Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6043,2,Mod(1,6043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6043, 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("6043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6043 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6043.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: | \(48.2535979415\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66716 | −1.88597 | −0.942984 | − | 0.332837i | \(-0.891994\pi\) | ||||
−0.942984 | + | 0.332837i | \(0.891994\pi\) | |||||||
\(3\) | 0.658905 | 0.380419 | 0.190210 | − | 0.981743i | \(-0.439083\pi\) | ||||
0.190210 | + | 0.981743i | \(0.439083\pi\) | |||||||
\(4\) | 5.11375 | 2.55688 | ||||||||
\(5\) | −0.783297 | −0.350301 | −0.175151 | − | 0.984542i | \(-0.556041\pi\) | ||||
−0.175151 | + | 0.984542i | \(0.556041\pi\) | |||||||
\(6\) | −1.75741 | −0.717459 | ||||||||
\(7\) | −0.338104 | −0.127791 | −0.0638957 | − | 0.997957i | \(-0.520352\pi\) | ||||
−0.0638957 | + | 0.997957i | \(0.520352\pi\) | |||||||
\(8\) | −8.30489 | −2.93622 | ||||||||
\(9\) | −2.56584 | −0.855281 | ||||||||
\(10\) | 2.08918 | 0.660657 | ||||||||
\(11\) | 4.66349 | 1.40610 | 0.703048 | − | 0.711143i | \(-0.251822\pi\) | ||||
0.703048 | + | 0.711143i | \(0.251822\pi\) | |||||||
\(12\) | 3.36948 | 0.972685 | ||||||||
\(13\) | 0.840231 | 0.233038 | 0.116519 | − | 0.993188i | \(-0.462826\pi\) | ||||
0.116519 | + | 0.993188i | \(0.462826\pi\) | |||||||
\(14\) | 0.901779 | 0.241011 | ||||||||
\(15\) | −0.516119 | −0.133261 | ||||||||
\(16\) | 11.9230 | 2.98074 | ||||||||
\(17\) | −1.70019 | −0.412358 | −0.206179 | − | 0.978514i | \(-0.566103\pi\) | ||||
−0.206179 | + | 0.978514i | \(0.566103\pi\) | |||||||
\(18\) | 6.84352 | 1.61303 | ||||||||
\(19\) | −5.80164 | −1.33099 | −0.665494 | − | 0.746404i | \(-0.731779\pi\) | ||||
−0.665494 | + | 0.746404i | \(0.731779\pi\) | |||||||
\(20\) | −4.00559 | −0.895677 | ||||||||
\(21\) | −0.222779 | −0.0486143 | ||||||||
\(22\) | −12.4383 | −2.65185 | ||||||||
\(23\) | −1.82105 | −0.379714 | −0.189857 | − | 0.981812i | \(-0.560802\pi\) | ||||
−0.189857 | + | 0.981812i | \(0.560802\pi\) | |||||||
\(24\) | −5.47214 | −1.11700 | ||||||||
\(25\) | −4.38645 | −0.877289 | ||||||||
\(26\) | −2.24103 | −0.439502 | ||||||||
\(27\) | −3.66736 | −0.705785 | ||||||||
\(28\) | −1.72898 | −0.326747 | ||||||||
\(29\) | −7.54922 | −1.40186 | −0.700928 | − | 0.713232i | \(-0.747230\pi\) | ||||
−0.700928 | + | 0.713232i | \(0.747230\pi\) | |||||||
\(30\) | 1.37657 | 0.251327 | ||||||||
\(31\) | −3.98375 | −0.715503 | −0.357751 | − | 0.933817i | \(-0.616456\pi\) | ||||
−0.357751 | + | 0.933817i | \(0.616456\pi\) | |||||||
\(32\) | −15.1907 | −2.68537 | ||||||||
\(33\) | 3.07280 | 0.534906 | ||||||||
\(34\) | 4.53469 | 0.777694 | ||||||||
\(35\) | 0.264836 | 0.0447655 | ||||||||
\(36\) | −13.1211 | −2.18685 | ||||||||
\(37\) | −5.81485 | −0.955956 | −0.477978 | − | 0.878372i | \(-0.658630\pi\) | ||||
−0.477978 | + | 0.878372i | \(0.658630\pi\) | |||||||
\(38\) | 15.4739 | 2.51020 | ||||||||
\(39\) | 0.553633 | 0.0886522 | ||||||||
\(40\) | 6.50520 | 1.02856 | ||||||||
\(41\) | 1.65231 | 0.258048 | 0.129024 | − | 0.991641i | \(-0.458816\pi\) | ||||
0.129024 | + | 0.991641i | \(0.458816\pi\) | |||||||
\(42\) | 0.594187 | 0.0916850 | ||||||||
\(43\) | 8.44116 | 1.28726 | 0.643632 | − | 0.765335i | \(-0.277427\pi\) | ||||
0.643632 | + | 0.765335i | \(0.277427\pi\) | |||||||
\(44\) | 23.8479 | 3.59521 | ||||||||
\(45\) | 2.00982 | 0.299606 | ||||||||
\(46\) | 4.85702 | 0.716129 | ||||||||
\(47\) | 6.97850 | 1.01792 | 0.508959 | − | 0.860791i | \(-0.330030\pi\) | ||||
0.508959 | + | 0.860791i | \(0.330030\pi\) | |||||||
\(48\) | 7.85611 | 1.13393 | ||||||||
\(49\) | −6.88569 | −0.983669 | ||||||||
\(50\) | 11.6994 | 1.65454 | ||||||||
\(51\) | −1.12027 | −0.156869 | ||||||||
\(52\) | 4.29673 | 0.595850 | ||||||||
\(53\) | −2.68221 | −0.368430 | −0.184215 | − | 0.982886i | \(-0.558974\pi\) | ||||
−0.184215 | + | 0.982886i | \(0.558974\pi\) | |||||||
\(54\) | 9.78146 | 1.33109 | ||||||||
\(55\) | −3.65290 | −0.492557 | ||||||||
\(56\) | 2.80792 | 0.375224 | ||||||||
\(57\) | −3.82273 | −0.506333 | ||||||||
\(58\) | 20.1350 | 2.64386 | ||||||||
\(59\) | −0.307295 | −0.0400064 | −0.0200032 | − | 0.999800i | \(-0.506368\pi\) | ||||
−0.0200032 | + | 0.999800i | \(0.506368\pi\) | |||||||
\(60\) | −2.63930 | −0.340733 | ||||||||
\(61\) | 11.5060 | 1.47319 | 0.736595 | − | 0.676334i | \(-0.236432\pi\) | ||||
0.736595 | + | 0.676334i | \(0.236432\pi\) | |||||||
\(62\) | 10.6253 | 1.34942 | ||||||||
\(63\) | 0.867523 | 0.109298 | ||||||||
\(64\) | 16.6702 | 2.08377 | ||||||||
\(65\) | −0.658150 | −0.0816335 | ||||||||
\(66\) | −8.19565 | −1.00882 | ||||||||
\(67\) | 5.64993 | 0.690248 | 0.345124 | − | 0.938557i | \(-0.387837\pi\) | ||||
0.345124 | + | 0.938557i | \(0.387837\pi\) | |||||||
\(68\) | −8.69438 | −1.05435 | ||||||||
\(69\) | −1.19990 | −0.144451 | ||||||||
\(70\) | −0.706361 | −0.0844263 | ||||||||
\(71\) | 10.9328 | 1.29748 | 0.648742 | − | 0.761009i | \(-0.275296\pi\) | ||||
0.648742 | + | 0.761009i | \(0.275296\pi\) | |||||||
\(72\) | 21.3090 | 2.51129 | ||||||||
\(73\) | −9.17667 | −1.07405 | −0.537024 | − | 0.843567i | \(-0.680452\pi\) | ||||
−0.537024 | + | 0.843567i | \(0.680452\pi\) | |||||||
\(74\) | 15.5092 | 1.80290 | ||||||||
\(75\) | −2.89025 | −0.333738 | ||||||||
\(76\) | −29.6682 | −3.40317 | ||||||||
\(77\) | −1.57675 | −0.179687 | ||||||||
\(78\) | −1.47663 | −0.167195 | ||||||||
\(79\) | −2.76935 | −0.311576 | −0.155788 | − | 0.987790i | \(-0.549792\pi\) | ||||
−0.155788 | + | 0.987790i | \(0.549792\pi\) | |||||||
\(80\) | −9.33923 | −1.04416 | ||||||||
\(81\) | 5.28108 | 0.586787 | ||||||||
\(82\) | −4.40699 | −0.486670 | ||||||||
\(83\) | 6.69087 | 0.734418 | 0.367209 | − | 0.930138i | \(-0.380313\pi\) | ||||
0.367209 | + | 0.930138i | \(0.380313\pi\) | |||||||
\(84\) | −1.13924 | −0.124301 | ||||||||
\(85\) | 1.33176 | 0.144449 | ||||||||
\(86\) | −22.5139 | −2.42774 | ||||||||
\(87\) | −4.97422 | −0.533293 | ||||||||
\(88\) | −38.7298 | −4.12861 | ||||||||
\(89\) | 6.43339 | 0.681938 | 0.340969 | − | 0.940075i | \(-0.389245\pi\) | ||||
0.340969 | + | 0.940075i | \(0.389245\pi\) | |||||||
\(90\) | −5.36051 | −0.565047 | ||||||||
\(91\) | −0.284086 | −0.0297803 | ||||||||
\(92\) | −9.31238 | −0.970883 | ||||||||
\(93\) | −2.62492 | −0.272191 | ||||||||
\(94\) | −18.6128 | −1.91976 | ||||||||
\(95\) | 4.54441 | 0.466246 | ||||||||
\(96\) | −10.0093 | −1.02157 | ||||||||
\(97\) | −14.3260 | −1.45458 | −0.727291 | − | 0.686330i | \(-0.759221\pi\) | ||||
−0.727291 | + | 0.686330i | \(0.759221\pi\) | |||||||
\(98\) | 18.3652 | 1.85517 | ||||||||
\(99\) | −11.9658 | −1.20261 | ||||||||
\(100\) | −22.4312 | −2.24312 | ||||||||
\(101\) | 6.51742 | 0.648508 | 0.324254 | − | 0.945970i | \(-0.394887\pi\) | ||||
0.324254 | + | 0.945970i | \(0.394887\pi\) | |||||||
\(102\) | 2.98794 | 0.295850 | ||||||||
\(103\) | 14.5790 | 1.43651 | 0.718257 | − | 0.695778i | \(-0.244940\pi\) | ||||
0.718257 | + | 0.695778i | \(0.244940\pi\) | |||||||
\(104\) | −6.97802 | −0.684251 | ||||||||
\(105\) | 0.174502 | 0.0170296 | ||||||||
