Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6002,2,Mod(1,6002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6002 = 2 \cdot 3001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6002.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: | \(47.9262112932\) |
Analytic rank: | \(0\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.27666 | −1.89178 | −0.945890 | − | 0.324487i | \(-0.894808\pi\) | ||||
−0.945890 | + | 0.324487i | \(0.894808\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.56247 | 1.59318 | 0.796592 | − | 0.604518i | \(-0.206634\pi\) | ||||
0.796592 | + | 0.604518i | \(0.206634\pi\) | |||||||
\(6\) | −3.27666 | −1.33769 | ||||||||
\(7\) | 2.04525 | 0.773032 | 0.386516 | − | 0.922283i | \(-0.373678\pi\) | ||||
0.386516 | + | 0.922283i | \(0.373678\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.73650 | 2.57883 | ||||||||
\(10\) | 3.56247 | 1.12655 | ||||||||
\(11\) | 0.471336 | 0.142113 | 0.0710566 | − | 0.997472i | \(-0.477363\pi\) | ||||
0.0710566 | + | 0.997472i | \(0.477363\pi\) | |||||||
\(12\) | −3.27666 | −0.945890 | ||||||||
\(13\) | −2.29668 | −0.636986 | −0.318493 | − | 0.947925i | \(-0.603177\pi\) | ||||
−0.318493 | + | 0.947925i | \(0.603177\pi\) | |||||||
\(14\) | 2.04525 | 0.546616 | ||||||||
\(15\) | −11.6730 | −3.01395 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.845777 | −0.205131 | −0.102565 | − | 0.994726i | \(-0.532705\pi\) | ||||
−0.102565 | + | 0.994726i | \(0.532705\pi\) | |||||||
\(18\) | 7.73650 | 1.82351 | ||||||||
\(19\) | −6.71359 | −1.54020 | −0.770102 | − | 0.637921i | \(-0.779795\pi\) | ||||
−0.770102 | + | 0.637921i | \(0.779795\pi\) | |||||||
\(20\) | 3.56247 | 0.796592 | ||||||||
\(21\) | −6.70159 | −1.46241 | ||||||||
\(22\) | 0.471336 | 0.100489 | ||||||||
\(23\) | −0.936843 | −0.195345 | −0.0976726 | − | 0.995219i | \(-0.531140\pi\) | ||||
−0.0976726 | + | 0.995219i | \(0.531140\pi\) | |||||||
\(24\) | −3.27666 | −0.668845 | ||||||||
\(25\) | 7.69116 | 1.53823 | ||||||||
\(26\) | −2.29668 | −0.450417 | ||||||||
\(27\) | −15.5199 | −2.98681 | ||||||||
\(28\) | 2.04525 | 0.386516 | ||||||||
\(29\) | 5.58919 | 1.03789 | 0.518943 | − | 0.854809i | \(-0.326326\pi\) | ||||
0.518943 | + | 0.854809i | \(0.326326\pi\) | |||||||
\(30\) | −11.6730 | −2.13119 | ||||||||
\(31\) | 7.95563 | 1.42887 | 0.714437 | − | 0.699700i | \(-0.246683\pi\) | ||||
0.714437 | + | 0.699700i | \(0.246683\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.54441 | −0.268847 | ||||||||
\(34\) | −0.845777 | −0.145049 | ||||||||
\(35\) | 7.28613 | 1.23158 | ||||||||
\(36\) | 7.73650 | 1.28942 | ||||||||
\(37\) | −1.11578 | −0.183433 | −0.0917163 | − | 0.995785i | \(-0.529235\pi\) | ||||
−0.0917163 | + | 0.995785i | \(0.529235\pi\) | |||||||
\(38\) | −6.71359 | −1.08909 | ||||||||
\(39\) | 7.52545 | 1.20504 | ||||||||
\(40\) | 3.56247 | 0.563275 | ||||||||
\(41\) | 1.90954 | 0.298220 | 0.149110 | − | 0.988821i | \(-0.452359\pi\) | ||||
0.149110 | + | 0.988821i | \(0.452359\pi\) | |||||||
\(42\) | −6.70159 | −1.03408 | ||||||||
\(43\) | 11.3011 | 1.72340 | 0.861700 | − | 0.507418i | \(-0.169400\pi\) | ||||
0.861700 | + | 0.507418i | \(0.169400\pi\) | |||||||
\(44\) | 0.471336 | 0.0710566 | ||||||||
\(45\) | 27.5610 | 4.10855 | ||||||||
\(46\) | −0.936843 | −0.138130 | ||||||||
\(47\) | −4.71665 | −0.687995 | −0.343997 | − | 0.938971i | \(-0.611781\pi\) | ||||
−0.343997 | + | 0.938971i | \(0.611781\pi\) | |||||||
\(48\) | −3.27666 | −0.472945 | ||||||||
\(49\) | −2.81695 | −0.402422 | ||||||||
\(50\) | 7.69116 | 1.08769 | ||||||||
\(51\) | 2.77132 | 0.388063 | ||||||||
\(52\) | −2.29668 | −0.318493 | ||||||||
\(53\) | 11.6804 | 1.60443 | 0.802216 | − | 0.597034i | \(-0.203654\pi\) | ||||
0.802216 | + | 0.597034i | \(0.203654\pi\) | |||||||
\(54\) | −15.5199 | −2.11199 | ||||||||
\(55\) | 1.67912 | 0.226412 | ||||||||
\(56\) | 2.04525 | 0.273308 | ||||||||
\(57\) | 21.9982 | 2.91373 | ||||||||
\(58\) | 5.58919 | 0.733897 | ||||||||
\(59\) | −9.77373 | −1.27243 | −0.636216 | − | 0.771511i | \(-0.719501\pi\) | ||||
−0.636216 | + | 0.771511i | \(0.719501\pi\) | |||||||
\(60\) | −11.6730 | −1.50698 | ||||||||
\(61\) | −2.54567 | −0.325939 | −0.162970 | − | 0.986631i | \(-0.552107\pi\) | ||||
−0.162970 | + | 0.986631i | \(0.552107\pi\) | |||||||
\(62\) | 7.95563 | 1.01037 | ||||||||
\(63\) | 15.8231 | 1.99352 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.18186 | −1.01483 | ||||||||
\(66\) | −1.54441 | −0.190103 | ||||||||
\(67\) | 13.5921 | 1.66054 | 0.830271 | − | 0.557360i | \(-0.188186\pi\) | ||||
0.830271 | + | 0.557360i | \(0.188186\pi\) | |||||||
\(68\) | −0.845777 | −0.102565 | ||||||||
\(69\) | 3.06972 | 0.369550 | ||||||||
\(70\) | 7.28613 | 0.870859 | ||||||||
\(71\) | −8.96504 | −1.06395 | −0.531977 | − | 0.846759i | \(-0.678551\pi\) | ||||
−0.531977 | + | 0.846759i | \(0.678551\pi\) | |||||||
\(72\) | 7.73650 | 0.911755 | ||||||||
\(73\) | 12.8974 | 1.50953 | 0.754764 | − | 0.655996i | \(-0.227751\pi\) | ||||
0.754764 | + | 0.655996i | \(0.227751\pi\) | |||||||
\(74\) | −1.11578 | −0.129706 | ||||||||
\(75\) | −25.2013 | −2.91000 | ||||||||
\(76\) | −6.71359 | −0.770102 | ||||||||
\(77\) | 0.964000 | 0.109858 | ||||||||
\(78\) | 7.52545 | 0.852090 | ||||||||
\(79\) | 16.9174 | 1.90335 | 0.951676 | − | 0.307103i | \(-0.0993597\pi\) | ||||
0.951676 | + | 0.307103i | \(0.0993597\pi\) | |||||||
\(80\) | 3.56247 | 0.398296 | ||||||||
\(81\) | 27.6439 | 3.07155 | ||||||||
\(82\) | 1.90954 | 0.210874 | ||||||||
\(83\) | −13.8011 | −1.51487 | −0.757435 | − | 0.652910i | \(-0.773548\pi\) | ||||
−0.757435 | + | 0.652910i | \(0.773548\pi\) | |||||||
\(84\) | −6.70159 | −0.731203 | ||||||||
\(85\) | −3.01305 | −0.326811 | ||||||||
\(86\) | 11.3011 | 1.21863 | ||||||||
\(87\) | −18.3139 | −1.96345 | ||||||||
\(88\) | 0.471336 | 0.0502446 | ||||||||
\(89\) | −7.63995 | −0.809833 | −0.404916 | − | 0.914354i | \(-0.632699\pi\) | ||||
−0.404916 | + | 0.914354i | \(0.632699\pi\) | |||||||
\(90\) | 27.5610 | 2.90519 | ||||||||
\(91\) | −4.69729 | −0.492410 | ||||||||
\(92\) | −0.936843 | −0.0976726 | ||||||||
\(93\) | −26.0679 | −2.70312 | ||||||||
\(94\) | −4.71665 | −0.486486 | ||||||||
\(95\) | −23.9169 | −2.45383 | ||||||||
\(96\) | −3.27666 | −0.334423 | ||||||||
\(97\) | 1.68621 | 0.171209 | 0.0856045 | − | 0.996329i | \(-0.472718\pi\) | ||||
0.0856045 | + | 0.996329i | \(0.472718\pi\) | |||||||
\(98\) | −2.81695 | −0.284555 | ||||||||
\(99\) | 3.64649 | 0.366486 | ||||||||
\(100\) | 7.69116 | 0.769116 | ||||||||
\(101\) | 14.0715 | 1.40017 | 0.700084 | − | 0.714061i | \(-0.253146\pi\) | ||||
0.700084 | + | 0.714061i | \(0.253146\pi\) | |||||||
\(102\) | 2.77132 | 0.274402 | ||||||||
\(103\) | −13.3315 | −1.31359 | −0.656797 | − | 0.754068i | \(-0.728089\pi\) | ||||
−0.656797 | + | 0.754068i | \(0.728089\pi\) | |||||||
\(104\) | −2.29668 | −0.225208 | ||||||||
\(105\) | −23.8742 | −2.32988 | ||||||||
\(106\) | 11.6804 | 1.13450 | ||||||||
\(107\) | 16.5427 | 1.59925 | 0.799623 | − | 0.600502i | \(-0.205033\pi\) | ||||
0.799623 | + | 0.600502i | \(0.205033\pi\) | |||||||
\(108\) | −15.5199 | −1.49340 | ||||||||
