | − | 0.750637i | \(-0.729747\pi\) | ||||
−0.660715 | + | 0.750637i | \(0.729747\pi\) | |||||||
\(788\) | 15.3874 | 0.548152 | ||||||||
\(789\) | −12.8633 | −0.457946 | ||||||||
\(790\) | −4.51034 | −0.160471 | ||||||||
\(791\) | −1.76974 | −0.0629249 | ||||||||
\(792\) | −11.0229 | −0.391682 | ||||||||
\(793\) | 10.7361 | 0.381251 | ||||||||
\(794\) | −16.1128 | −0.571821 | ||||||||
\(795\) | 9.45901 | 0.335476 | ||||||||
\(796\) | 15.7452 | 0.558072 | ||||||||
\(797\) | −34.8433 | −1.23421 | −0.617107 | − | 0.786879i | \(-0.711695\pi\) | ||||
−0.617107 | + | 0.786879i | \(0.711695\pi\) | |||||||
\(798\) | 6.09994 | 0.215936 | ||||||||
\(799\) | 6.53186 | 0.231081 | ||||||||
\(800\) | 17.8429 | 0.630841 | ||||||||
\(801\) | −4.31048 | −0.152303 | ||||||||
\(802\) | 18.9618 | 0.669564 | ||||||||
\(803\) | 8.49811 | 0.299892 | ||||||||
\(804\) | −14.3825 | −0.507230 | ||||||||
\(805\) | −4.95495 | −0.174639 | ||||||||
\(806\) | −9.44035 | −0.332522 | ||||||||
\(807\) | 25.0295 | 0.881079 | ||||||||
\(808\) | −57.5971 | −2.02626 | ||||||||
\(809\) | 0.459425 | 0.0161525 | 0.00807626 | − | 0.999967i | \(-0.497429\pi\) | ||||
0.00807626 | + | 0.999967i | \(0.497429\pi\) | |||||||
\(810\) | 1.14595 | 0.0402647 | ||||||||
\(811\) | 5.84158 | 0.205125 | 0.102563 | − | 0.994727i | \(-0.467296\pi\) | ||||
0.102563 | + | 0.994727i | \(0.467296\pi\) | |||||||
\(812\) | −0.192324 | −0.00674925 | ||||||||
\(813\) | −21.1717 | −0.742524 | ||||||||
\(814\) | 39.1522 | 1.37229 | ||||||||
\(815\) | −21.5316 | −0.754219 | ||||||||
\(816\) | −1.22746 | −0.0429698 | ||||||||
\(817\) | 32.8264 | 1.14845 | ||||||||
\(818\) | 12.8648 | 0.449805 | ||||||||
\(819\) | 3.11689 | 0.108913 | ||||||||
\(820\) | 4.50489 | 0.157318 | ||||||||
\(821\) | 36.5554 | 1.27579 | 0.637895 | − | 0.770123i | \(-0.279805\pi\) | ||||
0.637895 | + | 0.770123i | \(0.279805\pi\) | |||||||
\(822\) | −15.7975 | −0.551002 | ||||||||
\(823\) | −11.2049 | −0.390579 | −0.195290 | − | 0.980746i | \(-0.562565\pi\) | ||||
−0.195290 | + | 0.980746i | \(0.562565\pi\) | |||||||
\(824\) | −7.17041 | −0.249793 | ||||||||
\(825\) | −13.7344 | −0.478169 | ||||||||
\(826\) | −12.5520 | −0.436742 | ||||||||
\(827\) | −28.9897 | −1.00807 | −0.504036 | − | 0.863683i | \(-0.668152\pi\) | ||||
−0.504036 | + | 0.863683i | \(0.668152\pi\) | |||||||
\(828\) | 4.14576 | 0.144075 | ||||||||
\(829\) | 22.3728 | 0.777040 | 0.388520 | − | 0.921440i | \(-0.372987\pi\) | ||||
0.388520 | + | 0.921440i | \(0.372987\pi\) | |||||||
\(830\) | −9.98944 | −0.346738 | ||||||||
\(831\) | 8.31613 | 0.288483 | ||||||||
\(832\) | −23.3411 | −0.809206 | ||||||||
\(833\) | −0.947106 | −0.0328153 | ||||||||
\(834\) | 19.4263 | 0.672676 | ||||||||
\(835\) | −1.63779 | −0.0566779 | ||||||||
\(836\) | −19.7661 | −0.683625 | ||||||||
\(837\) | 2.92063 | 0.100952 | ||||||||
\(838\) | 24.2667 | 0.838280 | ||||||||
\(839\) | −44.5582 | −1.53832 | −0.769159 | − | 0.639057i | \(-0.779325\pi\) | ||||