\(106\) | 7.15390 | 0.694848 | ||||||||
\(107\) | 5.88326 | 0.568757 | 0.284378 | − | 0.958712i | \(-0.408213\pi\) | ||||
0.284378 | + | 0.958712i | \(0.408213\pi\) | |||||||
\(108\) | −18.7540 | −1.80460 | ||||||||
\(109\) | −18.8375 | −1.80430 | −0.902151 | − | 0.431420i | \(-0.858013\pi\) | ||||
−0.902151 | + | 0.431420i | \(0.858013\pi\) | |||||||
\(110\) | 9.74287 | 0.928947 | ||||||||
\(111\) | −3.83144 | −0.363664 | ||||||||
\(112\) | −4.03121 | −0.380913 | ||||||||
\(113\) | 19.7823 | 1.86097 | 0.930483 | − | 0.366335i | \(-0.119388\pi\) | ||||
0.930483 | + | 0.366335i | \(0.119388\pi\) | |||||||
\(114\) | 10.1958 | 0.954928 | ||||||||
\(115\) | 1.42642 | 0.133014 | ||||||||
\(116\) | −38.6049 | −3.58437 | ||||||||
\(117\) | −2.15590 | −0.199313 | ||||||||
\(118\) | 0.819606 | 0.0754508 | ||||||||
\(119\) | 0.574843 | 0.0526958 | ||||||||
\(120\) | 4.28631 | 0.391285 | ||||||||
\(121\) | 10.7481 | 0.977103 | ||||||||
\(122\) | −30.6883 | −2.77839 | ||||||||
\(123\) | 1.08872 | 0.0981664 | ||||||||
\(124\) | −20.3719 | −1.82945 | ||||||||
\(125\) | 7.35238 | 0.657617 | ||||||||
\(126\) | −2.31382 | −0.206132 | ||||||||
\(127\) | 1.54761 | 0.137328 | 0.0686641 | − | 0.997640i | \(-0.478126\pi\) | ||||
0.0686641 | + | 0.997640i | \(0.478126\pi\) | |||||||
\(128\) | −14.0807 | −1.24457 | ||||||||
\(129\) | 5.56192 | 0.489700 | ||||||||
\(130\) | 1.75539 | 0.153958 | ||||||||
\(131\) | −0.567558 | −0.0495878 | −0.0247939 | − | 0.999693i | \(-0.507893\pi\) | ||||
−0.0247939 | + | 0.999693i | \(0.507893\pi\) | |||||||
\(132\) | 15.7135 | 1.36769 | ||||||||
\(133\) | 1.96156 | 0.170089 | ||||||||
\(134\) | −15.0693 | −1.30179 | ||||||||
\(135\) | 2.87264 | 0.247237 | ||||||||
\(136\) | 14.1199 | 1.21077 | ||||||||
\(137\) | −14.0557 | −1.20086 | −0.600430 | − | 0.799677i | \(-0.705004\pi\) | ||||
−0.600430 | + | 0.799677i | \(0.705004\pi\) | |||||||
\(138\) | 3.20032 | 0.272429 | ||||||||
\(139\) | −1.08081 | −0.0916734 | −0.0458367 | − | 0.998949i | \(-0.514595\pi\) | ||||
−0.0458367 | + | 0.998949i | \(0.514595\pi\) | |||||||
\(140\) | 1.35431 | 0.114460 | ||||||||
\(141\) | 4.59817 | 0.387236 | ||||||||
\(142\) | −29.1595 | −2.44701 | ||||||||
\(143\) | 3.91841 | 0.327674 | ||||||||
\(144\) | −30.5925 | −2.54937 | ||||||||
\(145\) | 5.91328 | 0.491072 | ||||||||
\(146\) | 24.4757 | 2.02562 | ||||||||
\(147\) | −4.53702 | −0.374207 | ||||||||
\(148\) | −29.7357 | −2.44426 | ||||||||
\(149\) | 13.5882 | 1.11319 | 0.556596 | − | 0.830783i | \(-0.312107\pi\) | ||||
0.556596 | + | 0.830783i | \(0.312107\pi\) | |||||||
\(150\) | 7.70877 | 0.629419 | ||||||||
\(151\) | 7.33710 | 0.597084 | 0.298542 | − | 0.954396i | \(-0.403500\pi\) | ||||
0.298542 | + | 0.954396i | \(0.403500\pi\) | |||||||
\(152\) | 48.1820 | 3.90807 | ||||||||
\(153\) | 4.36243 | 0.352682 | ||||||||
\(154\) | 4.20544 | 0.338884 | ||||||||
\(155\) | 3.12046 | 0.250642 | ||||||||
\(156\) | 2.83114 | 0.226673 | ||||||||
\(157\) | 9.04328 | 0.721733 | 0.360866 | − | 0.932618i | \(-0.382481\pi\) | ||||
0.360866 | + | 0.932618i | \(0.382481\pi\) | |||||||
\(158\) | 7.38631 | 0.587623 | ||||||||
\(159\) | −1.76733 | −0.140158 | ||||||||
\(160\) | 11.8989 | 0.940687 | ||||||||
\(161\) | 0.615703 | 0.0485242 | ||||||||
\(162\) | −14.0855 | −1.10666 | ||||||||
\(163\) | 16.7719 | 1.31368 | 0.656839 | − | 0.754031i | \(-0.271893\pi\) | ||||
0.656839 | + | 0.754031i | \(0.271893\pi\) | |||||||
\(164\) | 8.44953 | 0.659797 | ||||||||
\(165\) | −2.40691 | −0.187378 | ||||||||
\(166\) | −17.8456 | −1.38509 | ||||||||
\(167\) | 14.9991 | 1.16067 | 0.580333 | − | 0.814379i | \(-0.302922\pi\) | ||||
0.580333 | + | 0.814379i | \(0.302922\pi\) | |||||||
\(168\) | 1.85015 | 0.142742 | ||||||||
\(169\) | −12.2940 | −0.945693 | ||||||||
\(170\) | −3.55201 | −0.272427 | ||||||||
\(171\) | 14.8861 | 1.13837 | ||||||||
\(172\) | 43.1660 | 3.29138 | ||||||||
\(173\) | −7.11361 | −0.540838 | −0.270419 | − | 0.962743i | \(-0.587162\pi\) | ||||
−0.270419 | + | 0.962743i | \(0.587162\pi\) | |||||||
\(174\) | 13.2671 | 1.00577 | ||||||||
\(175\) | 1.48308 | 0.112110 | ||||||||
\(176\) | 55.6027 | 4.19121 | ||||||||
\(177\) | −0.202478 | −0.0152192 | ||||||||
\(178\) | −17.1589 | −1.28611 | ||||||||
\(179\) | 4.15683 | 0.310696 | 0.155348 | − | 0.987860i | \(-0.450350\pi\) | ||||
0.155348 | + | 0.987860i | \(0.450350\pi\) | |||||||
\(180\) | 10.2777 | 0.766056 | ||||||||
\(181\) | 4.11016 | 0.305506 | 0.152753 | − | 0.988264i | \(-0.451186\pi\) | ||||
0.152753 | + | 0.988264i | \(0.451186\pi\) | |||||||
\(182\) | 0.757702 | 0.0561646 | ||||||||
\(183\) | 7.58135 | 0.560430 | ||||||||
\(184\) | 15.1236 | 1.11493 | ||||||||
\(185\) | 4.55476 | 0.334872 | ||||||||
\(186\) | 7.00108 | 0.513344 | ||||||||
\(187\) | −7.92884 | −0.579814 | ||||||||
\(188\) | 35.6863 | 2.60269 | ||||||||
\(189\) | 1.23995 | 0.0901932 | ||||||||
\(190\) | −12.1207 | −0.879326 | ||||||||
\(191\) | −15.1417 | −1.09561 | −0.547807 | − | 0.836605i | \(-0.684537\pi\) | ||||
−0.547807 | + | 0.836605i | \(0.684537\pi\) | |||||||
\(192\) | 10.9841 | 0.792708 | ||||||||
\(193\) | 12.9098 | 0.929266 | 0.464633 | − | 0.885503i | \(-0.346186\pi\) | ||||
0.464633 | + | 0.885503i | \(0.346186\pi\) | |||||||
\(194\) | 38.2097 | 2.74329 | ||||||||
\(195\) | −0.433659 | −0.0310550 | ||||||||
\(196\) | −35.2117 | −2.51512 | ||||||||
\(197\) | −24.0649 | −1.71455 | −0.857277 | − | 0.514855i | \(-0.827846\pi\) | ||||
−0.857277 | + | 0.514855i | \(0.827846\pi\) | |||||||
\(198\) | 31.9147 | 2.26808 | ||||||||
\(199\) | −13.0942 | −0.928220 | −0.464110 | − | 0.885778i | \(-0.653626\pi\) | ||||
−0.464110 | + | 0.885778i | \(0.653626\pi\) | |||||||
\(200\) | 36.4289 | 2.57591 | ||||||||
\(201\) | 3.72277 | 0.262584 | ||||||||
\(202\) | −17.3830 | −1.22307 | ||||||||
\(203\) | 2.55242 | 0.179145 | ||||||||
\(204\) | −5.72877 | −0.401094 | ||||||||
\(205\) | −1.29425 | −0.0903945 | ||||||||
\(206\) | −38.8846 | −2.70922 | ||||||||
\(207\) | 4.67252 | 0.324763 | ||||||||
\(208\) | 10.0181 | 0.694627 | ||||||||
\(209\) | −27.0559 | −1.87149 | ||||||||
\(210\) | −0.465425 | −0.0321174 | ||||||||
\(211\) | 22.7148 | 1.56375 | 0.781875 | − | 0.623436i | \(-0.214264\pi\) | ||||
0.781875 | + | 0.623436i | \(0.214264\pi\) | |||||||
\(212\) | −13.7162 | −0.942031 | ||||||||
\(213\) | 7.20367 | 0.493588 | ||||||||
\(214\) | −15.6916 | −1.07266 | ||||||||
\(215\) | −6.61193 | −0.450930 | ||||||||
\(216\) | 30.4571 | 2.07234 | ||||||||
\(217\) | 1.34692 | 0.0914351 | ||||||||
\(218\) | 50.2426 | 3.40286 | ||||||||
\(219\) | −6.04656 | −0.408589 | ||||||||
\(220\) | −18.6800 | −1.25941 | ||||||||
\(221\) | −1.42856 | −0.0960951 | ||||||||
\(222\) | 10.2191 | 0.685859 | ||||||||
\(223\) | 1.44039 | 0.0964559 | 0.0482279 | − | 0.998836i | \(-0.484643\pi\) | ||||
0.0482279 | + | 0.998836i | \(0.484643\pi\) | |||||||
\(224\) | 5.13605 | 0.343167 | ||||||||
\(225\) | 11.2549 | 0.750329 | ||||||||
\(226\) | −52.7627 | −3.50972 | ||||||||
\(227\) | −15.4980 | −1.02864 | −0.514318 | − | 0.857599i | \(-0.671955\pi\) | ||||
−0.514318 | + | 0.857599i | \(0.671955\pi\) | |||||||
\(228\) | −19.5485 | −1.29463 | ||||||||
\(229\) | 6.00576 | 0.396872 | 0.198436 | − | 0.980114i | \(-0.436414\pi\) | ||||
