Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.73802 | 1.93607 | 0.968037 | − | 0.250807i | \(-0.0806960\pi\) | ||||
0.968037 | + | 0.250807i | \(0.0806960\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.49677 | 2.74838 | ||||||||
\(5\) | 2.25213 | 1.00718 | 0.503591 | − | 0.863942i | \(-0.332012\pi\) | ||||
0.503591 | + | 0.863942i | \(0.332012\pi\) | |||||||
\(6\) | −2.73802 | −1.11779 | ||||||||
\(7\) | −2.23039 | −0.843008 | −0.421504 | − | 0.906827i | \(-0.638498\pi\) | ||||
−0.421504 | + | 0.906827i | \(0.638498\pi\) | |||||||
\(8\) | 9.57422 | 3.38500 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.16638 | 1.94998 | ||||||||
\(11\) | 4.01232 | 1.20976 | 0.604880 | − | 0.796317i | \(-0.293221\pi\) | ||||
0.604880 | + | 0.796317i | \(0.293221\pi\) | |||||||
\(12\) | −5.49677 | −1.58678 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −6.10685 | −1.63213 | ||||||||
\(15\) | −2.25213 | −0.581497 | ||||||||
\(16\) | 15.2209 | 3.80523 | ||||||||
\(17\) | 1.93575 | 0.469487 | 0.234744 | − | 0.972057i | \(-0.424575\pi\) | ||||
0.234744 | + | 0.972057i | \(0.424575\pi\) | |||||||
\(18\) | 2.73802 | 0.645358 | ||||||||
\(19\) | −3.89952 | −0.894611 | −0.447306 | − | 0.894381i | \(-0.647616\pi\) | ||||
−0.447306 | + | 0.894381i | \(0.647616\pi\) | |||||||
\(20\) | 12.3794 | 2.76812 | ||||||||
\(21\) | 2.23039 | 0.486711 | ||||||||
\(22\) | 10.9858 | 2.34218 | ||||||||
\(23\) | 1.46506 | 0.305486 | 0.152743 | − | 0.988266i | \(-0.451189\pi\) | ||||
0.152743 | + | 0.988266i | \(0.451189\pi\) | |||||||
\(24\) | −9.57422 | −1.95433 | ||||||||
\(25\) | 0.0720843 | 0.0144169 | ||||||||
\(26\) | 2.73802 | 0.536970 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −12.2599 | −2.31691 | ||||||||
\(29\) | −0.0392005 | −0.00727935 | −0.00363968 | − | 0.999993i | \(-0.501159\pi\) | ||||
−0.00363968 | + | 0.999993i | \(0.501159\pi\) | |||||||
\(30\) | −6.16638 | −1.12582 | ||||||||
\(31\) | −0.286582 | −0.0514716 | −0.0257358 | − | 0.999669i | \(-0.508193\pi\) | ||||
−0.0257358 | + | 0.999669i | \(0.508193\pi\) | |||||||
\(32\) | 22.5267 | 3.98220 | ||||||||
\(33\) | −4.01232 | −0.698455 | ||||||||
\(34\) | 5.30011 | 0.908962 | ||||||||
\(35\) | −5.02312 | −0.849063 | ||||||||
\(36\) | 5.49677 | 0.916128 | ||||||||
\(37\) | 0.862130 | 0.141733 | 0.0708667 | − | 0.997486i | \(-0.477424\pi\) | ||||
0.0708667 | + | 0.997486i | \(0.477424\pi\) | |||||||
\(38\) | −10.6770 | −1.73203 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 21.5624 | 3.40931 | ||||||||
\(41\) | −6.36427 | −0.993932 | −0.496966 | − | 0.867770i | \(-0.665553\pi\) | ||||
−0.496966 | + | 0.867770i | \(0.665553\pi\) | |||||||
\(42\) | 6.10685 | 0.942308 | ||||||||
\(43\) | 2.68261 | 0.409094 | 0.204547 | − | 0.978857i | \(-0.434428\pi\) | ||||
0.204547 | + | 0.978857i | \(0.434428\pi\) | |||||||
\(44\) | 22.0548 | 3.32488 | ||||||||
\(45\) | 2.25213 | 0.335728 | ||||||||
\(46\) | 4.01136 | 0.591443 | ||||||||
\(47\) | 3.27883 | 0.478267 | 0.239133 | − | 0.970987i | \(-0.423137\pi\) | ||||
0.239133 | + | 0.970987i | \(0.423137\pi\) | |||||||
\(48\) | −15.2209 | −2.19695 | ||||||||
\(49\) | −2.02537 | −0.289338 | ||||||||
\(50\) | 0.197368 | 0.0279121 | ||||||||
\(51\) | −1.93575 | −0.271059 | ||||||||
\(52\) | 5.49677 | 0.762264 | ||||||||
\(53\) | −11.3322 | −1.55660 | −0.778298 | − | 0.627895i | \(-0.783917\pi\) | ||||
−0.778298 | + | 0.627895i | \(0.783917\pi\) | |||||||
\(54\) | −2.73802 | −0.372598 | ||||||||
\(55\) | 9.03626 | 1.21845 | ||||||||
\(56\) | −21.3542 | −2.85358 | ||||||||
\(57\) | 3.89952 | 0.516504 | ||||||||
\(58\) | −0.107332 | −0.0140934 | ||||||||
\(59\) | 12.5156 | 1.62940 | 0.814698 | − | 0.579886i | \(-0.196903\pi\) | ||||
0.814698 | + | 0.579886i | \(0.196903\pi\) | |||||||
\(60\) | −12.3794 | −1.59818 | ||||||||
\(61\) | 1.47526 | 0.188888 | 0.0944439 | − | 0.995530i | \(-0.469893\pi\) | ||||
0.0944439 | + | 0.995530i | \(0.469893\pi\) | |||||||
\(62\) | −0.784668 | −0.0996529 | ||||||||
\(63\) | −2.23039 | −0.281003 | ||||||||
\(64\) | 31.2369 | 3.90461 | ||||||||
\(65\) | 2.25213 | 0.279342 | ||||||||
\(66\) | −10.9858 | −1.35226 | ||||||||
\(67\) | 3.33628 | 0.407591 | 0.203796 | − | 0.979013i | \(-0.434672\pi\) | ||||
0.203796 | + | 0.979013i | \(0.434672\pi\) | |||||||
\(68\) | 10.6403 | 1.29033 | ||||||||
\(69\) | −1.46506 | −0.176372 | ||||||||
\(70\) | −13.7534 | −1.64385 | ||||||||
\(71\) | −4.53598 | −0.538321 | −0.269161 | − | 0.963095i | \(-0.586746\pi\) | ||||
−0.269161 | + | 0.963095i | \(0.586746\pi\) | |||||||
\(72\) | 9.57422 | 1.12833 | ||||||||
\(73\) | 7.69775 | 0.900954 | 0.450477 | − | 0.892788i | \(-0.351254\pi\) | ||||
0.450477 | + | 0.892788i | \(0.351254\pi\) | |||||||
\(74\) | 2.36053 | 0.274406 | ||||||||
\(75\) | −0.0720843 | −0.00832358 | ||||||||
\(76\) | −21.4347 | −2.45873 | ||||||||
\(77\) | −8.94903 | −1.01984 | ||||||||
\(78\) | −2.73802 | −0.310020 | ||||||||
\(79\) | 3.50200 | 0.394005 | 0.197003 | − | 0.980403i | \(-0.436879\pi\) | ||||
0.197003 | + | 0.980403i | \(0.436879\pi\) | |||||||
\(80\) | 34.2794 | 3.83256 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −17.4255 | −1.92433 | ||||||||
\(83\) | −6.37677 | −0.699941 | −0.349970 | − | 0.936761i | \(-0.613808\pi\) | ||||
−0.349970 | + | 0.936761i | \(0.613808\pi\) | |||||||
\(84\) | 12.2599 | 1.33767 | ||||||||
\(85\) | 4.35955 | 0.472859 | ||||||||
\(86\) | 7.34504 | 0.792036 | ||||||||
\(87\) | 0.0392005 | 0.00420274 | ||||||||
\(88\) | 38.4148 | 4.09503 | ||||||||
\(89\) | −9.23478 | −0.978885 | −0.489442 | − | 0.872036i | \(-0.662800\pi\) | ||||
−0.489442 | + | 0.872036i | \(0.662800\pi\) | |||||||
\(90\) | 6.16638 | 0.649993 | ||||||||
\(91\) | −2.23039 | −0.233808 | ||||||||
\(92\) | 8.05309 | 0.839592 | ||||||||
\(93\) | 0.286582 | 0.0297172 | ||||||||
\(94\) | 8.97752 | 0.925960 | ||||||||
\(95\) | −8.78222 | −0.901037 | ||||||||
\(96\) | −22.5267 | −2.29912 | ||||||||
\(97\) | −17.3424 | −1.76086 | −0.880428 | − | 0.474180i | \(-0.842744\pi\) | ||||
−0.880428 | + | 0.474180i | \(0.842744\pi\) | |||||||
\(98\) | −5.54550 | −0.560180 | ||||||||
\(99\) | 4.01232 | 0.403253 | ||||||||
\(100\) | 0.396230 | 0.0396230 | ||||||||
\(101\) | −2.92744 | −0.291291 | −0.145646 | − | 0.989337i | \(-0.546526\pi\) | ||||
−0.145646 | + | 0.989337i | \(0.546526\pi\) | |||||||
\(102\) | −5.30011 | −0.524789 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 9.57422 | 0.938830 | ||||||||
\(105\) | 5.02312 | 0.490207 | ||||||||
\(106\) | −31.0278 | −3.01369 | ||||||||
\(107\) | −6.90978 | −0.667994 | −0.333997 | − | 0.942574i | \(-0.608398\pi\) | ||||
−0.333997 | + | 0.942574i | \(0.608398\pi\) | |||||||
\(108\) | −5.49677 | −0.528927 | ||||||||
\(109\) | 1.29481 | 0.124020 | 0.0620100 | − | 0.998076i | \(-0.480249\pi\) | ||||
0.0620100 | + | 0.998076i | \(0.480249\pi\) | |||||||
\(110\) | 24.7415 | 2.35901 | ||||||||
\(111\) | −0.862130 | −0.0818298 | ||||||||
\(112\) | −33.9485 | −3.20783 | ||||||||
\(113\) | 13.8148 | 1.29959 | 0.649795 | − | 0.760109i | \(-0.274855\pi\) | ||||
0.649795 | + | 0.760109i | \(0.274855\pi\) | |||||||
\(114\) | 10.6770 | 0.999990 | ||||||||