\(109\) | 17.2086 | 1.64828 | 0.824142 | − | 0.566383i | \(-0.191658\pi\) | ||||
0.824142 | + | 0.566383i | \(0.191658\pi\) | |||||||
\(110\) | 1.67912 | 0.160098 | ||||||||
\(111\) | 3.65602 | 0.347014 | ||||||||
\(112\) | 2.04525 | 0.193258 | ||||||||
\(113\) | 12.6791 | 1.19275 | 0.596374 | − | 0.802706i | \(-0.296607\pi\) | ||||
0.596374 | + | 0.802706i | \(0.296607\pi\) | |||||||
\(114\) | 21.9982 | 2.06032 | ||||||||
\(115\) | −3.33747 | −0.311221 | ||||||||
\(116\) | 5.58919 | 0.518943 | ||||||||
\(117\) | −17.7683 | −1.64268 | ||||||||
\(118\) | −9.77373 | −0.899745 | ||||||||
\(119\) | −1.72982 | −0.158573 | ||||||||
\(120\) | −11.6730 | −1.06559 | ||||||||
\(121\) | −10.7778 | −0.979804 | ||||||||
\(122\) | −2.54567 | −0.230474 | ||||||||
\(123\) | −6.25692 | −0.564167 | ||||||||
\(124\) | 7.95563 | 0.714437 | ||||||||
\(125\) | 9.58717 | 0.857502 | ||||||||
\(126\) | 15.8231 | 1.40963 | ||||||||
\(127\) | −5.09659 | −0.452249 | −0.226124 | − | 0.974098i | \(-0.572606\pi\) | ||||
−0.226124 | + | 0.974098i | \(0.572606\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −37.0298 | −3.26029 | ||||||||
\(130\) | −8.18186 | −0.717596 | ||||||||
\(131\) | −1.53453 | −0.134072 | −0.0670360 | − | 0.997751i | \(-0.521354\pi\) | ||||
−0.0670360 | + | 0.997751i | \(0.521354\pi\) | |||||||
\(132\) | −1.54441 | −0.134423 | ||||||||
\(133\) | −13.7310 | −1.19063 | ||||||||
\(134\) | 13.5921 | 1.17418 | ||||||||
\(135\) | −55.2891 | −4.75853 | ||||||||
\(136\) | −0.845777 | −0.0725247 | ||||||||
\(137\) | −17.6053 | −1.50412 | −0.752061 | − | 0.659094i | \(-0.770940\pi\) | ||||
−0.752061 | + | 0.659094i | \(0.770940\pi\) | |||||||
\(138\) | 3.06972 | 0.261312 | ||||||||
\(139\) | −8.48784 | −0.719929 | −0.359965 | − | 0.932966i | \(-0.617211\pi\) | ||||
−0.359965 | + | 0.932966i | \(0.617211\pi\) | |||||||
\(140\) | 7.28613 | 0.615791 | ||||||||
\(141\) | 15.4549 | 1.30153 | ||||||||
\(142\) | −8.96504 | −0.752330 | ||||||||
\(143\) | −1.08251 | −0.0905240 | ||||||||
\(144\) | 7.73650 | 0.644708 | ||||||||
\(145\) | 19.9113 | 1.65354 | ||||||||
\(146\) | 12.8974 | 1.06740 | ||||||||
\(147\) | 9.23020 | 0.761294 | ||||||||
\(148\) | −1.11578 | −0.0917163 | ||||||||
\(149\) | −0.583085 | −0.0477682 | −0.0238841 | − | 0.999715i | \(-0.507603\pi\) | ||||
−0.0238841 | + | 0.999715i | \(0.507603\pi\) | |||||||
\(150\) | −25.2013 | −2.05768 | ||||||||
\(151\) | −11.5921 | −0.943355 | −0.471677 | − | 0.881771i | \(-0.656351\pi\) | ||||
−0.471677 | + | 0.881771i | \(0.656351\pi\) | |||||||
\(152\) | −6.71359 | −0.544544 | ||||||||
\(153\) | −6.54335 | −0.528998 | ||||||||
\(154\) | 0.964000 | 0.0776813 | ||||||||
\(155\) | 28.3417 | 2.27646 | ||||||||
\(156\) | 7.52545 | 0.602518 | ||||||||
\(157\) | 1.81603 | 0.144935 | 0.0724676 | − | 0.997371i | \(-0.476913\pi\) | ||||
0.0724676 | + | 0.997371i | \(0.476913\pi\) | |||||||
\(158\) | 16.9174 | 1.34587 | ||||||||
\(159\) | −38.2728 | −3.03523 | ||||||||
\(160\) | 3.56247 | 0.281638 | ||||||||
\(161\) | −1.91608 | −0.151008 | ||||||||
\(162\) | 27.6439 | 2.17191 | ||||||||
\(163\) | −3.62185 | −0.283686 | −0.141843 | − | 0.989889i | \(-0.545303\pi\) | ||||
−0.141843 | + | 0.989889i | \(0.545303\pi\) | |||||||
\(164\) | 1.90954 | 0.149110 | ||||||||
\(165\) | −5.50190 | −0.428322 | ||||||||
\(166\) | −13.8011 | −1.07118 | ||||||||
\(167\) | 8.99378 | 0.695960 | 0.347980 | − | 0.937502i | \(-0.386868\pi\) | ||||
0.347980 | + | 0.937502i | \(0.386868\pi\) | |||||||
\(168\) | −6.70159 | −0.517039 | ||||||||
\(169\) | −7.72524 | −0.594249 | ||||||||
\(170\) | −3.01305 | −0.231090 | ||||||||
\(171\) | −51.9397 | −3.97193 | ||||||||
\(172\) | 11.3011 | 0.861700 | ||||||||
\(173\) | 17.6342 | 1.34071 | 0.670353 | − | 0.742043i | \(-0.266143\pi\) | ||||
0.670353 | + | 0.742043i | \(0.266143\pi\) | |||||||
\(174\) | −18.3139 | −1.38837 | ||||||||
\(175\) | 15.7303 | 1.18910 | ||||||||
\(176\) | 0.471336 | 0.0355283 | ||||||||
\(177\) | 32.0252 | 2.40716 | ||||||||
\(178\) | −7.63995 | −0.572638 | ||||||||
\(179\) | 26.3068 | 1.96627 | 0.983133 | − | 0.182894i | \(-0.0585464\pi\) | ||||
0.983133 | + | 0.182894i | \(0.0585464\pi\) | |||||||
\(180\) | 27.5610 | 2.05428 | ||||||||
\(181\) | 11.3135 | 0.840928 | 0.420464 | − | 0.907309i | \(-0.361867\pi\) | ||||
0.420464 | + | 0.907309i | \(0.361867\pi\) | |||||||
\(182\) | −4.69729 | −0.348187 | ||||||||
\(183\) | 8.34128 | 0.616605 | ||||||||
\(184\) | −0.936843 | −0.0690650 | ||||||||
\(185\) | −3.97492 | −0.292242 | ||||||||
\(186\) | −26.0679 | −1.91139 | ||||||||
\(187\) | −0.398645 | −0.0291518 | ||||||||
\(188\) | −4.71665 | −0.343997 | ||||||||
\(189\) | −31.7421 | −2.30890 | ||||||||
\(190\) | −23.9169 | −1.73512 | ||||||||
\(191\) | 5.66197 | 0.409686 | 0.204843 | − | 0.978795i | \(-0.434332\pi\) | ||||
0.204843 | + | 0.978795i | \(0.434332\pi\) | |||||||
\(192\) | −3.27666 | −0.236473 | ||||||||
\(193\) | −23.8043 | −1.71347 | −0.856735 | − | 0.515757i | \(-0.827511\pi\) | ||||
−0.856735 | + | 0.515757i | \(0.827511\pi\) | |||||||
\(194\) | 1.68621 | 0.121063 | ||||||||
\(195\) | 26.8092 | 1.91984 | ||||||||
\(196\) | −2.81695 | −0.201211 | ||||||||
\(197\) | 23.7215 | 1.69008 | 0.845042 | − | 0.534700i | \(-0.179575\pi\) | ||||
0.845042 | + | 0.534700i | \(0.179575\pi\) | |||||||
\(198\) | 3.64649 | 0.259145 | ||||||||
\(199\) | −15.8567 | −1.12405 | −0.562026 | − | 0.827119i | \(-0.689978\pi\) | ||||
−0.562026 | + | 0.827119i | \(0.689978\pi\) | |||||||
\(200\) | 7.69116 | 0.543847 | ||||||||
\(201\) | −44.5368 | −3.14138 | ||||||||
\(202\) | 14.0715 | 0.990068 | ||||||||
\(203\) | 11.4313 | 0.802319 | ||||||||
\(204\) | 2.77132 | 0.194031 | ||||||||
\(205\) | 6.80267 | 0.475119 | ||||||||
\(206\) | −13.3315 | −0.928851 | ||||||||
\(207\) | −7.24788 | −0.503763 | ||||||||
\(208\) | −2.29668 | −0.159246 | ||||||||
\(209\) | −3.16436 | −0.218883 | ||||||||
\(210\) | −23.8742 | −1.64747 | ||||||||
\(211\) | −19.5749 | −1.34759 | −0.673797 | − | 0.738916i | \(-0.735338\pi\) | ||||
−0.673797 | + | 0.738916i | \(0.735338\pi\) | |||||||
\(212\) | 11.6804 | 0.802216 | ||||||||
\(213\) | 29.3754 | 2.01277 | ||||||||
\(214\) | 16.5427 | 1.13084 | ||||||||
\(215\) | 40.2597 | 2.74569 | ||||||||
\(216\) | −15.5199 | −1.05600 | ||||||||
\(217\) | 16.2713 | 1.10457 | ||||||||
\(218\) | 17.2086 | 1.16551 | ||||||||
\(219\) | −42.2605 | −2.85570 | ||||||||
\(220\) | 1.67912 | 0.113206 | ||||||||
\(221\) | 1.94248 | 0.130665 | ||||||||
\(222\) | 3.65602 | 0.245376 | ||||||||
\(223\) | 10.8650 | 0.727576 | 0.363788 | − | 0.931482i | \(-0.381483\pi\) | ||||
0.363788 | + | 0.931482i | \(0.381483\pi\) | |||||||
\(224\) | 2.04525 | 0.136654 | ||||||||
\(225\) | 59.5027 | 3.96684 | ||||||||
\(226\) | 12.6791 | 0.843401 | ||||||||
\(227\) | 2.55851 | 0.169814 | 0.0849071 | − | 0.996389i | \(-0.472941\pi\) | ||||
0.0849071 | + | 0.996389i | \(0.472941\pi\) | |||||||
\(228\) | 21.9982 | 1.45686 | ||||||||
\(229\) | −1.11411 | −0.0736227 | −0.0368114 | − | 0.999322i | \(-0.511720\pi\) | ||||
−0.0368114 | + | 0.999322i | \(0.511720\pi\) | |||||||
\(230\) | −3.33747 | −0.220066 | ||||||||
\(231\) | −3.15870 | −0.207827 | ||||||||
\(232\) | 5.58919 | 0.366948 | ||||||||