0.198436 | + | 0.980114i | \(0.436414\pi\) | |||||||
\(230\) | −3.80449 | −0.250861 | ||||||||
\(231\) | −1.03893 | −0.0683563 | ||||||||
\(232\) | 62.6954 | 4.11616 | ||||||||
\(233\) | 19.6645 | 1.28827 | 0.644133 | − | 0.764913i | \(-0.277218\pi\) | ||||
0.644133 | + | 0.764913i | \(0.277218\pi\) | |||||||
\(234\) | 5.75014 | 0.375898 | ||||||||
\(235\) | −5.46624 | −0.356578 | ||||||||
\(236\) | −1.57143 | −0.102291 | ||||||||
\(237\) | −1.82474 | −0.118530 | ||||||||
\(238\) | −1.53320 | −0.0993826 | ||||||||
\(239\) | 30.4487 | 1.96956 | 0.984781 | − | 0.173800i | \(-0.0556047\pi\) | ||||
0.984781 | + | 0.173800i | \(0.0556047\pi\) | |||||||
\(240\) | −6.15367 | −0.397218 | ||||||||
\(241\) | −13.7247 | −0.884085 | −0.442043 | − | 0.896994i | \(-0.645746\pi\) | ||||
−0.442043 | + | 0.896994i | \(0.645746\pi\) | |||||||
\(242\) | −28.6670 | −1.84279 | ||||||||
\(243\) | 14.4818 | 0.929010 | ||||||||
\(244\) | 58.8388 | 3.76677 | ||||||||
\(245\) | 5.39354 | 0.344581 | ||||||||
\(246\) | −2.90379 | −0.185139 | ||||||||
\(247\) | −4.87471 | −0.310171 | ||||||||
\(248\) | 33.0846 | 2.10087 | ||||||||
\(249\) | 4.40865 | 0.279387 | ||||||||
\(250\) | −19.6100 | −1.24024 | ||||||||
\(251\) | 5.14687 | 0.324868 | 0.162434 | − | 0.986719i | \(-0.448066\pi\) | ||||
0.162434 | + | 0.986719i | \(0.448066\pi\) | |||||||
\(252\) | 4.43630 | 0.279460 | ||||||||
\(253\) | −8.49243 | −0.533914 | ||||||||
\(254\) | −4.12772 | −0.258996 | ||||||||
\(255\) | 0.877502 | 0.0549513 | ||||||||
\(256\) | 4.21500 | 0.263437 | ||||||||
\(257\) | 24.4557 | 1.52551 | 0.762753 | − | 0.646690i | \(-0.223847\pi\) | ||||
0.762753 | + | 0.646690i | \(0.223847\pi\) | |||||||
\(258\) | −14.8346 | −0.923559 | ||||||||
\(259\) | 1.96603 | 0.122163 | ||||||||
\(260\) | −3.36562 | −0.208727 | ||||||||
\(261\) | 19.3701 | 1.19898 | ||||||||
\(262\) | 1.51377 | 0.0935210 | ||||||||
\(263\) | 1.30307 | 0.0803506 | 0.0401753 | − | 0.999193i | \(-0.487208\pi\) | ||||
0.0401753 | + | 0.999193i | \(0.487208\pi\) | |||||||
\(264\) | −25.5193 | −1.57060 | ||||||||
\(265\) | 2.10097 | 0.129062 | ||||||||
\(266\) | −5.23179 | −0.320782 | ||||||||
\(267\) | 4.23900 | 0.259422 | ||||||||
\(268\) | 28.8923 | 1.76488 | ||||||||
\(269\) | 4.66565 | 0.284470 | 0.142235 | − | 0.989833i | \(-0.454571\pi\) | ||||
0.142235 | + | 0.989833i | \(0.454571\pi\) | |||||||
\(270\) | −7.66179 | −0.466282 | ||||||||
\(271\) | −13.7281 | −0.833923 | −0.416962 | − | 0.908924i | \(-0.636905\pi\) | ||||
−0.416962 | + | 0.908924i | \(0.636905\pi\) | |||||||
\(272\) | −20.2714 | −1.22913 | ||||||||
\(273\) | −0.187186 | −0.0113290 | ||||||||
\(274\) | 37.4889 | 2.26478 | ||||||||
\(275\) | −20.4561 | −1.23355 | ||||||||
\(276\) | −6.13598 | −0.369343 | ||||||||
\(277\) | 2.03111 | 0.122038 | 0.0610189 | − | 0.998137i | \(-0.480565\pi\) | ||||
0.0610189 | + | 0.998137i | \(0.480565\pi\) | |||||||
\(278\) | 2.88271 | 0.172893 | ||||||||
\(279\) | 10.2217 | 0.611956 | ||||||||
\(280\) | −2.19943 | −0.131441 | ||||||||
\(281\) | −9.57763 | −0.571353 | −0.285677 | − | 0.958326i | \(-0.592218\pi\) | ||||
−0.285677 | + | 0.958326i | \(0.592218\pi\) | |||||||
\(282\) | −12.2641 | −0.730315 | ||||||||
\(283\) | −33.1514 | −1.97065 | −0.985323 | − | 0.170702i | \(-0.945396\pi\) | ||||
−0.985323 | + | 0.170702i | \(0.945396\pi\) | |||||||
\(284\) | 55.9076 | 3.31750 | ||||||||
\(285\) | 2.99433 | 0.177369 | ||||||||
\(286\) | −10.4510 | −0.617982 | ||||||||
\(287\) | −0.558654 | −0.0329763 | ||||||||
\(288\) | 38.9770 | 2.29674 | ||||||||
\(289\) | −14.1093 | −0.829961 | ||||||||
\(290\) | −15.7717 | −0.926146 | ||||||||
\(291\) | −9.43945 | −0.553351 | ||||||||
\(292\) | −46.9272 | −2.74621 | ||||||||
\(293\) | −4.48756 | −0.262166 | −0.131083 | − | 0.991371i | \(-0.541845\pi\) | ||||
−0.131083 | + | 0.991371i | \(0.541845\pi\) | |||||||
\(294\) | 12.1010 | 0.705742 | ||||||||
\(295\) | 0.240703 | 0.0140143 | ||||||||
\(296\) | 48.2917 | 2.80690 | ||||||||
\(297\) | −17.1027 | −0.992400 | ||||||||
\(298\) | −36.2420 | −2.09944 | ||||||||
\(299\) | −1.53010 | −0.0884879 | ||||||||
\(300\) | −14.7800 | −0.853326 | ||||||||
\(301\) | −2.85399 | −0.164501 | ||||||||
\(302\) | −19.5692 | −1.12608 | ||||||||
\(303\) | 4.29437 | 0.246705 | ||||||||
\(304\) | −69.1728 | −3.96733 | ||||||||
\(305\) | −9.01260 | −0.516060 | ||||||||
\(306\) | −11.6353 | −0.665147 | ||||||||
\(307\) | 32.7166 | 1.86723 | 0.933617 | − | 0.358273i | \(-0.116634\pi\) | ||||
0.933617 | + | 0.358273i | \(0.116634\pi\) | |||||||
\(308\) | −8.06309 | −0.459437 | ||||||||
\(309\) | 9.60619 | 0.546477 | ||||||||
\(310\) | −8.32278 | −0.472702 | ||||||||
\(311\) | −9.79968 | −0.555689 | −0.277844 | − | 0.960626i | \(-0.589620\pi\) | ||||
−0.277844 | + | 0.960626i | \(0.589620\pi\) | |||||||
\(312\) | −4.59786 | −0.260302 | ||||||||
\(313\) | 4.98240 | 0.281622 | 0.140811 | − | 0.990036i | \(-0.455029\pi\) | ||||
0.140811 | + | 0.990036i | \(0.455029\pi\) | |||||||
\(314\) | −24.1199 | −1.36116 | ||||||||
\(315\) | −0.679528 | −0.0382871 | ||||||||
\(316\) | −14.1618 | −0.796663 | ||||||||
\(317\) | −17.8350 | −1.00171 | −0.500856 | − | 0.865531i | \(-0.666981\pi\) | ||||
−0.500856 | + | 0.865531i | \(0.666981\pi\) | |||||||
\(318\) | 4.71374 | 0.264334 | ||||||||
\(319\) | −35.2057 | −1.97114 | ||||||||
\(320\) | −13.0577 | −0.729949 | ||||||||
\(321\) | 3.87652 | 0.216366 | ||||||||
\(322\) | −1.64218 | −0.0915151 | ||||||||
\(323\) | 9.86391 | 0.548843 | ||||||||
\(324\) | 27.0062 | 1.50034 | ||||||||
\(325\) | −3.68563 | −0.204442 | ||||||||
\(326\) | −44.7334 | −2.47756 | ||||||||
\(327\) | −12.4121 | −0.686391 | ||||||||
\(328\) | −13.7223 | −0.757686 | ||||||||
\(329\) | −2.35946 | −0.130081 | ||||||||
\(330\) | 6.41963 | 0.353389 | ||||||||
\(331\) | 8.74743 | 0.480802 | 0.240401 | − | 0.970674i | \(-0.422721\pi\) | ||||
0.240401 | + | 0.970674i | \(0.422721\pi\) | |||||||
\(332\) | 34.2155 | 1.87782 | ||||||||
\(333\) | 14.9200 | 0.817611 | ||||||||
\(334\) | −40.0051 | −2.18898 | ||||||||
\(335\) | −4.42557 | −0.241795 | ||||||||
\(336\) | −2.65619 | −0.144907 | ||||||||
\(337\) | −8.97010 | −0.488632 | −0.244316 | − | 0.969696i | \(-0.578563\pi\) | ||||
−0.244316 | + | 0.969696i | \(0.578563\pi\) | |||||||
\(338\) | 32.7901 | 1.78355 | ||||||||
\(339\) | 13.0347 | 0.707947 | ||||||||
\(340\) | 6.81028 | 0.369339 | ||||||||
\(341\) | −18.5782 | −1.00607 | ||||||||
\(342\) | −39.7036 | −2.14693 | ||||||||
\(343\) | 4.69481 | 0.253496 | ||||||||
\(344\) | −70.1028 | −3.77969 | ||||||||
\(345\) | 0.939876 | 0.0506012 | ||||||||
\(346\) | 18.9732 | 1.02000 | ||||||||
\(347\) | 22.6667 | 1.21681 | 0.608406 | − | 0.793626i | \(-0.291809\pi\) | ||||
0.608406 | + | 0.793626i | \(0.291809\pi\) | |||||||
\(348\) | −25.4370 | −1.36356 | ||||||||
\(349\) | −25.3419 | −1.35652 | −0.678261 | − | 0.734821i | \(-0.737266\pi\) | ||||
−0.678261 | + | 0.734821i | \(0.737266\pi\) | |||||||
\(350\) | −3.95560 | −0.211436 | ||||||||
\(351\) | −3.08143 | −0.164475 | ||||||||
\(352\) | −70.8418 | −3.77588 | ||||||||
\(353\) | 32.5598 | 1.73298 | 0.866492 | − | 0.499191i | \(-0.166370\pi\) | ||||
0.866492 | + | 0.499191i | \(0.166370\pi\) | |||||||