\(115\) | 3.29950 | 0.307680 | ||||||||
\(116\) | −0.215476 | −0.0200064 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 34.2681 | 3.15463 | ||||||||
\(119\) | −4.31746 | −0.395781 | ||||||||
\(120\) | −21.5624 | −1.96837 | ||||||||
\(121\) | 5.09870 | 0.463518 | ||||||||
\(122\) | 4.03930 | 0.365701 | ||||||||
\(123\) | 6.36427 | 0.573847 | ||||||||
\(124\) | −1.57527 | −0.141464 | ||||||||
\(125\) | −11.0983 | −0.992662 | ||||||||
\(126\) | −6.10685 | −0.544042 | ||||||||
\(127\) | 18.7055 | 1.65984 | 0.829922 | − | 0.557879i | \(-0.188385\pi\) | ||||
0.829922 | + | 0.557879i | \(0.188385\pi\) | |||||||
\(128\) | 40.4738 | 3.57741 | ||||||||
\(129\) | −2.68261 | −0.236190 | ||||||||
\(130\) | 6.16638 | 0.540827 | ||||||||
\(131\) | 16.8203 | 1.46959 | 0.734797 | − | 0.678287i | \(-0.237277\pi\) | ||||
0.734797 | + | 0.678287i | \(0.237277\pi\) | |||||||
\(132\) | −22.0548 | −1.91962 | ||||||||
\(133\) | 8.69744 | 0.754164 | ||||||||
\(134\) | 9.13481 | 0.789127 | ||||||||
\(135\) | −2.25213 | −0.193832 | ||||||||
\(136\) | 18.5333 | 1.58921 | ||||||||
\(137\) | −5.88521 | −0.502808 | −0.251404 | − | 0.967882i | \(-0.580892\pi\) | ||||
−0.251404 | + | 0.967882i | \(0.580892\pi\) | |||||||
\(138\) | −4.01136 | −0.341470 | ||||||||
\(139\) | −4.02739 | −0.341599 | −0.170799 | − | 0.985306i | \(-0.554635\pi\) | ||||
−0.170799 | + | 0.985306i | \(0.554635\pi\) | |||||||
\(140\) | −27.6109 | −2.33355 | ||||||||
\(141\) | −3.27883 | −0.276127 | ||||||||
\(142\) | −12.4196 | −1.04223 | ||||||||
\(143\) | 4.01232 | 0.335527 | ||||||||
\(144\) | 15.2209 | 1.26841 | ||||||||
\(145\) | −0.0882846 | −0.00733164 | ||||||||
\(146\) | 21.0766 | 1.74431 | ||||||||
\(147\) | 2.02537 | 0.167050 | ||||||||
\(148\) | 4.73893 | 0.389537 | ||||||||
\(149\) | 19.3486 | 1.58510 | 0.792549 | − | 0.609809i | \(-0.208754\pi\) | ||||
0.792549 | + | 0.609809i | \(0.208754\pi\) | |||||||
\(150\) | −0.197368 | −0.0161151 | ||||||||
\(151\) | 7.51787 | 0.611796 | 0.305898 | − | 0.952064i | \(-0.401043\pi\) | ||||
0.305898 | + | 0.952064i | \(0.401043\pi\) | |||||||
\(152\) | −37.3349 | −3.02826 | ||||||||
\(153\) | 1.93575 | 0.156496 | ||||||||
\(154\) | −24.5026 | −1.97448 | ||||||||
\(155\) | −0.645420 | −0.0518414 | ||||||||
\(156\) | −5.49677 | −0.440093 | ||||||||
\(157\) | 6.80666 | 0.543231 | 0.271615 | − | 0.962406i | \(-0.412442\pi\) | ||||
0.271615 | + | 0.962406i | \(0.412442\pi\) | |||||||
\(158\) | 9.58854 | 0.762823 | ||||||||
\(159\) | 11.3322 | 0.898701 | ||||||||
\(160\) | 50.7331 | 4.01080 | ||||||||
\(161\) | −3.26765 | −0.257527 | ||||||||
\(162\) | 2.73802 | 0.215119 | ||||||||
\(163\) | 25.0489 | 1.96198 | 0.980989 | − | 0.194064i | \(-0.0621671\pi\) | ||||
0.980989 | + | 0.194064i | \(0.0621671\pi\) | |||||||
\(164\) | −34.9829 | −2.73171 | ||||||||
\(165\) | −9.03626 | −0.703472 | ||||||||
\(166\) | −17.4597 | −1.35514 | ||||||||
\(167\) | −12.1377 | −0.939241 | −0.469620 | − | 0.882868i | \(-0.655609\pi\) | ||||
−0.469620 | + | 0.882868i | \(0.655609\pi\) | |||||||
\(168\) | 21.3542 | 1.64751 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 11.9365 | 0.915491 | ||||||||
\(171\) | −3.89952 | −0.298204 | ||||||||
\(172\) | 14.7457 | 1.12435 | ||||||||
\(173\) | −10.3059 | −0.783545 | −0.391773 | − | 0.920062i | \(-0.628138\pi\) | ||||
−0.391773 | + | 0.920062i | \(0.628138\pi\) | |||||||
\(174\) | 0.107332 | 0.00813681 | ||||||||
\(175\) | −0.160776 | −0.0121535 | ||||||||
\(176\) | 61.0711 | 4.60341 | ||||||||
\(177\) | −12.5156 | −0.940732 | ||||||||
\(178\) | −25.2850 | −1.89519 | ||||||||
\(179\) | −24.9691 | −1.86628 | −0.933140 | − | 0.359514i | \(-0.882943\pi\) | ||||
−0.933140 | + | 0.359514i | \(0.882943\pi\) | |||||||
\(180\) | 12.3794 | 0.922708 | ||||||||
\(181\) | −19.6972 | −1.46408 | −0.732042 | − | 0.681260i | \(-0.761433\pi\) | ||||
−0.732042 | + | 0.681260i | \(0.761433\pi\) | |||||||
\(182\) | −6.10685 | −0.452670 | ||||||||
\(183\) | −1.47526 | −0.109054 | ||||||||
\(184\) | 14.0268 | 1.03407 | ||||||||
\(185\) | 1.94163 | 0.142751 | ||||||||
\(186\) | 0.784668 | 0.0575346 | ||||||||
\(187\) | 7.76683 | 0.567967 | ||||||||
\(188\) | 18.0230 | 1.31446 | ||||||||
\(189\) | 2.23039 | 0.162237 | ||||||||
\(190\) | −24.0459 | −1.74447 | ||||||||
\(191\) | −16.8097 | −1.21631 | −0.608153 | − | 0.793820i | \(-0.708089\pi\) | ||||
−0.608153 | + | 0.793820i | \(0.708089\pi\) | |||||||
\(192\) | −31.2369 | −2.25433 | ||||||||
\(193\) | −13.7159 | −0.987292 | −0.493646 | − | 0.869663i | \(-0.664336\pi\) | ||||
−0.493646 | + | 0.869663i | \(0.664336\pi\) | |||||||
\(194\) | −47.4839 | −3.40915 | ||||||||
\(195\) | −2.25213 | −0.161278 | ||||||||
\(196\) | −11.1330 | −0.795212 | ||||||||
\(197\) | −3.72352 | −0.265290 | −0.132645 | − | 0.991164i | \(-0.542347\pi\) | ||||
−0.132645 | + | 0.991164i | \(0.542347\pi\) | |||||||
\(198\) | 10.9858 | 0.780728 | ||||||||
\(199\) | 21.3145 | 1.51094 | 0.755472 | − | 0.655181i | \(-0.227408\pi\) | ||||
0.755472 | + | 0.655181i | \(0.227408\pi\) | |||||||
\(200\) | 0.690151 | 0.0488010 | ||||||||
\(201\) | −3.33628 | −0.235323 | ||||||||
\(202\) | −8.01540 | −0.563961 | ||||||||
\(203\) | 0.0874324 | 0.00613655 | ||||||||
\(204\) | −10.6403 | −0.744973 | ||||||||
\(205\) | −14.3332 | −1.00107 | ||||||||
\(206\) | −2.73802 | −0.190767 | ||||||||
\(207\) | 1.46506 | 0.101829 | ||||||||
\(208\) | 15.2209 | 1.05538 | ||||||||
\(209\) | −15.6461 | −1.08226 | ||||||||
\(210\) | 13.7534 | 0.949076 | ||||||||
\(211\) | −0.347438 | −0.0239186 | −0.0119593 | − | 0.999928i | \(-0.503807\pi\) | ||||
−0.0119593 | + | 0.999928i | \(0.503807\pi\) | |||||||
\(212\) | −62.2904 | −4.27812 | ||||||||
\(213\) | 4.53598 | 0.310800 | ||||||||
\(214\) | −18.9191 | −1.29329 | ||||||||
\(215\) | 6.04158 | 0.412032 | ||||||||
\(216\) | −9.57422 | −0.651443 | ||||||||
\(217\) | 0.639189 | 0.0433910 | ||||||||
\(218\) | 3.54521 | 0.240112 | ||||||||
\(219\) | −7.69775 | −0.520166 | ||||||||
\(220\) | 49.6702 | 3.34876 | ||||||||
\(221\) | 1.93575 | 0.130212 | ||||||||
\(222\) | −2.36053 | −0.158429 | ||||||||
\(223\) | −8.88346 | −0.594880 | −0.297440 | − | 0.954740i | \(-0.596133\pi\) | ||||
−0.297440 | + | 0.954740i | \(0.596133\pi\) | |||||||
\(224\) | −50.2433 | −3.35702 | ||||||||
\(225\) | 0.0720843 | 0.00480562 | ||||||||
\(226\) | 37.8253 | 2.51610 | ||||||||
\(227\) | −15.3482 | −1.01870 | −0.509349 | − | 0.860560i | \(-0.670114\pi\) | ||||
−0.509349 | + | 0.860560i | \(0.670114\pi\) | |||||||
\(228\) | 21.4347 | 1.41955 | ||||||||
\(229\) | −11.4562 | −0.757044 | −0.378522 | − | 0.925592i | \(-0.623568\pi\) | ||||
−0.378522 | + | 0.925592i | \(0.623568\pi\) | |||||||
\(230\) | 9.03411 | 0.595692 | ||||||||
\(231\) | 8.94903 | 0.588803 | ||||||||
\(232\) | −0.375314 | −0.0246406 | ||||||||
\(233\) | 10.4366 | 0.683724 | 0.341862 | − | 0.939750i | \(-0.388942\pi\) | ||||
0.341862 | + | 0.939750i | \(0.388942\pi\) | |||||||
\(234\) | 2.73802 | 0.178990 | ||||||||
\(235\) | 7.38435 | 0.481702 | ||||||||
\(236\) | 68.7955 | 4.47820 | ||||||||
\(237\) | −3.50200 | −0.227479 | ||||||||
\(238\) | −11.8213 | −0.766262 | ||||||||