\(233\) | 17.6860 | 1.15865 | 0.579323 | − | 0.815098i | \(-0.303317\pi\) | ||||
0.579323 | + | 0.815098i | \(0.303317\pi\) | |||||||
\(234\) | −17.7683 | −1.16155 | ||||||||
\(235\) | −16.8029 | −1.09610 | ||||||||
\(236\) | −9.77373 | −0.636216 | ||||||||
\(237\) | −55.4325 | −3.60072 | ||||||||
\(238\) | −1.72982 | −0.112128 | ||||||||
\(239\) | −9.39637 | −0.607801 | −0.303900 | − | 0.952704i | \(-0.598289\pi\) | ||||
−0.303900 | + | 0.952704i | \(0.598289\pi\) | |||||||
\(240\) | −11.6730 | −0.753488 | ||||||||
\(241\) | 17.6099 | 1.13435 | 0.567176 | − | 0.823597i | \(-0.308036\pi\) | ||||
0.567176 | + | 0.823597i | \(0.308036\pi\) | |||||||
\(242\) | −10.7778 | −0.692826 | ||||||||
\(243\) | −44.0200 | −2.82389 | ||||||||
\(244\) | −2.54567 | −0.162970 | ||||||||
\(245\) | −10.0353 | −0.641132 | ||||||||
\(246\) | −6.25692 | −0.398926 | ||||||||
\(247\) | 15.4190 | 0.981087 | ||||||||
\(248\) | 7.95563 | 0.505183 | ||||||||
\(249\) | 45.2216 | 2.86580 | ||||||||
\(250\) | 9.58717 | 0.606346 | ||||||||
\(251\) | 25.6215 | 1.61721 | 0.808607 | − | 0.588349i | \(-0.200222\pi\) | ||||
0.808607 | + | 0.588349i | \(0.200222\pi\) | |||||||
\(252\) | 15.8231 | 0.996760 | ||||||||
\(253\) | −0.441568 | −0.0277611 | ||||||||
\(254\) | −5.09659 | −0.319788 | ||||||||
\(255\) | 9.87274 | 0.618255 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.63639 | 0.164454 | 0.0822269 | − | 0.996614i | \(-0.473797\pi\) | ||||
0.0822269 | + | 0.996614i | \(0.473797\pi\) | |||||||
\(258\) | −37.0298 | −2.30538 | ||||||||
\(259\) | −2.28204 | −0.141799 | ||||||||
\(260\) | −8.18186 | −0.507417 | ||||||||
\(261\) | 43.2408 | 2.67654 | ||||||||
\(262\) | −1.53453 | −0.0948033 | ||||||||
\(263\) | −18.4191 | −1.13577 | −0.567884 | − | 0.823108i | \(-0.692238\pi\) | ||||
−0.567884 | + | 0.823108i | \(0.692238\pi\) | |||||||
\(264\) | −1.54441 | −0.0950517 | ||||||||
\(265\) | 41.6112 | 2.55615 | ||||||||
\(266\) | −13.7310 | −0.841900 | ||||||||
\(267\) | 25.0335 | 1.53203 | ||||||||
\(268\) | 13.5921 | 0.830271 | ||||||||
\(269\) | 1.06313 | 0.0648201 | 0.0324100 | − | 0.999475i | \(-0.489682\pi\) | ||||
0.0324100 | + | 0.999475i | \(0.489682\pi\) | |||||||
\(270\) | −55.2891 | −3.36479 | ||||||||
\(271\) | 20.5714 | 1.24963 | 0.624813 | − | 0.780775i | \(-0.285175\pi\) | ||||
0.624813 | + | 0.780775i | \(0.285175\pi\) | |||||||
\(272\) | −0.845777 | −0.0512827 | ||||||||
\(273\) | 15.3914 | 0.931532 | ||||||||
\(274\) | −17.6053 | −1.06357 | ||||||||
\(275\) | 3.62512 | 0.218603 | ||||||||
\(276\) | 3.06972 | 0.184775 | ||||||||
\(277\) | 22.3471 | 1.34271 | 0.671354 | − | 0.741137i | \(-0.265713\pi\) | ||||
0.671354 | + | 0.741137i | \(0.265713\pi\) | |||||||
\(278\) | −8.48784 | −0.509067 | ||||||||
\(279\) | 61.5488 | 3.68483 | ||||||||
\(280\) | 7.28613 | 0.435430 | ||||||||
\(281\) | −30.5708 | −1.82370 | −0.911851 | − | 0.410521i | \(-0.865347\pi\) | ||||
−0.911851 | + | 0.410521i | \(0.865347\pi\) | |||||||
\(282\) | 15.4549 | 0.920324 | ||||||||
\(283\) | −3.21210 | −0.190940 | −0.0954699 | − | 0.995432i | \(-0.530435\pi\) | ||||
−0.0954699 | + | 0.995432i | \(0.530435\pi\) | |||||||
\(284\) | −8.96504 | −0.531977 | ||||||||
\(285\) | 78.3677 | 4.64210 | ||||||||
\(286\) | −1.08251 | −0.0640102 | ||||||||
\(287\) | 3.90549 | 0.230534 | ||||||||
\(288\) | 7.73650 | 0.455878 | ||||||||
\(289\) | −16.2847 | −0.957921 | ||||||||
\(290\) | 19.9113 | 1.16923 | ||||||||
\(291\) | −5.52515 | −0.323890 | ||||||||
\(292\) | 12.8974 | 0.754764 | ||||||||
\(293\) | −10.9476 | −0.639564 | −0.319782 | − | 0.947491i | \(-0.603610\pi\) | ||||
−0.319782 | + | 0.947491i | \(0.603610\pi\) | |||||||
\(294\) | 9.23020 | 0.538316 | ||||||||
\(295\) | −34.8186 | −2.02722 | ||||||||
\(296\) | −1.11578 | −0.0648532 | ||||||||
\(297\) | −7.31509 | −0.424464 | ||||||||
\(298\) | −0.583085 | −0.0337772 | ||||||||
\(299\) | 2.15163 | 0.124432 | ||||||||
\(300\) | −25.2013 | −1.45500 | ||||||||
\(301\) | 23.1136 | 1.33224 | ||||||||
\(302\) | −11.5921 | −0.667052 | ||||||||
\(303\) | −46.1076 | −2.64881 | ||||||||
\(304\) | −6.71359 | −0.385051 | ||||||||
\(305\) | −9.06885 | −0.519281 | ||||||||
\(306\) | −6.54335 | −0.374058 | ||||||||
\(307\) | −11.9302 | −0.680894 | −0.340447 | − | 0.940264i | \(-0.610578\pi\) | ||||
−0.340447 | + | 0.940264i | \(0.610578\pi\) | |||||||
\(308\) | 0.964000 | 0.0549290 | ||||||||
\(309\) | 43.6828 | 2.48503 | ||||||||
\(310\) | 28.3417 | 1.60970 | ||||||||
\(311\) | −22.0615 | −1.25099 | −0.625495 | − | 0.780228i | \(-0.715103\pi\) | ||||
−0.625495 | + | 0.780228i | \(0.715103\pi\) | |||||||
\(312\) | 7.52545 | 0.426045 | ||||||||
\(313\) | 19.8960 | 1.12459 | 0.562295 | − | 0.826937i | \(-0.309918\pi\) | ||||
0.562295 | + | 0.826937i | \(0.309918\pi\) | |||||||
\(314\) | 1.81603 | 0.102485 | ||||||||
\(315\) | 56.3692 | 3.17604 | ||||||||
\(316\) | 16.9174 | 0.951676 | ||||||||
\(317\) | 8.61942 | 0.484115 | 0.242057 | − | 0.970262i | \(-0.422178\pi\) | ||||
0.242057 | + | 0.970262i | \(0.422178\pi\) | |||||||
\(318\) | −38.2728 | −2.14623 | ||||||||
\(319\) | 2.63439 | 0.147497 | ||||||||
\(320\) | 3.56247 | 0.199148 | ||||||||
\(321\) | −54.2049 | −3.02542 | ||||||||
\(322\) | −1.91608 | −0.106779 | ||||||||
\(323\) | 5.67820 | 0.315943 | ||||||||
\(324\) | 27.6439 | 1.53577 | ||||||||
\(325\) | −17.6642 | −0.979832 | ||||||||
\(326\) | −3.62185 | −0.200596 | ||||||||
\(327\) | −56.3867 | −3.11819 | ||||||||
\(328\) | 1.90954 | 0.105437 | ||||||||
\(329\) | −9.64673 | −0.531842 | ||||||||
\(330\) | −5.50190 | −0.302870 | ||||||||
\(331\) | −24.9534 | −1.37156 | −0.685782 | − | 0.727807i | \(-0.740540\pi\) | ||||
−0.685782 | + | 0.727807i | \(0.740540\pi\) | |||||||
\(332\) | −13.8011 | −0.757435 | ||||||||
\(333\) | −8.63221 | −0.473042 | ||||||||
\(334\) | 8.99378 | 0.492118 | ||||||||
\(335\) | 48.4215 | 2.64555 | ||||||||
\(336\) | −6.70159 | −0.365602 | ||||||||
\(337\) | 27.0511 | 1.47357 | 0.736785 | − | 0.676127i | \(-0.236343\pi\) | ||||
0.736785 | + | 0.676127i | \(0.236343\pi\) | |||||||
\(338\) | −7.72524 | −0.420198 | ||||||||
\(339\) | −41.5451 | −2.25642 | ||||||||
\(340\) | −3.01305 | −0.163406 | ||||||||
\(341\) | 3.74978 | 0.203062 | ||||||||
\(342\) | −51.9397 | −2.80858 | ||||||||
\(343\) | −20.0781 | −1.08412 | ||||||||
\(344\) | 11.3011 | 0.609314 | ||||||||
\(345\) | 10.9358 | 0.588761 | ||||||||
\(346\) | 17.6342 | 0.948022 | ||||||||
\(347\) | −0.206449 | −0.0110828 | −0.00554139 | − | 0.999985i | \(-0.501764\pi\) | ||||
−0.00554139 | + | 0.999985i | \(0.501764\pi\) | |||||||
\(348\) | −18.3139 | −0.981727 | ||||||||
\(349\) | 29.5719 | 1.58295 | 0.791474 | − | 0.611202i | \(-0.209314\pi\) | ||||
0.791474 | + | 0.611202i | \(0.209314\pi\) | |||||||
\(350\) | 15.7303 | 0.840822 | ||||||||
\(351\) | 35.6443 | 1.90255 | ||||||||
\(352\) | 0.471336 | 0.0251223 | ||||||||
\(353\) | −28.6723 | −1.52607 | −0.763035 | − | 0.646357i | \(-0.776292\pi\) | ||||
−0.763035 | + | 0.646357i | \(0.776292\pi\) | |||||||
\(354\) | 32.0252 | 1.70212 | ||||||||
\(355\) | −31.9377 | −1.69507 | ||||||||
\(356\) | −7.63995 | −0.404916 | ||||||||
\(357\) | 5.66805 | 0.299985 | ||||||||
\(358\) | 26.3068 | 1.39036 | ||||||||