\(354\) | 0.540043 | 0.0287029 | ||||||||
\(355\) | −8.56362 | −0.454510 | ||||||||
\(356\) | 32.8988 | 1.74363 | ||||||||
\(357\) | 0.378767 | 0.0200465 | ||||||||
\(358\) | −11.0869 | −0.585963 | ||||||||
\(359\) | −16.0245 | −0.845739 | −0.422870 | − | 0.906191i | \(-0.638977\pi\) | ||||
−0.422870 | + | 0.906191i | \(0.638977\pi\) | |||||||
\(360\) | −16.6913 | −0.879710 | ||||||||
\(361\) | 14.6590 | 0.771527 | ||||||||
\(362\) | −10.9625 | −0.576175 | ||||||||
\(363\) | 7.08201 | 0.371709 | ||||||||
\(364\) | −1.45274 | −0.0761445 | ||||||||
\(365\) | 7.18806 | 0.376240 | ||||||||
\(366\) | −20.2207 | −1.05695 | ||||||||
\(367\) | 16.9357 | 0.884034 | 0.442017 | − | 0.897007i | \(-0.354263\pi\) | ||||
0.442017 | + | 0.897007i | \(0.354263\pi\) | |||||||
\(368\) | −21.7123 | −1.13183 | ||||||||
\(369\) | −4.23958 | −0.220704 | ||||||||
\(370\) | −12.1483 | −0.631559 | ||||||||
\(371\) | 0.906868 | 0.0470822 | ||||||||
\(372\) | −13.4232 | −0.695959 | ||||||||
\(373\) | −6.66990 | −0.345354 | −0.172677 | − | 0.984978i | \(-0.555242\pi\) | ||||
−0.172677 | + | 0.984978i | \(0.555242\pi\) | |||||||
\(374\) | 21.1475 | 1.09351 | ||||||||
\(375\) | 4.84452 | 0.250170 | ||||||||
\(376\) | −57.9556 | −2.98883 | ||||||||
\(377\) | −6.34309 | −0.326686 | ||||||||
\(378\) | −3.30715 | −0.170102 | ||||||||
\(379\) | 6.15599 | 0.316212 | 0.158106 | − | 0.987422i | \(-0.449461\pi\) | ||||
0.158106 | + | 0.987422i | \(0.449461\pi\) | |||||||
\(380\) | 23.2390 | 1.19213 | ||||||||
\(381\) | 1.01973 | 0.0522423 | ||||||||
\(382\) | 40.3853 | 2.06629 | ||||||||
\(383\) | 32.0748 | 1.63894 | 0.819472 | − | 0.573120i | \(-0.194267\pi\) | ||||
0.819472 | + | 0.573120i | \(0.194267\pi\) | |||||||
\(384\) | −9.27782 | −0.473457 | ||||||||
\(385\) | 1.23506 | 0.0629445 | ||||||||
\(386\) | −34.4325 | −1.75257 | ||||||||
\(387\) | −21.6587 | −1.10097 | ||||||||
\(388\) | −73.2594 | −3.71919 | ||||||||
\(389\) | −15.7346 | −0.797777 | −0.398889 | − | 0.916999i | \(-0.630604\pi\) | ||||
−0.398889 | + | 0.916999i | \(0.630604\pi\) | |||||||
\(390\) | 1.15664 | 0.0585687 | ||||||||
\(391\) | 3.09613 | 0.156578 | ||||||||
\(392\) | 57.1848 | 2.88827 | ||||||||
\(393\) | −0.373967 | −0.0188641 | ||||||||
\(394\) | 64.1850 | 3.23360 | ||||||||
\(395\) | 2.16923 | 0.109146 | ||||||||
\(396\) | −61.1901 | −3.07492 | ||||||||
\(397\) | 31.4175 | 1.57680 | 0.788400 | − | 0.615164i | \(-0.210910\pi\) | ||||
0.788400 | + | 0.615164i | \(0.210910\pi\) | |||||||
\(398\) | 34.9242 | 1.75059 | ||||||||
\(399\) | 1.29248 | 0.0647050 | ||||||||
\(400\) | −52.2995 | −2.61497 | ||||||||
\(401\) | −30.8159 | −1.53887 | −0.769435 | − | 0.638725i | \(-0.779462\pi\) | ||||
−0.769435 | + | 0.638725i | \(0.779462\pi\) | |||||||
\(402\) | −9.92922 | −0.495225 | ||||||||
\(403\) | −3.34727 | −0.166739 | ||||||||
\(404\) | 33.3285 | 1.65815 | ||||||||
\(405\) | −4.13666 | −0.205552 | ||||||||
\(406\) | −6.80773 | −0.337862 | ||||||||
\(407\) | −27.1175 | −1.34416 | ||||||||
\(408\) | 9.30370 | 0.460602 | ||||||||
\(409\) | 0.790454 | 0.0390854 | 0.0195427 | − | 0.999809i | \(-0.493779\pi\) | ||||
0.0195427 | + | 0.999809i | \(0.493779\pi\) | |||||||
\(410\) | 3.45198 | 0.170481 | ||||||||
\(411\) | −9.26138 | −0.456830 | ||||||||
\(412\) | 74.5535 | 3.67299 | ||||||||
\(413\) | 0.103898 | 0.00511247 | ||||||||
\(414\) | −12.4624 | −0.612492 | ||||||||
\(415\) | −5.24094 | −0.257268 | ||||||||
\(416\) | −12.7637 | −0.625793 | ||||||||
\(417\) | −0.712154 | −0.0348743 | ||||||||
\(418\) | 72.1624 | 3.52958 | ||||||||
\(419\) | 3.01651 | 0.147366 | 0.0736830 | − | 0.997282i | \(-0.476525\pi\) | ||||
0.0736830 | + | 0.997282i | \(0.476525\pi\) | |||||||
\(420\) | 0.892360 | 0.0435427 | ||||||||
\(421\) | −0.396298 | −0.0193144 | −0.00965719 | − | 0.999953i | \(-0.503074\pi\) | ||||
−0.00965719 | + | 0.999953i | \(0.503074\pi\) | |||||||
\(422\) | −60.5840 | −2.94918 | ||||||||
\(423\) | −17.9057 | −0.870607 | ||||||||
\(424\) | 22.2755 | 1.08179 | ||||||||
\(425\) | 7.45781 | 0.361757 | ||||||||
\(426\) | −19.2134 | −0.930891 | ||||||||
\(427\) | −3.89022 | −0.188261 | ||||||||
\(428\) | 30.0856 | 1.45424 | ||||||||
\(429\) | 2.58186 | 0.124653 | ||||||||
\(430\) | 17.6351 | 0.850440 | ||||||||
\(431\) | 29.8848 | 1.43950 | 0.719751 | − | 0.694232i | \(-0.244256\pi\) | ||||
0.719751 | + | 0.694232i | \(0.244256\pi\) | |||||||
\(432\) | −43.7259 | −2.10376 | ||||||||
\(433\) | −6.20389 | −0.298140 | −0.149070 | − | 0.988827i | \(-0.547628\pi\) | ||||
−0.149070 | + | 0.988827i | \(0.547628\pi\) | |||||||
\(434\) | −3.59246 | −0.172444 | ||||||||
\(435\) | 3.89630 | 0.186813 | ||||||||
\(436\) | −96.3302 | −4.61338 | ||||||||
\(437\) | 10.5650 | 0.505395 | ||||||||
\(438\) | 16.1272 | 0.770585 | ||||||||
\(439\) | 13.6075 | 0.649450 | 0.324725 | − | 0.945808i | \(-0.394728\pi\) | ||||
0.324725 | + | 0.945808i | \(0.394728\pi\) | |||||||
\(440\) | 30.3369 | 1.44626 | ||||||||
\(441\) | 17.6676 | 0.841314 | ||||||||
\(442\) | 3.81019 | 0.181232 | ||||||||
\(443\) | −24.2713 | −1.15317 | −0.576583 | − | 0.817038i | \(-0.695614\pi\) | ||||
−0.576583 | + | 0.817038i | \(0.695614\pi\) | |||||||
\(444\) | −19.5930 | −0.929844 | ||||||||
\(445\) | −5.03926 | −0.238884 | ||||||||
\(446\) | −3.84176 | −0.181913 | ||||||||
\(447\) | 8.95336 | 0.423480 | ||||||||
\(448\) | −5.63626 | −0.266288 | ||||||||
\(449\) | 16.5839 | 0.782641 | 0.391321 | − | 0.920254i | \(-0.372018\pi\) | ||||
0.391321 | + | 0.920254i | \(0.372018\pi\) | |||||||
\(450\) | −30.0187 | −1.41510 | ||||||||
\(451\) | 7.70555 | 0.362840 | ||||||||
\(452\) | 101.162 | 4.75826 | ||||||||
\(453\) | 4.83445 | 0.227142 | ||||||||
\(454\) | 41.3356 | 1.93998 | ||||||||
\(455\) | 0.222523 | 0.0104321 | ||||||||
\(456\) | 31.7474 | 1.48671 | ||||||||
\(457\) | −3.45205 | −0.161480 | −0.0807401 | − | 0.996735i | \(-0.525728\pi\) | ||||
−0.0807401 | + | 0.996735i | \(0.525728\pi\) | |||||||
\(458\) | −16.0183 | −0.748488 | ||||||||
\(459\) | 6.23523 | 0.291036 | ||||||||
\(460\) | 7.29436 | 0.340101 | ||||||||
\(461\) | −18.3585 | −0.855040 | −0.427520 | − | 0.904006i | \(-0.640613\pi\) | ||||
−0.427520 | + | 0.904006i | \(0.640613\pi\) | |||||||
\(462\) | 2.77098 | 0.128918 | ||||||||
\(463\) | 7.11049 | 0.330453 | 0.165226 | − | 0.986256i | \(-0.447165\pi\) | ||||
0.165226 | + | 0.986256i | \(0.447165\pi\) | |||||||
\(464\) | −90.0092 | −4.17857 | ||||||||
\(465\) | 2.05609 | 0.0953489 | ||||||||
\(466\) | −52.4485 | −2.42963 | ||||||||
\(467\) | −5.21192 | −0.241179 | −0.120589 | − | 0.992702i | \(-0.538478\pi\) | ||||
−0.120589 | + | 0.992702i | \(0.538478\pi\) | |||||||
\(468\) | −11.0247 | −0.509619 | ||||||||
\(469\) | −1.91026 | −0.0882078 | ||||||||
\(470\) | 14.5793 | 0.672495 | ||||||||
\(471\) | 5.95867 | 0.274561 | ||||||||
\(472\) | 2.55205 | 0.117468 | ||||||||
\(473\) | 39.3652 | 1.81002 | ||||||||
\(474\) | 4.86688 | 0.223543 | ||||||||
\(475\) | 25.4486 | 1.16766 | ||||||||
\(476\) | 2.93961 | 0.134737 | ||||||||
\(477\) | 6.88214 | 0.315112 | ||||||||
\(478\) | −81.2116 | −3.71453 | ||||||||
\(479\) | 15.2102 | 0.694972 | 0.347486 | − | 0.937685i | \(-0.387035\pi\) | ||||
0.347486 | + | 0.937685i | \(0.387035\pi\) | |||||||