−0.769159 | + | 0.639057i | \(0.779325\pi\) | |||||||
\(840\) | −3.35143 | −0.115635 | ||||||||
\(841\) | −28.9567 | −0.998508 | ||||||||
\(842\) | 29.1760 | 1.00547 | ||||||||
\(843\) | −7.02617 | −0.241994 | ||||||||
\(844\) | −19.7689 | −0.680474 | ||||||||
\(845\) | 3.63008 | 0.124878 | ||||||||
\(846\) | 7.15202 | 0.245891 | ||||||||
\(847\) | −2.20953 | −0.0759204 | ||||||||
\(848\) | −11.0938 | −0.380961 | ||||||||
\(849\) | 12.8768 | 0.441930 | ||||||||
\(850\) | −3.71153 | −0.127305 | ||||||||
\(851\) | −46.5785 | −1.59669 | ||||||||
\(852\) | −14.7686 | −0.505962 | ||||||||
\(853\) | −57.6634 | −1.97436 | −0.987179 | − | 0.159620i | \(-0.948973\pi\) | ||||
−0.987179 | + | 0.159620i | \(0.948973\pi\) | |||||||
\(854\) | −3.57204 | −0.122233 | ||||||||
\(855\) | 6.49999 | 0.222295 | ||||||||
\(856\) | 9.76983 | 0.333926 | ||||||||
\(857\) | −46.7267 | −1.59615 | −0.798077 | − | 0.602555i | \(-0.794149\pi\) | ||||
−0.798077 | + | 0.602555i | \(0.794149\pi\) | |||||||
\(858\) | 11.7478 | 0.401062 | ||||||||
\(859\) | −32.3796 | −1.10478 | −0.552389 | − | 0.833587i | \(-0.686284\pi\) | ||||
−0.552389 | + | 0.833587i | \(0.686284\pi\) | |||||||
\(860\) | −5.70173 | −0.194427 | ||||||||
\(861\) | 4.40926 | 0.150267 | ||||||||
\(862\) | 16.5680 | 0.564307 | ||||||||
\(863\) | 19.3716 | 0.659418 | 0.329709 | − | 0.944083i | \(-0.393049\pi\) | ||||
0.329709 | + | 0.944083i | \(0.393049\pi\) | |||||||
\(864\) | 4.72172 | 0.160636 | ||||||||
\(865\) | 12.1968 | 0.414702 | ||||||||
\(866\) | −6.33505 | −0.215274 | ||||||||
\(867\) | 16.1030 | 0.546886 | ||||||||
\(868\) | −2.70034 | −0.0916556 | ||||||||
\(869\) | 14.3049 | 0.485261 | ||||||||
\(870\) | 0.238374 | 0.00808164 | ||||||||
\(871\) | 48.4856 | 1.64287 | ||||||||
\(872\) | −1.60662 | −0.0544069 | ||||||||
\(873\) | 1.19390 | 0.0404074 | ||||||||
\(874\) | −27.3520 | −0.925194 | ||||||||
\(875\) | −9.70100 | −0.327954 | ||||||||
\(876\) | −2.16182 | −0.0730413 | ||||||||
\(877\) | −1.03135 | −0.0348261 | −0.0174130 | − | 0.999848i | \(-0.505543\pi\) | ||||
−0.0174130 | + | 0.999848i | \(0.505543\pi\) | |||||||
\(878\) | 28.1516 | 0.950072 | ||||||||
\(879\) | 1.60819 | 0.0542428 | ||||||||
\(880\) | −5.20512 | −0.175465 | ||||||||
\(881\) | 32.3845 | 1.09106 | 0.545530 | − | 0.838091i | \(-0.316328\pi\) | ||||
0.545530 | + | 0.838091i | \(0.316328\pi\) | |||||||
\(882\) | −1.03703 | −0.0349185 | ||||||||
\(883\) | 23.8220 | 0.801673 | 0.400837 | − | 0.916150i | \(-0.368719\pi\) | ||||
0.400837 | + | 0.916150i | \(0.368719\pi\) | |||||||
\(884\) | −2.72936 | −0.0917984 | ||||||||
\(885\) | −13.3752 | −0.449603 | ||||||||
\(886\) | 0.737215 | 0.0247672 | ||||||||
\(887\) | −15.0118 | −0.504046 | −0.252023 | − | 0.967721i | \(-0.581096\pi\) | ||||
−0.252023 | + | 0.967721i | \(0.581096\pi\) | |||||||
\(888\) | −31.5047 | −1.05723 | ||||||||
\(889\) | 1.32367 | 0.0443944 | ||||||||
\(890\) | −4.93962 | −0.165576 | ||||||||
\(891\) | −3.63449 | −0.121760 | ||||||||
\(892\) | 5.48846 | 0.183767 | ||||||||