\(239\) | 4.27431 | 0.276482 | 0.138241 | − | 0.990399i | \(-0.455855\pi\) | ||||
0.138241 | + | 0.990399i | \(0.455855\pi\) | |||||||
\(240\) | −34.2794 | −2.21273 | ||||||||
\(241\) | −15.5365 | −1.00080 | −0.500398 | − | 0.865796i | \(-0.666813\pi\) | ||||
−0.500398 | + | 0.865796i | \(0.666813\pi\) | |||||||
\(242\) | 13.9603 | 0.897405 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 8.10916 | 0.519136 | ||||||||
\(245\) | −4.56139 | −0.291416 | ||||||||
\(246\) | 17.4255 | 1.11101 | ||||||||
\(247\) | −3.89952 | −0.248121 | ||||||||
\(248\) | −2.74380 | −0.174231 | ||||||||
\(249\) | 6.37677 | 0.404111 | ||||||||
\(250\) | −30.3874 | −1.92187 | ||||||||
\(251\) | −3.10336 | −0.195882 | −0.0979412 | − | 0.995192i | \(-0.531226\pi\) | ||||
−0.0979412 | + | 0.995192i | \(0.531226\pi\) | |||||||
\(252\) | −12.2599 | −0.772303 | ||||||||
\(253\) | 5.87828 | 0.369565 | ||||||||
\(254\) | 51.2161 | 3.21358 | ||||||||
\(255\) | −4.35955 | −0.273005 | ||||||||
\(256\) | 48.3444 | 3.02152 | ||||||||
\(257\) | −17.7908 | −1.10976 | −0.554879 | − | 0.831931i | \(-0.687236\pi\) | ||||
−0.554879 | + | 0.831931i | \(0.687236\pi\) | |||||||
\(258\) | −7.34504 | −0.457282 | ||||||||
\(259\) | −1.92289 | −0.119482 | ||||||||
\(260\) | 12.3794 | 0.767739 | ||||||||
\(261\) | −0.0392005 | −0.00242645 | ||||||||
\(262\) | 46.0543 | 2.84524 | ||||||||
\(263\) | −6.04045 | −0.372470 | −0.186235 | − | 0.982505i | \(-0.559629\pi\) | ||||
−0.186235 | + | 0.982505i | \(0.559629\pi\) | |||||||
\(264\) | −38.4148 | −2.36427 | ||||||||
\(265\) | −25.5216 | −1.56778 | ||||||||
\(266\) | 23.8138 | 1.46012 | ||||||||
\(267\) | 9.23478 | 0.565159 | ||||||||
\(268\) | 18.3387 | 1.12022 | ||||||||
\(269\) | −16.9184 | −1.03153 | −0.515766 | − | 0.856729i | \(-0.672493\pi\) | ||||
−0.515766 | + | 0.856729i | \(0.672493\pi\) | |||||||
\(270\) | −6.16638 | −0.375274 | ||||||||
\(271\) | −16.4202 | −0.997456 | −0.498728 | − | 0.866758i | \(-0.666199\pi\) | ||||
−0.498728 | + | 0.866758i | \(0.666199\pi\) | |||||||
\(272\) | 29.4638 | 1.78650 | ||||||||
\(273\) | 2.23039 | 0.134989 | ||||||||
\(274\) | −16.1138 | −0.973473 | ||||||||
\(275\) | 0.289225 | 0.0174409 | ||||||||
\(276\) | −8.05309 | −0.484739 | ||||||||
\(277\) | −7.13667 | −0.428801 | −0.214401 | − | 0.976746i | \(-0.568780\pi\) | ||||
−0.214401 | + | 0.976746i | \(0.568780\pi\) | |||||||
\(278\) | −11.0271 | −0.661360 | ||||||||
\(279\) | −0.286582 | −0.0171572 | ||||||||
\(280\) | −48.0925 | −2.87408 | ||||||||
\(281\) | −8.08608 | −0.482375 | −0.241188 | − | 0.970479i | \(-0.577537\pi\) | ||||
−0.241188 | + | 0.970479i | \(0.577537\pi\) | |||||||
\(282\) | −8.97752 | −0.534603 | ||||||||
\(283\) | 1.86933 | 0.111120 | 0.0555600 | − | 0.998455i | \(-0.482306\pi\) | ||||
0.0555600 | + | 0.998455i | \(0.482306\pi\) | |||||||
\(284\) | −24.9332 | −1.47951 | ||||||||
\(285\) | 8.78222 | 0.520214 | ||||||||
\(286\) | 10.9858 | 0.649605 | ||||||||
\(287\) | 14.1948 | 0.837893 | ||||||||
\(288\) | 22.5267 | 1.32740 | ||||||||
\(289\) | −13.2529 | −0.779582 | ||||||||
\(290\) | −0.241725 | −0.0141946 | ||||||||
\(291\) | 17.3424 | 1.01663 | ||||||||
\(292\) | 42.3127 | 2.47617 | ||||||||
\(293\) | −2.61365 | −0.152691 | −0.0763455 | − | 0.997081i | \(-0.524325\pi\) | ||||
−0.0763455 | + | 0.997081i | \(0.524325\pi\) | |||||||
\(294\) | 5.54550 | 0.323420 | ||||||||
\(295\) | 28.1868 | 1.64110 | ||||||||
\(296\) | 8.25423 | 0.479767 | ||||||||
\(297\) | −4.01232 | −0.232818 | ||||||||
\(298\) | 52.9768 | 3.06887 | ||||||||
\(299\) | 1.46506 | 0.0847266 | ||||||||
\(300\) | −0.396230 | −0.0228764 | ||||||||
\(301\) | −5.98325 | −0.344869 | ||||||||
\(302\) | 20.5841 | 1.18448 | ||||||||
\(303\) | 2.92744 | 0.168177 | ||||||||
\(304\) | −59.3542 | −3.40420 | ||||||||
\(305\) | 3.32248 | 0.190244 | ||||||||
\(306\) | 5.30011 | 0.302987 | ||||||||
\(307\) | 13.8308 | 0.789366 | 0.394683 | − | 0.918817i | \(-0.370854\pi\) | ||||
0.394683 | + | 0.918817i | \(0.370854\pi\) | |||||||
\(308\) | −49.1907 | −2.80290 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −1.76717 | −0.100369 | ||||||||
\(311\) | 1.27395 | 0.0722389 | 0.0361195 | − | 0.999347i | \(-0.488500\pi\) | ||||
0.0361195 | + | 0.999347i | \(0.488500\pi\) | |||||||
\(312\) | −9.57422 | −0.542034 | ||||||||
\(313\) | 2.55357 | 0.144336 | 0.0721681 | − | 0.997392i | \(-0.477008\pi\) | ||||
0.0721681 | + | 0.997392i | \(0.477008\pi\) | |||||||
\(314\) | 18.6368 | 1.05173 | ||||||||
\(315\) | −5.02312 | −0.283021 | ||||||||
\(316\) | 19.2496 | 1.08288 | ||||||||
\(317\) | 17.1973 | 0.965894 | 0.482947 | − | 0.875649i | \(-0.339566\pi\) | ||||
0.482947 | + | 0.875649i | \(0.339566\pi\) | |||||||
\(318\) | 31.0278 | 1.73995 | ||||||||
\(319\) | −0.157285 | −0.00880627 | ||||||||
\(320\) | 70.3494 | 3.93265 | ||||||||
\(321\) | 6.90978 | 0.385666 | ||||||||
\(322\) | −8.94690 | −0.498591 | ||||||||
\(323\) | −7.54848 | −0.420009 | ||||||||
\(324\) | 5.49677 | 0.305376 | ||||||||
\(325\) | 0.0720843 | 0.00399852 | ||||||||
\(326\) | 68.5843 | 3.79853 | ||||||||
\(327\) | −1.29481 | −0.0716029 | ||||||||
\(328\) | −60.9330 | −3.36446 | ||||||||
\(329\) | −7.31307 | −0.403183 | ||||||||
\(330\) | −24.7415 | −1.36197 | ||||||||
\(331\) | 6.63238 | 0.364548 | 0.182274 | − | 0.983248i | \(-0.441654\pi\) | ||||
0.182274 | + | 0.983248i | \(0.441654\pi\) | |||||||
\(332\) | −35.0516 | −1.92371 | ||||||||
\(333\) | 0.862130 | 0.0472444 | ||||||||
\(334\) | −33.2332 | −1.81844 | ||||||||
\(335\) | 7.51373 | 0.410519 | ||||||||
\(336\) | 33.9485 | 1.85204 | ||||||||
\(337\) | 8.19212 | 0.446253 | 0.223127 | − | 0.974789i | \(-0.428374\pi\) | ||||
0.223127 | + | 0.974789i | \(0.428374\pi\) | |||||||
\(338\) | 2.73802 | 0.148929 | ||||||||
\(339\) | −13.8148 | −0.750319 | ||||||||
\(340\) | 23.9634 | 1.29960 | ||||||||
\(341\) | −1.14986 | −0.0622683 | ||||||||
\(342\) | −10.6770 | −0.577345 | ||||||||
\(343\) | 20.1301 | 1.08692 | ||||||||
\(344\) | 25.6839 | 1.38478 | ||||||||
\(345\) | −3.29950 | −0.177639 | ||||||||
\(346\) | −28.2179 | −1.51700 | ||||||||
\(347\) | 14.9052 | 0.800153 | 0.400076 | − | 0.916482i | \(-0.368984\pi\) | ||||
0.400076 | + | 0.916482i | \(0.368984\pi\) | |||||||
\(348\) | 0.215476 | 0.0115507 | ||||||||
\(349\) | −0.206241 | −0.0110398 | −0.00551990 | − | 0.999985i | \(-0.501757\pi\) | ||||
−0.00551990 | + | 0.999985i | \(0.501757\pi\) | |||||||
\(350\) | −0.440208 | −0.0235301 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 90.3844 | 4.81750 | ||||||||
\(353\) | 15.8088 | 0.841416 | 0.420708 | − | 0.907196i | \(-0.361782\pi\) | ||||
0.420708 | + | 0.907196i | \(0.361782\pi\) | |||||||
\(354\) | −34.2681 | −1.82133 | ||||||||
\(355\) | −10.2156 | −0.542188 | ||||||||
\(356\) | −50.7614 | −2.69035 | ||||||||
\(357\) | 4.31746 | 0.228504 | ||||||||
\(358\) | −68.3660 | −3.61326 | ||||||||
\(359\) | 22.9336 | 1.21039 | 0.605195 | − | 0.796077i | \(-0.293095\pi\) | ||||
0.605195 | + | 0.796077i | \(0.293095\pi\) | |||||||
\(360\) | 21.5624 | 1.13644 | ||||||||
\(361\) | −3.79375 | −0.199671 | ||||||||
\(362\) | −53.9315 | −2.83457 | ||||||||
