Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6005,2,Mod(1,6005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6005 = 5 \cdot 1201 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6005.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: | \(47.9501664138\) |
Analytic rank: | \(0\) |
Dimension: | \(113\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.18171 | −1.54270 | −0.771352 | − | 0.636409i | \(-0.780419\pi\) | ||||
−0.771352 | + | 0.636409i | \(0.780419\pi\) | |||||||
\(3\) | 2.09909 | 1.21191 | 0.605955 | − | 0.795499i | \(-0.292791\pi\) | ||||
0.605955 | + | 0.795499i | \(0.292791\pi\) | |||||||
\(4\) | 2.75987 | 1.37993 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −4.57961 | −1.86962 | ||||||||
\(7\) | −2.68153 | −1.01352 | −0.506762 | − | 0.862086i | \(-0.669158\pi\) | ||||
−0.506762 | + | 0.862086i | \(0.669158\pi\) | |||||||
\(8\) | −1.65781 | −0.586125 | ||||||||
\(9\) | 1.40617 | 0.468724 | ||||||||
\(10\) | 2.18171 | 0.689918 | ||||||||
\(11\) | 0.412490 | 0.124370 | 0.0621852 | − | 0.998065i | \(-0.480193\pi\) | ||||
0.0621852 | + | 0.998065i | \(0.480193\pi\) | |||||||
\(12\) | 5.79321 | 1.67235 | ||||||||
\(13\) | 1.83522 | 0.508998 | 0.254499 | − | 0.967073i | \(-0.418089\pi\) | ||||
0.254499 | + | 0.967073i | \(0.418089\pi\) | |||||||
\(14\) | 5.85033 | 1.56357 | ||||||||
\(15\) | −2.09909 | −0.541982 | ||||||||
\(16\) | −1.90287 | −0.475716 | ||||||||
\(17\) | 0.163414 | 0.0396338 | 0.0198169 | − | 0.999804i | \(-0.493692\pi\) | ||||
0.0198169 | + | 0.999804i | \(0.493692\pi\) | |||||||
\(18\) | −3.06786 | −0.723102 | ||||||||
\(19\) | 7.14152 | 1.63838 | 0.819188 | − | 0.573525i | \(-0.194425\pi\) | ||||
0.819188 | + | 0.573525i | \(0.194425\pi\) | |||||||
\(20\) | −2.75987 | −0.617125 | ||||||||
\(21\) | −5.62877 | −1.22830 | ||||||||
\(22\) | −0.899935 | −0.191867 | ||||||||
\(23\) | −5.22422 | −1.08932 | −0.544662 | − | 0.838655i | \(-0.683342\pi\) | ||||
−0.544662 | + | 0.838655i | \(0.683342\pi\) | |||||||
\(24\) | −3.47990 | −0.710331 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.00392 | −0.785233 | ||||||||
\(27\) | −3.34559 | −0.643858 | ||||||||
\(28\) | −7.40067 | −1.39860 | ||||||||
\(29\) | 9.21346 | 1.71090 | 0.855448 | − | 0.517888i | \(-0.173282\pi\) | ||||
0.855448 | + | 0.517888i | \(0.173282\pi\) | |||||||
\(30\) | 4.57961 | 0.836118 | ||||||||
\(31\) | −10.6409 | −1.91117 | −0.955583 | − | 0.294722i | \(-0.904773\pi\) | ||||
−0.955583 | + | 0.294722i | \(0.904773\pi\) | |||||||
\(32\) | 7.46713 | 1.32001 | ||||||||
\(33\) | 0.865853 | 0.150726 | ||||||||
\(34\) | −0.356523 | −0.0611431 | ||||||||
\(35\) | 2.68153 | 0.453262 | ||||||||
\(36\) | 3.88085 | 0.646808 | ||||||||
\(37\) | 1.57980 | 0.259718 | 0.129859 | − | 0.991532i | \(-0.458548\pi\) | ||||
0.129859 | + | 0.991532i | \(0.458548\pi\) | |||||||
\(38\) | −15.5807 | −2.52753 | ||||||||
\(39\) | 3.85229 | 0.616860 | ||||||||
\(40\) | 1.65781 | 0.262123 | ||||||||
\(41\) | 7.59348 | 1.18590 | 0.592951 | − | 0.805239i | \(-0.297963\pi\) | ||||
0.592951 | + | 0.805239i | \(0.297963\pi\) | |||||||
\(42\) | 12.2804 | 1.89490 | ||||||||
\(43\) | −9.07160 | −1.38341 | −0.691703 | − | 0.722182i | \(-0.743139\pi\) | ||||
−0.691703 | + | 0.722182i | \(0.743139\pi\) | |||||||
\(44\) | 1.13842 | 0.171623 | ||||||||
\(45\) | −1.40617 | −0.209620 | ||||||||
\(46\) | 11.3977 | 1.68050 | ||||||||
\(47\) | −1.76996 | −0.258175 | −0.129087 | − | 0.991633i | \(-0.541205\pi\) | ||||
−0.129087 | + | 0.991633i | \(0.541205\pi\) | |||||||
\(48\) | −3.99428 | −0.576525 | ||||||||
\(49\) | 0.190616 | 0.0272309 | ||||||||
\(50\) | −2.18171 | −0.308541 | ||||||||
\(51\) | 0.343021 | 0.0480325 | ||||||||
\(52\) | 5.06496 | 0.702384 | ||||||||
\(53\) | −3.12694 | −0.429519 | −0.214759 | − | 0.976667i | \(-0.568897\pi\) | ||||
−0.214759 | + | 0.976667i | \(0.568897\pi\) | |||||||
\(54\) | 7.29911 | 0.993283 | ||||||||
\(55\) | −0.412490 | −0.0556202 | ||||||||
\(56\) | 4.44548 | 0.594052 | ||||||||
\(57\) | 14.9907 | 1.98556 | ||||||||
\(58\) | −20.1011 | −2.63941 | ||||||||
\(59\) | 5.64814 | 0.735325 | 0.367663 | − | 0.929959i | \(-0.380158\pi\) | ||||
0.367663 | + | 0.929959i | \(0.380158\pi\) | |||||||
\(60\) | −5.79321 | −0.747900 | ||||||||
\(61\) | 12.9160 | 1.65372 | 0.826862 | − | 0.562404i | \(-0.190124\pi\) | ||||
0.826862 | + | 0.562404i | \(0.190124\pi\) | |||||||
\(62\) | 23.2154 | 2.94836 | ||||||||
\(63\) | −3.77069 | −0.475063 | ||||||||
\(64\) | −12.4854 | −1.56067 | ||||||||
\(65\) | −1.83522 | −0.227631 | ||||||||
\(66\) | −1.88904 | −0.232525 | ||||||||
\(67\) | 9.28256 | 1.13405 | 0.567023 | − | 0.823702i | \(-0.308095\pi\) | ||||
0.567023 | + | 0.823702i | \(0.308095\pi\) | |||||||
\(68\) | 0.451002 | 0.0546920 | ||||||||
\(69\) | −10.9661 | −1.32016 | ||||||||
\(70\) | −5.85033 | −0.699248 | ||||||||
\(71\) | −10.2797 | −1.21998 | −0.609991 | − | 0.792409i | \(-0.708827\pi\) | ||||
−0.609991 | + | 0.792409i | \(0.708827\pi\) | |||||||
\(72\) | −2.33117 | −0.274731 | ||||||||
\(73\) | 8.34284 | 0.976456 | 0.488228 | − | 0.872716i | \(-0.337644\pi\) | ||||
0.488228 | + | 0.872716i | \(0.337644\pi\) | |||||||
\(74\) | −3.44667 | −0.400668 | ||||||||
\(75\) | 2.09909 | 0.242382 | ||||||||
\(76\) | 19.7096 | 2.26085 | ||||||||
\(77\) | −1.10611 | −0.126052 | ||||||||
\(78\) | −8.40458 | −0.951632 | ||||||||
\(79\) | 7.62559 | 0.857946 | 0.428973 | − | 0.903317i | \(-0.358875\pi\) | ||||
0.428973 | + | 0.903317i | \(0.358875\pi\) | |||||||
\(80\) | 1.90287 | 0.212747 | ||||||||
\(81\) | −11.2412 | −1.24902 | ||||||||
\(82\) | −16.5668 | −1.82950 | ||||||||
\(83\) | 0.362022 | 0.0397371 | 0.0198685 | − | 0.999803i | \(-0.493675\pi\) | ||||
0.0198685 | + | 0.999803i | \(0.493675\pi\) | |||||||
\(84\) | −15.5347 | −1.69497 | ||||||||
\(85\) | −0.163414 | −0.0177248 | ||||||||
\(86\) | 19.7916 | 2.13418 | ||||||||
\(87\) | 19.3399 | 2.07345 | ||||||||
\(88\) | −0.683831 | −0.0728967 | ||||||||
\(89\) | −11.2820 | −1.19589 | −0.597944 | − | 0.801538i | \(-0.704015\pi\) | ||||
−0.597944 | + | 0.801538i | \(0.704015\pi\) | |||||||
\(90\) | 3.06786 | 0.323381 | ||||||||
\(91\) | −4.92120 | −0.515882 | ||||||||
\(92\) | −14.4181 | −1.50320 | ||||||||
\(93\) | −22.3362 | −2.31616 | ||||||||
\(94\) | 3.86154 | 0.398287 | ||||||||
\(95\) | −7.14152 | −0.732704 | ||||||||
\(96\) | 15.6742 | 1.59974 | ||||||||
\(97\) | −4.67679 | −0.474857 | −0.237428 | − | 0.971405i | \(-0.576304\pi\) | ||||
−0.237428 | + | 0.971405i | \(0.576304\pi\) | |||||||
\(98\) | −0.415869 | −0.0420091 | ||||||||
\(99\) | 0.580032 | 0.0582954 | ||||||||
\(100\) | 2.75987 | 0.275987 | ||||||||
\(101\) | −6.74742 | −0.671393 | −0.335697 | − | 0.941970i | \(-0.608972\pi\) | ||||
−0.335697 | + | 0.941970i | \(0.608972\pi\) | |||||||
\(102\) | −0.748373 | −0.0740999 | ||||||||
\(103\) | 15.0154 | 1.47951 | 0.739755 | − | 0.672877i | \(-0.234941\pi\) | ||||
0.739755 | + | 0.672877i | \(0.234941\pi\) | |||||||
\(104\) | −3.04245 | −0.298337 | ||||||||
\(105\) | 5.62877 | 0.549312 | ||||||||
\(106\) | 6.82209 | 0.662620 | ||||||||
\(107\) | −4.82653 | −0.466598 | −0.233299 | − | 0.972405i | \(-0.574952\pi\) | ||||
−0.233299 | + | 0.972405i | \(0.574952\pi\) | |||||||