\(893\) | 40.5671 | 1.35753 | ||||||||
\(894\) | 6.15711 | 0.205925 | ||||||||
\(895\) | −24.2350 | −0.810087 | ||||||||
\(896\) | −1.67758 | −0.0560439 | ||||||||
\(897\) | −13.9760 | −0.466646 | ||||||||
\(898\) | −9.20865 | −0.307297 | ||||||||
\(899\) | 0.607532 | 0.0202623 | ||||||||
\(900\) | 3.49387 | 0.116462 | ||||||||
\(901\) | −8.10713 | −0.270088 | ||||||||
\(902\) | 16.6188 | 0.553345 | ||||||||
\(903\) | −5.58070 | −0.185714 | ||||||||
\(904\) | 5.36739 | 0.178517 | ||||||||
\(905\) | −4.29853 | −0.142888 | ||||||||
\(906\) | −8.14956 | −0.270751 | ||||||||
\(907\) | −55.8019 | −1.85287 | −0.926436 | − | 0.376453i | \(-0.877144\pi\) | ||||
−0.926436 | + | 0.376453i | \(0.877144\pi\) | |||||||
\(908\) | −6.92597 | −0.229847 | ||||||||
\(909\) | −18.9910 | −0.629892 | ||||||||
\(910\) | 3.57181 | 0.118404 | ||||||||
\(911\) | 16.4212 | 0.544058 | 0.272029 | − | 0.962289i | \(-0.412305\pi\) | ||||
0.272029 | + | 0.962289i | \(0.412305\pi\) | |||||||
\(912\) | −7.62335 | −0.252434 | ||||||||
\(913\) | 31.6824 | 1.04853 | ||||||||
\(914\) | −12.4939 | −0.413260 | ||||||||
\(915\) | −3.80630 | −0.125833 | ||||||||
\(916\) | −27.0464 | −0.893638 | ||||||||
\(917\) | 0.795161 | 0.0262585 | ||||||||
\(918\) | −0.982175 | −0.0324166 | ||||||||
\(919\) | 27.8004 | 0.917050 | 0.458525 | − | 0.888682i | \(-0.348378\pi\) | ||||
0.458525 | + | 0.888682i | \(0.348378\pi\) | |||||||
\(920\) | 15.0277 | 0.495449 | ||||||||
\(921\) | −13.6333 | −0.449231 | ||||||||
\(922\) | −27.5114 | −0.906038 | ||||||||
\(923\) | 49.7871 | 1.63876 | ||||||||
\(924\) | 3.36036 | 0.110548 | ||||||||
\(925\) | −39.2543 | −1.29067 | ||||||||
\(926\) | −16.8718 | −0.554442 | ||||||||
\(927\) | −2.36424 | −0.0776518 | ||||||||
\(928\) | 0.982184 | 0.0322418 | ||||||||
\(929\) | −0.361276 | −0.0118531 | −0.00592654 | − | 0.999982i | \(-0.501886\pi\) | ||||
−0.00592654 | + | 0.999982i | \(0.501886\pi\) | |||||||
\(930\) | 3.34691 | 0.109750 | ||||||||
\(931\) | −5.88214 | −0.192779 | ||||||||
\(932\) | 10.3037 | 0.337508 | ||||||||
\(933\) | 21.1376 | 0.692015 | ||||||||
\(934\) | 12.0727 | 0.395032 | ||||||||
\(935\) | −3.80381 | −0.124398 | ||||||||
\(936\) | −9.45309 | −0.308984 | ||||||||
\(937\) | −21.6264 | −0.706504 | −0.353252 | − | 0.935528i | \(-0.614924\pi\) | ||||
−0.353252 | + | 0.935528i | \(0.614924\pi\) | |||||||
\(938\) | −16.1318 | −0.526721 | ||||||||
\(939\) | −21.6650 | −0.707011 | ||||||||
\(940\) | −7.04623 | −0.229823 | ||||||||
\(941\) | 23.9308 | 0.780123 | 0.390061 | − | 0.920789i | \(-0.372454\pi\) | ||||
0.390061 | + | 0.920789i | \(0.372454\pi\) | |||||||
\(942\) | 6.44042 | 0.209840 | ||||||||
\(943\) | −19.7710 | −0.643832 | ||||||||
\(944\) | 15.6868 | 0.510562 | ||||||||
\(945\) | −1.10504 | −0.0359469 | ||||||||
\(946\) | −21.0340 | −0.683875 | ||||||||
\(947\) | −53.5317 | −1.73955 | −0.869774 | − | 0.493451i | \(-0.835735\pi\) | ||||
−0.869774 | + | 0.493451i | \(0.835735\pi\) | |||||||