\(480\) | 7.84022 | 0.357856 | ||||||||
\(481\) | −4.88582 | −0.222774 | ||||||||
\(482\) | 36.6060 | 1.66736 | ||||||||
\(483\) | 0.405690 | 0.0184595 | ||||||||
\(484\) | 54.9633 | 2.49833 | ||||||||
\(485\) | 11.2215 | 0.509541 | ||||||||
\(486\) | −38.6254 | −1.75208 | ||||||||
\(487\) | 23.8701 | 1.08166 | 0.540828 | − | 0.841133i | \(-0.318111\pi\) | ||||
0.540828 | + | 0.841133i | \(0.318111\pi\) | |||||||
\(488\) | −95.5559 | −4.32561 | ||||||||
\(489\) | 11.0511 | 0.499748 | ||||||||
\(490\) | −14.3854 | −0.649868 | ||||||||
\(491\) | 26.0327 | 1.17484 | 0.587420 | − | 0.809282i | \(-0.300144\pi\) | ||||
0.587420 | + | 0.809282i | \(0.300144\pi\) | |||||||
\(492\) | 5.56744 | 0.251000 | ||||||||
\(493\) | 12.8351 | 0.578066 | ||||||||
\(494\) | 13.0017 | 0.584972 | ||||||||
\(495\) | 9.37277 | 0.421275 | ||||||||
\(496\) | −47.4982 | −2.13273 | ||||||||
\(497\) | −3.69642 | −0.165807 | ||||||||
\(498\) | −11.7586 | −0.526915 | ||||||||
\(499\) | −37.5991 | −1.68317 | −0.841583 | − | 0.540128i | \(-0.818376\pi\) | ||||
−0.841583 | + | 0.540128i | \(0.818376\pi\) | |||||||
\(500\) | 37.5982 | 1.68144 | ||||||||
\(501\) | 9.88300 | 0.441540 | ||||||||
\(502\) | −13.7275 | −0.612690 | ||||||||
\(503\) | −25.9909 | −1.15887 | −0.579437 | − | 0.815017i | \(-0.696728\pi\) | ||||
−0.579437 | + | 0.815017i | \(0.696728\pi\) | |||||||
\(504\) | −7.20468 | −0.320922 | ||||||||
\(505\) | −5.10508 | −0.227173 | ||||||||
\(506\) | 22.6507 | 1.00695 | ||||||||
\(507\) | −8.10059 | −0.359760 | ||||||||
\(508\) | 7.91409 | 0.351131 | ||||||||
\(509\) | 39.9172 | 1.76930 | 0.884650 | − | 0.466256i | \(-0.154397\pi\) | ||||
0.884650 | + | 0.466256i | \(0.154397\pi\) | |||||||
\(510\) | −2.34044 | −0.103636 | ||||||||
\(511\) | 3.10267 | 0.137254 | ||||||||
\(512\) | 16.9192 | 0.747731 | ||||||||
\(513\) | 21.2767 | 0.939390 | ||||||||
\(514\) | −65.2274 | −2.87706 | ||||||||
\(515\) | −11.4197 | −0.503212 | ||||||||
\(516\) | 28.4423 | 1.25210 | ||||||||
\(517\) | 32.5442 | 1.43129 | ||||||||
\(518\) | −5.24371 | −0.230395 | ||||||||
\(519\) | −4.68720 | −0.205745 | ||||||||
\(520\) | 5.46587 | 0.239694 | ||||||||
\(521\) | −41.9531 | −1.83800 | −0.918999 | − | 0.394260i | \(-0.871001\pi\) | ||||
−0.918999 | + | 0.394260i | \(0.871001\pi\) | |||||||
\(522\) | −51.6633 | −2.26124 | ||||||||
\(523\) | 20.4098 | 0.892459 | 0.446230 | − | 0.894919i | \(-0.352766\pi\) | ||||
0.446230 | + | 0.894919i | \(0.352766\pi\) | |||||||
\(524\) | −2.90235 | −0.126790 | ||||||||
\(525\) | 0.977207 | 0.0426488 | ||||||||
\(526\) | −3.47549 | −0.151539 | ||||||||
\(527\) | 6.77315 | 0.295043 | ||||||||
\(528\) | 36.6369 | 1.59442 | ||||||||
\(529\) | −19.6838 | −0.855817 | ||||||||
\(530\) | −5.60363 | −0.243406 | ||||||||
\(531\) | 0.788471 | 0.0342167 | ||||||||
\(532\) | 10.0309 | 0.434896 | ||||||||
\(533\) | 1.38832 | 0.0601350 | ||||||||
\(534\) | −11.3061 | −0.489262 | ||||||||
\(535\) | −4.60834 | −0.199236 | ||||||||
\(536\) | −46.9220 | −2.02672 | ||||||||
\(537\) | 2.73896 | 0.118195 | ||||||||
\(538\) | −12.4441 | −0.536501 | ||||||||
\(539\) | −32.1113 | −1.38313 | ||||||||
\(540\) | 14.6900 | 0.632155 | ||||||||
\(541\) | 10.6155 | 0.456395 | 0.228197 | − | 0.973615i | \(-0.426717\pi\) | ||||
0.228197 | + | 0.973615i | \(0.426717\pi\) | |||||||
\(542\) | 36.6151 | 1.57275 | ||||||||
\(543\) | 2.70821 | 0.116220 | ||||||||
\(544\) | 25.8272 | 1.10733 | ||||||||
\(545\) | 14.7553 | 0.632049 | ||||||||
\(546\) | 0.499254 | 0.0213661 | ||||||||
\(547\) | 4.14173 | 0.177088 | 0.0885438 | − | 0.996072i | \(-0.471779\pi\) | ||||
0.0885438 | + | 0.996072i | \(0.471779\pi\) | |||||||
\(548\) | −71.8774 | −3.07045 | ||||||||
\(549\) | −29.5225 | −1.25999 | ||||||||
\(550\) | 54.5599 | 2.32644 | ||||||||
\(551\) | 43.7979 | 1.86585 | ||||||||
\(552\) | 9.96501 | 0.424139 | ||||||||
\(553\) | 0.936330 | 0.0398168 | ||||||||
\(554\) | −5.41731 | −0.230159 | ||||||||
\(555\) | 3.00116 | 0.127392 | ||||||||
\(556\) | −5.52702 | −0.234398 | ||||||||
\(557\) | 23.1200 | 0.979627 | 0.489814 | − | 0.871827i | \(-0.337065\pi\) | ||||
0.489814 | + | 0.871827i | \(0.337065\pi\) | |||||||
\(558\) | −27.2629 | −1.15413 | ||||||||
\(559\) | 7.09252 | 0.299982 | ||||||||
\(560\) | 3.15763 | 0.133434 | ||||||||
\(561\) | −5.22436 | −0.220572 | ||||||||
\(562\) | 25.5451 | 1.07755 | ||||||||
\(563\) | 1.11215 | 0.0468714 | 0.0234357 | − | 0.999725i | \(-0.492539\pi\) | ||||
0.0234357 | + | 0.999725i | \(0.492539\pi\) | |||||||
\(564\) | 23.5139 | 0.990114 | ||||||||
\(565\) | −15.4955 | −0.651899 | ||||||||
\(566\) | 88.4201 | 3.71658 | ||||||||
\(567\) | −1.78556 | −0.0749863 | ||||||||
\(568\) | −90.7956 | −3.80970 | ||||||||
\(569\) | 37.3755 | 1.56686 | 0.783431 | − | 0.621479i | \(-0.213468\pi\) | ||||
0.783431 | + | 0.621479i | \(0.213468\pi\) | |||||||
\(570\) | −7.98638 | −0.334513 | ||||||||
\(571\) | 10.9105 | 0.456592 | 0.228296 | − | 0.973592i | \(-0.426685\pi\) | ||||
0.228296 | + | 0.973592i | \(0.426685\pi\) | |||||||
\(572\) | 20.0378 | 0.837821 | ||||||||
\(573\) | −9.97694 | −0.416793 | ||||||||
\(574\) | 1.49002 | 0.0621923 | ||||||||
\(575\) | 7.98792 | 0.333119 | ||||||||
\(576\) | −42.7731 | −1.78221 | ||||||||
\(577\) | −36.5277 | −1.52067 | −0.760334 | − | 0.649533i | \(-0.774965\pi\) | ||||
−0.760334 | + | 0.649533i | \(0.774965\pi\) | |||||||
\(578\) | 37.6319 | 1.56528 | ||||||||
\(579\) | 8.50632 | 0.353511 | ||||||||
\(580\) | 30.2391 | 1.25561 | ||||||||
\(581\) | −2.26221 | −0.0938523 | ||||||||
\(582\) | 25.1766 | 1.04360 | ||||||||
\(583\) | −12.5085 | −0.518048 | ||||||||
\(584\) | 76.2112 | 3.15364 | ||||||||
\(585\) | 1.68871 | 0.0698196 | ||||||||
\(586\) | 11.9690 | 0.494437 | ||||||||
\(587\) | 30.6482 | 1.26499 | 0.632494 | − | 0.774565i | \(-0.282031\pi\) | ||||
0.632494 | + | 0.774565i | \(0.282031\pi\) | |||||||
\(588\) | −23.2012 | −0.956801 | ||||||||
\(589\) | 23.1123 | 0.952325 | ||||||||
\(590\) | −0.641995 | −0.0264305 | ||||||||
\(591\) | −15.8565 | −0.652250 | ||||||||
\(592\) | −69.3303 | −2.84946 | ||||||||
\(593\) | 41.4959 | 1.70403 | 0.852016 | − | 0.523515i | \(-0.175380\pi\) | ||||
0.852016 | + | 0.523515i | \(0.175380\pi\) | |||||||
\(594\) | 45.6157 | 1.87164 | ||||||||
\(595\) | −0.450273 | −0.0184594 | ||||||||
\(596\) | 69.4869 | 2.84629 | ||||||||
\(597\) | −8.62781 | −0.353113 | ||||||||
\(598\) | 4.08102 | 0.166885 | ||||||||
\(599\) | −11.2225 | −0.458538 | −0.229269 | − | 0.973363i | \(-0.573634\pi\) | ||||
−0.229269 | + | 0.973363i | \(0.573634\pi\) | |||||||
\(600\) | 24.0032 | 0.979928 | ||||||||
\(601\) | −15.3837 | −0.627515 | −0.313757 | − | 0.949503i | \(-0.601588\pi\) | ||||
−0.313757 | + | 0.949503i | \(0.601588\pi\) | |||||||
\(602\) | 7.61205 | 0.310244 | ||||||||
\(603\) | −14.4968 | −0.590356 | ||||||||
\(604\) | 37.5201 | 1.52667 | ||||||||
\(605\) | −8.41899 | −0.342280 | ||||||||
\(606\) | −11.4538 | −0.465278 | ||||||||
\(607\) | −1.20035 | −0.0487205 | −0.0243603 | − | 0.999703i | \(-0.507755\pi\) | ||||
−0.0243603 | + | 0.999703i | \(0.507755\pi\) | |||||||
\(608\) | 88.1311 | 3.57419 | ||||||||
\(609\) | 1.68181 | 0.0681502 | ||||||||
\(610\) | 24.0381 | 0.973273 | ||||||||
\(611\) | 5.86355 | 0.237214 | ||||||||