\(108\) | −9.23338 | −0.888482 | ||||||||
\(109\) | 5.54853 | 0.531453 | 0.265726 | − | 0.964048i | \(-0.414388\pi\) | ||||
0.265726 | + | 0.964048i | \(0.414388\pi\) | |||||||
\(110\) | 0.899935 | 0.0858054 | ||||||||
\(111\) | 3.31614 | 0.314754 | ||||||||
\(112\) | 5.10260 | 0.482150 | ||||||||
\(113\) | 7.99808 | 0.752396 | 0.376198 | − | 0.926539i | \(-0.377231\pi\) | ||||
0.376198 | + | 0.926539i | \(0.377231\pi\) | |||||||
\(114\) | −32.7053 | −3.06313 | ||||||||
\(115\) | 5.22422 | 0.487161 | ||||||||
\(116\) | 25.4279 | 2.36092 | ||||||||
\(117\) | 2.58063 | 0.238580 | ||||||||
\(118\) | −12.3226 | −1.13439 | ||||||||
\(119\) | −0.438200 | −0.0401698 | ||||||||
\(120\) | 3.47990 | 0.317670 | ||||||||
\(121\) | −10.8299 | −0.984532 | ||||||||
\(122\) | −28.1790 | −2.55121 | ||||||||
\(123\) | 15.9394 | 1.43721 | ||||||||
\(124\) | −29.3675 | −2.63728 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 8.22657 | 0.732881 | ||||||||
\(127\) | −6.13550 | −0.544438 | −0.272219 | − | 0.962235i | \(-0.587757\pi\) | ||||
−0.272219 | + | 0.962235i | \(0.587757\pi\) | |||||||
\(128\) | 12.3053 | 1.08764 | ||||||||
\(129\) | −19.0421 | −1.67656 | ||||||||
\(130\) | 4.00392 | 0.351167 | ||||||||
\(131\) | 0.575780 | 0.0503061 | 0.0251530 | − | 0.999684i | \(-0.491993\pi\) | ||||
0.0251530 | + | 0.999684i | \(0.491993\pi\) | |||||||
\(132\) | 2.38964 | 0.207991 | ||||||||
\(133\) | −19.1502 | −1.66053 | ||||||||
\(134\) | −20.2519 | −1.74950 | ||||||||
\(135\) | 3.34559 | 0.287942 | ||||||||
\(136\) | −0.270910 | −0.0232303 | ||||||||
\(137\) | −10.5516 | −0.901482 | −0.450741 | − | 0.892655i | \(-0.648840\pi\) | ||||
−0.450741 | + | 0.892655i | \(0.648840\pi\) | |||||||
\(138\) | 23.9249 | 2.03662 | ||||||||
\(139\) | 12.2636 | 1.04019 | 0.520093 | − | 0.854110i | \(-0.325897\pi\) | ||||
0.520093 | + | 0.854110i | \(0.325897\pi\) | |||||||
\(140\) | 7.40067 | 0.625471 | ||||||||
\(141\) | −3.71530 | −0.312884 | ||||||||
\(142\) | 22.4274 | 1.88207 | ||||||||
\(143\) | 0.757010 | 0.0633043 | ||||||||
\(144\) | −2.67576 | −0.222980 | ||||||||
\(145\) | −9.21346 | −0.765136 | ||||||||
\(146\) | −18.2017 | −1.50638 | ||||||||
\(147\) | 0.400120 | 0.0330013 | ||||||||
\(148\) | 4.36004 | 0.358393 | ||||||||
\(149\) | −15.6300 | −1.28046 | −0.640228 | − | 0.768185i | \(-0.721160\pi\) | ||||
−0.640228 | + | 0.768185i | \(0.721160\pi\) | |||||||
\(150\) | −4.57961 | −0.373923 | ||||||||
\(151\) | 15.7045 | 1.27802 | 0.639008 | − | 0.769200i | \(-0.279345\pi\) | ||||
0.639008 | + | 0.769200i | \(0.279345\pi\) | |||||||
\(152\) | −11.8393 | −0.960294 | ||||||||
\(153\) | 0.229788 | 0.0185773 | ||||||||
\(154\) | 2.41320 | 0.194462 | ||||||||
\(155\) | 10.6409 | 0.854700 | ||||||||
\(156\) | 10.6318 | 0.851226 | ||||||||
\(157\) | −14.0678 | −1.12273 | −0.561364 | − | 0.827569i | \(-0.689723\pi\) | ||||
−0.561364 | + | 0.827569i | \(0.689723\pi\) | |||||||
\(158\) | −16.6369 | −1.32356 | ||||||||
\(159\) | −6.56373 | −0.520538 | ||||||||
\(160\) | −7.46713 | −0.590328 | ||||||||
\(161\) | 14.0089 | 1.10406 | ||||||||
\(162\) | 24.5251 | 1.92687 | ||||||||
\(163\) | 23.4405 | 1.83600 | 0.918001 | − | 0.396578i | \(-0.129803\pi\) | ||||
0.918001 | + | 0.396578i | \(0.129803\pi\) | |||||||
\(164\) | 20.9570 | 1.63647 | ||||||||
\(165\) | −0.865853 | −0.0674066 | ||||||||
\(166\) | −0.789828 | −0.0613025 | ||||||||
\(167\) | 20.0398 | 1.55073 | 0.775364 | − | 0.631515i | \(-0.217566\pi\) | ||||
0.775364 | + | 0.631515i | \(0.217566\pi\) | |||||||
\(168\) | 9.33145 | 0.719937 | ||||||||
\(169\) | −9.63197 | −0.740921 | ||||||||
\(170\) | 0.356523 | 0.0273440 | ||||||||
\(171\) | 10.0422 | 0.767946 | ||||||||
\(172\) | −25.0364 | −1.90901 | ||||||||
\(173\) | −1.17842 | −0.0895934 | −0.0447967 | − | 0.998996i | \(-0.514264\pi\) | ||||
−0.0447967 | + | 0.998996i | \(0.514264\pi\) | |||||||
\(174\) | −42.1940 | −3.19872 | ||||||||
\(175\) | −2.68153 | −0.202705 | ||||||||
\(176\) | −0.784913 | −0.0591651 | ||||||||
\(177\) | 11.8559 | 0.891147 | ||||||||
\(178\) | 24.6140 | 1.84490 | ||||||||
\(179\) | 25.7489 | 1.92456 | 0.962281 | − | 0.272057i | \(-0.0877040\pi\) | ||||
0.962281 | + | 0.272057i | \(0.0877040\pi\) | |||||||
\(180\) | −3.88085 | −0.289261 | ||||||||
\(181\) | 10.0896 | 0.749951 | 0.374976 | − | 0.927035i | \(-0.377651\pi\) | ||||
0.374976 | + | 0.927035i | \(0.377651\pi\) | |||||||
\(182\) | 10.7366 | 0.795853 | ||||||||
\(183\) | 27.1118 | 2.00416 | ||||||||
\(184\) | 8.66077 | 0.638481 | ||||||||
\(185\) | −1.57980 | −0.116149 | ||||||||
\(186\) | 48.7312 | 3.57315 | ||||||||
\(187\) | 0.0674067 | 0.00492927 | ||||||||
\(188\) | −4.88485 | −0.356264 | ||||||||
\(189\) | 8.97130 | 0.652566 | ||||||||
\(190\) | 15.5807 | 1.13034 | ||||||||
\(191\) | 0.850433 | 0.0615352 | 0.0307676 | − | 0.999527i | \(-0.490205\pi\) | ||||
0.0307676 | + | 0.999527i | \(0.490205\pi\) | |||||||
\(192\) | −26.2080 | −1.89140 | ||||||||
\(193\) | −9.89347 | −0.712148 | −0.356074 | − | 0.934458i | \(-0.615885\pi\) | ||||
−0.356074 | + | 0.934458i | \(0.615885\pi\) | |||||||
\(194\) | 10.2034 | 0.732563 | ||||||||
\(195\) | −3.85229 | −0.275868 | ||||||||
\(196\) | 0.526075 | 0.0375768 | ||||||||
\(197\) | −3.85789 | −0.274863 | −0.137431 | − | 0.990511i | \(-0.543885\pi\) | ||||
−0.137431 | + | 0.990511i | \(0.543885\pi\) | |||||||
\(198\) | −1.26546 | −0.0899325 | ||||||||
\(199\) | 15.0938 | 1.06997 | 0.534985 | − | 0.844861i | \(-0.320317\pi\) | ||||
0.534985 | + | 0.844861i | \(0.320317\pi\) | |||||||
\(200\) | −1.65781 | −0.117225 | ||||||||
\(201\) | 19.4849 | 1.37436 | ||||||||
\(202\) | 14.7209 | 1.03576 | ||||||||
\(203\) | −24.7062 | −1.73403 | ||||||||
\(204\) | 0.946692 | 0.0662817 | ||||||||
\(205\) | −7.59348 | −0.530352 | ||||||||
\(206\) | −32.7592 | −2.28244 | ||||||||
\(207\) | −7.34614 | −0.510592 | ||||||||
\(208\) | −3.49218 | −0.242139 | ||||||||
\(209\) | 2.94580 | 0.203766 | ||||||||
\(210\) | −12.2804 | −0.847426 | ||||||||
\(211\) | −0.645352 | −0.0444279 | −0.0222139 | − | 0.999753i | \(-0.507071\pi\) | ||||
−0.0222139 | + | 0.999753i | \(0.507071\pi\) | |||||||
\(212\) | −8.62995 | −0.592708 | ||||||||
\(213\) | −21.5781 | −1.47851 | ||||||||
\(214\) | 10.5301 | 0.719823 | ||||||||
\(215\) | 9.07160 | 0.618678 | ||||||||
\(216\) | 5.54636 | 0.377382 | ||||||||
\(217\) | 28.5340 | 1.93701 | ||||||||
\(218\) | −12.1053 | −0.819874 | ||||||||
\(219\) | 17.5124 | 1.18338 | ||||||||
\(220\) | −1.13842 | −0.0767521 | ||||||||
\(221\) | 0.299901 | 0.0201735 | ||||||||
\(222\) | −7.23487 | −0.485573 | ||||||||
\(223\) | −7.35555 | −0.492564 | −0.246282 | − | 0.969198i | \(-0.579209\pi\) | ||||
−0.246282 | + | 0.969198i | \(0.579209\pi\) | |||||||
\(224\) | −20.0234 | −1.33787 | ||||||||
\(225\) | 1.40617 | 0.0937448 | ||||||||
\(226\) | −17.4495 | −1.16072 | ||||||||
\(227\) | 10.3846 | 0.689252 | 0.344626 | − | 0.938740i | \(-0.388006\pi\) | ||||
0.344626 | + | 0.938740i | \(0.388006\pi\) | |||||||
\(228\) | 41.3723 | 2.73995 | ||||||||
\(229\) | 21.5471 | 1.42387 | 0.711937 | − | 0.702243i | \(-0.247818\pi\) | ||||
0.711937 | + | 0.702243i | \(0.247818\pi\) | |||||||
\(230\) | −11.3977 | −0.751545 | ||||||||