\(948\) | −3.63901 | −0.118190 | ||||||||
\(949\) | 7.28785 | 0.236574 | ||||||||
\(950\) | −23.0510 | −0.747874 | ||||||||
\(951\) | 4.02993 | 0.130679 | ||||||||
\(952\) | 2.87244 | 0.0930964 | ||||||||
\(953\) | −8.96549 | −0.290421 | −0.145210 | − | 0.989401i | \(-0.546386\pi\) | ||||
−0.145210 | + | 0.989401i | \(0.546386\pi\) | |||||||
\(954\) | −8.87685 | −0.287399 | ||||||||
\(955\) | −1.10504 | −0.0357582 | ||||||||
\(956\) | −26.5642 | −0.859146 | ||||||||
\(957\) | −0.756025 | −0.0244388 | ||||||||
\(958\) | 14.4190 | 0.465857 | ||||||||
\(959\) | 15.2335 | 0.491915 | ||||||||
\(960\) | 8.27517 | 0.267080 | ||||||||
\(961\) | −22.4699 | −0.724835 | ||||||||
\(962\) | 33.5764 | 1.08255 | ||||||||
\(963\) | 3.22132 | 0.103806 | ||||||||
\(964\) | −19.2700 | −0.620646 | ||||||||
\(965\) | −18.3862 | −0.591874 | ||||||||
\(966\) | 4.65000 | 0.149611 | ||||||||
\(967\) | −55.2643 | −1.77718 | −0.888590 | − | 0.458703i | \(-0.848314\pi\) | ||||
−0.888590 | + | 0.458703i | \(0.848314\pi\) | |||||||
\(968\) | 6.70121 | 0.215385 | ||||||||
\(969\) | −5.57101 | −0.178967 | ||||||||
\(970\) | 1.36815 | 0.0439288 | ||||||||
\(971\) | −7.68789 | −0.246716 | −0.123358 | − | 0.992362i | \(-0.539366\pi\) | ||||
−0.123358 | + | 0.992362i | \(0.539366\pi\) | |||||||
\(972\) | 0.924574 | 0.0296557 | ||||||||
\(973\) | −18.7326 | −0.600541 | ||||||||
\(974\) | −20.8146 | −0.666942 | ||||||||
\(975\) | −11.7784 | −0.377210 | ||||||||
\(976\) | 4.46413 | 0.142893 | ||||||||
\(977\) | 17.2569 | 0.552098 | 0.276049 | − | 0.961144i | \(-0.410975\pi\) | ||||
0.276049 | + | 0.961144i | \(0.410975\pi\) | |||||||
\(978\) | 20.2064 | 0.646130 | ||||||||
\(979\) | 15.6664 | 0.500701 | ||||||||
\(980\) | 1.02169 | 0.0326366 | ||||||||
\(981\) | −0.529736 | −0.0169132 | ||||||||
\(982\) | 26.7260 | 0.852862 | ||||||||
\(983\) | 2.96957 | 0.0947147 | 0.0473574 | − | 0.998878i | \(-0.484920\pi\) | ||||
0.0473574 | + | 0.998878i | \(0.484920\pi\) | |||||||
\(984\) | −13.3727 | −0.426305 | ||||||||
\(985\) | 18.3908 | 0.585978 | ||||||||
\(986\) | −0.204306 | −0.00650643 | ||||||||
\(987\) | −6.89665 | −0.219523 | ||||||||
\(988\) | −16.9511 | −0.539286 | ||||||||
\(989\) | 25.0237 | 0.795706 | ||||||||
\(990\) | −4.16496 | −0.132371 | ||||||||
\(991\) | 6.79748 | 0.215929 | 0.107965 | − | 0.994155i | \(-0.465567\pi\) | ||||
0.107965 | + | 0.994155i | \(0.465567\pi\) | |||||||
\(992\) | 13.7904 | 0.437847 | ||||||||
\(993\) | −32.3774 | −1.02746 | ||||||||
\(994\) | −16.5648 | −0.525404 | ||||||||
\(995\) | 18.8184 | 0.596583 | ||||||||
\(996\) | −8.05964 | −0.255379 | ||||||||
\(997\) | 12.8536 | 0.407079 | 0.203540 | − | 0.979067i | \(-0.434755\pi\) | ||||
0.203540 | + | 0.979067i | \(0.434755\pi\) | |||||||
\(998\) | 10.4749 | 0.331578 | ||||||||
\(999\) | −10.3878 | −0.328655 |
(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 | 4011.2.a.j.1.10 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.j.1.10 | ✓ | 26 | 1.1 | even | 1 | trivial |