\(612\) | 22.3084 | 0.901764 | ||||||||
\(613\) | −28.9911 | −1.17094 | −0.585470 | − | 0.810694i | \(-0.699090\pi\) | ||||
−0.585470 | + | 0.810694i | \(0.699090\pi\) | |||||||
\(614\) | −87.2604 | −3.52154 | ||||||||
\(615\) | −0.852790 | −0.0343878 | ||||||||
\(616\) | 13.0947 | 0.527600 | ||||||||
\(617\) | 24.0305 | 0.967433 | 0.483717 | − | 0.875225i | \(-0.339287\pi\) | ||||
0.483717 | + | 0.875225i | \(0.339287\pi\) | |||||||
\(618\) | −25.6213 | −1.03064 | ||||||||
\(619\) | −1.52246 | −0.0611929 | −0.0305964 | − | 0.999532i | \(-0.509741\pi\) | ||||
−0.0305964 | + | 0.999532i | \(0.509741\pi\) | |||||||
\(620\) | 15.9573 | 0.640860 | ||||||||
\(621\) | 6.67844 | 0.267997 | ||||||||
\(622\) | 26.1373 | 1.04801 | ||||||||
\(623\) | −2.17516 | −0.0871458 | ||||||||
\(624\) | 6.60095 | 0.264249 | ||||||||
\(625\) | 16.1731 | 0.646925 | ||||||||
\(626\) | −13.2889 | −0.531130 | ||||||||
\(627\) | −17.8273 | −0.711953 | ||||||||
\(628\) | 46.2451 | 1.84538 | ||||||||
\(629\) | 9.88638 | 0.394196 | ||||||||
\(630\) | 1.81241 | 0.0722082 | ||||||||
\(631\) | 6.44483 | 0.256564 | 0.128282 | − | 0.991738i | \(-0.459054\pi\) | ||||
0.128282 | + | 0.991738i | \(0.459054\pi\) | |||||||
\(632\) | 22.9992 | 0.914858 | ||||||||
\(633\) | 14.9669 | 0.594880 | ||||||||
\(634\) | 47.5688 | 1.88920 | ||||||||
\(635\) | −1.21224 | −0.0481062 | ||||||||
\(636\) | −9.03767 | −0.358367 | ||||||||
\(637\) | −5.78556 | −0.229232 | ||||||||
\(638\) | 93.8994 | 3.71751 | ||||||||
\(639\) | −28.0518 | −1.10971 | ||||||||
\(640\) | 11.0293 | 0.435973 | ||||||||
\(641\) | −18.0724 | −0.713817 | −0.356908 | − | 0.934139i | \(-0.616169\pi\) | ||||
−0.356908 | + | 0.934139i | \(0.616169\pi\) | |||||||
\(642\) | −10.3393 | −0.408059 | ||||||||
\(643\) | −39.9559 | −1.57571 | −0.787854 | − | 0.615862i | \(-0.788808\pi\) | ||||
−0.787854 | + | 0.615862i | \(0.788808\pi\) | |||||||
\(644\) | 3.14856 | 0.124070 | ||||||||
\(645\) | −4.35664 | −0.171543 | ||||||||
\(646\) | −26.3087 | −1.03510 | ||||||||
\(647\) | 2.90440 | 0.114184 | 0.0570920 | − | 0.998369i | \(-0.481817\pi\) | ||||
0.0570920 | + | 0.998369i | \(0.481817\pi\) | |||||||
\(648\) | −43.8588 | −1.72294 | ||||||||
\(649\) | −1.43307 | −0.0562528 | ||||||||
\(650\) | 9.83016 | 0.385571 | ||||||||
\(651\) | 0.887495 | 0.0347837 | ||||||||
\(652\) | 85.7675 | 3.35891 | ||||||||
\(653\) | −21.4532 | −0.839527 | −0.419763 | − | 0.907634i | \(-0.637887\pi\) | ||||
−0.419763 | + | 0.907634i | \(0.637887\pi\) | |||||||
\(654\) | 33.1051 | 1.29451 | ||||||||
\(655\) | 0.444567 | 0.0173707 | ||||||||
\(656\) | 19.7005 | 0.769175 | ||||||||
\(657\) | 23.5459 | 0.918613 | ||||||||
\(658\) | 6.29306 | 0.245329 | ||||||||
\(659\) | 31.1338 | 1.21280 | 0.606401 | − | 0.795159i | \(-0.292613\pi\) | ||||
0.606401 | + | 0.795159i | \(0.292613\pi\) | |||||||
\(660\) | −12.3084 | −0.479103 | ||||||||
\(661\) | −29.2519 | −1.13777 | −0.568883 | − | 0.822418i | \(-0.692624\pi\) | ||||
−0.568883 | + | 0.822418i | \(0.692624\pi\) | |||||||
\(662\) | −23.3308 | −0.906778 | ||||||||
\(663\) | −0.941283 | −0.0365564 | ||||||||
\(664\) | −55.5669 | −2.15641 | ||||||||
\(665\) | −1.53648 | −0.0595823 | ||||||||
\(666\) | −39.7941 | −1.54199 | ||||||||
\(667\) | 13.7475 | 0.532305 | ||||||||
\(668\) | 76.7018 | 2.96768 | ||||||||
\(669\) | 0.949083 | 0.0366937 | ||||||||
\(670\) | 11.8037 | 0.456017 | ||||||||
\(671\) | 53.6580 | 2.07145 | ||||||||
\(672\) | 3.38417 | 0.130547 | ||||||||
\(673\) | 36.2871 | 1.39877 | 0.699383 | − | 0.714747i | \(-0.253458\pi\) | ||||
0.699383 | + | 0.714747i | \(0.253458\pi\) | |||||||
\(674\) | 23.9247 | 0.921545 | ||||||||
\(675\) | 16.0867 | 0.619177 | ||||||||
\(676\) | −62.8686 | −2.41802 | ||||||||
\(677\) | 7.88088 | 0.302887 | 0.151443 | − | 0.988466i | \(-0.451608\pi\) | ||||
0.151443 | + | 0.988466i | \(0.451608\pi\) | |||||||
\(678\) | −34.7656 | −1.33517 | ||||||||
\(679\) | 4.84367 | 0.185883 | ||||||||
\(680\) | −11.0601 | −0.424135 | ||||||||
\(681\) | −10.2117 | −0.391313 | ||||||||
\(682\) | 49.5510 | 1.89741 | ||||||||
\(683\) | 2.54041 | 0.0972061 | 0.0486031 | − | 0.998818i | \(-0.484523\pi\) | ||||
0.0486031 | + | 0.998818i | \(0.484523\pi\) | |||||||
\(684\) | 76.1238 | 2.91067 | ||||||||
\(685\) | 11.0098 | 0.420663 | ||||||||
\(686\) | −12.5218 | −0.478085 | ||||||||
\(687\) | 3.95723 | 0.150978 | ||||||||
\(688\) | 100.644 | 3.83700 | ||||||||
\(689\) | −2.25368 | −0.0858583 | ||||||||
\(690\) | −2.50680 | −0.0954323 | ||||||||
\(691\) | 4.47391 | 0.170195 | 0.0850977 | − | 0.996373i | \(-0.472880\pi\) | ||||
0.0850977 | + | 0.996373i | \(0.472880\pi\) | |||||||
\(692\) | −36.3773 | −1.38286 | ||||||||
\(693\) | 4.04568 | 0.153683 | ||||||||
\(694\) | −60.4557 | −2.29487 | ||||||||
\(695\) | 0.846599 | 0.0321133 | ||||||||
\(696\) | 41.3104 | 1.56587 | ||||||||
\(697\) | −2.80925 | −0.106408 | ||||||||
\(698\) | 67.5910 | 2.55836 | ||||||||
\(699\) | 12.9571 | 0.490081 | ||||||||
\(700\) | 7.58408 | 0.286651 | ||||||||
\(701\) | −39.9123 | −1.50747 | −0.753733 | − | 0.657181i | \(-0.771749\pi\) | ||||
−0.753733 | + | 0.657181i | \(0.771749\pi\) | |||||||
\(702\) | 8.21868 | 0.310194 | ||||||||
\(703\) | 33.7357 | 1.27237 | ||||||||
\(704\) | 77.7413 | 2.92999 | ||||||||
\(705\) | −3.60173 | −0.135649 | ||||||||
\(706\) | −86.8423 | −3.26835 | ||||||||
\(707\) | −2.20357 | −0.0828737 | ||||||||
\(708\) | −1.03542 | −0.0389136 | ||||||||
\(709\) | 5.14595 | 0.193260 | 0.0966300 | − | 0.995320i | \(-0.469194\pi\) | ||||
0.0966300 | + | 0.995320i | \(0.469194\pi\) | |||||||
\(710\) | 22.8406 | 0.857191 | ||||||||
\(711\) | 7.10573 | 0.266486 | ||||||||
\(712\) | −53.4286 | −2.00232 | ||||||||
\(713\) | 7.25459 | 0.271687 | ||||||||
\(714\) | −1.01023 | −0.0378070 | ||||||||
\(715\) | −3.06928 | −0.114784 | ||||||||
\(716\) | 21.2570 | 0.794411 | ||||||||
\(717\) | 20.0628 | 0.749259 | ||||||||
\(718\) | 42.7399 | 1.59504 | ||||||||
\(719\) | 41.1369 | 1.53415 | 0.767074 | − | 0.641559i | \(-0.221712\pi\) | ||||
0.767074 | + | 0.641559i | \(0.221712\pi\) | |||||||
\(720\) | 23.9630 | 0.893049 | ||||||||
\(721\) | −4.92923 | −0.183574 | ||||||||
\(722\) | −39.0979 | −1.45507 | ||||||||
\(723\) | −9.04327 | −0.336323 | ||||||||
\(724\) | 21.0184 | 0.781142 | ||||||||
\(725\) | 33.1143 | 1.22983 | ||||||||
\(726\) | −18.8889 | −0.701031 | ||||||||
\(727\) | 13.0398 | 0.483619 | 0.241810 | − | 0.970324i | \(-0.422259\pi\) | ||||
0.241810 | + | 0.970324i | \(0.422259\pi\) | |||||||
\(728\) | 2.35930 | 0.0874414 | ||||||||
\(729\) | −6.30109 | −0.233374 | ||||||||
\(730\) | −19.1717 | −0.709577 | ||||||||
\(731\) | −14.3516 | −0.530813 | ||||||||
\(732\) | 38.7692 | 1.43295 | ||||||||
\(733\) | −1.85333 | −0.0684541 | −0.0342271 | − | 0.999414i | \(-0.510897\pi\) | ||||
−0.0342271 | + | 0.999414i | \(0.510897\pi\) | |||||||
\(734\) | −45.1702 | −1.66726 | ||||||||
\(735\) | 3.55383 | 0.131085 | ||||||||
\(736\) | 27.6630 | 1.01967 | ||||||||
\(737\) | 26.3484 | 0.970555 | ||||||||
\(738\) | 11.3076 | 0.416240 | ||||||||
\(739\) | 25.8555 | 0.951111 | 0.475556 | − | 0.879686i | \(-0.342247\pi\) | ||||
0.475556 | + | 0.879686i | \(0.342247\pi\) | |||||||
\(740\) | 23.2919 | 0.856228 | ||||||||