\(359\) | −17.4411 | −0.920508 | −0.460254 | − | 0.887787i | \(-0.652242\pi\) | ||||
−0.460254 | + | 0.887787i | \(0.652242\pi\) | |||||||
\(360\) | 27.5610 | 1.45259 | ||||||||
\(361\) | 26.0723 | 1.37223 | ||||||||
\(362\) | 11.3135 | 0.594626 | ||||||||
\(363\) | 35.3153 | 1.85357 | ||||||||
\(364\) | −4.69729 | −0.246205 | ||||||||
\(365\) | 45.9466 | 2.40496 | ||||||||
\(366\) | 8.34128 | 0.436006 | ||||||||
\(367\) | 30.2560 | 1.57935 | 0.789676 | − | 0.613524i | \(-0.210249\pi\) | ||||
0.789676 | + | 0.613524i | \(0.210249\pi\) | |||||||
\(368\) | −0.936843 | −0.0488363 | ||||||||
\(369\) | 14.7732 | 0.769060 | ||||||||
\(370\) | −3.97492 | −0.206646 | ||||||||
\(371\) | 23.8894 | 1.24028 | ||||||||
\(372\) | −26.0679 | −1.35156 | ||||||||
\(373\) | −16.2820 | −0.843052 | −0.421526 | − | 0.906816i | \(-0.638505\pi\) | ||||
−0.421526 | + | 0.906816i | \(0.638505\pi\) | |||||||
\(374\) | −0.398645 | −0.0206134 | ||||||||
\(375\) | −31.4139 | −1.62221 | ||||||||
\(376\) | −4.71665 | −0.243243 | ||||||||
\(377\) | −12.8366 | −0.661119 | ||||||||
\(378\) | −31.7421 | −1.63264 | ||||||||
\(379\) | 21.0865 | 1.08314 | 0.541570 | − | 0.840655i | \(-0.317830\pi\) | ||||
0.541570 | + | 0.840655i | \(0.317830\pi\) | |||||||
\(380\) | −23.9169 | −1.22691 | ||||||||
\(381\) | 16.6998 | 0.855556 | ||||||||
\(382\) | 5.66197 | 0.289691 | ||||||||
\(383\) | 22.5117 | 1.15029 | 0.575146 | − | 0.818051i | \(-0.304945\pi\) | ||||
0.575146 | + | 0.818051i | \(0.304945\pi\) | |||||||
\(384\) | −3.27666 | −0.167211 | ||||||||
\(385\) | 3.43422 | 0.175024 | ||||||||
\(386\) | −23.8043 | −1.21161 | ||||||||
\(387\) | 87.4309 | 4.44436 | ||||||||
\(388\) | 1.68621 | 0.0856045 | ||||||||
\(389\) | 10.3804 | 0.526308 | 0.263154 | − | 0.964754i | \(-0.415237\pi\) | ||||
0.263154 | + | 0.964754i | \(0.415237\pi\) | |||||||
\(390\) | 26.8092 | 1.35753 | ||||||||
\(391\) | 0.792360 | 0.0400714 | ||||||||
\(392\) | −2.81695 | −0.142278 | ||||||||
\(393\) | 5.02812 | 0.253635 | ||||||||
\(394\) | 23.7215 | 1.19507 | ||||||||
\(395\) | 60.2675 | 3.03239 | ||||||||
\(396\) | 3.64649 | 0.183243 | ||||||||
\(397\) | 2.44123 | 0.122522 | 0.0612609 | − | 0.998122i | \(-0.480488\pi\) | ||||
0.0612609 | + | 0.998122i | \(0.480488\pi\) | |||||||
\(398\) | −15.8567 | −0.794825 | ||||||||
\(399\) | 44.9917 | 2.25240 | ||||||||
\(400\) | 7.69116 | 0.384558 | ||||||||
\(401\) | 1.44526 | 0.0721729 | 0.0360864 | − | 0.999349i | \(-0.488511\pi\) | ||||
0.0360864 | + | 0.999349i | \(0.488511\pi\) | |||||||
\(402\) | −44.5368 | −2.22129 | ||||||||
\(403\) | −18.2716 | −0.910172 | ||||||||
\(404\) | 14.0715 | 0.700084 | ||||||||
\(405\) | 98.4805 | 4.89354 | ||||||||
\(406\) | 11.4313 | 0.567325 | ||||||||
\(407\) | −0.525906 | −0.0260682 | ||||||||
\(408\) | 2.77132 | 0.137201 | ||||||||
\(409\) | −1.28590 | −0.0635837 | −0.0317918 | − | 0.999495i | \(-0.510121\pi\) | ||||
−0.0317918 | + | 0.999495i | \(0.510121\pi\) | |||||||
\(410\) | 6.80267 | 0.335960 | ||||||||
\(411\) | 57.6865 | 2.84547 | ||||||||
\(412\) | −13.3315 | −0.656797 | ||||||||
\(413\) | −19.9897 | −0.983630 | ||||||||
\(414\) | −7.24788 | −0.356214 | ||||||||
\(415\) | −49.1661 | −2.41347 | ||||||||
\(416\) | −2.29668 | −0.112604 | ||||||||
\(417\) | 27.8118 | 1.36195 | ||||||||
\(418\) | −3.16436 | −0.154774 | ||||||||
\(419\) | 9.90362 | 0.483824 | 0.241912 | − | 0.970298i | \(-0.422226\pi\) | ||||
0.241912 | + | 0.970298i | \(0.422226\pi\) | |||||||
\(420\) | −23.8742 | −1.16494 | ||||||||
\(421\) | −5.87673 | −0.286414 | −0.143207 | − | 0.989693i | \(-0.545741\pi\) | ||||
−0.143207 | + | 0.989693i | \(0.545741\pi\) | |||||||
\(422\) | −19.5749 | −0.952893 | ||||||||
\(423\) | −36.4904 | −1.77422 | ||||||||
\(424\) | 11.6804 | 0.567252 | ||||||||
\(425\) | −6.50500 | −0.315539 | ||||||||
\(426\) | 29.3754 | 1.42324 | ||||||||
\(427\) | −5.20652 | −0.251961 | ||||||||
\(428\) | 16.5427 | 0.799623 | ||||||||
\(429\) | 3.54702 | 0.171252 | ||||||||
\(430\) | 40.2597 | 1.94150 | ||||||||
\(431\) | 6.53342 | 0.314704 | 0.157352 | − | 0.987543i | \(-0.449704\pi\) | ||||
0.157352 | + | 0.987543i | \(0.449704\pi\) | |||||||
\(432\) | −15.5199 | −0.746701 | ||||||||
\(433\) | −16.7479 | −0.804854 | −0.402427 | − | 0.915452i | \(-0.631833\pi\) | ||||
−0.402427 | + | 0.915452i | \(0.631833\pi\) | |||||||
\(434\) | 16.2713 | 0.781045 | ||||||||
\(435\) | −65.2426 | −3.12814 | ||||||||
\(436\) | 17.2086 | 0.824142 | ||||||||
\(437\) | 6.28958 | 0.300871 | ||||||||
\(438\) | −42.2605 | −2.01928 | ||||||||
\(439\) | 8.76042 | 0.418112 | 0.209056 | − | 0.977904i | \(-0.432961\pi\) | ||||
0.209056 | + | 0.977904i | \(0.432961\pi\) | |||||||
\(440\) | 1.67912 | 0.0800488 | ||||||||
\(441\) | −21.7934 | −1.03778 | ||||||||
\(442\) | 1.94248 | 0.0923944 | ||||||||
\(443\) | 16.4273 | 0.780483 | 0.390241 | − | 0.920713i | \(-0.372392\pi\) | ||||
0.390241 | + | 0.920713i | \(0.372392\pi\) | |||||||
\(444\) | 3.65602 | 0.173507 | ||||||||
\(445\) | −27.2171 | −1.29021 | ||||||||
\(446\) | 10.8650 | 0.514474 | ||||||||
\(447\) | 1.91057 | 0.0903669 | ||||||||
\(448\) | 2.04525 | 0.0966290 | ||||||||
\(449\) | −0.923403 | −0.0435781 | −0.0217890 | − | 0.999763i | \(-0.506936\pi\) | ||||
−0.0217890 | + | 0.999763i | \(0.506936\pi\) | |||||||
\(450\) | 59.5027 | 2.80498 | ||||||||
\(451\) | 0.900035 | 0.0423810 | ||||||||
\(452\) | 12.6791 | 0.596374 | ||||||||
\(453\) | 37.9835 | 1.78462 | ||||||||
\(454\) | 2.55851 | 0.120077 | ||||||||
\(455\) | −16.7339 | −0.784499 | ||||||||
\(456\) | 21.9982 | 1.03016 | ||||||||
\(457\) | 4.48696 | 0.209891 | 0.104945 | − | 0.994478i | \(-0.466533\pi\) | ||||
0.104945 | + | 0.994478i | \(0.466533\pi\) | |||||||
\(458\) | −1.11411 | −0.0520591 | ||||||||
\(459\) | 13.1264 | 0.612686 | ||||||||
\(460\) | −3.33747 | −0.155610 | ||||||||
\(461\) | 18.3102 | 0.852791 | 0.426395 | − | 0.904537i | \(-0.359783\pi\) | ||||
0.426395 | + | 0.904537i | \(0.359783\pi\) | |||||||
\(462\) | −3.15870 | −0.146956 | ||||||||
\(463\) | 0.366767 | 0.0170451 | 0.00852255 | − | 0.999964i | \(-0.497287\pi\) | ||||
0.00852255 | + | 0.999964i | \(0.497287\pi\) | |||||||
\(464\) | 5.58919 | 0.259472 | ||||||||
\(465\) | −92.8660 | −4.30656 | ||||||||
\(466\) | 17.6860 | 0.819286 | ||||||||
\(467\) | 19.9240 | 0.921974 | 0.460987 | − | 0.887407i | \(-0.347496\pi\) | ||||
0.460987 | + | 0.887407i | \(0.347496\pi\) | |||||||
\(468\) | −17.7683 | −0.821340 | ||||||||
\(469\) | 27.7993 | 1.28365 | ||||||||
\(470\) | −16.8029 | −0.775061 | ||||||||
\(471\) | −5.95052 | −0.274185 | ||||||||
\(472\) | −9.77373 | −0.449873 | ||||||||
\(473\) | 5.32661 | 0.244918 | ||||||||
\(474\) | −55.4325 | −2.54610 | ||||||||
\(475\) | −51.6353 | −2.36919 | ||||||||
\(476\) | −1.72982 | −0.0792864 | ||||||||
\(477\) | 90.3657 | 4.13756 | ||||||||
\(478\) | −9.39637 | −0.429780 | ||||||||
\(479\) | −19.0667 | −0.871182 | −0.435591 | − | 0.900145i | \(-0.643461\pi\) | ||||
−0.435591 | + | 0.900145i | \(0.643461\pi\) | |||||||
\(480\) | −11.6730 | −0.532797 | ||||||||
\(481\) | 2.56259 | 0.116844 | ||||||||
\(482\) | 17.6099 | 0.802108 | ||||||||
\(483\) | 6.27834 | 0.285674 | ||||||||