\(231\) | −2.32181 | −0.152764 | ||||||||
\(232\) | −15.2742 | −1.00280 | ||||||||
\(233\) | −1.63338 | −0.107006 | −0.0535032 | − | 0.998568i | \(-0.517039\pi\) | ||||
−0.0535032 | + | 0.998568i | \(0.517039\pi\) | |||||||
\(234\) | −5.63020 | −0.368058 | ||||||||
\(235\) | 1.76996 | 0.115459 | ||||||||
\(236\) | 15.5881 | 1.01470 | ||||||||
\(237\) | 16.0068 | 1.03975 | ||||||||
\(238\) | 0.956027 | 0.0619700 | ||||||||
\(239\) | −7.92983 | −0.512938 | −0.256469 | − | 0.966552i | \(-0.582559\pi\) | ||||
−0.256469 | + | 0.966552i | \(0.582559\pi\) | |||||||
\(240\) | 3.99428 | 0.257830 | ||||||||
\(241\) | 23.5440 | 1.51660 | 0.758301 | − | 0.651905i | \(-0.226030\pi\) | ||||
0.758301 | + | 0.651905i | \(0.226030\pi\) | |||||||
\(242\) | 23.6276 | 1.51884 | ||||||||
\(243\) | −13.5595 | −0.869842 | ||||||||
\(244\) | 35.6465 | 2.28203 | ||||||||
\(245\) | −0.190616 | −0.0121780 | ||||||||
\(246\) | −34.7751 | −2.21718 | ||||||||
\(247\) | 13.1062 | 0.833931 | ||||||||
\(248\) | 17.6407 | 1.12018 | ||||||||
\(249\) | 0.759916 | 0.0481577 | ||||||||
\(250\) | 2.18171 | 0.137984 | ||||||||
\(251\) | 31.2993 | 1.97559 | 0.987796 | − | 0.155756i | \(-0.0497813\pi\) | ||||
0.987796 | + | 0.155756i | \(0.0497813\pi\) | |||||||
\(252\) | −10.4066 | −0.655555 | ||||||||
\(253\) | −2.15494 | −0.135480 | ||||||||
\(254\) | 13.3859 | 0.839906 | ||||||||
\(255\) | −0.343021 | −0.0214808 | ||||||||
\(256\) | −1.87579 | −0.117237 | ||||||||
\(257\) | 13.7076 | 0.855058 | 0.427529 | − | 0.904002i | \(-0.359384\pi\) | ||||
0.427529 | + | 0.904002i | \(0.359384\pi\) | |||||||
\(258\) | 41.5444 | 2.58644 | ||||||||
\(259\) | −4.23629 | −0.263230 | ||||||||
\(260\) | −5.06496 | −0.314116 | ||||||||
\(261\) | 12.9557 | 0.801938 | ||||||||
\(262\) | −1.25619 | −0.0776074 | ||||||||
\(263\) | 2.12966 | 0.131320 | 0.0656602 | − | 0.997842i | \(-0.479085\pi\) | ||||
0.0656602 | + | 0.997842i | \(0.479085\pi\) | |||||||
\(264\) | −1.43542 | −0.0883441 | ||||||||
\(265\) | 3.12694 | 0.192087 | ||||||||
\(266\) | 41.7802 | 2.56171 | ||||||||
\(267\) | −23.6819 | −1.44931 | ||||||||
\(268\) | 25.6186 | 1.56491 | ||||||||
\(269\) | 4.65888 | 0.284057 | 0.142028 | − | 0.989863i | \(-0.454638\pi\) | ||||
0.142028 | + | 0.989863i | \(0.454638\pi\) | |||||||
\(270\) | −7.29911 | −0.444210 | ||||||||
\(271\) | 12.4820 | 0.758226 | 0.379113 | − | 0.925350i | \(-0.376229\pi\) | ||||
0.379113 | + | 0.925350i | \(0.376229\pi\) | |||||||
\(272\) | −0.310955 | −0.0188544 | ||||||||
\(273\) | −10.3300 | −0.625202 | ||||||||
\(274\) | 23.0205 | 1.39072 | ||||||||
\(275\) | 0.412490 | 0.0248741 | ||||||||
\(276\) | −30.2650 | −1.82174 | ||||||||
\(277\) | 4.72817 | 0.284088 | 0.142044 | − | 0.989860i | \(-0.454633\pi\) | ||||
0.142044 | + | 0.989860i | \(0.454633\pi\) | |||||||
\(278\) | −26.7556 | −1.60470 | ||||||||
\(279\) | −14.9630 | −0.895809 | ||||||||
\(280\) | −4.44548 | −0.265668 | ||||||||
\(281\) | −8.04840 | −0.480127 | −0.240064 | − | 0.970757i | \(-0.577168\pi\) | ||||
−0.240064 | + | 0.970757i | \(0.577168\pi\) | |||||||
\(282\) | 8.10571 | 0.482688 | ||||||||
\(283\) | 17.8203 | 1.05931 | 0.529653 | − | 0.848214i | \(-0.322322\pi\) | ||||
0.529653 | + | 0.848214i | \(0.322322\pi\) | |||||||
\(284\) | −28.3707 | −1.68349 | ||||||||
\(285\) | −14.9907 | −0.887971 | ||||||||
\(286\) | −1.65158 | −0.0976598 | ||||||||
\(287\) | −20.3622 | −1.20194 | ||||||||
\(288\) | 10.5001 | 0.618722 | ||||||||
\(289\) | −16.9733 | −0.998429 | ||||||||
\(290\) | 20.1011 | 1.18038 | ||||||||
\(291\) | −9.81700 | −0.575483 | ||||||||
\(292\) | 23.0251 | 1.34744 | ||||||||
\(293\) | −10.4735 | −0.611867 | −0.305933 | − | 0.952053i | \(-0.598968\pi\) | ||||
−0.305933 | + | 0.952053i | \(0.598968\pi\) | |||||||
\(294\) | −0.872946 | −0.0509113 | ||||||||
\(295\) | −5.64814 | −0.328847 | ||||||||
\(296\) | −2.61902 | −0.152227 | ||||||||
\(297\) | −1.38002 | −0.0800770 | ||||||||
\(298\) | 34.1001 | 1.97536 | ||||||||
\(299\) | −9.58758 | −0.554464 | ||||||||
\(300\) | 5.79321 | 0.334471 | ||||||||
\(301\) | 24.3258 | 1.40212 | ||||||||
\(302\) | −34.2628 | −1.97160 | ||||||||
\(303\) | −14.1634 | −0.813667 | ||||||||
\(304\) | −13.5893 | −0.779402 | ||||||||
\(305\) | −12.9160 | −0.739568 | ||||||||
\(306\) | −0.501332 | −0.0286592 | ||||||||
\(307\) | 8.10659 | 0.462668 | 0.231334 | − | 0.972874i | \(-0.425691\pi\) | ||||
0.231334 | + | 0.972874i | \(0.425691\pi\) | |||||||
\(308\) | −3.05271 | −0.173944 | ||||||||
\(309\) | 31.5186 | 1.79303 | ||||||||
\(310\) | −23.2154 | −1.31855 | ||||||||
\(311\) | 10.3454 | 0.586634 | 0.293317 | − | 0.956015i | \(-0.405241\pi\) | ||||
0.293317 | + | 0.956015i | \(0.405241\pi\) | |||||||
\(312\) | −6.38637 | −0.361557 | ||||||||
\(313\) | 16.5124 | 0.933338 | 0.466669 | − | 0.884432i | \(-0.345454\pi\) | ||||
0.466669 | + | 0.884432i | \(0.345454\pi\) | |||||||
\(314\) | 30.6918 | 1.73204 | ||||||||
\(315\) | 3.77069 | 0.212455 | ||||||||
\(316\) | 21.0456 | 1.18391 | ||||||||
\(317\) | −7.75811 | −0.435739 | −0.217869 | − | 0.975978i | \(-0.569911\pi\) | ||||
−0.217869 | + | 0.975978i | \(0.569911\pi\) | |||||||
\(318\) | 14.3202 | 0.803035 | ||||||||
\(319\) | 3.80046 | 0.212785 | ||||||||
\(320\) | 12.4854 | 0.697955 | ||||||||
\(321\) | −10.1313 | −0.565475 | ||||||||
\(322\) | −30.5634 | −1.70323 | ||||||||
\(323\) | 1.16702 | 0.0649350 | ||||||||
\(324\) | −31.0242 | −1.72357 | ||||||||
\(325\) | 1.83522 | 0.101800 | ||||||||
\(326\) | −51.1404 | −2.83241 | ||||||||
\(327\) | 11.6469 | 0.644073 | ||||||||
\(328\) | −12.5886 | −0.695087 | ||||||||
\(329\) | 4.74620 | 0.261666 | ||||||||
\(330\) | 1.88904 | 0.103988 | ||||||||
\(331\) | 7.26729 | 0.399446 | 0.199723 | − | 0.979852i | \(-0.435996\pi\) | ||||
0.199723 | + | 0.979852i | \(0.435996\pi\) | |||||||
\(332\) | 0.999133 | 0.0548345 | ||||||||
\(333\) | 2.22147 | 0.121736 | ||||||||
\(334\) | −43.7211 | −2.39231 | ||||||||
\(335\) | −9.28256 | −0.507160 | ||||||||
\(336\) | 10.7108 | 0.584322 | ||||||||
\(337\) | 22.5005 | 1.22568 | 0.612839 | − | 0.790208i | \(-0.290027\pi\) | ||||
0.612839 | + | 0.790208i | \(0.290027\pi\) | |||||||
\(338\) | 21.0142 | 1.14302 | ||||||||
\(339\) | 16.7887 | 0.911836 | ||||||||
\(340\) | −0.451002 | −0.0244590 | ||||||||
\(341\) | −4.38928 | −0.237693 | ||||||||
\(342\) | −21.9092 | −1.18471 | ||||||||
\(343\) | 18.2596 | 0.985925 | ||||||||
\(344\) | 15.0390 | 0.810849 | ||||||||
\(345\) | 10.9661 | 0.590395 | ||||||||
\(346\) | 2.57097 | 0.138216 | ||||||||
\(347\) | −4.15850 | −0.223240 | −0.111620 | − | 0.993751i | \(-0.535604\pi\) | ||||
−0.111620 | + | 0.993751i | \(0.535604\pi\) | |||||||
\(348\) | 53.3755 | 2.86123 | ||||||||
\(349\) | 23.7678 | 1.27226 | 0.636132 | − | 0.771581i | \(-0.280534\pi\) | ||||
0.636132 | + | 0.771581i | \(0.280534\pi\) | |||||||
\(350\) | 5.85033 | 0.312713 | ||||||||
\(351\) | −6.13989 | −0.327723 | ||||||||
\(352\) | 3.08012 | 0.164171 | ||||||||
\(353\) | −15.5948 | −0.830025 | −0.415012 | − | 0.909816i | \(-0.636223\pi\) | ||||
−0.415012 | + | 0.909816i | \(0.636223\pi\) | |||||||
\(354\) | −25.8663 | −1.37478 | ||||||||
\(355\) | 10.2797 | 0.545592 | ||||||||
\(356\) | −31.1368 | −1.65025 | ||||||||