\(363\) | −5.09870 | −0.267612 | ||||||||
\(364\) | −12.2599 | −0.642595 | ||||||||
\(365\) | 17.3363 | 0.907425 | ||||||||
\(366\) | −4.03930 | −0.211137 | ||||||||
\(367\) | −21.8950 | −1.14291 | −0.571455 | − | 0.820633i | \(-0.693621\pi\) | ||||
−0.571455 | + | 0.820633i | \(0.693621\pi\) | |||||||
\(368\) | 22.2995 | 1.16244 | ||||||||
\(369\) | −6.36427 | −0.331311 | ||||||||
\(370\) | 5.31622 | 0.276377 | ||||||||
\(371\) | 25.2752 | 1.31222 | ||||||||
\(372\) | 1.57527 | 0.0816742 | ||||||||
\(373\) | −28.3129 | −1.46599 | −0.732994 | − | 0.680235i | \(-0.761878\pi\) | ||||
−0.732994 | + | 0.680235i | \(0.761878\pi\) | |||||||
\(374\) | 21.2657 | 1.09963 | ||||||||
\(375\) | 11.0983 | 0.573114 | ||||||||
\(376\) | 31.3923 | 1.61893 | ||||||||
\(377\) | −0.0392005 | −0.00201893 | ||||||||
\(378\) | 6.10685 | 0.314103 | ||||||||
\(379\) | −4.66157 | −0.239449 | −0.119724 | − | 0.992807i | \(-0.538201\pi\) | ||||
−0.119724 | + | 0.992807i | \(0.538201\pi\) | |||||||
\(380\) | −48.2738 | −2.47639 | ||||||||
\(381\) | −18.7055 | −0.958312 | ||||||||
\(382\) | −46.0253 | −2.35486 | ||||||||
\(383\) | −25.4152 | −1.29866 | −0.649328 | − | 0.760509i | \(-0.724950\pi\) | ||||
−0.649328 | + | 0.760509i | \(0.724950\pi\) | |||||||
\(384\) | −40.4738 | −2.06542 | ||||||||
\(385\) | −20.1544 | −1.02716 | ||||||||
\(386\) | −37.5544 | −1.91147 | ||||||||
\(387\) | 2.68261 | 0.136365 | ||||||||
\(388\) | −95.3272 | −4.83950 | ||||||||
\(389\) | 22.8812 | 1.16012 | 0.580060 | − | 0.814573i | \(-0.303029\pi\) | ||||
0.580060 | + | 0.814573i | \(0.303029\pi\) | |||||||
\(390\) | −6.16638 | −0.312247 | ||||||||
\(391\) | 2.83598 | 0.143422 | ||||||||
\(392\) | −19.3913 | −0.979410 | ||||||||
\(393\) | −16.8203 | −0.848471 | ||||||||
\(394\) | −10.1951 | −0.513621 | ||||||||
\(395\) | 7.88694 | 0.396835 | ||||||||
\(396\) | 22.0548 | 1.10829 | ||||||||
\(397\) | 8.76949 | 0.440128 | 0.220064 | − | 0.975485i | \(-0.429373\pi\) | ||||
0.220064 | + | 0.975485i | \(0.429373\pi\) | |||||||
\(398\) | 58.3596 | 2.92530 | ||||||||
\(399\) | −8.69744 | −0.435417 | ||||||||
\(400\) | 1.09719 | 0.0548594 | ||||||||
\(401\) | −10.3080 | −0.514757 | −0.257379 | − | 0.966311i | \(-0.582859\pi\) | ||||
−0.257379 | + | 0.966311i | \(0.582859\pi\) | |||||||
\(402\) | −9.13481 | −0.455603 | ||||||||
\(403\) | −0.286582 | −0.0142757 | ||||||||
\(404\) | −16.0915 | −0.800580 | ||||||||
\(405\) | 2.25213 | 0.111909 | ||||||||
\(406\) | 0.239392 | 0.0118808 | ||||||||
\(407\) | 3.45914 | 0.171463 | ||||||||
\(408\) | −18.5333 | −0.917533 | ||||||||
\(409\) | −30.9929 | −1.53250 | −0.766250 | − | 0.642543i | \(-0.777879\pi\) | ||||
−0.766250 | + | 0.642543i | \(0.777879\pi\) | |||||||
\(410\) | −39.2445 | −1.93815 | ||||||||
\(411\) | 5.88521 | 0.290296 | ||||||||
\(412\) | −5.49677 | −0.270806 | ||||||||
\(413\) | −27.9147 | −1.37359 | ||||||||
\(414\) | 4.01136 | 0.197148 | ||||||||
\(415\) | −14.3613 | −0.704968 | ||||||||
\(416\) | 22.5267 | 1.10446 | ||||||||
\(417\) | 4.02739 | 0.197222 | ||||||||
\(418\) | −42.8394 | −2.09534 | ||||||||
\(419\) | 26.0310 | 1.27170 | 0.635850 | − | 0.771813i | \(-0.280650\pi\) | ||||
0.635850 | + | 0.771813i | \(0.280650\pi\) | |||||||
\(420\) | 27.6109 | 1.34728 | ||||||||
\(421\) | 5.86010 | 0.285604 | 0.142802 | − | 0.989751i | \(-0.454389\pi\) | ||||
0.142802 | + | 0.989751i | \(0.454389\pi\) | |||||||
\(422\) | −0.951293 | −0.0463082 | ||||||||
\(423\) | 3.27883 | 0.159422 | ||||||||
\(424\) | −108.497 | −5.26908 | ||||||||
\(425\) | 0.139537 | 0.00676853 | ||||||||
\(426\) | 12.4196 | 0.601732 | ||||||||
\(427\) | −3.29040 | −0.159234 | ||||||||
\(428\) | −37.9815 | −1.83590 | ||||||||
\(429\) | −4.01232 | −0.193717 | ||||||||
\(430\) | 16.5420 | 0.797725 | ||||||||
\(431\) | 22.3070 | 1.07449 | 0.537244 | − | 0.843427i | \(-0.319465\pi\) | ||||
0.537244 | + | 0.843427i | \(0.319465\pi\) | |||||||
\(432\) | −15.2209 | −0.732316 | ||||||||
\(433\) | 12.5592 | 0.603559 | 0.301779 | − | 0.953378i | \(-0.402419\pi\) | ||||
0.301779 | + | 0.953378i | \(0.402419\pi\) | |||||||
\(434\) | 1.75011 | 0.0840082 | ||||||||
\(435\) | 0.0882846 | 0.00423292 | ||||||||
\(436\) | 7.11724 | 0.340854 | ||||||||
\(437\) | −5.71303 | −0.273291 | ||||||||
\(438\) | −21.0766 | −1.00708 | ||||||||
\(439\) | 20.4122 | 0.974223 | 0.487112 | − | 0.873340i | \(-0.338050\pi\) | ||||
0.487112 | + | 0.873340i | \(0.338050\pi\) | |||||||
\(440\) | 86.5151 | 4.12445 | ||||||||
\(441\) | −2.02537 | −0.0964461 | ||||||||
\(442\) | 5.30011 | 0.252101 | ||||||||
\(443\) | −6.84950 | −0.325430 | −0.162715 | − | 0.986673i | \(-0.552025\pi\) | ||||
−0.162715 | + | 0.986673i | \(0.552025\pi\) | |||||||
\(444\) | −4.73893 | −0.224900 | ||||||||
\(445\) | −20.7979 | −0.985916 | ||||||||
\(446\) | −24.3231 | −1.15173 | ||||||||
\(447\) | −19.3486 | −0.915156 | ||||||||
\(448\) | −69.6703 | −3.29161 | ||||||||
\(449\) | 19.0147 | 0.897359 | 0.448679 | − | 0.893693i | \(-0.351894\pi\) | ||||
0.448679 | + | 0.893693i | \(0.351894\pi\) | |||||||
\(450\) | 0.197368 | 0.00930403 | ||||||||
\(451\) | −25.5355 | −1.20242 | ||||||||
\(452\) | 75.9369 | 3.57177 | ||||||||
\(453\) | −7.51787 | −0.353220 | ||||||||
\(454\) | −42.0238 | −1.97227 | ||||||||
\(455\) | −5.02312 | −0.235488 | ||||||||
\(456\) | 37.3349 | 1.74837 | ||||||||
\(457\) | 29.2712 | 1.36925 | 0.684624 | − | 0.728897i | \(-0.259967\pi\) | ||||
0.684624 | + | 0.728897i | \(0.259967\pi\) | |||||||
\(458\) | −31.3672 | −1.46569 | ||||||||
\(459\) | −1.93575 | −0.0903529 | ||||||||
\(460\) | 18.1366 | 0.845623 | ||||||||
\(461\) | −31.9394 | −1.48757 | −0.743784 | − | 0.668420i | \(-0.766971\pi\) | ||||
−0.743784 | + | 0.668420i | \(0.766971\pi\) | |||||||
\(462\) | 24.5026 | 1.13997 | ||||||||
\(463\) | 7.27286 | 0.337998 | 0.168999 | − | 0.985616i | \(-0.445946\pi\) | ||||
0.168999 | + | 0.985616i | \(0.445946\pi\) | |||||||
\(464\) | −0.596667 | −0.0276996 | ||||||||
\(465\) | 0.645420 | 0.0299306 | ||||||||
\(466\) | 28.5756 | 1.32374 | ||||||||
\(467\) | 19.9052 | 0.921101 | 0.460551 | − | 0.887633i | \(-0.347652\pi\) | ||||
0.460551 | + | 0.887633i | \(0.347652\pi\) | |||||||
\(468\) | 5.49677 | 0.254088 | ||||||||
\(469\) | −7.44120 | −0.343603 | ||||||||
\(470\) | 20.2185 | 0.932611 | ||||||||
\(471\) | −6.80666 | −0.313634 | ||||||||
\(472\) | 119.827 | 5.51550 | ||||||||
\(473\) | 10.7635 | 0.494905 | ||||||||
\(474\) | −9.58854 | −0.440416 | ||||||||
\(475\) | −0.281094 | −0.0128975 | ||||||||
\(476\) | −23.7321 | −1.08776 | ||||||||
\(477\) | −11.3322 | −0.518866 | ||||||||
\(478\) | 11.7032 | 0.535290 | ||||||||
\(479\) | −42.0670 | −1.92209 | −0.961046 | − | 0.276389i | \(-0.910862\pi\) | ||||
−0.961046 | + | 0.276389i | \(0.910862\pi\) | |||||||
\(480\) | −50.7331 | −2.31564 | ||||||||
\(481\) | 0.862130 | 0.0393098 | ||||||||
\(482\) | −42.5394 | −1.93761 | ||||||||
\(483\) | 3.26765 | 0.148683 | ||||||||
\(484\) | 28.0263 | 1.27392 | ||||||||
\(485\) | −39.0574 | −1.77350 | ||||||||
\(486\) | −2.73802 | −0.124199 | ||||||||
\(487\) | −31.9367 | −1.44719 | −0.723596 | − | 0.690224i | \(-0.757512\pi\) | ||||