\(484\) | −10.7778 | −0.489902 | ||||||||
\(485\) | 6.00708 | 0.272767 | ||||||||
\(486\) | −44.0200 | −1.99679 | ||||||||
\(487\) | −17.6870 | −0.801473 | −0.400737 | − | 0.916193i | \(-0.631246\pi\) | ||||
−0.400737 | + | 0.916193i | \(0.631246\pi\) | |||||||
\(488\) | −2.54567 | −0.115237 | ||||||||
\(489\) | 11.8676 | 0.536671 | ||||||||
\(490\) | −10.0353 | −0.453349 | ||||||||
\(491\) | −23.0384 | −1.03971 | −0.519854 | − | 0.854255i | \(-0.674014\pi\) | ||||
−0.519854 | + | 0.854255i | \(0.674014\pi\) | |||||||
\(492\) | −6.25692 | −0.282084 | ||||||||
\(493\) | −4.72721 | −0.212903 | ||||||||
\(494\) | 15.4190 | 0.693734 | ||||||||
\(495\) | 12.9905 | 0.583879 | ||||||||
\(496\) | 7.95563 | 0.357219 | ||||||||
\(497\) | −18.3358 | −0.822471 | ||||||||
\(498\) | 45.2216 | 2.02643 | ||||||||
\(499\) | −14.1952 | −0.635466 | −0.317733 | − | 0.948180i | \(-0.602922\pi\) | ||||
−0.317733 | + | 0.948180i | \(0.602922\pi\) | |||||||
\(500\) | 9.58717 | 0.428751 | ||||||||
\(501\) | −29.4696 | −1.31660 | ||||||||
\(502\) | 25.6215 | 1.14354 | ||||||||
\(503\) | −3.71122 | −0.165475 | −0.0827375 | − | 0.996571i | \(-0.526366\pi\) | ||||
−0.0827375 | + | 0.996571i | \(0.526366\pi\) | |||||||
\(504\) | 15.8231 | 0.704816 | ||||||||
\(505\) | 50.1293 | 2.23072 | ||||||||
\(506\) | −0.441568 | −0.0196301 | ||||||||
\(507\) | 25.3130 | 1.12419 | ||||||||
\(508\) | −5.09659 | −0.226124 | ||||||||
\(509\) | 5.24058 | 0.232285 | 0.116142 | − | 0.993233i | \(-0.462947\pi\) | ||||
0.116142 | + | 0.993233i | \(0.462947\pi\) | |||||||
\(510\) | 9.87274 | 0.437172 | ||||||||
\(511\) | 26.3784 | 1.16691 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 104.194 | 4.60029 | ||||||||
\(514\) | 2.63639 | 0.116286 | ||||||||
\(515\) | −47.4931 | −2.09279 | ||||||||
\(516\) | −37.0298 | −1.63015 | ||||||||
\(517\) | −2.22313 | −0.0977731 | ||||||||
\(518\) | −2.28204 | −0.100267 | ||||||||
\(519\) | −57.7814 | −2.53632 | ||||||||
\(520\) | −8.18186 | −0.358798 | ||||||||
\(521\) | −24.2581 | −1.06277 | −0.531383 | − | 0.847132i | \(-0.678328\pi\) | ||||
−0.531383 | + | 0.847132i | \(0.678328\pi\) | |||||||
\(522\) | 43.2408 | 1.89260 | ||||||||
\(523\) | 37.8312 | 1.65424 | 0.827121 | − | 0.562024i | \(-0.189977\pi\) | ||||
0.827121 | + | 0.562024i | \(0.189977\pi\) | |||||||
\(524\) | −1.53453 | −0.0670360 | ||||||||
\(525\) | −51.5430 | −2.24952 | ||||||||
\(526\) | −18.4191 | −0.803110 | ||||||||
\(527\) | −6.72869 | −0.293106 | ||||||||
\(528\) | −1.54441 | −0.0672117 | ||||||||
\(529\) | −22.1223 | −0.961840 | ||||||||
\(530\) | 41.6112 | 1.80747 | ||||||||
\(531\) | −75.6145 | −3.28139 | ||||||||
\(532\) | −13.7310 | −0.595313 | ||||||||
\(533\) | −4.38561 | −0.189962 | ||||||||
\(534\) | 25.0335 | 1.08331 | ||||||||
\(535\) | 58.9329 | 2.54789 | ||||||||
\(536\) | 13.5921 | 0.587090 | ||||||||
\(537\) | −86.1986 | −3.71974 | ||||||||
\(538\) | 1.06313 | 0.0458347 | ||||||||
\(539\) | −1.32773 | −0.0571894 | ||||||||
\(540\) | −55.2891 | −2.37926 | ||||||||
\(541\) | −39.2704 | −1.68836 | −0.844182 | − | 0.536056i | \(-0.819914\pi\) | ||||
−0.844182 | + | 0.536056i | \(0.819914\pi\) | |||||||
\(542\) | 20.5714 | 0.883618 | ||||||||
\(543\) | −37.0706 | −1.59085 | ||||||||
\(544\) | −0.845777 | −0.0362624 | ||||||||
\(545\) | 61.3050 | 2.62602 | ||||||||
\(546\) | 15.3914 | 0.658692 | ||||||||
\(547\) | −1.52187 | −0.0650703 | −0.0325351 | − | 0.999471i | \(-0.510358\pi\) | ||||
−0.0325351 | + | 0.999471i | \(0.510358\pi\) | |||||||
\(548\) | −17.6053 | −0.752061 | ||||||||
\(549\) | −19.6945 | −0.840543 | ||||||||
\(550\) | 3.62512 | 0.154576 | ||||||||
\(551\) | −37.5235 | −1.59856 | ||||||||
\(552\) | 3.06972 | 0.130656 | ||||||||
\(553\) | 34.6002 | 1.47135 | ||||||||
\(554\) | 22.3471 | 0.949438 | ||||||||
\(555\) | 13.0245 | 0.552857 | ||||||||
\(556\) | −8.48784 | −0.359965 | ||||||||
\(557\) | −45.2088 | −1.91556 | −0.957780 | − | 0.287502i | \(-0.907175\pi\) | ||||
−0.957780 | + | 0.287502i | \(0.907175\pi\) | |||||||
\(558\) | 61.5488 | 2.60557 | ||||||||
\(559\) | −25.9550 | −1.09778 | ||||||||
\(560\) | 7.28613 | 0.307895 | ||||||||
\(561\) | 1.30622 | 0.0551488 | ||||||||
\(562\) | −30.5708 | −1.28955 | ||||||||
\(563\) | −14.6315 | −0.616646 | −0.308323 | − | 0.951282i | \(-0.599768\pi\) | ||||
−0.308323 | + | 0.951282i | \(0.599768\pi\) | |||||||
\(564\) | 15.4549 | 0.650767 | ||||||||
\(565\) | 45.1688 | 1.90027 | ||||||||
\(566\) | −3.21210 | −0.135015 | ||||||||
\(567\) | 56.5387 | 2.37440 | ||||||||
\(568\) | −8.96504 | −0.376165 | ||||||||
\(569\) | 24.0122 | 1.00664 | 0.503322 | − | 0.864099i | \(-0.332111\pi\) | ||||
0.503322 | + | 0.864099i | \(0.332111\pi\) | |||||||
\(570\) | 78.3677 | 3.28246 | ||||||||
\(571\) | −5.63877 | −0.235975 | −0.117988 | − | 0.993015i | \(-0.537644\pi\) | ||||
−0.117988 | + | 0.993015i | \(0.537644\pi\) | |||||||
\(572\) | −1.08251 | −0.0452620 | ||||||||
\(573\) | −18.5523 | −0.775035 | ||||||||
\(574\) | 3.90549 | 0.163012 | ||||||||
\(575\) | −7.20541 | −0.300486 | ||||||||
\(576\) | 7.73650 | 0.322354 | ||||||||
\(577\) | −14.4960 | −0.603478 | −0.301739 | − | 0.953391i | \(-0.597567\pi\) | ||||
−0.301739 | + | 0.953391i | \(0.597567\pi\) | |||||||
\(578\) | −16.2847 | −0.677353 | ||||||||
\(579\) | 77.9985 | 3.24151 | ||||||||
\(580\) | 19.9113 | 0.826772 | ||||||||
\(581\) | −28.2268 | −1.17104 | ||||||||
\(582\) | −5.52515 | −0.229025 | ||||||||
\(583\) | 5.50541 | 0.228011 | ||||||||
\(584\) | 12.8974 | 0.533699 | ||||||||
\(585\) | −63.2989 | −2.61709 | ||||||||
\(586\) | −10.9476 | −0.452240 | ||||||||
\(587\) | −1.74785 | −0.0721415 | −0.0360708 | − | 0.999349i | \(-0.511484\pi\) | ||||
−0.0360708 | + | 0.999349i | \(0.511484\pi\) | |||||||
\(588\) | 9.23020 | 0.380647 | ||||||||
\(589\) | −53.4109 | −2.20076 | ||||||||
\(590\) | −34.8186 | −1.43346 | ||||||||
\(591\) | −77.7272 | −3.19727 | ||||||||
\(592\) | −1.11578 | −0.0458582 | ||||||||
\(593\) | 10.2000 | 0.418864 | 0.209432 | − | 0.977823i | \(-0.432839\pi\) | ||||
0.209432 | + | 0.977823i | \(0.432839\pi\) | |||||||
\(594\) | −7.31509 | −0.300142 | ||||||||
\(595\) | −6.16244 | −0.252635 | ||||||||
\(596\) | −0.583085 | −0.0238841 | ||||||||
\(597\) | 51.9571 | 2.12646 | ||||||||
\(598\) | 2.15163 | 0.0879868 | ||||||||
\(599\) | −7.36660 | −0.300991 | −0.150496 | − | 0.988611i | \(-0.548087\pi\) | ||||
−0.150496 | + | 0.988611i | \(0.548087\pi\) | |||||||
\(600\) | −25.2013 | −1.02884 | ||||||||
\(601\) | −44.8588 | −1.82983 | −0.914914 | − | 0.403649i | \(-0.867742\pi\) | ||||
−0.914914 | + | 0.403649i | \(0.867742\pi\) | |||||||
\(602\) | 23.1136 | 0.942038 | ||||||||
\(603\) | 105.155 | 4.28226 | ||||||||
\(604\) | −11.5921 | −0.471677 | ||||||||
\(605\) | −38.3957 | −1.56101 | ||||||||
\(606\) | −46.1076 | −1.87299 | ||||||||
\(607\) | 10.7337 | 0.435668 | 0.217834 | − | 0.975986i | \(-0.430101\pi\) | ||||
0.217834 | + | 0.975986i | \(0.430101\pi\) | |||||||
\(608\) | −6.71359 | −0.272272 | ||||||||
\(609\) | −37.4565 | −1.51781 | ||||||||
\(610\) | −9.06885 | −0.367187 | ||||||||
\(611\) | 10.8327 | 0.438243 | ||||||||
\(612\) | −6.54335 | −0.264499 | ||||||||