\(741\) | −3.21198 | −0.117995 | ||||||||
\(742\) | −2.41876 | −0.0887956 | ||||||||
\(743\) | 39.4269 | 1.44643 | 0.723217 | − | 0.690621i | \(-0.242663\pi\) | ||||
0.723217 | + | 0.690621i | \(0.242663\pi\) | |||||||
\(744\) | 21.7996 | 0.799213 | ||||||||
\(745\) | −10.6436 | −0.389952 | ||||||||
\(746\) | 17.7897 | 0.651327 | ||||||||
\(747\) | −17.1677 | −0.628134 | ||||||||
\(748\) | −40.5461 | −1.48251 | ||||||||
\(749\) | −1.98916 | −0.0726822 | ||||||||
\(750\) | −12.9211 | −0.471813 | ||||||||
\(751\) | −7.85358 | −0.286581 | −0.143291 | − | 0.989681i | \(-0.545768\pi\) | ||||
−0.143291 | + | 0.989681i | \(0.545768\pi\) | |||||||
\(752\) | 83.2045 | 3.03415 | ||||||||
\(753\) | 3.39130 | 0.123586 | ||||||||
\(754\) | 16.9180 | 0.616119 | ||||||||
\(755\) | −5.74713 | −0.209159 | ||||||||
\(756\) | 6.34081 | 0.230613 | ||||||||
\(757\) | −21.1649 | −0.769251 | −0.384626 | − | 0.923073i | \(-0.625669\pi\) | ||||
−0.384626 | + | 0.923073i | \(0.625669\pi\) | |||||||
\(758\) | −16.4190 | −0.596366 | ||||||||
\(759\) | −5.59571 | −0.203111 | ||||||||
\(760\) | −37.7408 | −1.36900 | ||||||||
\(761\) | −17.0686 | −0.618738 | −0.309369 | − | 0.950942i | \(-0.600118\pi\) | ||||
−0.309369 | + | 0.950942i | \(0.600118\pi\) | |||||||
\(762\) | −2.71978 | −0.0985272 | ||||||||
\(763\) | 6.36903 | 0.230574 | ||||||||
\(764\) | −77.4308 | −2.80135 | ||||||||
\(765\) | −3.41708 | −0.123545 | ||||||||
\(766\) | −85.5486 | −3.09100 | ||||||||
\(767\) | −0.258199 | −0.00932302 | ||||||||
\(768\) | 2.77729 | 0.100217 | ||||||||
\(769\) | −3.26523 | −0.117747 | −0.0588736 | − | 0.998265i | \(-0.518751\pi\) | ||||
−0.0588736 | + | 0.998265i | \(0.518751\pi\) | |||||||
\(770\) | −3.29411 | −0.118711 | ||||||||
\(771\) | 16.1140 | 0.580332 | ||||||||
\(772\) | 66.0174 | 2.37602 | ||||||||
\(773\) | −51.1621 | −1.84017 | −0.920086 | − | 0.391715i | \(-0.871882\pi\) | ||||
−0.920086 | + | 0.391715i | \(0.871882\pi\) | |||||||
\(774\) | 57.7672 | 2.07640 | ||||||||
\(775\) | 17.4745 | 0.627703 | ||||||||
\(776\) | 118.976 | 4.27097 | ||||||||
\(777\) | 1.29543 | 0.0464731 | ||||||||
\(778\) | 41.9668 | 1.50458 | ||||||||
\(779\) | −9.58613 | −0.343459 | ||||||||
\(780\) | −2.21763 | −0.0794037 | ||||||||
\(781\) | 50.9849 | 1.82438 | ||||||||
\(782\) | −8.25789 | −0.295301 | ||||||||
\(783\) | 27.6858 | 0.989408 | ||||||||
\(784\) | −82.0979 | −2.93207 | ||||||||
\(785\) | −7.08358 | −0.252824 | ||||||||
\(786\) | 0.997431 | 0.0355772 | ||||||||
\(787\) | 25.7064 | 0.916334 | 0.458167 | − | 0.888866i | \(-0.348506\pi\) | ||||
0.458167 | + | 0.888866i | \(0.348506\pi\) | |||||||
\(788\) | −123.062 | −4.38391 | ||||||||
\(789\) | 0.858599 | 0.0305669 | ||||||||
\(790\) | −5.78568 | −0.205845 | ||||||||
\(791\) | −6.68849 | −0.237815 | ||||||||
\(792\) | 99.3745 | 3.53112 | ||||||||
\(793\) | 9.66768 | 0.343309 | ||||||||
\(794\) | −83.7956 | −2.97379 | ||||||||
\(795\) | 1.38434 | 0.0490975 | ||||||||
\(796\) | −66.9603 | −2.37334 | ||||||||
\(797\) | 39.3099 | 1.39243 | 0.696214 | − | 0.717834i | \(-0.254866\pi\) | ||||
0.696214 | + | 0.717834i | \(0.254866\pi\) | |||||||
\(798\) | −3.44726 | −0.122032 | ||||||||
\(799\) | −11.8648 | −0.419747 | ||||||||
\(800\) | 66.6333 | 2.35584 | ||||||||
\(801\) | −16.5071 | −0.583249 | ||||||||
\(802\) | 82.1909 | 2.90226 | ||||||||
\(803\) | −42.7953 | −1.51021 | ||||||||
\(804\) | 19.0373 | 0.671394 | ||||||||
\(805\) | −0.482279 | −0.0169981 | ||||||||
\(806\) | 8.92771 | 0.314465 | ||||||||
\(807\) | 3.07422 | 0.108218 | ||||||||
\(808\) | −54.1265 | −1.90416 | ||||||||
\(809\) | −10.9338 | −0.384412 | −0.192206 | − | 0.981355i | \(-0.561564\pi\) | ||||
−0.192206 | + | 0.981355i | \(0.561564\pi\) | |||||||
\(810\) | 11.0331 | 0.387665 | ||||||||
\(811\) | 37.9895 | 1.33399 | 0.666995 | − | 0.745062i | \(-0.267580\pi\) | ||||
0.666995 | + | 0.745062i | \(0.267580\pi\) | |||||||
\(812\) | 13.0525 | 0.458052 | ||||||||
\(813\) | −9.04553 | −0.317241 | ||||||||
\(814\) | 72.3268 | 2.53505 | ||||||||
\(815\) | −13.1374 | −0.460183 | ||||||||
\(816\) | −13.3569 | −0.467586 | ||||||||
\(817\) | −48.9725 | −1.71333 | ||||||||
\(818\) | −2.10827 | −0.0737139 | ||||||||
\(819\) | 0.728919 | 0.0254705 | ||||||||
\(820\) | −6.61849 | −0.231128 | ||||||||
\(821\) | 38.8748 | 1.35674 | 0.678370 | − | 0.734720i | \(-0.262686\pi\) | ||||
0.678370 | + | 0.734720i | \(0.262686\pi\) | |||||||
\(822\) | 24.7016 | 0.861568 | ||||||||
\(823\) | 54.0363 | 1.88359 | 0.941794 | − | 0.336190i | \(-0.109138\pi\) | ||||
0.941794 | + | 0.336190i | \(0.109138\pi\) | |||||||
\(824\) | −121.077 | −4.21792 | ||||||||
\(825\) | −13.4787 | −0.469267 | ||||||||
\(826\) | −0.277112 | −0.00964196 | ||||||||
\(827\) | 46.3264 | 1.61093 | 0.805463 | − | 0.592646i | \(-0.201917\pi\) | ||||
0.805463 | + | 0.592646i | \(0.201917\pi\) | |||||||
\(828\) | 23.8941 | 0.830378 | ||||||||
\(829\) | −19.8963 | −0.691027 | −0.345513 | − | 0.938414i | \(-0.612295\pi\) | ||||
−0.345513 | + | 0.938414i | \(0.612295\pi\) | |||||||
\(830\) | 13.9784 | 0.485199 | ||||||||
\(831\) | 1.33831 | 0.0464255 | ||||||||
\(832\) | 14.0068 | 0.485599 | ||||||||
\(833\) | 11.7070 | 0.405624 | ||||||||
\(834\) | 1.89943 | 0.0657719 | ||||||||
\(835\) | −11.7488 | −0.406583 | ||||||||
\(836\) | −138.357 | −4.78518 | ||||||||
\(837\) | 14.6099 | 0.504991 | ||||||||
\(838\) | −8.04551 | −0.277928 | ||||||||
\(839\) | −26.7054 | −0.921973 | −0.460987 | − | 0.887407i | \(-0.652504\pi\) | ||||
−0.460987 | + | 0.887407i | \(0.652504\pi\) | |||||||
\(840\) | −1.44922 | −0.0500028 | ||||||||
\(841\) | 27.9908 | 0.965198 | ||||||||
\(842\) | 1.05699 | 0.0364263 | ||||||||
\(843\) | −6.31075 | −0.217354 | ||||||||
\(844\) | 116.158 | 3.99832 | ||||||||
\(845\) | 9.62987 | 0.331277 | ||||||||
\(846\) | 47.7575 | 1.64194 | ||||||||
\(847\) | −3.63399 | −0.124865 | ||||||||
\(848\) | −31.9800 | −1.09820 | ||||||||
\(849\) | −21.8436 | −0.749671 | ||||||||
\(850\) | −19.8912 | −0.682262 | ||||||||
\(851\) | 10.5891 | 0.362990 | ||||||||
\(852\) | 36.8378 | 1.26204 | ||||||||
\(853\) | 7.29645 | 0.249826 | 0.124913 | − | 0.992168i | \(-0.460135\pi\) | ||||
0.124913 | + | 0.992168i | \(0.460135\pi\) | |||||||
\(854\) | 10.3759 | 0.355054 | ||||||||
\(855\) | −11.6602 | −0.398772 | ||||||||
\(856\) | −48.8599 | −1.67000 | ||||||||
\(857\) | −33.7955 | −1.15443 | −0.577216 | − | 0.816592i | \(-0.695861\pi\) | ||||
−0.577216 | + | 0.816592i | \(0.695861\pi\) | |||||||
\(858\) | −6.88624 | −0.235092 | ||||||||
\(859\) | −48.7499 | −1.66333 | −0.831663 | − | 0.555281i | \(-0.812611\pi\) | ||||
−0.831663 | + | 0.555281i | \(0.812611\pi\) | |||||||
\(860\) | −33.8118 | −1.15297 | ||||||||
\(861\) | −0.368100 | −0.0125448 | ||||||||
\(862\) | −79.7077 | −2.71486 | ||||||||
\(863\) | 0.778138 | 0.0264881 | 0.0132441 | − | 0.999912i | \(-0.495784\pi\) | ||||
0.0132441 | + | 0.999912i | \(0.495784\pi\) | |||||||
\(864\) | 55.7100 | 1.89529 | ||||||||
\(865\) | 5.57207 | 0.189456 | ||||||||
\(866\) | 16.5468 | 0.562283 | ||||||||
\(867\) | −9.29672 | −0.315733 | ||||||||
\(868\) | 6.88783 | 0.233788 | ||||||||
\(869\) | −12.9148 | −0.438106 | ||||||||
\(870\) | −10.3921 | −0.352324 | ||||||||