−0.723596 | + | 0.690224i | \(0.757512\pi\) | |||||||
\(488\) | 14.1245 | 0.639385 | ||||||||
\(489\) | −25.0489 | −1.13275 | ||||||||
\(490\) | −12.4892 | −0.564204 | ||||||||
\(491\) | −12.9039 | −0.582347 | −0.291173 | − | 0.956670i | \(-0.594046\pi\) | ||||
−0.291173 | + | 0.956670i | \(0.594046\pi\) | |||||||
\(492\) | 34.9829 | 1.57715 | ||||||||
\(493\) | −0.0758822 | −0.00341756 | ||||||||
\(494\) | −10.6770 | −0.480380 | ||||||||
\(495\) | 9.03626 | 0.406150 | ||||||||
\(496\) | −4.36204 | −0.195861 | ||||||||
\(497\) | 10.1170 | 0.453809 | ||||||||
\(498\) | 17.4597 | 0.782389 | ||||||||
\(499\) | 34.8983 | 1.56226 | 0.781130 | − | 0.624368i | \(-0.214643\pi\) | ||||
0.781130 | + | 0.624368i | \(0.214643\pi\) | |||||||
\(500\) | −61.0048 | −2.72822 | ||||||||
\(501\) | 12.1377 | 0.542271 | ||||||||
\(502\) | −8.49707 | −0.379243 | ||||||||
\(503\) | −23.7413 | −1.05857 | −0.529287 | − | 0.848443i | \(-0.677540\pi\) | ||||
−0.529287 | + | 0.848443i | \(0.677540\pi\) | |||||||
\(504\) | −21.3542 | −0.951193 | ||||||||
\(505\) | −6.59297 | −0.293383 | ||||||||
\(506\) | 16.0949 | 0.715504 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 102.820 | 4.56189 | ||||||||
\(509\) | 20.9102 | 0.926828 | 0.463414 | − | 0.886142i | \(-0.346624\pi\) | ||||
0.463414 | + | 0.886142i | \(0.346624\pi\) | |||||||
\(510\) | −11.9365 | −0.528559 | ||||||||
\(511\) | −17.1690 | −0.759511 | ||||||||
\(512\) | 51.4204 | 2.27248 | ||||||||
\(513\) | 3.89952 | 0.172168 | ||||||||
\(514\) | −48.7116 | −2.14857 | ||||||||
\(515\) | −2.25213 | −0.0992407 | ||||||||
\(516\) | −14.7457 | −0.649141 | ||||||||
\(517\) | 13.1557 | 0.578588 | ||||||||
\(518\) | −5.26490 | −0.231327 | ||||||||
\(519\) | 10.3059 | 0.452380 | ||||||||
\(520\) | 21.5624 | 0.945573 | ||||||||
\(521\) | 11.4309 | 0.500799 | 0.250399 | − | 0.968143i | \(-0.419438\pi\) | ||||
0.250399 | + | 0.968143i | \(0.419438\pi\) | |||||||
\(522\) | −0.107332 | −0.00469779 | ||||||||
\(523\) | −26.2467 | −1.14769 | −0.573844 | − | 0.818965i | \(-0.694548\pi\) | ||||
−0.573844 | + | 0.818965i | \(0.694548\pi\) | |||||||
\(524\) | 92.4571 | 4.03901 | ||||||||
\(525\) | 0.160776 | 0.00701684 | ||||||||
\(526\) | −16.5389 | −0.721130 | ||||||||
\(527\) | −0.554750 | −0.0241653 | ||||||||
\(528\) | −61.0711 | −2.65778 | ||||||||
\(529\) | −20.8536 | −0.906678 | ||||||||
\(530\) | −69.8786 | −3.03533 | ||||||||
\(531\) | 12.5156 | 0.543132 | ||||||||
\(532\) | 47.8078 | 2.07273 | ||||||||
\(533\) | −6.36427 | −0.275667 | ||||||||
\(534\) | 25.2850 | 1.09419 | ||||||||
\(535\) | −15.5617 | −0.672792 | ||||||||
\(536\) | 31.9423 | 1.37970 | ||||||||
\(537\) | 24.9691 | 1.07750 | ||||||||
\(538\) | −46.3229 | −1.99712 | ||||||||
\(539\) | −8.12642 | −0.350030 | ||||||||
\(540\) | −12.3794 | −0.532726 | ||||||||
\(541\) | −6.81108 | −0.292831 | −0.146416 | − | 0.989223i | \(-0.546774\pi\) | ||||
−0.146416 | + | 0.989223i | \(0.546774\pi\) | |||||||
\(542\) | −44.9589 | −1.93115 | ||||||||
\(543\) | 19.6972 | 0.845289 | ||||||||
\(544\) | 43.6060 | 1.86959 | ||||||||
\(545\) | 2.91607 | 0.124911 | ||||||||
\(546\) | 6.10685 | 0.261349 | ||||||||
\(547\) | 14.1543 | 0.605193 | 0.302597 | − | 0.953119i | \(-0.402146\pi\) | ||||
0.302597 | + | 0.953119i | \(0.402146\pi\) | |||||||
\(548\) | −32.3496 | −1.38191 | ||||||||
\(549\) | 1.47526 | 0.0629626 | ||||||||
\(550\) | 0.791905 | 0.0337669 | ||||||||
\(551\) | 0.152863 | 0.00651219 | ||||||||
\(552\) | −14.0268 | −0.597020 | ||||||||
\(553\) | −7.81081 | −0.332149 | ||||||||
\(554\) | −19.5404 | −0.830191 | ||||||||
\(555\) | −1.94163 | −0.0824175 | ||||||||
\(556\) | −22.1376 | −0.938843 | ||||||||
\(557\) | −23.5680 | −0.998608 | −0.499304 | − | 0.866427i | \(-0.666411\pi\) | ||||
−0.499304 | + | 0.866427i | \(0.666411\pi\) | |||||||
\(558\) | −0.784668 | −0.0332176 | ||||||||
\(559\) | 2.68261 | 0.113462 | ||||||||
\(560\) | −76.4564 | −3.23087 | ||||||||
\(561\) | −7.76683 | −0.327916 | ||||||||
\(562\) | −22.1399 | −0.933914 | ||||||||
\(563\) | −2.79150 | −0.117648 | −0.0588239 | − | 0.998268i | \(-0.518735\pi\) | ||||
−0.0588239 | + | 0.998268i | \(0.518735\pi\) | |||||||
\(564\) | −18.0230 | −0.758904 | ||||||||
\(565\) | 31.1128 | 1.30893 | ||||||||
\(566\) | 5.11826 | 0.215137 | ||||||||
\(567\) | −2.23039 | −0.0936675 | ||||||||
\(568\) | −43.4284 | −1.82222 | ||||||||
\(569\) | −0.812193 | −0.0340489 | −0.0170245 | − | 0.999855i | \(-0.505419\pi\) | ||||
−0.0170245 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(570\) | 24.0459 | 1.00717 | ||||||||
\(571\) | −12.4909 | −0.522729 | −0.261365 | − | 0.965240i | \(-0.584172\pi\) | ||||
−0.261365 | + | 0.965240i | \(0.584172\pi\) | |||||||
\(572\) | 22.0548 | 0.922156 | ||||||||
\(573\) | 16.8097 | 0.702235 | ||||||||
\(574\) | 38.8657 | 1.62222 | ||||||||
\(575\) | 0.105608 | 0.00440415 | ||||||||
\(576\) | 31.2369 | 1.30154 | ||||||||
\(577\) | −12.8212 | −0.533756 | −0.266878 | − | 0.963730i | \(-0.585992\pi\) | ||||
−0.266878 | + | 0.963730i | \(0.585992\pi\) | |||||||
\(578\) | −36.2867 | −1.50933 | ||||||||
\(579\) | 13.7159 | 0.570013 | ||||||||
\(580\) | −0.485280 | −0.0201501 | ||||||||
\(581\) | 14.2227 | 0.590056 | ||||||||
\(582\) | 47.4839 | 1.96827 | ||||||||
\(583\) | −45.4684 | −1.88311 | ||||||||
\(584\) | 73.7000 | 3.04973 | ||||||||
\(585\) | 2.25213 | 0.0931141 | ||||||||
\(586\) | −7.15623 | −0.295621 | ||||||||
\(587\) | 27.6397 | 1.14081 | 0.570405 | − | 0.821363i | \(-0.306786\pi\) | ||||
0.570405 | + | 0.821363i | \(0.306786\pi\) | |||||||
\(588\) | 11.1330 | 0.459116 | ||||||||
\(589\) | 1.11753 | 0.0460471 | ||||||||
\(590\) | 77.1761 | 3.17729 | ||||||||
\(591\) | 3.72352 | 0.153165 | ||||||||
\(592\) | 13.1224 | 0.539327 | ||||||||
\(593\) | 29.5963 | 1.21538 | 0.607688 | − | 0.794176i | \(-0.292097\pi\) | ||||
0.607688 | + | 0.794176i | \(0.292097\pi\) | |||||||
\(594\) | −10.9858 | −0.450753 | ||||||||
\(595\) | −9.72349 | −0.398624 | ||||||||
\(596\) | 106.355 | 4.35645 | ||||||||
\(597\) | −21.3145 | −0.872344 | ||||||||
\(598\) | 4.01136 | 0.164037 | ||||||||
\(599\) | −30.6489 | −1.25228 | −0.626141 | − | 0.779710i | \(-0.715367\pi\) | ||||
−0.626141 | + | 0.779710i | \(0.715367\pi\) | |||||||
\(600\) | −0.690151 | −0.0281753 | ||||||||
\(601\) | 12.0523 | 0.491623 | 0.245811 | − | 0.969318i | \(-0.420946\pi\) | ||||
0.245811 | + | 0.969318i | \(0.420946\pi\) | |||||||
\(602\) | −16.3823 | −0.667692 | ||||||||
\(603\) | 3.33628 | 0.135864 | ||||||||
\(604\) | 41.3240 | 1.68145 | ||||||||
\(605\) | 11.4829 | 0.466847 | ||||||||
\(606\) | 8.01540 | 0.325603 | ||||||||
\(607\) | 33.6940 | 1.36760 | 0.683799 | − | 0.729671i | \(-0.260327\pi\) | ||||
0.683799 | + | 0.729671i | \(0.260327\pi\) | |||||||
\(608\) | −87.8434 | −3.56252 | ||||||||
\(609\) | −0.0874324 | −0.00354294 | ||||||||
\(610\) | 9.09702 | 0.368327 | ||||||||
\(611\) | 3.27883 | 0.132647 | ||||||||
\(612\) | 10.6403 | 0.430110 | ||||||||
\(613\) | −1.33551 | −0.0539407 | −0.0269704 | − | 0.999636i | \(-0.508586\pi\) | ||||
−0.0269704 | + | 0.999636i | \(0.508586\pi\) | |||||||
\(614\) | 37.8691 | 1.52827 | ||||||||
\(615\) | 14.3332 | 0.577969 | ||||||||