\(613\) | −4.27600 | −0.172706 | −0.0863530 | − | 0.996265i | \(-0.527521\pi\) | ||||
−0.0863530 | + | 0.996265i | \(0.527521\pi\) | |||||||
\(614\) | −11.9302 | −0.481465 | ||||||||
\(615\) | −22.2900 | −0.898821 | ||||||||
\(616\) | 0.964000 | 0.0388407 | ||||||||
\(617\) | 1.39353 | 0.0561014 | 0.0280507 | − | 0.999607i | \(-0.491070\pi\) | ||||
0.0280507 | + | 0.999607i | \(0.491070\pi\) | |||||||
\(618\) | 43.6828 | 1.75718 | ||||||||
\(619\) | −33.9034 | −1.36269 | −0.681347 | − | 0.731961i | \(-0.738605\pi\) | ||||
−0.681347 | + | 0.731961i | \(0.738605\pi\) | |||||||
\(620\) | 28.3417 | 1.13823 | ||||||||
\(621\) | 14.5397 | 0.583458 | ||||||||
\(622\) | −22.0615 | −0.884584 | ||||||||
\(623\) | −15.6256 | −0.626027 | ||||||||
\(624\) | 7.52545 | 0.301259 | ||||||||
\(625\) | −4.30185 | −0.172074 | ||||||||
\(626\) | 19.8960 | 0.795206 | ||||||||
\(627\) | 10.3685 | 0.414079 | ||||||||
\(628\) | 1.81603 | 0.0724676 | ||||||||
\(629\) | 0.943698 | 0.0376277 | ||||||||
\(630\) | 56.3692 | 2.24580 | ||||||||
\(631\) | 4.31000 | 0.171578 | 0.0857892 | − | 0.996313i | \(-0.472659\pi\) | ||||
0.0857892 | + | 0.996313i | \(0.472659\pi\) | |||||||
\(632\) | 16.9174 | 0.672937 | ||||||||
\(633\) | 64.1404 | 2.54935 | ||||||||
\(634\) | 8.61942 | 0.342321 | ||||||||
\(635\) | −18.1564 | −0.720515 | ||||||||
\(636\) | −38.2728 | −1.51762 | ||||||||
\(637\) | 6.46965 | 0.256337 | ||||||||
\(638\) | 2.63439 | 0.104296 | ||||||||
\(639\) | −69.3580 | −2.74376 | ||||||||
\(640\) | 3.56247 | 0.140819 | ||||||||
\(641\) | −32.6126 | −1.28812 | −0.644060 | − | 0.764975i | \(-0.722751\pi\) | ||||
−0.644060 | + | 0.764975i | \(0.722751\pi\) | |||||||
\(642\) | −54.2049 | −2.13930 | ||||||||
\(643\) | 21.3863 | 0.843393 | 0.421697 | − | 0.906737i | \(-0.361435\pi\) | ||||
0.421697 | + | 0.906737i | \(0.361435\pi\) | |||||||
\(644\) | −1.91608 | −0.0755040 | ||||||||
\(645\) | −131.917 | −5.19425 | ||||||||
\(646\) | 5.67820 | 0.223406 | ||||||||
\(647\) | 21.0434 | 0.827302 | 0.413651 | − | 0.910436i | \(-0.364253\pi\) | ||||
0.413651 | + | 0.910436i | \(0.364253\pi\) | |||||||
\(648\) | 27.6439 | 1.08596 | ||||||||
\(649\) | −4.60671 | −0.180829 | ||||||||
\(650\) | −17.6642 | −0.692846 | ||||||||
\(651\) | −53.3154 | −2.08959 | ||||||||
\(652\) | −3.62185 | −0.141843 | ||||||||
\(653\) | −7.46964 | −0.292310 | −0.146155 | − | 0.989262i | \(-0.546690\pi\) | ||||
−0.146155 | + | 0.989262i | \(0.546690\pi\) | |||||||
\(654\) | −56.3867 | −2.20489 | ||||||||
\(655\) | −5.46669 | −0.213601 | ||||||||
\(656\) | 1.90954 | 0.0745550 | ||||||||
\(657\) | 99.7809 | 3.89282 | ||||||||
\(658\) | −9.64673 | −0.376069 | ||||||||
\(659\) | 19.3845 | 0.755114 | 0.377557 | − | 0.925986i | \(-0.376764\pi\) | ||||
0.377557 | + | 0.925986i | \(0.376764\pi\) | |||||||
\(660\) | −5.50190 | −0.214161 | ||||||||
\(661\) | −15.9933 | −0.622068 | −0.311034 | − | 0.950399i | \(-0.600675\pi\) | ||||
−0.311034 | + | 0.950399i | \(0.600675\pi\) | |||||||
\(662\) | −24.9534 | −0.969843 | ||||||||
\(663\) | −6.36485 | −0.247190 | ||||||||
\(664\) | −13.8011 | −0.535588 | ||||||||
\(665\) | −48.9161 | −1.89689 | ||||||||
\(666\) | −8.63221 | −0.334491 | ||||||||
\(667\) | −5.23619 | −0.202746 | ||||||||
\(668\) | 8.99378 | 0.347980 | ||||||||
\(669\) | −35.6010 | −1.37641 | ||||||||
\(670\) | 48.4215 | 1.87068 | ||||||||
\(671\) | −1.19986 | −0.0463202 | ||||||||
\(672\) | −6.70159 | −0.258519 | ||||||||
\(673\) | 12.4468 | 0.479790 | 0.239895 | − | 0.970799i | \(-0.422887\pi\) | ||||
0.239895 | + | 0.970799i | \(0.422887\pi\) | |||||||
\(674\) | 27.0511 | 1.04197 | ||||||||
\(675\) | −119.366 | −4.59440 | ||||||||
\(676\) | −7.72524 | −0.297125 | ||||||||
\(677\) | −26.2182 | −1.00765 | −0.503823 | − | 0.863807i | \(-0.668074\pi\) | ||||
−0.503823 | + | 0.863807i | \(0.668074\pi\) | |||||||
\(678\) | −41.5451 | −1.59553 | ||||||||
\(679\) | 3.44873 | 0.132350 | ||||||||
\(680\) | −3.01305 | −0.115545 | ||||||||
\(681\) | −8.38336 | −0.321251 | ||||||||
\(682\) | 3.74978 | 0.143586 | ||||||||
\(683\) | 40.5984 | 1.55345 | 0.776727 | − | 0.629838i | \(-0.216879\pi\) | ||||
0.776727 | + | 0.629838i | \(0.216879\pi\) | |||||||
\(684\) | −51.9397 | −1.98596 | ||||||||
\(685\) | −62.7182 | −2.39634 | ||||||||
\(686\) | −20.0781 | −0.766586 | ||||||||
\(687\) | 3.65057 | 0.139278 | ||||||||
\(688\) | 11.3011 | 0.430850 | ||||||||
\(689\) | −26.8263 | −1.02200 | ||||||||
\(690\) | 10.9358 | 0.416317 | ||||||||
\(691\) | −23.9742 | −0.912020 | −0.456010 | − | 0.889975i | \(-0.650722\pi\) | ||||
−0.456010 | + | 0.889975i | \(0.650722\pi\) | |||||||
\(692\) | 17.6342 | 0.670353 | ||||||||
\(693\) | 7.45798 | 0.283305 | ||||||||
\(694\) | −0.206449 | −0.00783670 | ||||||||
\(695\) | −30.2376 | −1.14698 | ||||||||
\(696\) | −18.3139 | −0.694186 | ||||||||
\(697\) | −1.61504 | −0.0611742 | ||||||||
\(698\) | 29.5719 | 1.11931 | ||||||||
\(699\) | −57.9508 | −2.19190 | ||||||||
\(700\) | 15.7303 | 0.594551 | ||||||||
\(701\) | −20.7561 | −0.783948 | −0.391974 | − | 0.919976i | \(-0.628208\pi\) | ||||
−0.391974 | + | 0.919976i | \(0.628208\pi\) | |||||||
\(702\) | 35.6443 | 1.34531 | ||||||||
\(703\) | 7.49087 | 0.282524 | ||||||||
\(704\) | 0.471336 | 0.0177641 | ||||||||
\(705\) | 55.0574 | 2.07358 | ||||||||
\(706\) | −28.6723 | −1.07909 | ||||||||
\(707\) | 28.7798 | 1.08237 | ||||||||
\(708\) | 32.0252 | 1.20358 | ||||||||
\(709\) | 49.9311 | 1.87520 | 0.937601 | − | 0.347712i | \(-0.113041\pi\) | ||||
0.937601 | + | 0.347712i | \(0.113041\pi\) | |||||||
\(710\) | −31.9377 | −1.19860 | ||||||||
\(711\) | 130.881 | 4.90843 | ||||||||
\(712\) | −7.63995 | −0.286319 | ||||||||
\(713\) | −7.45318 | −0.279124 | ||||||||
\(714\) | 5.66805 | 0.212121 | ||||||||
\(715\) | −3.85640 | −0.144221 | ||||||||
\(716\) | 26.3068 | 0.983133 | ||||||||
\(717\) | 30.7887 | 1.14983 | ||||||||
\(718\) | −17.4411 | −0.650898 | ||||||||
\(719\) | −4.80534 | −0.179209 | −0.0896045 | − | 0.995977i | \(-0.528560\pi\) | ||||
−0.0896045 | + | 0.995977i | \(0.528560\pi\) | |||||||
\(720\) | 27.5610 | 1.02714 | ||||||||
\(721\) | −27.2663 | −1.01545 | ||||||||
\(722\) | 26.0723 | 0.970311 | ||||||||
\(723\) | −57.7016 | −2.14594 | ||||||||
\(724\) | 11.3135 | 0.420464 | ||||||||
\(725\) | 42.9874 | 1.59651 | ||||||||
\(726\) | 35.3153 | 1.31067 | ||||||||
\(727\) | −32.5873 | −1.20859 | −0.604297 | − | 0.796759i | \(-0.706546\pi\) | ||||
−0.604297 | + | 0.796759i | \(0.706546\pi\) | |||||||
\(728\) | −4.69729 | −0.174093 | ||||||||
\(729\) | 61.3069 | 2.27063 | ||||||||
\(730\) | 45.9466 | 1.70056 | ||||||||
\(731\) | −9.55820 | −0.353523 | ||||||||
\(732\) | 8.34128 | 0.308303 | ||||||||
\(733\) | −35.4866 | −1.31073 | −0.655364 | − | 0.755313i | \(-0.727485\pi\) | ||||
−0.655364 | + | 0.755313i | \(0.727485\pi\) | |||||||
\(734\) | 30.2560 | 1.11677 | ||||||||
\(735\) | 32.8823 | 1.21288 | ||||||||
\(736\) | −0.936843 | −0.0345325 | ||||||||
\(737\) | 6.40646 | 0.235985 | ||||||||
\(738\) | 14.7732 | 0.543808 | ||||||||
\(739\) | 3.93090 | 0.144600 | 0.0723002 | − | 0.997383i | \(-0.476966\pi\) | ||||
0.0723002 | + | 0.997383i | \(0.476966\pi\) | |||||||
\(740\) | −3.97492 | −0.146121 | ||||||||
\(741\) | −50.5228 | −1.85600 | ||||||||