\(357\) | −0.919821 | −0.0486821 | ||||||||
\(358\) | −56.1767 | −2.96903 | ||||||||
\(359\) | −12.1179 | −0.639561 | −0.319780 | − | 0.947492i | \(-0.603609\pi\) | ||||
−0.319780 | + | 0.947492i | \(0.603609\pi\) | |||||||
\(360\) | 2.33117 | 0.122863 | ||||||||
\(361\) | 32.0012 | 1.68428 | ||||||||
\(362\) | −22.0125 | −1.15695 | ||||||||
\(363\) | −22.7328 | −1.19316 | ||||||||
\(364\) | −13.5819 | −0.711883 | ||||||||
\(365\) | −8.34284 | −0.436684 | ||||||||
\(366\) | −59.1502 | −3.09183 | ||||||||
\(367\) | −5.55057 | −0.289738 | −0.144869 | − | 0.989451i | \(-0.546276\pi\) | ||||
−0.144869 | + | 0.989451i | \(0.546276\pi\) | |||||||
\(368\) | 9.94098 | 0.518210 | ||||||||
\(369\) | 10.6777 | 0.555861 | ||||||||
\(370\) | 3.44667 | 0.179184 | ||||||||
\(371\) | 8.38500 | 0.435328 | ||||||||
\(372\) | −61.6451 | −3.19615 | ||||||||
\(373\) | −13.8265 | −0.715908 | −0.357954 | − | 0.933739i | \(-0.616526\pi\) | ||||
−0.357954 | + | 0.933739i | \(0.616526\pi\) | |||||||
\(374\) | −0.147062 | −0.00760440 | ||||||||
\(375\) | −2.09909 | −0.108396 | ||||||||
\(376\) | 2.93426 | 0.151323 | ||||||||
\(377\) | 16.9087 | 0.870844 | ||||||||
\(378\) | −19.5728 | −1.00672 | ||||||||
\(379\) | −0.771167 | −0.0396122 | −0.0198061 | − | 0.999804i | \(-0.506305\pi\) | ||||
−0.0198061 | + | 0.999804i | \(0.506305\pi\) | |||||||
\(380\) | −19.7096 | −1.01108 | ||||||||
\(381\) | −12.8790 | −0.659809 | ||||||||
\(382\) | −1.85540 | −0.0949305 | ||||||||
\(383\) | −11.5295 | −0.589130 | −0.294565 | − | 0.955631i | \(-0.595175\pi\) | ||||
−0.294565 | + | 0.955631i | \(0.595175\pi\) | |||||||
\(384\) | 25.8299 | 1.31813 | ||||||||
\(385\) | 1.10611 | 0.0563724 | ||||||||
\(386\) | 21.5847 | 1.09863 | ||||||||
\(387\) | −12.7562 | −0.648435 | ||||||||
\(388\) | −12.9073 | −0.655271 | ||||||||
\(389\) | −8.62762 | −0.437437 | −0.218719 | − | 0.975788i | \(-0.570188\pi\) | ||||
−0.218719 | + | 0.975788i | \(0.570188\pi\) | |||||||
\(390\) | 8.40458 | 0.425583 | ||||||||
\(391\) | −0.853711 | −0.0431740 | ||||||||
\(392\) | −0.316006 | −0.0159607 | ||||||||
\(393\) | 1.20861 | 0.0609664 | ||||||||
\(394\) | 8.41680 | 0.424032 | ||||||||
\(395\) | −7.62559 | −0.383685 | ||||||||
\(396\) | 1.60081 | 0.0804438 | ||||||||
\(397\) | −26.2096 | −1.31542 | −0.657712 | − | 0.753269i | \(-0.728476\pi\) | ||||
−0.657712 | + | 0.753269i | \(0.728476\pi\) | |||||||
\(398\) | −32.9303 | −1.65065 | ||||||||
\(399\) | −40.1980 | −2.01242 | ||||||||
\(400\) | −1.90287 | −0.0951433 | ||||||||
\(401\) | 8.37489 | 0.418222 | 0.209111 | − | 0.977892i | \(-0.432943\pi\) | ||||
0.209111 | + | 0.977892i | \(0.432943\pi\) | |||||||
\(402\) | −42.5105 | −2.12023 | ||||||||
\(403\) | −19.5284 | −0.972780 | ||||||||
\(404\) | −18.6220 | −0.926478 | ||||||||
\(405\) | 11.2412 | 0.558580 | ||||||||
\(406\) | 53.9018 | 2.67510 | ||||||||
\(407\) | 0.651653 | 0.0323012 | ||||||||
\(408\) | −0.568664 | −0.0281531 | ||||||||
\(409\) | 21.2094 | 1.04874 | 0.524368 | − | 0.851492i | \(-0.324302\pi\) | ||||
0.524368 | + | 0.851492i | \(0.324302\pi\) | |||||||
\(410\) | 16.5668 | 0.818175 | ||||||||
\(411\) | −22.1487 | −1.09251 | ||||||||
\(412\) | 41.4405 | 2.04163 | ||||||||
\(413\) | −15.1457 | −0.745270 | ||||||||
\(414\) | 16.0272 | 0.787693 | ||||||||
\(415\) | −0.362022 | −0.0177710 | ||||||||
\(416\) | 13.7038 | 0.671885 | ||||||||
\(417\) | 25.7424 | 1.26061 | ||||||||
\(418\) | −6.42690 | −0.314350 | ||||||||
\(419\) | 14.2591 | 0.696604 | 0.348302 | − | 0.937382i | \(-0.386758\pi\) | ||||
0.348302 | + | 0.937382i | \(0.386758\pi\) | |||||||
\(420\) | 15.5347 | 0.758014 | ||||||||
\(421\) | −6.51538 | −0.317540 | −0.158770 | − | 0.987316i | \(-0.550753\pi\) | ||||
−0.158770 | + | 0.987316i | \(0.550753\pi\) | |||||||
\(422\) | 1.40797 | 0.0685390 | ||||||||
\(423\) | −2.48886 | −0.121013 | ||||||||
\(424\) | 5.18389 | 0.251752 | ||||||||
\(425\) | 0.163414 | 0.00792675 | ||||||||
\(426\) | 47.0772 | 2.28090 | ||||||||
\(427\) | −34.6347 | −1.67609 | ||||||||
\(428\) | −13.3206 | −0.643875 | ||||||||
\(429\) | 1.58903 | 0.0767191 | ||||||||
\(430\) | −19.7916 | −0.954437 | ||||||||
\(431\) | −10.7471 | −0.517670 | −0.258835 | − | 0.965922i | \(-0.583339\pi\) | ||||
−0.258835 | + | 0.965922i | \(0.583339\pi\) | |||||||
\(432\) | 6.36620 | 0.306294 | ||||||||
\(433\) | 4.83537 | 0.232373 | 0.116187 | − | 0.993227i | \(-0.462933\pi\) | ||||
0.116187 | + | 0.993227i | \(0.462933\pi\) | |||||||
\(434\) | −62.2529 | −2.98824 | ||||||||
\(435\) | −19.3399 | −0.927276 | ||||||||
\(436\) | 15.3132 | 0.733370 | ||||||||
\(437\) | −37.3088 | −1.78472 | ||||||||
\(438\) | −38.2069 | −1.82560 | ||||||||
\(439\) | −11.5831 | −0.552831 | −0.276416 | − | 0.961038i | \(-0.589147\pi\) | ||||
−0.276416 | + | 0.961038i | \(0.589147\pi\) | |||||||
\(440\) | 0.683831 | 0.0326004 | ||||||||
\(441\) | 0.268039 | 0.0127638 | ||||||||
\(442\) | −0.654297 | −0.0311218 | ||||||||
\(443\) | −5.34739 | −0.254062 | −0.127031 | − | 0.991899i | \(-0.540545\pi\) | ||||
−0.127031 | + | 0.991899i | \(0.540545\pi\) | |||||||
\(444\) | 9.15212 | 0.434340 | ||||||||
\(445\) | 11.2820 | 0.534817 | ||||||||
\(446\) | 16.0477 | 0.759880 | ||||||||
\(447\) | −32.8087 | −1.55180 | ||||||||
\(448\) | 33.4800 | 1.58178 | ||||||||
\(449\) | 17.0683 | 0.805503 | 0.402752 | − | 0.915309i | \(-0.368054\pi\) | ||||
0.402752 | + | 0.915309i | \(0.368054\pi\) | |||||||
\(450\) | −3.06786 | −0.144620 | ||||||||
\(451\) | 3.13223 | 0.147491 | ||||||||
\(452\) | 22.0736 | 1.03826 | ||||||||
\(453\) | 32.9652 | 1.54884 | ||||||||
\(454\) | −22.6563 | −1.06331 | ||||||||
\(455\) | 4.92120 | 0.230709 | ||||||||
\(456\) | −24.8517 | −1.16379 | ||||||||
\(457\) | −40.2217 | −1.88149 | −0.940745 | − | 0.339114i | \(-0.889873\pi\) | ||||
−0.940745 | + | 0.339114i | \(0.889873\pi\) | |||||||
\(458\) | −47.0096 | −2.19662 | ||||||||
\(459\) | −0.546716 | −0.0255185 | ||||||||
\(460\) | 14.4181 | 0.672250 | ||||||||
\(461\) | 13.4737 | 0.627535 | 0.313768 | − | 0.949500i | \(-0.398409\pi\) | ||||
0.313768 | + | 0.949500i | \(0.398409\pi\) | |||||||
\(462\) | 5.06553 | 0.235670 | ||||||||
\(463\) | 11.1515 | 0.518253 | 0.259127 | − | 0.965843i | \(-0.416565\pi\) | ||||
0.259127 | + | 0.965843i | \(0.416565\pi\) | |||||||
\(464\) | −17.5320 | −0.813902 | ||||||||
\(465\) | 22.3362 | 1.03582 | ||||||||
\(466\) | 3.56357 | 0.165079 | ||||||||
\(467\) | 26.1996 | 1.21237 | 0.606186 | − | 0.795323i | \(-0.292699\pi\) | ||||
0.606186 | + | 0.795323i | \(0.292699\pi\) | |||||||
\(468\) | 7.12221 | 0.329224 | ||||||||
\(469\) | −24.8915 | −1.14938 | ||||||||
\(470\) | −3.86154 | −0.178119 | ||||||||
\(471\) | −29.5295 | −1.36065 | ||||||||
\(472\) | −9.36356 | −0.430993 | ||||||||
\(473\) | −3.74194 | −0.172055 | ||||||||
\(474\) | −34.9222 | −1.60403 | ||||||||
\(475\) | 7.14152 | 0.327675 | ||||||||
\(476\) | −1.20938 | −0.0554316 | ||||||||
\(477\) | −4.39702 | −0.201326 | ||||||||
\(478\) | 17.3006 | 0.791311 | ||||||||
\(479\) | 14.7105 | 0.672140 | 0.336070 | − | 0.941837i | \(-0.390902\pi\) | ||||
0.336070 | + | 0.941837i | \(0.390902\pi\) | |||||||
\(480\) | −15.6742 | −0.715424 | ||||||||
\(481\) | 2.89928 | 0.132196 | ||||||||