\(616\) | −85.6800 | −3.45214 | ||||||||
\(617\) | −32.8870 | −1.32398 | −0.661991 | − | 0.749512i | \(-0.730288\pi\) | ||||
−0.661991 | + | 0.749512i | \(0.730288\pi\) | |||||||
\(618\) | 2.73802 | 0.110139 | ||||||||
\(619\) | −20.5063 | −0.824217 | −0.412108 | − | 0.911135i | \(-0.635208\pi\) | ||||
−0.412108 | + | 0.911135i | \(0.635208\pi\) | |||||||
\(620\) | −3.54772 | −0.142480 | ||||||||
\(621\) | −1.46506 | −0.0587908 | ||||||||
\(622\) | 3.48810 | 0.139860 | ||||||||
\(623\) | 20.5971 | 0.825207 | ||||||||
\(624\) | −15.2209 | −0.609324 | ||||||||
\(625\) | −25.3552 | −1.01421 | ||||||||
\(626\) | 6.99173 | 0.279446 | ||||||||
\(627\) | 15.6461 | 0.624846 | ||||||||
\(628\) | 37.4146 | 1.49301 | ||||||||
\(629\) | 1.66886 | 0.0665420 | ||||||||
\(630\) | −13.7534 | −0.547949 | ||||||||
\(631\) | 39.4988 | 1.57242 | 0.786211 | − | 0.617958i | \(-0.212040\pi\) | ||||
0.786211 | + | 0.617958i | \(0.212040\pi\) | |||||||
\(632\) | 33.5289 | 1.33371 | ||||||||
\(633\) | 0.347438 | 0.0138094 | ||||||||
\(634\) | 47.0865 | 1.87004 | ||||||||
\(635\) | 42.1272 | 1.67177 | ||||||||
\(636\) | 62.2904 | 2.46998 | ||||||||
\(637\) | −2.02537 | −0.0802480 | ||||||||
\(638\) | −0.430650 | −0.0170496 | ||||||||
\(639\) | −4.53598 | −0.179440 | ||||||||
\(640\) | 91.1522 | 3.60311 | ||||||||
\(641\) | −42.0904 | −1.66247 | −0.831236 | − | 0.555919i | \(-0.812366\pi\) | ||||
−0.831236 | + | 0.555919i | \(0.812366\pi\) | |||||||
\(642\) | 18.9191 | 0.746679 | ||||||||
\(643\) | 36.5921 | 1.44305 | 0.721525 | − | 0.692388i | \(-0.243441\pi\) | ||||
0.721525 | + | 0.692388i | \(0.243441\pi\) | |||||||
\(644\) | −17.9615 | −0.707783 | ||||||||
\(645\) | −6.04158 | −0.237887 | ||||||||
\(646\) | −20.6679 | −0.813168 | ||||||||
\(647\) | 0.150619 | 0.00592144 | 0.00296072 | − | 0.999996i | \(-0.499058\pi\) | ||||
0.00296072 | + | 0.999996i | \(0.499058\pi\) | |||||||
\(648\) | 9.57422 | 0.376111 | ||||||||
\(649\) | 50.2167 | 1.97118 | ||||||||
\(650\) | 0.197368 | 0.00774142 | ||||||||
\(651\) | −0.639189 | −0.0250518 | ||||||||
\(652\) | 137.688 | 5.39227 | ||||||||
\(653\) | 7.77619 | 0.304306 | 0.152153 | − | 0.988357i | \(-0.451379\pi\) | ||||
0.152153 | + | 0.988357i | \(0.451379\pi\) | |||||||
\(654\) | −3.54521 | −0.138629 | ||||||||
\(655\) | 37.8814 | 1.48015 | ||||||||
\(656\) | −96.8700 | −3.78214 | ||||||||
\(657\) | 7.69775 | 0.300318 | ||||||||
\(658\) | −20.0233 | −0.780591 | ||||||||
\(659\) | −10.7563 | −0.419004 | −0.209502 | − | 0.977808i | \(-0.567184\pi\) | ||||
−0.209502 | + | 0.977808i | \(0.567184\pi\) | |||||||
\(660\) | −49.6702 | −1.93341 | ||||||||
\(661\) | 32.8404 | 1.27734 | 0.638671 | − | 0.769480i | \(-0.279485\pi\) | ||||
0.638671 | + | 0.769480i | \(0.279485\pi\) | |||||||
\(662\) | 18.1596 | 0.705793 | ||||||||
\(663\) | −1.93575 | −0.0751781 | ||||||||
\(664\) | −61.0526 | −2.36930 | ||||||||
\(665\) | 19.5878 | 0.759581 | ||||||||
\(666\) | 2.36053 | 0.0914687 | ||||||||
\(667\) | −0.0574311 | −0.00222374 | ||||||||
\(668\) | −66.7179 | −2.58139 | ||||||||
\(669\) | 8.88346 | 0.343454 | ||||||||
\(670\) | 20.5728 | 0.794795 | ||||||||
\(671\) | 5.91921 | 0.228509 | ||||||||
\(672\) | 50.2433 | 1.93818 | ||||||||
\(673\) | 14.0879 | 0.543047 | 0.271523 | − | 0.962432i | \(-0.412473\pi\) | ||||
0.271523 | + | 0.962432i | \(0.412473\pi\) | |||||||
\(674\) | 22.4302 | 0.863979 | ||||||||
\(675\) | −0.0720843 | −0.00277453 | ||||||||
\(676\) | 5.49677 | 0.211414 | ||||||||
\(677\) | 31.2527 | 1.20114 | 0.600569 | − | 0.799573i | \(-0.294941\pi\) | ||||
0.600569 | + | 0.799573i | \(0.294941\pi\) | |||||||
\(678\) | −37.8253 | −1.45267 | ||||||||
\(679\) | 38.6803 | 1.48441 | ||||||||
\(680\) | 41.7393 | 1.60063 | ||||||||
\(681\) | 15.3482 | 0.588145 | ||||||||
\(682\) | −3.14834 | −0.120556 | ||||||||
\(683\) | −45.8345 | −1.75381 | −0.876904 | − | 0.480665i | \(-0.840395\pi\) | ||||
−0.876904 | + | 0.480665i | \(0.840395\pi\) | |||||||
\(684\) | −21.4347 | −0.819578 | ||||||||
\(685\) | −13.2543 | −0.506419 | ||||||||
\(686\) | 55.1166 | 2.10436 | ||||||||
\(687\) | 11.4562 | 0.437080 | ||||||||
\(688\) | 40.8317 | 1.55669 | ||||||||
\(689\) | −11.3322 | −0.431722 | ||||||||
\(690\) | −9.03411 | −0.343923 | ||||||||
\(691\) | −43.0759 | −1.63869 | −0.819343 | − | 0.573304i | \(-0.805661\pi\) | ||||
−0.819343 | + | 0.573304i | \(0.805661\pi\) | |||||||
\(692\) | −56.6493 | −2.15348 | ||||||||
\(693\) | −8.94903 | −0.339945 | ||||||||
\(694\) | 40.8107 | 1.54915 | ||||||||
\(695\) | −9.07019 | −0.344052 | ||||||||
\(696\) | 0.375314 | 0.0142263 | ||||||||
\(697\) | −12.3196 | −0.466639 | ||||||||
\(698\) | −0.564691 | −0.0213739 | ||||||||
\(699\) | −10.4366 | −0.394748 | ||||||||
\(700\) | −0.883748 | −0.0334025 | ||||||||
\(701\) | 30.4099 | 1.14857 | 0.574283 | − | 0.818657i | \(-0.305281\pi\) | ||||
0.574283 | + | 0.818657i | \(0.305281\pi\) | |||||||
\(702\) | −2.73802 | −0.103340 | ||||||||
\(703\) | −3.36189 | −0.126796 | ||||||||
\(704\) | 125.332 | 4.72364 | ||||||||
\(705\) | −7.38435 | −0.278111 | ||||||||
\(706\) | 43.2848 | 1.62904 | ||||||||
\(707\) | 6.52933 | 0.245561 | ||||||||
\(708\) | −68.7955 | −2.58549 | ||||||||
\(709\) | 8.91063 | 0.334646 | 0.167323 | − | 0.985902i | \(-0.446488\pi\) | ||||
0.167323 | + | 0.985902i | \(0.446488\pi\) | |||||||
\(710\) | −27.9705 | −1.04972 | ||||||||
\(711\) | 3.50200 | 0.131335 | ||||||||
\(712\) | −88.4158 | −3.31352 | ||||||||
\(713\) | −0.419860 | −0.0157239 | ||||||||
\(714\) | 11.8213 | 0.442401 | ||||||||
\(715\) | 9.03626 | 0.337937 | ||||||||
\(716\) | −137.249 | −5.12925 | ||||||||
\(717\) | −4.27431 | −0.159627 | ||||||||
\(718\) | 62.7928 | 2.34341 | ||||||||
\(719\) | 4.70263 | 0.175379 | 0.0876893 | − | 0.996148i | \(-0.472052\pi\) | ||||
0.0876893 | + | 0.996148i | \(0.472052\pi\) | |||||||
\(720\) | 34.2794 | 1.27752 | ||||||||
\(721\) | 2.23039 | 0.0830640 | ||||||||
\(722\) | −10.3874 | −0.386577 | ||||||||
\(723\) | 15.5365 | 0.577810 | ||||||||
\(724\) | −108.271 | −4.02386 | ||||||||
\(725\) | −0.00282574 | −0.000104945 0 | ||||||||
\(726\) | −13.9603 | −0.518117 | ||||||||
\(727\) | −41.4810 | −1.53844 | −0.769222 | − | 0.638981i | \(-0.779356\pi\) | ||||
−0.769222 | + | 0.638981i | \(0.779356\pi\) | |||||||
\(728\) | −21.3542 | −0.791441 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 47.4673 | 1.75684 | ||||||||
\(731\) | 5.19284 | 0.192064 | ||||||||
\(732\) | −8.10916 | −0.299723 | ||||||||
\(733\) | −24.8936 | −0.919465 | −0.459733 | − | 0.888057i | \(-0.652055\pi\) | ||||
−0.459733 | + | 0.888057i | \(0.652055\pi\) | |||||||
\(734\) | −59.9491 | −2.21276 | ||||||||
\(735\) | 4.56139 | 0.168249 | ||||||||
\(736\) | 33.0030 | 1.21651 | ||||||||
\(737\) | 13.3862 | 0.493088 | ||||||||
\(738\) | −17.4255 | −0.641442 | ||||||||
\(739\) | −11.6467 | −0.428431 | −0.214216 | − | 0.976786i | \(-0.568720\pi\) | ||||
−0.214216 | + | 0.976786i | \(0.568720\pi\) | |||||||
\(740\) | 10.6727 | 0.392335 | ||||||||
\(741\) | 3.89952 | 0.143252 | ||||||||
\(742\) | 69.2040 | 2.54056 | ||||||||
\(743\) | −30.6055 | −1.12281 | −0.561403 | − | 0.827543i | \(-0.689738\pi\) | ||||