\(742\) | 23.8894 | 0.877008 | ||||||||
\(743\) | 40.9247 | 1.50138 | 0.750690 | − | 0.660654i | \(-0.229721\pi\) | ||||
0.750690 | + | 0.660654i | \(0.229721\pi\) | |||||||
\(744\) | −26.0679 | −0.955696 | ||||||||
\(745\) | −2.07722 | −0.0761034 | ||||||||
\(746\) | −16.2820 | −0.596128 | ||||||||
\(747\) | −106.772 | −3.90660 | ||||||||
\(748\) | −0.398645 | −0.0145759 | ||||||||
\(749\) | 33.8340 | 1.23627 | ||||||||
\(750\) | −31.4139 | −1.14707 | ||||||||
\(751\) | 27.4971 | 1.00338 | 0.501691 | − | 0.865047i | \(-0.332711\pi\) | ||||
0.501691 | + | 0.865047i | \(0.332711\pi\) | |||||||
\(752\) | −4.71665 | −0.171999 | ||||||||
\(753\) | −83.9529 | −3.05941 | ||||||||
\(754\) | −12.8366 | −0.467482 | ||||||||
\(755\) | −41.2966 | −1.50294 | ||||||||
\(756\) | −31.7421 | −1.15445 | ||||||||
\(757\) | 16.4204 | 0.596811 | 0.298406 | − | 0.954439i | \(-0.403545\pi\) | ||||
0.298406 | + | 0.954439i | \(0.403545\pi\) | |||||||
\(758\) | 21.0865 | 0.765896 | ||||||||
\(759\) | 1.44687 | 0.0525180 | ||||||||
\(760\) | −23.9169 | −0.867559 | ||||||||
\(761\) | 24.2726 | 0.879882 | 0.439941 | − | 0.898027i | \(-0.354999\pi\) | ||||
0.439941 | + | 0.898027i | \(0.354999\pi\) | |||||||
\(762\) | 16.6998 | 0.604969 | ||||||||
\(763\) | 35.1959 | 1.27418 | ||||||||
\(764\) | 5.66197 | 0.204843 | ||||||||
\(765\) | −23.3105 | −0.842791 | ||||||||
\(766\) | 22.5117 | 0.813379 | ||||||||
\(767\) | 22.4472 | 0.810521 | ||||||||
\(768\) | −3.27666 | −0.118236 | ||||||||
\(769\) | 30.3008 | 1.09267 | 0.546337 | − | 0.837566i | \(-0.316022\pi\) | ||||
0.546337 | + | 0.837566i | \(0.316022\pi\) | |||||||
\(770\) | 3.43422 | 0.123761 | ||||||||
\(771\) | −8.63857 | −0.311110 | ||||||||
\(772\) | −23.8043 | −0.856735 | ||||||||
\(773\) | −2.83667 | −0.102028 | −0.0510139 | − | 0.998698i | \(-0.516245\pi\) | ||||
−0.0510139 | + | 0.998698i | \(0.516245\pi\) | |||||||
\(774\) | 87.4309 | 3.14264 | ||||||||
\(775\) | 61.1881 | 2.19794 | ||||||||
\(776\) | 1.68621 | 0.0605315 | ||||||||
\(777\) | 7.47748 | 0.268253 | ||||||||
\(778\) | 10.3804 | 0.372156 | ||||||||
\(779\) | −12.8199 | −0.459320 | ||||||||
\(780\) | 26.8092 | 0.959922 | ||||||||
\(781\) | −4.22555 | −0.151202 | ||||||||
\(782\) | 0.792360 | 0.0283347 | ||||||||
\(783\) | −86.7437 | −3.09997 | ||||||||
\(784\) | −2.81695 | −0.100605 | ||||||||
\(785\) | 6.46955 | 0.230908 | ||||||||
\(786\) | 5.02812 | 0.179347 | ||||||||
\(787\) | 9.80178 | 0.349396 | 0.174698 | − | 0.984622i | \(-0.444105\pi\) | ||||
0.174698 | + | 0.984622i | \(0.444105\pi\) | |||||||
\(788\) | 23.7215 | 0.845042 | ||||||||
\(789\) | 60.3530 | 2.14862 | ||||||||
\(790\) | 60.2675 | 2.14422 | ||||||||
\(791\) | 25.9319 | 0.922033 | ||||||||
\(792\) | 3.64649 | 0.129572 | ||||||||
\(793\) | 5.84659 | 0.207619 | ||||||||
\(794\) | 2.44123 | 0.0866359 | ||||||||
\(795\) | −136.346 | −4.83568 | ||||||||
\(796\) | −15.8567 | −0.562026 | ||||||||
\(797\) | 6.13117 | 0.217177 | 0.108589 | − | 0.994087i | \(-0.465367\pi\) | ||||
0.108589 | + | 0.994087i | \(0.465367\pi\) | |||||||
\(798\) | 44.9917 | 1.59269 | ||||||||
\(799\) | 3.98923 | 0.141129 | ||||||||
\(800\) | 7.69116 | 0.271924 | ||||||||
\(801\) | −59.1065 | −2.08842 | ||||||||
\(802\) | 1.44526 | 0.0510339 | ||||||||
\(803\) | 6.07902 | 0.214524 | ||||||||
\(804\) | −44.5368 | −1.57069 | ||||||||
\(805\) | −6.82596 | −0.240584 | ||||||||
\(806\) | −18.2716 | −0.643589 | ||||||||
\(807\) | −3.48351 | −0.122625 | ||||||||
\(808\) | 14.0715 | 0.495034 | ||||||||
\(809\) | −19.0418 | −0.669476 | −0.334738 | − | 0.942311i | \(-0.608648\pi\) | ||||
−0.334738 | + | 0.942311i | \(0.608648\pi\) | |||||||
\(810\) | 98.4805 | 3.46025 | ||||||||
\(811\) | 11.9108 | 0.418244 | 0.209122 | − | 0.977890i | \(-0.432939\pi\) | ||||
0.209122 | + | 0.977890i | \(0.432939\pi\) | |||||||
\(812\) | 11.4313 | 0.401160 | ||||||||
\(813\) | −67.4056 | −2.36402 | ||||||||
\(814\) | −0.525906 | −0.0184330 | ||||||||
\(815\) | −12.9027 | −0.451963 | ||||||||
\(816\) | 2.77132 | 0.0970157 | ||||||||
\(817\) | −75.8709 | −2.65439 | ||||||||
\(818\) | −1.28590 | −0.0449604 | ||||||||
\(819\) | −36.3406 | −1.26984 | ||||||||
\(820\) | 6.80267 | 0.237560 | ||||||||
\(821\) | −11.8408 | −0.413247 | −0.206624 | − | 0.978421i | \(-0.566248\pi\) | ||||
−0.206624 | + | 0.978421i | \(0.566248\pi\) | |||||||
\(822\) | 57.6865 | 2.01205 | ||||||||
\(823\) | 8.96652 | 0.312553 | 0.156277 | − | 0.987713i | \(-0.450051\pi\) | ||||
0.156277 | + | 0.987713i | \(0.450051\pi\) | |||||||
\(824\) | −13.3315 | −0.464425 | ||||||||
\(825\) | −11.8783 | −0.413549 | ||||||||
\(826\) | −19.9897 | −0.695532 | ||||||||
\(827\) | −37.4133 | −1.30099 | −0.650494 | − | 0.759511i | \(-0.725438\pi\) | ||||
−0.650494 | + | 0.759511i | \(0.725438\pi\) | |||||||
\(828\) | −7.24788 | −0.251881 | ||||||||
\(829\) | 3.31799 | 0.115239 | 0.0576193 | − | 0.998339i | \(-0.481649\pi\) | ||||
0.0576193 | + | 0.998339i | \(0.481649\pi\) | |||||||
\(830\) | −49.1661 | −1.70658 | ||||||||
\(831\) | −73.2239 | −2.54011 | ||||||||
\(832\) | −2.29668 | −0.0796232 | ||||||||
\(833\) | 2.38251 | 0.0825492 | ||||||||
\(834\) | 27.8118 | 0.963043 | ||||||||
\(835\) | 32.0400 | 1.10879 | ||||||||
\(836\) | −3.16436 | −0.109442 | ||||||||
\(837\) | −123.471 | −4.26777 | ||||||||
\(838\) | 9.90362 | 0.342115 | ||||||||
\(839\) | 29.5697 | 1.02086 | 0.510429 | − | 0.859920i | \(-0.329487\pi\) | ||||
0.510429 | + | 0.859920i | \(0.329487\pi\) | |||||||
\(840\) | −23.8742 | −0.823737 | ||||||||
\(841\) | 2.23905 | 0.0772087 | ||||||||
\(842\) | −5.87673 | −0.202525 | ||||||||
\(843\) | 100.170 | 3.45004 | ||||||||
\(844\) | −19.5749 | −0.673797 | ||||||||
\(845\) | −27.5209 | −0.946748 | ||||||||
\(846\) | −36.4904 | −1.25457 | ||||||||
\(847\) | −22.0434 | −0.757420 | ||||||||
\(848\) | 11.6804 | 0.401108 | ||||||||
\(849\) | 10.5250 | 0.361216 | ||||||||
\(850\) | −6.50500 | −0.223120 | ||||||||
\(851\) | 1.04531 | 0.0358327 | ||||||||
\(852\) | 29.3754 | 1.00638 | ||||||||
\(853\) | −35.4884 | −1.21510 | −0.607550 | − | 0.794282i | \(-0.707847\pi\) | ||||
−0.607550 | + | 0.794282i | \(0.707847\pi\) | |||||||
\(854\) | −5.20652 | −0.178164 | ||||||||
\(855\) | −185.033 | −6.32801 | ||||||||
\(856\) | 16.5427 | 0.565419 | ||||||||
\(857\) | 40.7442 | 1.39180 | 0.695898 | − | 0.718141i | \(-0.255007\pi\) | ||||
0.695898 | + | 0.718141i | \(0.255007\pi\) | |||||||
\(858\) | 3.54702 | 0.121093 | ||||||||
\(859\) | 1.87841 | 0.0640905 | 0.0320453 | − | 0.999486i | \(-0.489798\pi\) | ||||
0.0320453 | + | 0.999486i | \(0.489798\pi\) | |||||||
\(860\) | 40.2597 | 1.37285 | ||||||||
\(861\) | −12.7970 | −0.436119 | ||||||||
\(862\) | 6.53342 | 0.222529 | ||||||||
\(863\) | 10.8542 | 0.369481 | 0.184741 | − | 0.982787i | \(-0.440855\pi\) | ||||
0.184741 | + | 0.982787i | \(0.440855\pi\) | |||||||
\(864\) | −15.5199 | −0.527998 | ||||||||
\(865\) | 62.8213 | 2.13599 | ||||||||
\(866\) | −16.7479 | −0.569118 | ||||||||
\(867\) | 53.3593 | 1.81218 | ||||||||
\(868\) | 16.2713 | 0.552283 | ||||||||
\(869\) | 7.97376 | 0.270491 | ||||||||
\(870\) | −65.2426 | −2.21193 | ||||||||
\(871\) | −31.2168 | −1.05774 | ||||||||