\(482\) | −51.3662 | −2.33967 | ||||||||
\(483\) | 29.4059 | 1.33802 | ||||||||
\(484\) | −29.8890 | −1.35859 | ||||||||
\(485\) | 4.67679 | 0.212362 | ||||||||
\(486\) | 29.5829 | 1.34191 | ||||||||
\(487\) | −5.28058 | −0.239286 | −0.119643 | − | 0.992817i | \(-0.538175\pi\) | ||||
−0.119643 | + | 0.992817i | \(0.538175\pi\) | |||||||
\(488\) | −21.4123 | −0.969290 | ||||||||
\(489\) | 49.2037 | 2.22507 | ||||||||
\(490\) | 0.415869 | 0.0187871 | ||||||||
\(491\) | 12.1477 | 0.548217 | 0.274108 | − | 0.961699i | \(-0.411617\pi\) | ||||
0.274108 | + | 0.961699i | \(0.411617\pi\) | |||||||
\(492\) | 43.9906 | 1.98325 | ||||||||
\(493\) | 1.50561 | 0.0678093 | ||||||||
\(494\) | −28.5941 | −1.28651 | ||||||||
\(495\) | −0.580032 | −0.0260705 | ||||||||
\(496\) | 20.2482 | 0.909173 | ||||||||
\(497\) | 27.5655 | 1.23648 | ||||||||
\(498\) | −1.65792 | −0.0742931 | ||||||||
\(499\) | 20.6552 | 0.924653 | 0.462327 | − | 0.886710i | \(-0.347015\pi\) | ||||
0.462327 | + | 0.886710i | \(0.347015\pi\) | |||||||
\(500\) | −2.75987 | −0.123425 | ||||||||
\(501\) | 42.0653 | 1.87934 | ||||||||
\(502\) | −68.2860 | −3.04775 | ||||||||
\(503\) | −2.23118 | −0.0994833 | −0.0497417 | − | 0.998762i | \(-0.515840\pi\) | ||||
−0.0497417 | + | 0.998762i | \(0.515840\pi\) | |||||||
\(504\) | 6.25110 | 0.278446 | ||||||||
\(505\) | 6.74742 | 0.300256 | ||||||||
\(506\) | 4.70145 | 0.209005 | ||||||||
\(507\) | −20.2184 | −0.897929 | ||||||||
\(508\) | −16.9332 | −0.751288 | ||||||||
\(509\) | −33.8303 | −1.49950 | −0.749751 | − | 0.661720i | \(-0.769827\pi\) | ||||
−0.749751 | + | 0.661720i | \(0.769827\pi\) | |||||||
\(510\) | 0.748373 | 0.0331385 | ||||||||
\(511\) | −22.3716 | −0.989661 | ||||||||
\(512\) | −20.5181 | −0.906782 | ||||||||
\(513\) | −23.8926 | −1.05488 | ||||||||
\(514\) | −29.9061 | −1.31910 | ||||||||
\(515\) | −15.0154 | −0.661657 | ||||||||
\(516\) | −52.5536 | −2.31355 | ||||||||
\(517\) | −0.730090 | −0.0321093 | ||||||||
\(518\) | 9.24236 | 0.406086 | ||||||||
\(519\) | −2.47360 | −0.108579 | ||||||||
\(520\) | 3.04245 | 0.133420 | ||||||||
\(521\) | 15.4443 | 0.676626 | 0.338313 | − | 0.941034i | \(-0.390144\pi\) | ||||
0.338313 | + | 0.941034i | \(0.390144\pi\) | |||||||
\(522\) | −28.2656 | −1.23715 | ||||||||
\(523\) | 15.1533 | 0.662609 | 0.331305 | − | 0.943524i | \(-0.392511\pi\) | ||||
0.331305 | + | 0.943524i | \(0.392511\pi\) | |||||||
\(524\) | 1.58908 | 0.0694191 | ||||||||
\(525\) | −5.62877 | −0.245660 | ||||||||
\(526\) | −4.64630 | −0.202588 | ||||||||
\(527\) | −1.73888 | −0.0757467 | ||||||||
\(528\) | −1.64760 | −0.0717027 | ||||||||
\(529\) | 4.29244 | 0.186628 | ||||||||
\(530\) | −6.82209 | −0.296333 | ||||||||
\(531\) | 7.94225 | 0.344664 | ||||||||
\(532\) | −52.8520 | −2.29143 | ||||||||
\(533\) | 13.9357 | 0.603622 | ||||||||
\(534\) | 51.6670 | 2.23585 | ||||||||
\(535\) | 4.82653 | 0.208669 | ||||||||
\(536\) | −15.3887 | −0.664692 | ||||||||
\(537\) | 54.0492 | 2.33239 | ||||||||
\(538\) | −10.1643 | −0.438215 | ||||||||
\(539\) | 0.0786272 | 0.00338671 | ||||||||
\(540\) | 9.23338 | 0.397341 | ||||||||
\(541\) | 14.8129 | 0.636857 | 0.318428 | − | 0.947947i | \(-0.396845\pi\) | ||||
0.318428 | + | 0.947947i | \(0.396845\pi\) | |||||||
\(542\) | −27.2321 | −1.16972 | ||||||||
\(543\) | 21.1789 | 0.908873 | ||||||||
\(544\) | 1.22023 | 0.0523171 | ||||||||
\(545\) | −5.54853 | −0.237673 | ||||||||
\(546\) | 22.5372 | 0.964501 | ||||||||
\(547\) | 3.51714 | 0.150382 | 0.0751910 | − | 0.997169i | \(-0.476043\pi\) | ||||
0.0751910 | + | 0.997169i | \(0.476043\pi\) | |||||||
\(548\) | −29.1210 | −1.24399 | ||||||||
\(549\) | 18.1621 | 0.775140 | ||||||||
\(550\) | −0.899935 | −0.0383733 | ||||||||
\(551\) | 65.7981 | 2.80309 | ||||||||
\(552\) | 18.1797 | 0.773781 | ||||||||
\(553\) | −20.4483 | −0.869549 | ||||||||
\(554\) | −10.3155 | −0.438263 | ||||||||
\(555\) | −3.31614 | −0.140762 | ||||||||
\(556\) | 33.8459 | 1.43539 | ||||||||
\(557\) | 8.07874 | 0.342307 | 0.171154 | − | 0.985244i | \(-0.445251\pi\) | ||||
0.171154 | + | 0.985244i | \(0.445251\pi\) | |||||||
\(558\) | 32.6449 | 1.38197 | ||||||||
\(559\) | −16.6484 | −0.704151 | ||||||||
\(560\) | −5.10260 | −0.215624 | ||||||||
\(561\) | 0.141493 | 0.00597383 | ||||||||
\(562\) | 17.5593 | 0.740694 | ||||||||
\(563\) | 20.1854 | 0.850715 | 0.425357 | − | 0.905025i | \(-0.360148\pi\) | ||||
0.425357 | + | 0.905025i | \(0.360148\pi\) | |||||||
\(564\) | −10.2537 | −0.431760 | ||||||||
\(565\) | −7.99808 | −0.336482 | ||||||||
\(566\) | −38.8787 | −1.63420 | ||||||||
\(567\) | 30.1436 | 1.26591 | ||||||||
\(568\) | 17.0419 | 0.715062 | ||||||||
\(569\) | 13.3507 | 0.559690 | 0.279845 | − | 0.960045i | \(-0.409717\pi\) | ||||
0.279845 | + | 0.960045i | \(0.409717\pi\) | |||||||
\(570\) | 32.7053 | 1.36988 | ||||||||
\(571\) | 35.1768 | 1.47210 | 0.736052 | − | 0.676925i | \(-0.236688\pi\) | ||||
0.736052 | + | 0.676925i | \(0.236688\pi\) | |||||||
\(572\) | 2.08925 | 0.0873558 | ||||||||
\(573\) | 1.78513 | 0.0745750 | ||||||||
\(574\) | 44.4244 | 1.85424 | ||||||||
\(575\) | −5.22422 | −0.217865 | ||||||||
\(576\) | −17.5566 | −0.731525 | ||||||||
\(577\) | 2.88165 | 0.119965 | 0.0599823 | − | 0.998199i | \(-0.480896\pi\) | ||||
0.0599823 | + | 0.998199i | \(0.480896\pi\) | |||||||
\(578\) | 37.0308 | 1.54028 | ||||||||
\(579\) | −20.7673 | −0.863058 | ||||||||
\(580\) | −25.4279 | −1.05584 | ||||||||
\(581\) | −0.970774 | −0.0402745 | ||||||||
\(582\) | 21.4179 | 0.887800 | ||||||||
\(583\) | −1.28983 | −0.0534194 | ||||||||
\(584\) | −13.8309 | −0.572325 | ||||||||
\(585\) | −2.58063 | −0.106696 | ||||||||
\(586\) | 22.8501 | 0.943929 | ||||||||
\(587\) | −15.3878 | −0.635122 | −0.317561 | − | 0.948238i | \(-0.602864\pi\) | ||||
−0.317561 | + | 0.948238i | \(0.602864\pi\) | |||||||
\(588\) | 1.10428 | 0.0455396 | ||||||||
\(589\) | −75.9923 | −3.13121 | ||||||||
\(590\) | 12.3226 | 0.507314 | ||||||||
\(591\) | −8.09804 | −0.333109 | ||||||||
\(592\) | −3.00615 | −0.123552 | ||||||||
\(593\) | −28.9773 | −1.18995 | −0.594977 | − | 0.803742i | \(-0.702839\pi\) | ||||
−0.594977 | + | 0.803742i | \(0.702839\pi\) | |||||||
\(594\) | 3.01081 | 0.123535 | ||||||||
\(595\) | 0.438200 | 0.0179645 | ||||||||
\(596\) | −43.1366 | −1.76694 | ||||||||
\(597\) | 31.6832 | 1.29671 | ||||||||
\(598\) | 20.9173 | 0.855374 | ||||||||
\(599\) | 10.3313 | 0.422125 | 0.211062 | − | 0.977473i | \(-0.432308\pi\) | ||||
0.211062 | + | 0.977473i | \(0.432308\pi\) | |||||||
\(600\) | −3.47990 | −0.142066 | ||||||||
\(601\) | 27.5913 | 1.12547 | 0.562737 | − | 0.826636i | \(-0.309748\pi\) | ||||
0.562737 | + | 0.826636i | \(0.309748\pi\) | |||||||
\(602\) | −53.0719 | −2.16305 | ||||||||
\(603\) | 13.0529 | 0.531554 | ||||||||
\(604\) | 43.3424 | 1.76358 | ||||||||
\(605\) | 10.8299 | 0.440296 | ||||||||
\(606\) | 30.9005 | 1.25525 | ||||||||
\(607\) | 40.1345 | 1.62901 | 0.814505 | − | 0.580156i | \(-0.197008\pi\) | ||||
0.814505 | + | 0.580156i | \(0.197008\pi\) | |||||||
\(608\) | 53.3266 | 2.16268 | ||||||||
\(609\) | −51.8605 | −2.10149 | ||||||||
\(610\) | 28.1790 | 1.14093 | ||||||||
\(611\) | −3.24826 | −0.131411 | ||||||||
\(612\) | 0.634185 | 0.0256354 | ||||||||