−0.561403 | + | 0.827543i | \(0.689738\pi\) | |||||||
\(744\) | 2.74380 | 0.100593 | ||||||||
\(745\) | 43.5755 | 1.59648 | ||||||||
\(746\) | −77.5214 | −2.83826 | ||||||||
\(747\) | −6.37677 | −0.233314 | ||||||||
\(748\) | 42.6924 | 1.56099 | ||||||||
\(749\) | 15.4115 | 0.563124 | ||||||||
\(750\) | 30.3874 | 1.10959 | ||||||||
\(751\) | −29.1830 | −1.06490 | −0.532451 | − | 0.846461i | \(-0.678729\pi\) | ||||
−0.532451 | + | 0.846461i | \(0.678729\pi\) | |||||||
\(752\) | 49.9068 | 1.81991 | ||||||||
\(753\) | 3.10336 | 0.113093 | ||||||||
\(754\) | −0.107332 | −0.00390880 | ||||||||
\(755\) | 16.9312 | 0.616190 | ||||||||
\(756\) | 12.2599 | 0.445889 | ||||||||
\(757\) | 15.0268 | 0.546158 | 0.273079 | − | 0.961992i | \(-0.411958\pi\) | ||||
0.273079 | + | 0.961992i | \(0.411958\pi\) | |||||||
\(758\) | −12.7635 | −0.463590 | ||||||||
\(759\) | −5.87828 | −0.213368 | ||||||||
\(760\) | −84.0829 | −3.05001 | ||||||||
\(761\) | 12.0306 | 0.436111 | 0.218055 | − | 0.975936i | \(-0.430029\pi\) | ||||
0.218055 | + | 0.975936i | \(0.430029\pi\) | |||||||
\(762\) | −51.2161 | −1.85536 | ||||||||
\(763\) | −2.88792 | −0.104550 | ||||||||
\(764\) | −92.3989 | −3.34287 | ||||||||
\(765\) | 4.35955 | 0.157620 | ||||||||
\(766\) | −69.5873 | −2.51429 | ||||||||
\(767\) | 12.5156 | 0.451913 | ||||||||
\(768\) | −48.3444 | −1.74448 | ||||||||
\(769\) | −3.09469 | −0.111598 | −0.0557988 | − | 0.998442i | \(-0.517771\pi\) | ||||
−0.0557988 | + | 0.998442i | \(0.517771\pi\) | |||||||
\(770\) | −55.1831 | −1.98866 | ||||||||
\(771\) | 17.7908 | 0.640719 | ||||||||
\(772\) | −75.3931 | −2.71346 | ||||||||
\(773\) | −34.2136 | −1.23058 | −0.615289 | − | 0.788301i | \(-0.710961\pi\) | ||||
−0.615289 | + | 0.788301i | \(0.710961\pi\) | |||||||
\(774\) | 7.34504 | 0.264012 | ||||||||
\(775\) | −0.0206581 | −0.000742059 0 | ||||||||
\(776\) | −166.040 | −5.96049 | ||||||||
\(777\) | 1.92289 | 0.0689831 | ||||||||
\(778\) | 62.6491 | 2.24608 | ||||||||
\(779\) | 24.8176 | 0.889183 | ||||||||
\(780\) | −12.3794 | −0.443254 | ||||||||
\(781\) | −18.1998 | −0.651239 | ||||||||
\(782\) | 7.76498 | 0.277675 | ||||||||
\(783\) | 0.0392005 | 0.00140091 | ||||||||
\(784\) | −30.8279 | −1.10100 | ||||||||
\(785\) | 15.3295 | 0.547132 | ||||||||
\(786\) | −46.0543 | −1.64270 | ||||||||
\(787\) | 37.0412 | 1.32038 | 0.660188 | − | 0.751101i | \(-0.270477\pi\) | ||||
0.660188 | + | 0.751101i | \(0.270477\pi\) | |||||||
\(788\) | −20.4673 | −0.729118 | ||||||||
\(789\) | 6.04045 | 0.215046 | ||||||||
\(790\) | 21.5946 | 0.768302 | ||||||||
\(791\) | −30.8125 | −1.09556 | ||||||||
\(792\) | 38.4148 | 1.36501 | ||||||||
\(793\) | 1.47526 | 0.0523880 | ||||||||
\(794\) | 24.0111 | 0.852120 | ||||||||
\(795\) | 25.5216 | 0.905157 | ||||||||
\(796\) | 117.161 | 4.15265 | ||||||||
\(797\) | 35.2454 | 1.24846 | 0.624228 | − | 0.781242i | \(-0.285414\pi\) | ||||
0.624228 | + | 0.781242i | \(0.285414\pi\) | |||||||
\(798\) | −23.8138 | −0.842999 | ||||||||
\(799\) | 6.34698 | 0.224540 | ||||||||
\(800\) | 1.62382 | 0.0574108 | ||||||||
\(801\) | −9.23478 | −0.326295 | ||||||||
\(802\) | −28.2235 | −0.996608 | ||||||||
\(803\) | 30.8858 | 1.08994 | ||||||||
\(804\) | −18.3387 | −0.646758 | ||||||||
\(805\) | −7.35917 | −0.259377 | ||||||||
\(806\) | −0.784668 | −0.0276387 | ||||||||
\(807\) | 16.9184 | 0.595556 | ||||||||
\(808\) | −28.0280 | −0.986020 | ||||||||
\(809\) | 27.9356 | 0.982163 | 0.491082 | − | 0.871114i | \(-0.336602\pi\) | ||||
0.491082 | + | 0.871114i | \(0.336602\pi\) | |||||||
\(810\) | 6.16638 | 0.216664 | ||||||||
\(811\) | −15.2507 | −0.535524 | −0.267762 | − | 0.963485i | \(-0.586284\pi\) | ||||
−0.267762 | + | 0.963485i | \(0.586284\pi\) | |||||||
\(812\) | 0.480595 | 0.0168656 | ||||||||
\(813\) | 16.4202 | 0.575882 | ||||||||
\(814\) | 9.47120 | 0.331966 | ||||||||
\(815\) | 56.4132 | 1.97607 | ||||||||
\(816\) | −29.4638 | −1.03144 | ||||||||
\(817\) | −10.4609 | −0.365980 | ||||||||
\(818\) | −84.8592 | −2.96703 | ||||||||
\(819\) | −2.23039 | −0.0779361 | ||||||||
\(820\) | −78.7860 | −2.75133 | ||||||||
\(821\) | 5.78489 | 0.201894 | 0.100947 | − | 0.994892i | \(-0.467813\pi\) | ||||
0.100947 | + | 0.994892i | \(0.467813\pi\) | |||||||
\(822\) | 16.1138 | 0.562035 | ||||||||
\(823\) | 49.3605 | 1.72060 | 0.860299 | − | 0.509790i | \(-0.170277\pi\) | ||||
0.860299 | + | 0.509790i | \(0.170277\pi\) | |||||||
\(824\) | −9.57422 | −0.333534 | ||||||||
\(825\) | −0.289225 | −0.0100695 | ||||||||
\(826\) | −76.4311 | −2.65938 | ||||||||
\(827\) | −29.1946 | −1.01519 | −0.507597 | − | 0.861594i | \(-0.669466\pi\) | ||||
−0.507597 | + | 0.861594i | \(0.669466\pi\) | |||||||
\(828\) | 8.05309 | 0.279864 | ||||||||
\(829\) | 7.10218 | 0.246669 | 0.123335 | − | 0.992365i | \(-0.460641\pi\) | ||||
0.123335 | + | 0.992365i | \(0.460641\pi\) | |||||||
\(830\) | −39.3216 | −1.36487 | ||||||||
\(831\) | 7.13667 | 0.247568 | ||||||||
\(832\) | 31.2369 | 1.08294 | ||||||||
\(833\) | −3.92060 | −0.135841 | ||||||||
\(834\) | 11.0271 | 0.381836 | ||||||||
\(835\) | −27.3356 | −0.945987 | ||||||||
\(836\) | −86.0030 | −2.97448 | ||||||||
\(837\) | 0.286582 | 0.00990572 | ||||||||
\(838\) | 71.2736 | 2.46211 | ||||||||
\(839\) | −13.2473 | −0.457346 | −0.228673 | − | 0.973503i | \(-0.573439\pi\) | ||||
−0.228673 | + | 0.973503i | \(0.573439\pi\) | |||||||
\(840\) | 48.0925 | 1.65935 | ||||||||
\(841\) | −28.9985 | −0.999947 | ||||||||
\(842\) | 16.0451 | 0.552950 | ||||||||
\(843\) | 8.08608 | 0.278499 | ||||||||
\(844\) | −1.90978 | −0.0657375 | ||||||||
\(845\) | 2.25213 | 0.0774756 | ||||||||
\(846\) | 8.97752 | 0.308653 | ||||||||
\(847\) | −11.3721 | −0.390749 | ||||||||
\(848\) | −172.486 | −5.92320 | ||||||||
\(849\) | −1.86933 | −0.0641552 | ||||||||
\(850\) | 0.382055 | 0.0131044 | ||||||||
\(851\) | 1.26307 | 0.0432975 | ||||||||
\(852\) | 24.9332 | 0.854197 | ||||||||
\(853\) | 33.7902 | 1.15695 | 0.578477 | − | 0.815698i | \(-0.303647\pi\) | ||||
0.578477 | + | 0.815698i | \(0.303647\pi\) | |||||||
\(854\) | −9.00920 | −0.308288 | ||||||||
\(855\) | −8.78222 | −0.300346 | ||||||||
\(856\) | −66.1558 | −2.26116 | ||||||||
\(857\) | 0.434238 | 0.0148333 | 0.00741664 | − | 0.999972i | \(-0.497639\pi\) | ||||
0.00741664 | + | 0.999972i | \(0.497639\pi\) | |||||||
\(858\) | −10.9858 | −0.375050 | ||||||||
\(859\) | −28.5717 | −0.974855 | −0.487427 | − | 0.873164i | \(-0.662065\pi\) | ||||
−0.487427 | + | 0.873164i | \(0.662065\pi\) | |||||||
\(860\) | 33.2091 | 1.13242 | ||||||||
\(861\) | −14.1948 | −0.483757 | ||||||||
\(862\) | 61.0770 | 2.08029 | ||||||||
\(863\) | 48.2336 | 1.64189 | 0.820946 | − | 0.571007i | \(-0.193447\pi\) | ||||
0.820946 | + | 0.571007i | \(0.193447\pi\) | |||||||
\(864\) | −22.5267 | −0.766375 | ||||||||
\(865\) | −23.2103 | −0.789173 | ||||||||
\(866\) | 34.3875 | 1.16853 | ||||||||
\(867\) | 13.2529 | 0.450092 | ||||||||
\(868\) | 3.51347 | 0.119255 | ||||||||
\(869\) | 14.0511 | 0.476652 | ||||||||
\(870\) | 0.241725 | 0.00819525 | ||||||||
\(871\) | 3.33628 | 0.113046 | ||||||||
\(872\) | 12.3968 | 0.419807 | ||||||||