\(872\) | 17.2086 | 0.582757 | ||||||||
\(873\) | 13.0454 | 0.441519 | ||||||||
\(874\) | 6.28958 | 0.212748 | ||||||||
\(875\) | 19.6081 | 0.662876 | ||||||||
\(876\) | −42.2605 | −1.42785 | ||||||||
\(877\) | 5.12005 | 0.172892 | 0.0864459 | − | 0.996257i | \(-0.472449\pi\) | ||||
0.0864459 | + | 0.996257i | \(0.472449\pi\) | |||||||
\(878\) | 8.76042 | 0.295650 | ||||||||
\(879\) | 35.8715 | 1.20991 | ||||||||
\(880\) | 1.67912 | 0.0566031 | ||||||||
\(881\) | 5.25485 | 0.177040 | 0.0885202 | − | 0.996074i | \(-0.471786\pi\) | ||||
0.0885202 | + | 0.996074i | \(0.471786\pi\) | |||||||
\(882\) | −21.7934 | −0.733820 | ||||||||
\(883\) | −9.72610 | −0.327309 | −0.163655 | − | 0.986518i | \(-0.552328\pi\) | ||||
−0.163655 | + | 0.986518i | \(0.552328\pi\) | |||||||
\(884\) | 1.94248 | 0.0653327 | ||||||||
\(885\) | 114.089 | 3.83505 | ||||||||
\(886\) | 16.4273 | 0.551885 | ||||||||
\(887\) | 36.5362 | 1.22677 | 0.613383 | − | 0.789785i | \(-0.289808\pi\) | ||||
0.613383 | + | 0.789785i | \(0.289808\pi\) | |||||||
\(888\) | 3.65602 | 0.122688 | ||||||||
\(889\) | −10.4238 | −0.349603 | ||||||||
\(890\) | −27.2171 | −0.912318 | ||||||||
\(891\) | 13.0296 | 0.436507 | ||||||||
\(892\) | 10.8650 | 0.363788 | ||||||||
\(893\) | 31.6657 | 1.05965 | ||||||||
\(894\) | 1.91057 | 0.0638990 | ||||||||
\(895\) | 93.7172 | 3.13262 | ||||||||
\(896\) | 2.04525 | 0.0683270 | ||||||||
\(897\) | −7.05017 | −0.235398 | ||||||||
\(898\) | −0.923403 | −0.0308144 | ||||||||
\(899\) | 44.4656 | 1.48301 | ||||||||
\(900\) | 59.5027 | 1.98342 | ||||||||
\(901\) | −9.87904 | −0.329119 | ||||||||
\(902\) | 0.900035 | 0.0299679 | ||||||||
\(903\) | −75.7352 | −2.52031 | ||||||||
\(904\) | 12.6791 | 0.421700 | ||||||||
\(905\) | 40.3041 | 1.33975 | ||||||||
\(906\) | 37.9835 | 1.26192 | ||||||||
\(907\) | 39.2322 | 1.30268 | 0.651341 | − | 0.758785i | \(-0.274207\pi\) | ||||
0.651341 | + | 0.758785i | \(0.274207\pi\) | |||||||
\(908\) | 2.55851 | 0.0849071 | ||||||||
\(909\) | 108.864 | 3.61080 | ||||||||
\(910\) | −16.7339 | −0.554725 | ||||||||
\(911\) | −42.6189 | −1.41203 | −0.706014 | − | 0.708198i | \(-0.749508\pi\) | ||||
−0.706014 | + | 0.708198i | \(0.749508\pi\) | |||||||
\(912\) | 21.9982 | 0.728432 | ||||||||
\(913\) | −6.50497 | −0.215283 | ||||||||
\(914\) | 4.48696 | 0.148415 | ||||||||
\(915\) | 29.7155 | 0.982365 | ||||||||
\(916\) | −1.11411 | −0.0368114 | ||||||||
\(917\) | −3.13849 | −0.103642 | ||||||||
\(918\) | 13.1264 | 0.433235 | ||||||||
\(919\) | −50.2593 | −1.65790 | −0.828951 | − | 0.559322i | \(-0.811062\pi\) | ||||
−0.828951 | + | 0.559322i | \(0.811062\pi\) | |||||||
\(920\) | −3.33747 | −0.110033 | ||||||||
\(921\) | 39.0913 | 1.28810 | ||||||||
\(922\) | 18.3102 | 0.603014 | ||||||||
\(923\) | 20.5899 | 0.677724 | ||||||||
\(924\) | −3.15870 | −0.103914 | ||||||||
\(925\) | −8.58162 | −0.282162 | ||||||||
\(926\) | 0.366767 | 0.0120527 | ||||||||
\(927\) | −103.139 | −3.38754 | ||||||||
\(928\) | 5.58919 | 0.183474 | ||||||||
\(929\) | −11.0745 | −0.363342 | −0.181671 | − | 0.983359i | \(-0.558151\pi\) | ||||
−0.181671 | + | 0.983359i | \(0.558151\pi\) | |||||||
\(930\) | −92.8660 | −3.04520 | ||||||||
\(931\) | 18.9119 | 0.619812 | ||||||||
\(932\) | 17.6860 | 0.579323 | ||||||||
\(933\) | 72.2879 | 2.36660 | ||||||||
\(934\) | 19.9240 | 0.651934 | ||||||||
\(935\) | −1.42016 | −0.0464442 | ||||||||
\(936\) | −17.7683 | −0.580775 | ||||||||
\(937\) | 8.24204 | 0.269256 | 0.134628 | − | 0.990896i | \(-0.457016\pi\) | ||||
0.134628 | + | 0.990896i | \(0.457016\pi\) | |||||||
\(938\) | 27.7993 | 0.907679 | ||||||||
\(939\) | −65.1925 | −2.12748 | ||||||||
\(940\) | −16.8029 | −0.548051 | ||||||||
\(941\) | 4.99278 | 0.162760 | 0.0813799 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813799 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(942\) | −5.95052 | −0.193878 | ||||||||
\(943\) | −1.78894 | −0.0582559 | ||||||||
\(944\) | −9.77373 | −0.318108 | ||||||||
\(945\) | −113.080 | −3.67849 | ||||||||
\(946\) | 5.32661 | 0.173183 | ||||||||
\(947\) | 14.1834 | 0.460897 | 0.230449 | − | 0.973085i | \(-0.425981\pi\) | ||||
0.230449 | + | 0.973085i | \(0.425981\pi\) | |||||||
\(948\) | −55.4325 | −1.80036 | ||||||||
\(949\) | −29.6213 | −0.961548 | ||||||||
\(950\) | −51.6353 | −1.67527 | ||||||||
\(951\) | −28.2429 | −0.915839 | ||||||||
\(952\) | −1.72982 | −0.0560639 | ||||||||
\(953\) | 1.74320 | 0.0564679 | 0.0282340 | − | 0.999601i | \(-0.491012\pi\) | ||||
0.0282340 | + | 0.999601i | \(0.491012\pi\) | |||||||
\(954\) | 90.3657 | 2.92570 | ||||||||
\(955\) | 20.1706 | 0.652704 | ||||||||
\(956\) | −9.39637 | −0.303900 | ||||||||
\(957\) | −8.63199 | −0.279033 | ||||||||
\(958\) | −19.0667 | −0.616018 | ||||||||
\(959\) | −36.0072 | −1.16273 | ||||||||
\(960\) | −11.6730 | −0.376744 | ||||||||
\(961\) | 32.2921 | 1.04168 | ||||||||
\(962\) | 2.56259 | 0.0826212 | ||||||||
\(963\) | 127.983 | 4.12419 | ||||||||
\(964\) | 17.6099 | 0.567176 | ||||||||
\(965\) | −84.8019 | −2.72987 | ||||||||
\(966\) | 6.27834 | 0.202002 | ||||||||
\(967\) | −33.1406 | −1.06573 | −0.532865 | − | 0.846200i | \(-0.678885\pi\) | ||||
−0.532865 | + | 0.846200i | \(0.678885\pi\) | |||||||
\(968\) | −10.7778 | −0.346413 | ||||||||
\(969\) | −18.6055 | −0.597696 | ||||||||
\(970\) | 6.00708 | 0.192876 | ||||||||
\(971\) | −51.1828 | −1.64253 | −0.821266 | − | 0.570545i | \(-0.806732\pi\) | ||||
−0.821266 | + | 0.570545i | \(0.806732\pi\) | |||||||
\(972\) | −44.0200 | −1.41194 | ||||||||
\(973\) | −17.3598 | −0.556528 | ||||||||
\(974\) | −17.6870 | −0.566727 | ||||||||
\(975\) | 57.8795 | 1.85363 | ||||||||
\(976\) | −2.54567 | −0.0814848 | ||||||||
\(977\) | −11.5368 | −0.369094 | −0.184547 | − | 0.982824i | \(-0.559082\pi\) | ||||
−0.184547 | + | 0.982824i | \(0.559082\pi\) | |||||||
\(978\) | 11.8676 | 0.379484 | ||||||||
\(979\) | −3.60098 | −0.115088 | ||||||||
\(980\) | −10.0353 | −0.320566 | ||||||||
\(981\) | 133.134 | 4.25065 | ||||||||
\(982\) | −23.0384 | −0.735185 | ||||||||
\(983\) | −3.33851 | −0.106482 | −0.0532409 | − | 0.998582i | \(-0.516955\pi\) | ||||
−0.0532409 | + | 0.998582i | \(0.516955\pi\) | |||||||
\(984\) | −6.25692 | −0.199463 | ||||||||
\(985\) | 84.5069 | 2.69261 | ||||||||
\(986\) | −4.72721 | −0.150545 | ||||||||
\(987\) | 31.6091 | 1.00613 | ||||||||
\(988\) | 15.4190 | 0.490544 | ||||||||
\(989\) | −10.5873 | −0.336658 | ||||||||
\(990\) | 12.9905 | 0.412865 | ||||||||
\(991\) | 46.2203 | 1.46824 | 0.734118 | − | 0.679022i | \(-0.237596\pi\) | ||||
0.734118 | + | 0.679022i | \(0.237596\pi\) | |||||||
\(992\) | 7.95563 | 0.252592 | ||||||||
\(993\) | 81.7639 | 2.59470 | ||||||||
\(994\) | −18.3358 | −0.581575 | ||||||||
\(995\) | −56.4890 | −1.79082 | ||||||||
\(996\) | 45.2216 | 1.43290 | ||||||||
\(997\) | 33.2994 | 1.05460 | 0.527301 | − | 0.849678i | \(-0.323204\pi\) | ||||
0.527301 | + | 0.849678i | \(0.323204\pi\) | |||||||
\(998\) | −14.1952 | −0.449342 | ||||||||
\(999\) | 17.3167 | 0.547878 |
(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 | 6002.2.a.d.1.3 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6002.2.a.d.1.3 | ✓ | 79 | 1.1 | even | 1 | trivial |