\(613\) | 8.72394 | 0.352357 | 0.176178 | − | 0.984358i | \(-0.443626\pi\) | ||||
0.176178 | + | 0.984358i | \(0.443626\pi\) | |||||||
\(614\) | −17.6862 | −0.713759 | ||||||||
\(615\) | −15.9394 | −0.642738 | ||||||||
\(616\) | 1.83372 | 0.0738825 | ||||||||
\(617\) | 16.3340 | 0.657582 | 0.328791 | − | 0.944403i | \(-0.393359\pi\) | ||||
0.328791 | + | 0.944403i | \(0.393359\pi\) | |||||||
\(618\) | −68.7645 | −2.76612 | ||||||||
\(619\) | −31.2311 | −1.25528 | −0.627641 | − | 0.778503i | \(-0.715980\pi\) | ||||
−0.627641 | + | 0.778503i | \(0.715980\pi\) | |||||||
\(620\) | 29.3675 | 1.17943 | ||||||||
\(621\) | 17.4781 | 0.701371 | ||||||||
\(622\) | −22.5707 | −0.905003 | ||||||||
\(623\) | 30.2530 | 1.21206 | ||||||||
\(624\) | −7.33039 | −0.293450 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −36.0254 | −1.43986 | ||||||||
\(627\) | 6.18350 | 0.246945 | ||||||||
\(628\) | −38.8251 | −1.54929 | ||||||||
\(629\) | 0.258162 | 0.0102936 | ||||||||
\(630\) | −8.22657 | −0.327754 | ||||||||
\(631\) | −15.0017 | −0.597210 | −0.298605 | − | 0.954377i | \(-0.596521\pi\) | ||||
−0.298605 | + | 0.954377i | \(0.596521\pi\) | |||||||
\(632\) | −12.6418 | −0.502864 | ||||||||
\(633\) | −1.35465 | −0.0538425 | ||||||||
\(634\) | 16.9260 | 0.672216 | ||||||||
\(635\) | 6.13550 | 0.243480 | ||||||||
\(636\) | −18.1150 | −0.718308 | ||||||||
\(637\) | 0.349822 | 0.0138605 | ||||||||
\(638\) | −8.29151 | −0.328264 | ||||||||
\(639\) | −14.4551 | −0.571834 | ||||||||
\(640\) | −12.3053 | −0.486409 | ||||||||
\(641\) | 15.9636 | 0.630523 | 0.315261 | − | 0.949005i | \(-0.397908\pi\) | ||||
0.315261 | + | 0.949005i | \(0.397908\pi\) | |||||||
\(642\) | 22.1036 | 0.872360 | ||||||||
\(643\) | −16.5047 | −0.650881 | −0.325440 | − | 0.945563i | \(-0.605513\pi\) | ||||
−0.325440 | + | 0.945563i | \(0.605513\pi\) | |||||||
\(644\) | 38.6627 | 1.52353 | ||||||||
\(645\) | 19.0421 | 0.749781 | ||||||||
\(646\) | −2.54611 | −0.100175 | ||||||||
\(647\) | 25.5197 | 1.00328 | 0.501642 | − | 0.865075i | \(-0.332729\pi\) | ||||
0.501642 | + | 0.865075i | \(0.332729\pi\) | |||||||
\(648\) | 18.6358 | 0.732083 | ||||||||
\(649\) | 2.32980 | 0.0914527 | ||||||||
\(650\) | −4.00392 | −0.157047 | ||||||||
\(651\) | 59.8953 | 2.34748 | ||||||||
\(652\) | 64.6927 | 2.53356 | ||||||||
\(653\) | 16.3131 | 0.638383 | 0.319191 | − | 0.947690i | \(-0.396589\pi\) | ||||
0.319191 | + | 0.947690i | \(0.396589\pi\) | |||||||
\(654\) | −25.4101 | −0.993613 | ||||||||
\(655\) | −0.575780 | −0.0224976 | ||||||||
\(656\) | −14.4494 | −0.564153 | ||||||||
\(657\) | 11.7315 | 0.457688 | ||||||||
\(658\) | −10.3548 | −0.403674 | ||||||||
\(659\) | 9.11201 | 0.354954 | 0.177477 | − | 0.984125i | \(-0.443207\pi\) | ||||
0.177477 | + | 0.984125i | \(0.443207\pi\) | |||||||
\(660\) | −2.38964 | −0.0930166 | ||||||||
\(661\) | 24.9480 | 0.970363 | 0.485182 | − | 0.874413i | \(-0.338753\pi\) | ||||
0.485182 | + | 0.874413i | \(0.338753\pi\) | |||||||
\(662\) | −15.8551 | −0.616227 | ||||||||
\(663\) | 0.629518 | 0.0244485 | ||||||||
\(664\) | −0.600165 | −0.0232909 | ||||||||
\(665\) | 19.1502 | 0.742613 | ||||||||
\(666\) | −4.84661 | −0.187802 | ||||||||
\(667\) | −48.1331 | −1.86372 | ||||||||
\(668\) | 55.3072 | 2.13990 | ||||||||
\(669\) | −15.4399 | −0.596943 | ||||||||
\(670\) | 20.2519 | 0.782398 | ||||||||
\(671\) | 5.32772 | 0.205674 | ||||||||
\(672\) | −42.0308 | −1.62137 | ||||||||
\(673\) | 14.6152 | 0.563375 | 0.281687 | − | 0.959506i | \(-0.409106\pi\) | ||||
0.281687 | + | 0.959506i | \(0.409106\pi\) | |||||||
\(674\) | −49.0895 | −1.89086 | ||||||||
\(675\) | −3.34559 | −0.128772 | ||||||||
\(676\) | −26.5830 | −1.02242 | ||||||||
\(677\) | −21.5771 | −0.829274 | −0.414637 | − | 0.909987i | \(-0.636092\pi\) | ||||
−0.414637 | + | 0.909987i | \(0.636092\pi\) | |||||||
\(678\) | −36.6281 | −1.40669 | ||||||||
\(679\) | 12.5410 | 0.481279 | ||||||||
\(680\) | 0.270910 | 0.0103889 | ||||||||
\(681\) | 21.7983 | 0.835311 | ||||||||
\(682\) | 9.57614 | 0.366689 | ||||||||
\(683\) | −0.513188 | −0.0196366 | −0.00981829 | − | 0.999952i | \(-0.503125\pi\) | ||||
−0.00981829 | + | 0.999952i | \(0.503125\pi\) | |||||||
\(684\) | 27.7151 | 1.05971 | ||||||||
\(685\) | 10.5516 | 0.403155 | ||||||||
\(686\) | −39.8372 | −1.52099 | ||||||||
\(687\) | 45.2293 | 1.72561 | ||||||||
\(688\) | 17.2620 | 0.658109 | ||||||||
\(689\) | −5.73863 | −0.218624 | ||||||||
\(690\) | −23.9249 | −0.910804 | ||||||||
\(691\) | 2.16319 | 0.0822917 | 0.0411459 | − | 0.999153i | \(-0.486899\pi\) | ||||
0.0411459 | + | 0.999153i | \(0.486899\pi\) | |||||||
\(692\) | −3.25228 | −0.123633 | ||||||||
\(693\) | −1.55537 | −0.0590838 | ||||||||
\(694\) | 9.07266 | 0.344393 | ||||||||
\(695\) | −12.2636 | −0.465185 | ||||||||
\(696\) | −32.0619 | −1.21530 | ||||||||
\(697\) | 1.24088 | 0.0470018 | ||||||||
\(698\) | −51.8546 | −1.96272 | ||||||||
\(699\) | −3.42861 | −0.129682 | ||||||||
\(700\) | −7.40067 | −0.279719 | ||||||||
\(701\) | −35.7695 | −1.35100 | −0.675498 | − | 0.737361i | \(-0.736072\pi\) | ||||
−0.675498 | + | 0.737361i | \(0.736072\pi\) | |||||||
\(702\) | 13.3955 | 0.505579 | ||||||||
\(703\) | 11.2822 | 0.425515 | ||||||||
\(704\) | −5.15010 | −0.194102 | ||||||||
\(705\) | 3.71530 | 0.139926 | ||||||||
\(706\) | 34.0233 | 1.28048 | ||||||||
\(707\) | 18.0934 | 0.680473 | ||||||||
\(708\) | 32.7208 | 1.22972 | ||||||||
\(709\) | −25.0734 | −0.941650 | −0.470825 | − | 0.882227i | \(-0.656044\pi\) | ||||
−0.470825 | + | 0.882227i | \(0.656044\pi\) | |||||||
\(710\) | −22.4274 | −0.841687 | ||||||||
\(711\) | 10.7229 | 0.402140 | ||||||||
\(712\) | 18.7034 | 0.700940 | ||||||||
\(713\) | 55.5905 | 2.08188 | ||||||||
\(714\) | 2.00679 | 0.0751021 | ||||||||
\(715\) | −0.757010 | −0.0283106 | ||||||||
\(716\) | 71.0635 | 2.65577 | ||||||||
\(717\) | −16.6454 | −0.621634 | ||||||||
\(718\) | 26.4379 | 0.986652 | ||||||||
\(719\) | −3.84664 | −0.143456 | −0.0717278 | − | 0.997424i | \(-0.522851\pi\) | ||||
−0.0717278 | + | 0.997424i | \(0.522851\pi\) | |||||||
\(720\) | 2.67576 | 0.0997195 | ||||||||
\(721\) | −40.2642 | −1.49952 | ||||||||
\(722\) | −69.8175 | −2.59834 | ||||||||
\(723\) | 49.4209 | 1.83798 | ||||||||
\(724\) | 27.8459 | 1.03488 | ||||||||
\(725\) | 9.21346 | 0.342179 | ||||||||
\(726\) | 49.5965 | 1.84070 | ||||||||
\(727\) | 14.9477 | 0.554381 | 0.277190 | − | 0.960815i | \(-0.410597\pi\) | ||||
0.277190 | + | 0.960815i | \(0.410597\pi\) | |||||||
\(728\) | 8.15843 | 0.302371 | ||||||||
\(729\) | 5.26100 | 0.194852 | ||||||||
\(730\) | 18.2017 | 0.673674 | ||||||||
\(731\) | −1.48243 | −0.0548296 | ||||||||
\(732\) | 74.8251 | 2.76561 | ||||||||
\(733\) | −15.8984 | −0.587222 | −0.293611 | − | 0.955925i | \(-0.594857\pi\) | ||||
−0.293611 | + | 0.955925i | \(0.594857\pi\) | |||||||
\(734\) | 12.1098 | 0.446979 | ||||||||
\(735\) | −0.400120 | −0.0147586 | ||||||||
\(736\) | −39.0099 | −1.43792 | ||||||||
\(737\) | 3.82896 | 0.141042 | ||||||||
\(738\) | −23.2957 | −0.857528 | ||||||||
\(739\) | 36.0121 | 1.32473 | 0.662363 | − | 0.749183i | \(-0.269554\pi\) | ||||
0.662363 | + | 0.749183i | \(0.269554\pi\) | |||||||
\(740\) | −4.36004 | −0.160278 | ||||||||
\(741\) | 27.5112 | 1.01065 | ||||||||