\(873\) | −17.3424 | −0.586952 | ||||||||
\(874\) | −15.6424 | −0.529112 | ||||||||
\(875\) | 24.7535 | 0.836822 | ||||||||
\(876\) | −42.3127 | −1.42962 | ||||||||
\(877\) | −3.21501 | −0.108563 | −0.0542817 | − | 0.998526i | \(-0.517287\pi\) | ||||
−0.0542817 | + | 0.998526i | \(0.517287\pi\) | |||||||
\(878\) | 55.8892 | 1.88617 | ||||||||
\(879\) | 2.61365 | 0.0881562 | ||||||||
\(880\) | 137.540 | 4.63647 | ||||||||
\(881\) | 36.9025 | 1.24328 | 0.621639 | − | 0.783304i | \(-0.286467\pi\) | ||||
0.621639 | + | 0.783304i | \(0.286467\pi\) | |||||||
\(882\) | −5.54550 | −0.186727 | ||||||||
\(883\) | 22.2626 | 0.749196 | 0.374598 | − | 0.927187i | \(-0.377781\pi\) | ||||
0.374598 | + | 0.927187i | \(0.377781\pi\) | |||||||
\(884\) | 10.6403 | 0.357873 | ||||||||
\(885\) | −28.1868 | −0.947489 | ||||||||
\(886\) | −18.7541 | −0.630056 | ||||||||
\(887\) | −18.7149 | −0.628383 | −0.314192 | − | 0.949360i | \(-0.601733\pi\) | ||||
−0.314192 | + | 0.949360i | \(0.601733\pi\) | |||||||
\(888\) | −8.25423 | −0.276994 | ||||||||
\(889\) | −41.7205 | −1.39926 | ||||||||
\(890\) | −56.9451 | −1.90881 | ||||||||
\(891\) | 4.01232 | 0.134418 | ||||||||
\(892\) | −48.8303 | −1.63496 | ||||||||
\(893\) | −12.7859 | −0.427863 | ||||||||
\(894\) | −52.9768 | −1.77181 | ||||||||
\(895\) | −56.2337 | −1.87968 | ||||||||
\(896\) | −90.2722 | −3.01578 | ||||||||
\(897\) | −1.46506 | −0.0489169 | ||||||||
\(898\) | 52.0627 | 1.73735 | ||||||||
\(899\) | 0.0112342 | 0.000374680 0 | ||||||||
\(900\) | 0.396230 | 0.0132077 | ||||||||
\(901\) | −21.9362 | −0.730802 | ||||||||
\(902\) | −69.9167 | −2.32797 | ||||||||
\(903\) | 5.98325 | 0.199110 | ||||||||
\(904\) | 132.266 | 4.39911 | ||||||||
\(905\) | −44.3607 | −1.47460 | ||||||||
\(906\) | −20.5841 | −0.683861 | ||||||||
\(907\) | 27.6472 | 0.918009 | 0.459005 | − | 0.888434i | \(-0.348206\pi\) | ||||
0.459005 | + | 0.888434i | \(0.348206\pi\) | |||||||
\(908\) | −84.3656 | −2.79977 | ||||||||
\(909\) | −2.92744 | −0.0970971 | ||||||||
\(910\) | −13.7534 | −0.455921 | ||||||||
\(911\) | −56.2268 | −1.86288 | −0.931438 | − | 0.363899i | \(-0.881445\pi\) | ||||
−0.931438 | + | 0.363899i | \(0.881445\pi\) | |||||||
\(912\) | 59.3542 | 1.96541 | ||||||||
\(913\) | −25.5856 | −0.846760 | ||||||||
\(914\) | 80.1451 | 2.65096 | ||||||||
\(915\) | −3.32248 | −0.109838 | ||||||||
\(916\) | −62.9718 | −2.08065 | ||||||||
\(917\) | −37.5157 | −1.23888 | ||||||||
\(918\) | −5.30011 | −0.174930 | ||||||||
\(919\) | 49.4192 | 1.63019 | 0.815095 | − | 0.579327i | \(-0.196685\pi\) | ||||
0.815095 | + | 0.579327i | \(0.196685\pi\) | |||||||
\(920\) | 31.5902 | 1.04150 | ||||||||
\(921\) | −13.8308 | −0.455741 | ||||||||
\(922\) | −87.4509 | −2.88004 | ||||||||
\(923\) | −4.53598 | −0.149303 | ||||||||
\(924\) | 49.1907 | 1.61826 | ||||||||
\(925\) | 0.0621460 | 0.00204335 | ||||||||
\(926\) | 19.9132 | 0.654390 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −0.883059 | −0.0289878 | ||||||||
\(929\) | −6.98607 | −0.229206 | −0.114603 | − | 0.993411i | \(-0.536560\pi\) | ||||
−0.114603 | + | 0.993411i | \(0.536560\pi\) | |||||||
\(930\) | 1.76717 | 0.0579479 | ||||||||
\(931\) | 7.89796 | 0.258845 | ||||||||
\(932\) | 57.3675 | 1.87914 | ||||||||
\(933\) | −1.27395 | −0.0417072 | ||||||||
\(934\) | 54.5008 | 1.78332 | ||||||||
\(935\) | 17.4919 | 0.572046 | ||||||||
\(936\) | 9.57422 | 0.312943 | ||||||||
\(937\) | −53.0486 | −1.73302 | −0.866511 | − | 0.499158i | \(-0.833643\pi\) | ||||
−0.866511 | + | 0.499158i | \(0.833643\pi\) | |||||||
\(938\) | −20.3742 | −0.665240 | ||||||||
\(939\) | −2.55357 | −0.0833326 | ||||||||
\(940\) | 40.5901 | 1.32390 | ||||||||
\(941\) | 60.1422 | 1.96058 | 0.980290 | − | 0.197563i | \(-0.0633028\pi\) | ||||
0.980290 | + | 0.197563i | \(0.0633028\pi\) | |||||||
\(942\) | −18.6368 | −0.607219 | ||||||||
\(943\) | −9.32404 | −0.303632 | ||||||||
\(944\) | 190.499 | 6.20022 | ||||||||
\(945\) | 5.02312 | 0.163402 | ||||||||
\(946\) | 29.4706 | 0.958173 | ||||||||
\(947\) | 43.9056 | 1.42674 | 0.713370 | − | 0.700787i | \(-0.247168\pi\) | ||||
0.713370 | + | 0.700787i | \(0.247168\pi\) | |||||||
\(948\) | −19.2496 | −0.625199 | ||||||||
\(949\) | 7.69775 | 0.249880 | ||||||||
\(950\) | −0.769642 | −0.0249705 | ||||||||
\(951\) | −17.1973 | −0.557659 | ||||||||
\(952\) | −41.3364 | −1.33972 | ||||||||
\(953\) | −19.5581 | −0.633548 | −0.316774 | − | 0.948501i | \(-0.602600\pi\) | ||||
−0.316774 | + | 0.948501i | \(0.602600\pi\) | |||||||
\(954\) | −31.0278 | −1.00456 | ||||||||
\(955\) | −37.8576 | −1.22504 | ||||||||
\(956\) | 23.4949 | 0.759879 | ||||||||
\(957\) | 0.157285 | 0.00508430 | ||||||||
\(958\) | −115.180 | −3.72131 | ||||||||
\(959\) | 13.1263 | 0.423871 | ||||||||
\(960\) | −70.3494 | −2.27052 | ||||||||
\(961\) | −30.9179 | −0.997351 | ||||||||
\(962\) | 2.36053 | 0.0761066 | ||||||||
\(963\) | −6.90978 | −0.222665 | ||||||||
\(964\) | −85.4006 | −2.75057 | ||||||||
\(965\) | −30.8900 | −0.994383 | ||||||||
\(966\) | 8.94690 | 0.287862 | ||||||||
\(967\) | −8.97958 | −0.288764 | −0.144382 | − | 0.989522i | \(-0.546119\pi\) | ||||
−0.144382 | + | 0.989522i | \(0.546119\pi\) | |||||||
\(968\) | 48.8160 | 1.56901 | ||||||||
\(969\) | 7.54848 | 0.242492 | ||||||||
\(970\) | −106.940 | −3.43363 | ||||||||
\(971\) | −42.9997 | −1.37992 | −0.689962 | − | 0.723845i | \(-0.742373\pi\) | ||||
−0.689962 | + | 0.723845i | \(0.742373\pi\) | |||||||
\(972\) | −5.49677 | −0.176309 | ||||||||
\(973\) | 8.98264 | 0.287970 | ||||||||
\(974\) | −87.4435 | −2.80187 | ||||||||
\(975\) | −0.0720843 | −0.00230854 | ||||||||
\(976\) | 22.4548 | 0.718760 | ||||||||
\(977\) | 45.3026 | 1.44936 | 0.724680 | − | 0.689086i | \(-0.241988\pi\) | ||||
0.724680 | + | 0.689086i | \(0.241988\pi\) | |||||||
\(978\) | −68.5843 | −2.19308 | ||||||||
\(979\) | −37.0529 | −1.18421 | ||||||||
\(980\) | −25.0729 | −0.800924 | ||||||||
\(981\) | 1.29481 | 0.0413400 | ||||||||
\(982\) | −35.3313 | −1.12747 | ||||||||
\(983\) | 36.6821 | 1.16998 | 0.584988 | − | 0.811042i | \(-0.301099\pi\) | ||||
0.584988 | + | 0.811042i | \(0.301099\pi\) | |||||||
\(984\) | 60.9330 | 1.94247 | ||||||||
\(985\) | −8.38585 | −0.267195 | ||||||||
\(986\) | −0.207767 | −0.00661666 | ||||||||
\(987\) | 7.31307 | 0.232778 | ||||||||
\(988\) | −21.4347 | −0.681930 | ||||||||
\(989\) | 3.93018 | 0.124972 | ||||||||
\(990\) | 24.7415 | 0.786336 | ||||||||
\(991\) | −8.80711 | −0.279767 | −0.139884 | − | 0.990168i | \(-0.544673\pi\) | ||||
−0.139884 | + | 0.990168i | \(0.544673\pi\) | |||||||
\(992\) | −6.45575 | −0.204970 | ||||||||
\(993\) | −6.63238 | −0.210472 | ||||||||
\(994\) | 27.7005 | 0.878608 | ||||||||
\(995\) | 48.0030 | 1.52180 | ||||||||
\(996\) | 35.0516 | 1.11065 | ||||||||
\(997\) | −16.2359 | −0.514195 | −0.257098 | − | 0.966385i | \(-0.582766\pi\) | ||||
−0.257098 | + | 0.966385i | \(0.582766\pi\) | |||||||
\(998\) | 95.5522 | 3.02465 | ||||||||
\(999\) | −0.862130 | −0.0272766 |
(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 | 4017.2.a.j.1.25 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.25 | ✓ | 25 | 1.1 | even | 1 | trivial |