\(871\) | 4.74724 | 0.160854 | ||||||||
\(872\) | 156.443 | 5.29783 | ||||||||
\(873\) | 36.7582 | 1.24408 | ||||||||
\(874\) | −28.1787 | −0.953159 | ||||||||
\(875\) | −2.48587 | −0.0840377 | ||||||||
\(876\) | −30.9206 | −1.04471 | ||||||||
\(877\) | 45.5552 | 1.53829 | 0.769144 | − | 0.639075i | \(-0.220683\pi\) | ||||
0.769144 | + | 0.639075i | \(0.220683\pi\) | |||||||
\(878\) | −36.2934 | −1.22484 | ||||||||
\(879\) | −2.95688 | −0.0997330 | ||||||||
\(880\) | −43.5534 | −1.46819 | ||||||||
\(881\) | −35.2520 | −1.18767 | −0.593835 | − | 0.804587i | \(-0.702387\pi\) | ||||
−0.593835 | + | 0.804587i | \(0.702387\pi\) | |||||||
\(882\) | −47.1223 | −1.58669 | ||||||||
\(883\) | 24.5755 | 0.827030 | 0.413515 | − | 0.910497i | \(-0.364301\pi\) | ||||
0.413515 | + | 0.910497i | \(0.364301\pi\) | |||||||
\(884\) | −7.30528 | −0.245703 | ||||||||
\(885\) | 0.158601 | 0.00533131 | ||||||||
\(886\) | 64.7356 | 2.17484 | ||||||||
\(887\) | −42.5525 | −1.42877 | −0.714387 | − | 0.699751i | \(-0.753294\pi\) | ||||
−0.714387 | + | 0.699751i | \(0.753294\pi\) | |||||||
\(888\) | 31.8197 | 1.06780 | ||||||||
\(889\) | −0.523253 | −0.0175493 | ||||||||
\(890\) | 13.4405 | 0.450527 | ||||||||
\(891\) | 24.6283 | 0.825078 | ||||||||
\(892\) | 7.36582 | 0.246626 | ||||||||
\(893\) | −40.4867 | −1.35484 | ||||||||
\(894\) | −23.8801 | −0.798669 | ||||||||
\(895\) | −3.25603 | −0.108837 | ||||||||
\(896\) | 4.76073 | 0.159045 | ||||||||
\(897\) | −1.00819 | −0.0336625 | ||||||||
\(898\) | −44.2319 | −1.47604 | ||||||||
\(899\) | 30.0742 | 1.00303 | ||||||||
\(900\) | 57.5550 | 1.91850 | ||||||||
\(901\) | 4.56029 | 0.151925 | ||||||||
\(902\) | −20.5519 | −0.684305 | ||||||||
\(903\) | −1.88051 | −0.0625794 | ||||||||
\(904\) | −164.290 | −5.46421 | ||||||||
\(905\) | −3.21948 | −0.107019 | ||||||||
\(906\) | −12.8943 | −0.428383 | ||||||||
\(907\) | −31.8406 | −1.05725 | −0.528625 | − | 0.848855i | \(-0.677292\pi\) | ||||
−0.528625 | + | 0.848855i | \(0.677292\pi\) | |||||||
\(908\) | −79.2528 | −2.63010 | ||||||||
\(909\) | −16.7227 | −0.554657 | ||||||||
\(910\) | −0.593506 | −0.0196745 | ||||||||
\(911\) | 53.3020 | 1.76597 | 0.882986 | − | 0.469399i | \(-0.155529\pi\) | ||||
0.882986 | + | 0.469399i | \(0.155529\pi\) | |||||||
\(912\) | −45.5783 | −1.50925 | ||||||||
\(913\) | 31.2028 | 1.03266 | ||||||||
\(914\) | 9.20718 | 0.304547 | ||||||||
\(915\) | −5.93845 | −0.196319 | ||||||||
\(916\) | 30.7120 | 1.01475 | ||||||||
\(917\) | 0.191894 | 0.00633689 | ||||||||
\(918\) | −16.6304 | −0.548884 | ||||||||
\(919\) | 2.20502 | 0.0727370 | 0.0363685 | − | 0.999338i | \(-0.488421\pi\) | ||||
0.0363685 | + | 0.999338i | \(0.488421\pi\) | |||||||
\(920\) | −11.8463 | −0.390560 | ||||||||
\(921\) | 21.5571 | 0.710332 | ||||||||
\(922\) | 48.9651 | 1.61258 | ||||||||
\(923\) | 9.18606 | 0.302363 | ||||||||
\(924\) | −5.31281 | −0.174779 | ||||||||
\(925\) | 25.5065 | 0.838650 | ||||||||
\(926\) | −18.9648 | −0.623223 | ||||||||
\(927\) | −37.4075 | −1.22862 | ||||||||
\(928\) | 114.678 | 3.76450 | ||||||||
\(929\) | −32.5888 | −1.06920 | −0.534602 | − | 0.845104i | \(-0.679538\pi\) | ||||
−0.534602 | + | 0.845104i | \(0.679538\pi\) | |||||||
\(930\) | −5.48392 | −0.179825 | ||||||||
\(931\) | 39.9483 | 1.30925 | ||||||||
\(932\) | 100.560 | 3.29394 | ||||||||
\(933\) | −6.45706 | −0.211395 | ||||||||
\(934\) | 13.9010 | 0.454856 | ||||||||
\(935\) | 6.21064 | 0.203110 | ||||||||
\(936\) | 17.9045 | 0.585227 | ||||||||
\(937\) | 34.8932 | 1.13991 | 0.569956 | − | 0.821675i | \(-0.306960\pi\) | ||||
0.569956 | + | 0.821675i | \(0.306960\pi\) | |||||||
\(938\) | 5.09498 | 0.166357 | ||||||||
\(939\) | 3.28293 | 0.107134 | ||||||||
\(940\) | −27.9530 | −0.911726 | ||||||||
\(941\) | 18.8006 | 0.612882 | 0.306441 | − | 0.951890i | \(-0.400862\pi\) | ||||
0.306441 | + | 0.951890i | \(0.400862\pi\) | |||||||
\(942\) | −15.8927 | −0.517813 | ||||||||
\(943\) | −3.00894 | −0.0979845 | ||||||||
\(944\) | −3.66387 | −0.119249 | ||||||||
\(945\) | −0.971251 | −0.0315948 | ||||||||
\(946\) | −104.993 | −3.41363 | ||||||||
\(947\) | −41.2510 | −1.34048 | −0.670238 | − | 0.742146i | \(-0.733808\pi\) | ||||
−0.670238 | + | 0.742146i | \(0.733808\pi\) | |||||||
\(948\) | −9.33128 | −0.303066 | ||||||||
\(949\) | −7.71052 | −0.250294 | ||||||||
\(950\) | −67.8755 | −2.20217 | ||||||||
\(951\) | −11.7516 | −0.381071 | ||||||||
\(952\) | −4.77401 | −0.154726 | ||||||||
\(953\) | −15.0306 | −0.486888 | −0.243444 | − | 0.969915i | \(-0.578277\pi\) | ||||
−0.243444 | + | 0.969915i | \(0.578277\pi\) | |||||||
\(954\) | −18.3558 | −0.594291 | ||||||||
\(955\) | 11.8604 | 0.383795 | ||||||||
\(956\) | 155.707 | 5.03593 | ||||||||
\(957\) | −23.1972 | −0.749860 | ||||||||
\(958\) | −40.5681 | −1.31070 | ||||||||
\(959\) | 4.75229 | 0.153460 | ||||||||
\(960\) | −8.60380 | −0.277687 | ||||||||
\(961\) | −15.1297 | −0.488056 | ||||||||
\(962\) | 13.0313 | 0.420145 | ||||||||
\(963\) | −15.0955 | −0.486447 | ||||||||
\(964\) | −70.1847 | −2.26050 | ||||||||
\(965\) | −10.1122 | −0.325523 | ||||||||
\(966\) | −1.08204 | −0.0348141 | ||||||||
\(967\) | 26.1840 | 0.842020 | 0.421010 | − | 0.907056i | \(-0.361676\pi\) | ||||
0.421010 | + | 0.907056i | \(0.361676\pi\) | |||||||
\(968\) | −89.2621 | −2.86899 | ||||||||
\(969\) | 6.49939 | 0.208790 | ||||||||
\(970\) | −29.9295 | −0.960979 | ||||||||
\(971\) | 10.2956 | 0.330402 | 0.165201 | − | 0.986260i | \(-0.447173\pi\) | ||||
0.165201 | + | 0.986260i | \(0.447173\pi\) | |||||||
\(972\) | 74.0565 | 2.37536 | ||||||||
\(973\) | 0.365428 | 0.0117151 | ||||||||
\(974\) | −63.6653 | −2.03997 | ||||||||
\(975\) | −2.42848 | −0.0777736 | ||||||||
\(976\) | 137.186 | 4.39120 | ||||||||
\(977\) | 13.5033 | 0.432008 | 0.216004 | − | 0.976392i | \(-0.430698\pi\) | ||||
0.216004 | + | 0.976392i | \(0.430698\pi\) | |||||||
\(978\) | −29.4751 | −0.942510 | ||||||||
\(979\) | 30.0021 | 0.958870 | ||||||||
\(980\) | 27.5812 | 0.881050 | ||||||||
\(981\) | 48.3340 | 1.54319 | ||||||||
\(982\) | −69.4334 | −2.21571 | ||||||||
\(983\) | 33.8510 | 1.07968 | 0.539840 | − | 0.841768i | \(-0.318485\pi\) | ||||
0.539840 | + | 0.841768i | \(0.318485\pi\) | |||||||
\(984\) | −9.04169 | −0.288238 | ||||||||
\(985\) | 18.8500 | 0.600610 | ||||||||
\(986\) | −34.2334 | −1.09021 | ||||||||
\(987\) | −1.55466 | −0.0494854 | ||||||||
\(988\) | −24.9281 | −0.793068 | ||||||||
\(989\) | −15.3717 | −0.488793 | ||||||||
\(990\) | −24.9987 | −0.794510 | ||||||||
\(991\) | 39.6661 | 1.26004 | 0.630018 | − | 0.776581i | \(-0.283048\pi\) | ||||
0.630018 | + | 0.776581i | \(0.283048\pi\) | |||||||
\(992\) | 60.5161 | 1.92139 | ||||||||
\(993\) | 5.76373 | 0.182906 | ||||||||
\(994\) | 9.85895 | 0.312707 | ||||||||
\(995\) | 10.2566 | 0.325157 | ||||||||
\(996\) | 22.5448 | 0.714358 | ||||||||
\(997\) | 1.15607 | 0.0366131 | 0.0183065 | − | 0.999832i | \(-0.494173\pi\) | ||||
0.0183065 | + | 0.999832i | \(0.494173\pi\) | |||||||
\(998\) | 100.283 | 3.17440 | ||||||||
\(999\) | 21.3252 | 0.674699 |
(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 | 6043.2.a.c.1.4 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6043.2.a.c.1.4 | ✓ | 259 | 1.1 | even | 1 | trivial |