\(742\) | −18.2937 | −0.671581 | ||||||||
\(743\) | −26.0522 | −0.955763 | −0.477882 | − | 0.878424i | \(-0.658595\pi\) | ||||
−0.477882 | + | 0.878424i | \(0.658595\pi\) | |||||||
\(744\) | 37.0293 | 1.35756 | ||||||||
\(745\) | 15.6300 | 0.572637 | ||||||||
\(746\) | 30.1654 | 1.10443 | ||||||||
\(747\) | 0.509065 | 0.0186257 | ||||||||
\(748\) | 0.186034 | 0.00680206 | ||||||||
\(749\) | 12.9425 | 0.472909 | ||||||||
\(750\) | 4.57961 | 0.167224 | ||||||||
\(751\) | 1.75278 | 0.0639600 | 0.0319800 | − | 0.999489i | \(-0.489819\pi\) | ||||
0.0319800 | + | 0.999489i | \(0.489819\pi\) | |||||||
\(752\) | 3.36799 | 0.122818 | ||||||||
\(753\) | 65.6999 | 2.39424 | ||||||||
\(754\) | −36.8900 | −1.34345 | ||||||||
\(755\) | −15.7045 | −0.571546 | ||||||||
\(756\) | 24.7596 | 0.900498 | ||||||||
\(757\) | −15.8250 | −0.575171 | −0.287586 | − | 0.957755i | \(-0.592853\pi\) | ||||
−0.287586 | + | 0.957755i | \(0.592853\pi\) | |||||||
\(758\) | 1.68247 | 0.0611099 | ||||||||
\(759\) | −4.52340 | −0.164189 | ||||||||
\(760\) | 11.8393 | 0.429456 | ||||||||
\(761\) | −36.0339 | −1.30623 | −0.653113 | − | 0.757260i | \(-0.726537\pi\) | ||||
−0.653113 | + | 0.757260i | \(0.726537\pi\) | |||||||
\(762\) | 28.0982 | 1.01789 | ||||||||
\(763\) | −14.8786 | −0.538640 | ||||||||
\(764\) | 2.34708 | 0.0849145 | ||||||||
\(765\) | −0.229788 | −0.00830802 | ||||||||
\(766\) | 25.1541 | 0.908853 | ||||||||
\(767\) | 10.3656 | 0.374279 | ||||||||
\(768\) | −3.93745 | −0.142080 | ||||||||
\(769\) | 30.4982 | 1.09979 | 0.549896 | − | 0.835233i | \(-0.314667\pi\) | ||||
0.549896 | + | 0.835233i | \(0.314667\pi\) | |||||||
\(770\) | −2.41320 | −0.0869658 | ||||||||
\(771\) | 28.7735 | 1.03625 | ||||||||
\(772\) | −27.3047 | −0.982717 | ||||||||
\(773\) | −2.03719 | −0.0732725 | −0.0366362 | − | 0.999329i | \(-0.511664\pi\) | ||||
−0.0366362 | + | 0.999329i | \(0.511664\pi\) | |||||||
\(774\) | 27.8304 | 1.00034 | ||||||||
\(775\) | −10.6409 | −0.382233 | ||||||||
\(776\) | 7.75325 | 0.278325 | ||||||||
\(777\) | −8.89234 | −0.319011 | ||||||||
\(778\) | 18.8230 | 0.674836 | ||||||||
\(779\) | 54.2289 | 1.94295 | ||||||||
\(780\) | −10.6318 | −0.380680 | ||||||||
\(781\) | −4.24029 | −0.151730 | ||||||||
\(782\) | 1.86255 | 0.0666047 | ||||||||
\(783\) | −30.8244 | −1.10158 | ||||||||
\(784\) | −0.362717 | −0.0129542 | ||||||||
\(785\) | 14.0678 | 0.502100 | ||||||||
\(786\) | −2.63684 | −0.0940531 | ||||||||
\(787\) | 8.41615 | 0.300003 | 0.150002 | − | 0.988686i | \(-0.452072\pi\) | ||||
0.150002 | + | 0.988686i | \(0.452072\pi\) | |||||||
\(788\) | −10.6473 | −0.379293 | ||||||||
\(789\) | 4.47034 | 0.159148 | ||||||||
\(790\) | 16.6369 | 0.591913 | ||||||||
\(791\) | −21.4471 | −0.762572 | ||||||||
\(792\) | −0.961584 | −0.0341684 | ||||||||
\(793\) | 23.7037 | 0.841743 | ||||||||
\(794\) | 57.1819 | 2.02931 | ||||||||
\(795\) | 6.56373 | 0.232792 | ||||||||
\(796\) | 41.6569 | 1.47649 | ||||||||
\(797\) | −34.6815 | −1.22848 | −0.614240 | − | 0.789119i | \(-0.710537\pi\) | ||||
−0.614240 | + | 0.789119i | \(0.710537\pi\) | |||||||
\(798\) | 87.7004 | 3.10456 | ||||||||
\(799\) | −0.289236 | −0.0102324 | ||||||||
\(800\) | 7.46713 | 0.264003 | ||||||||
\(801\) | −15.8644 | −0.560541 | ||||||||
\(802\) | −18.2716 | −0.645192 | ||||||||
\(803\) | 3.44134 | 0.121442 | ||||||||
\(804\) | 53.7758 | 1.89653 | ||||||||
\(805\) | −14.0089 | −0.493749 | ||||||||
\(806\) | 42.6054 | 1.50071 | ||||||||
\(807\) | 9.77939 | 0.344251 | ||||||||
\(808\) | 11.1860 | 0.393520 | ||||||||
\(809\) | 33.1397 | 1.16513 | 0.582565 | − | 0.812784i | \(-0.302049\pi\) | ||||
0.582565 | + | 0.812784i | \(0.302049\pi\) | |||||||
\(810\) | −24.5251 | −0.861723 | ||||||||
\(811\) | 51.2766 | 1.80057 | 0.900283 | − | 0.435305i | \(-0.143359\pi\) | ||||
0.900283 | + | 0.435305i | \(0.143359\pi\) | |||||||
\(812\) | −68.1858 | −2.39285 | ||||||||
\(813\) | 26.2008 | 0.918901 | ||||||||
\(814\) | −1.42172 | −0.0498312 | ||||||||
\(815\) | −23.4405 | −0.821085 | ||||||||
\(816\) | −0.652722 | −0.0228499 | ||||||||
\(817\) | −64.7850 | −2.26654 | ||||||||
\(818\) | −46.2727 | −1.61789 | ||||||||
\(819\) | −6.92005 | −0.241806 | ||||||||
\(820\) | −20.9570 | −0.731850 | ||||||||
\(821\) | −45.7128 | −1.59539 | −0.797694 | − | 0.603063i | \(-0.793947\pi\) | ||||
−0.797694 | + | 0.603063i | \(0.793947\pi\) | |||||||
\(822\) | 48.3221 | 1.68543 | ||||||||
\(823\) | 0.890322 | 0.0310347 | 0.0155173 | − | 0.999880i | \(-0.495060\pi\) | ||||
0.0155173 | + | 0.999880i | \(0.495060\pi\) | |||||||
\(824\) | −24.8927 | −0.867178 | ||||||||
\(825\) | 0.865853 | 0.0301451 | ||||||||
\(826\) | 33.0435 | 1.14973 | ||||||||
\(827\) | −40.4417 | −1.40629 | −0.703147 | − | 0.711044i | \(-0.748223\pi\) | ||||
−0.703147 | + | 0.711044i | \(0.748223\pi\) | |||||||
\(828\) | −20.2744 | −0.704584 | ||||||||
\(829\) | 19.8894 | 0.690786 | 0.345393 | − | 0.938458i | \(-0.387746\pi\) | ||||
0.345393 | + | 0.938458i | \(0.387746\pi\) | |||||||
\(830\) | 0.789828 | 0.0274153 | ||||||||
\(831\) | 9.92484 | 0.344289 | ||||||||
\(832\) | −22.9134 | −0.794381 | ||||||||
\(833\) | 0.0311494 | 0.00107926 | ||||||||
\(834\) | −56.1625 | −1.94475 | ||||||||
\(835\) | −20.0398 | −0.693507 | ||||||||
\(836\) | 8.13003 | 0.281183 | ||||||||
\(837\) | 35.6001 | 1.23052 | ||||||||
\(838\) | −31.1093 | −1.07465 | ||||||||
\(839\) | −34.5482 | −1.19274 | −0.596368 | − | 0.802711i | \(-0.703390\pi\) | ||||
−0.596368 | + | 0.802711i | \(0.703390\pi\) | |||||||
\(840\) | −9.33145 | −0.321966 | ||||||||
\(841\) | 55.8879 | 1.92717 | ||||||||
\(842\) | 14.2147 | 0.489870 | ||||||||
\(843\) | −16.8943 | −0.581871 | ||||||||
\(844\) | −1.78109 | −0.0613075 | ||||||||
\(845\) | 9.63197 | 0.331350 | ||||||||
\(846\) | 5.42998 | 0.186687 | ||||||||
\(847\) | 29.0406 | 0.997847 | ||||||||
\(848\) | 5.95015 | 0.204329 | ||||||||
\(849\) | 37.4064 | 1.28378 | ||||||||
\(850\) | −0.356523 | −0.0122286 | ||||||||
\(851\) | −8.25323 | −0.282917 | ||||||||
\(852\) | −59.5527 | −2.04024 | ||||||||
\(853\) | −30.5568 | −1.04625 | −0.523123 | − | 0.852257i | \(-0.675233\pi\) | ||||
−0.523123 | + | 0.852257i | \(0.675233\pi\) | |||||||
\(854\) | 75.5629 | 2.58571 | ||||||||
\(855\) | −10.0422 | −0.343436 | ||||||||
\(856\) | 8.00149 | 0.273485 | ||||||||
\(857\) | 46.2745 | 1.58071 | 0.790354 | − | 0.612651i | \(-0.209897\pi\) | ||||
0.790354 | + | 0.612651i | \(0.209897\pi\) | |||||||
\(858\) | −3.46681 | −0.118355 | ||||||||
\(859\) | −21.5525 | −0.735361 | −0.367681 | − | 0.929952i | \(-0.619848\pi\) | ||||
−0.367681 | + | 0.929952i | \(0.619848\pi\) | |||||||
\(860\) | 25.0364 | 0.853735 | ||||||||
\(861\) | −42.7420 | −1.45664 | ||||||||
\(862\) | 23.4471 | 0.798611 | ||||||||
\(863\) | −16.6225 | −0.565837 | −0.282919 | − | 0.959144i | \(-0.591303\pi\) | ||||
−0.282919 | + | 0.959144i | \(0.591303\pi\) | |||||||
\(864\) | −24.9819 | −0.849903 | ||||||||
\(865\) | 1.17842 | 0.0400674 | ||||||||
\(866\) | −10.5494 | −0.358483 | ||||||||
\(867\) | −35.6284 | −1.21001 | ||||||||
\(868\) | 78.7500 | 2.67295 | ||||||||
\(869\) | 3.14548 | 0.106703 | ||||||||
\(870\) | 42.1940 | 1.43051 | ||||||||
\(871\) | 17.0355 | 0.577227 | ||||||||
\(872\) | −9.19842 | −0.311498 | ||||||||
\(873\) | −6.57638 | −0.222577 | ||||||||
\(874\) | 81.3971 | 2.75330 | ||||||||
\(875\) | 2.68153 | 0.0906523 | ||||||||
\(876\) | 48.3318 | 1.63298 | ||||||||
\(877\) | 27.2412 | 0.919869 | 0.459934 | − | 0.887953i | \(-0.347873\pi\) | ||||
0.459934 | + | 0.887953i | \(0.347873\pi\) | |||||||
\(878\) | 25.2710 | 0.852855 | ||||||||
\(879\) | −21.9847 | −0.741527 | ||||||||
\(880\) | 0.784913 | 0.0264594 | ||||||||
\(881\) | −3.58110 | −0.120650 | −0.0603251 | − | 0.998179i | \(-0.519214\pi\) | ||||
−0.0603251 | + | 0.998179i | \(0.519214\pi\) | |||||||
\(882\) | −0.584783 | −0.0196907 | ||||||||
\(883\) | 49.8593 | 1.67790 | 0.838949 | − | 0.544209i | \(-0.183170\pi\) | ||||
0.838949 | + | 0.544209i | \(0.183170\pi\) | |||||||
\(884\) | 0.827687 | 0.0278381 | ||||||||
\(885\) | −11.8559 | −0.398533 | ||||||||
\(886\) | 11.6665 | 0.391943 | ||||||||
\(887\) | 33.5973 | 1.12809 | 0.564043 | − | 0.825745i | \(-0.309245\pi\) | ||||
0.564043 | + | 0.825745i | \(0.309245\pi\) | |||||||
\(888\) | −5.49754 | −0.184485 | ||||||||
\(889\) | 16.4525 | 0.551801 | ||||||||
\(890\) | −24.6140 | −0.825064 | ||||||||
\(891\) | −4.63688 | −0.155341 | ||||||||
\(892\) | −20.3003 | −0.679706 | ||||||||
\(893\) | −12.6402 | −0.422987 | ||||||||
\(894\) | 71.5791 | 2.39396 | ||||||||
\(895\) | −25.7489 | −0.860690 | ||||||||
\(896\) | −32.9970 | −1.10235 | ||||||||
\(897\) | −20.1252 | −0.671960 | ||||||||
\(898\) | −37.2381 | −1.24265 | ||||||||
\(899\) | −98.0397 | −3.26981 | ||||||||
\(900\) | 3.88085 | 0.129362 | ||||||||
\(901\) | −0.510987 | −0.0170234 | ||||||||
\(902\) | −6.83363 | −0.227535 | ||||||||
\(903\) | 51.0620 | 1.69924 | ||||||||
\(904\) | −13.2593 | −0.440998 | ||||||||
\(905\) | −10.0896 | −0.335389 | ||||||||
\(906\) | −71.9205 | −2.38940 | ||||||||
\(907\) | −14.8891 | −0.494383 | −0.247191 | − | 0.968967i | \(-0.579508\pi\) | ||||
−0.247191 | + | 0.968967i | \(0.579508\pi\) | |||||||
\(908\) | 28.6602 | 0.951123 | ||||||||
\(909\) | −9.48803 | −0.314698 | ||||||||
\(910\) | −10.7366 | −0.355916 | ||||||||
\(911\) | 13.2749 | 0.439818 | 0.219909 | − | 0.975520i | \(-0.429424\pi\) | ||||
0.219909 | + | 0.975520i | \(0.429424\pi\) | |||||||
\(912\) | −28.5252 | −0.944565 | ||||||||
\(913\) | 0.149331 | 0.00494212 | ||||||||
\(914\) | 87.7521 | 2.90258 | ||||||||
\(915\) | −27.1118 | −0.896290 | ||||||||
\(916\) | 59.4672 | 1.96485 | ||||||||
\(917\) | −1.54397 | −0.0509864 | ||||||||
\(918\) | 1.19278 | 0.0393675 | ||||||||
\(919\) | 12.6882 | 0.418544 | 0.209272 | − | 0.977857i | \(-0.432891\pi\) | ||||
0.209272 | + | 0.977857i | \(0.432891\pi\) | |||||||
\(920\) | −8.66077 | −0.285537 | ||||||||
\(921\) | 17.0164 | 0.560711 | ||||||||
\(922\) | −29.3958 | −0.968100 | ||||||||
\(923\) | −18.8656 | −0.620968 | ||||||||
\(924\) | −6.40790 | −0.210804 | ||||||||
\(925\) | 1.57980 | 0.0519436 | ||||||||
\(926\) | −24.3293 | −0.799511 | ||||||||
\(927\) | 21.1142 | 0.693481 | ||||||||
\(928\) | 68.7981 | 2.25841 | ||||||||
\(929\) | −55.8616 | −1.83276 | −0.916380 | − | 0.400309i | \(-0.868903\pi\) | ||||
−0.916380 | + | 0.400309i | \(0.868903\pi\) | |||||||
\(930\) | −48.7312 | −1.59796 | ||||||||
\(931\) | 1.36129 | 0.0446144 | ||||||||
\(932\) | −4.50792 | −0.147662 | ||||||||
\(933\) | 21.7159 | 0.710947 | ||||||||
\(934\) | −57.1599 | −1.87033 | ||||||||
\(935\) | −0.0674067 | −0.00220444 | ||||||||
\(936\) | −4.27821 | −0.139838 | ||||||||
\(937\) | −9.92086 | −0.324100 | −0.162050 | − | 0.986783i | \(-0.551811\pi\) | ||||
−0.162050 | + | 0.986783i | \(0.551811\pi\) | |||||||
\(938\) | 54.3060 | 1.77316 | ||||||||
\(939\) | 34.6611 | 1.13112 | ||||||||
\(940\) | 4.88485 | 0.159326 | ||||||||
\(941\) | 32.8606 | 1.07123 | 0.535613 | − | 0.844464i | \(-0.320081\pi\) | ||||
0.535613 | + | 0.844464i | \(0.320081\pi\) | |||||||
\(942\) | 64.4248 | 2.09907 | ||||||||
\(943\) | −39.6700 | −1.29183 | ||||||||
\(944\) | −10.7477 | −0.349806 | ||||||||
\(945\) | −8.97130 | −0.291836 | ||||||||
\(946\) | 8.16385 | 0.265430 | ||||||||
\(947\) | 57.3764 | 1.86448 | 0.932242 | − | 0.361836i | \(-0.117850\pi\) | ||||
0.932242 | + | 0.361836i | \(0.117850\pi\) | |||||||
\(948\) | 44.1766 | 1.43479 | ||||||||
\(949\) | 15.3109 | 0.497014 | ||||||||
\(950\) | −15.5807 | −0.505506 | ||||||||
\(951\) | −16.2850 | −0.528076 | ||||||||
\(952\) | 0.726454 | 0.0235445 | ||||||||
\(953\) | −30.7280 | −0.995378 | −0.497689 | − | 0.867356i | \(-0.665818\pi\) | ||||
−0.497689 | + | 0.867356i | \(0.665818\pi\) | |||||||
\(954\) | 9.59303 | 0.310586 | ||||||||
\(955\) | −0.850433 | −0.0275194 | ||||||||
\(956\) | −21.8853 | −0.707820 | ||||||||
\(957\) | 7.97750 | 0.257876 | ||||||||
\(958\) | −32.0941 | −1.03691 | ||||||||
\(959\) | 28.2944 | 0.913674 | ||||||||
\(960\) | 26.2080 | 0.845858 | ||||||||
\(961\) | 82.2292 | 2.65256 | ||||||||
\(962\) | −6.32540 | −0.203939 | ||||||||
\(963\) | −6.78693 | −0.218706 | ||||||||
\(964\) | 64.9783 | 2.09281 | ||||||||
\(965\) | 9.89347 | 0.318482 | ||||||||
\(966\) | −64.1553 | −2.06416 | ||||||||
\(967\) | 39.2555 | 1.26237 | 0.631185 | − | 0.775632i | \(-0.282569\pi\) | ||||
0.631185 | + | 0.775632i | \(0.282569\pi\) | |||||||
\(968\) | 17.9539 | 0.577059 | ||||||||
\(969\) | 2.44969 | 0.0786953 | ||||||||
\(970\) | −10.2034 | −0.327612 | ||||||||
\(971\) | 50.8234 | 1.63100 | 0.815500 | − | 0.578757i | \(-0.196462\pi\) | ||||
0.815500 | + | 0.578757i | \(0.196462\pi\) | |||||||
\(972\) | −37.4224 | −1.20033 | ||||||||
\(973\) | −32.8852 | −1.05425 | ||||||||
\(974\) | 11.5207 | 0.369147 | ||||||||
\(975\) | 3.85229 | 0.123372 | ||||||||
\(976\) | −24.5774 | −0.786704 | ||||||||
\(977\) | −29.7903 | −0.953075 | −0.476537 | − | 0.879154i | \(-0.658108\pi\) | ||||
−0.476537 | + | 0.879154i | \(0.658108\pi\) | |||||||
\(978\) | −107.348 | −3.43262 | ||||||||
\(979\) | −4.65370 | −0.148733 | ||||||||
\(980\) | −0.526075 | −0.0168048 | ||||||||
\(981\) | 7.80218 | 0.249105 | ||||||||
\(982\) | −26.5027 | −0.845736 | ||||||||
\(983\) | −28.1487 | −0.897804 | −0.448902 | − | 0.893581i | \(-0.648185\pi\) | ||||
−0.448902 | + | 0.893581i | \(0.648185\pi\) | |||||||
\(984\) | −26.4245 | −0.842383 | ||||||||
\(985\) | 3.85789 | 0.122922 | ||||||||
\(986\) | −3.28481 | −0.104610 | ||||||||
\(987\) | 9.96269 | 0.317116 | ||||||||
\(988\) | 36.1715 | 1.15077 | ||||||||
\(989\) | 47.3920 | 1.50698 | ||||||||
\(990\) | 1.26546 | 0.0402190 | ||||||||
\(991\) | −40.1637 | −1.27584 | −0.637921 | − | 0.770102i | \(-0.720206\pi\) | ||||
−0.637921 | + | 0.770102i | \(0.720206\pi\) | |||||||
\(992\) | −79.4572 | −2.52277 | ||||||||
\(993\) | 15.2547 | 0.484093 | ||||||||
\(994\) | −60.1399 | −1.90752 | ||||||||
\(995\) | −15.0938 | −0.478505 | ||||||||
\(996\) | 2.09727 | 0.0664545 | ||||||||
\(997\) | 40.2155 | 1.27364 | 0.636819 | − | 0.771013i | \(-0.280250\pi\) | ||||
0.636819 | + | 0.771013i | \(0.280250\pi\) | |||||||
\(998\) | −45.0637 | −1.42647 | ||||||||
\(999\) | −5.28536 | −0.167221 |
(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 | 6005.2.a.g.1.17 | ✓ | 113 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6005.2.a.g.1.17 | ✓ | 113 | 1.1 | even | 1 | trivial |