Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, 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("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(0\) |
Dimension: | \(179\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54699 | −1.80100 | −0.900498 | − | 0.434860i | \(-0.856798\pi\) | ||||
−0.900498 | + | 0.434860i | \(0.856798\pi\) | |||||||
\(3\) | −0.919443 | −0.530841 | −0.265420 | − | 0.964133i | \(-0.585511\pi\) | ||||
−0.265420 | + | 0.964133i | \(0.585511\pi\) | |||||||
\(4\) | 4.48717 | 2.24359 | ||||||||
\(5\) | −0.00498874 | −0.00223103 | −0.00111552 | − | 0.999999i | \(-0.500355\pi\) | ||||
−0.00111552 | + | 0.999999i | \(0.500355\pi\) | |||||||
\(6\) | 2.34182 | 0.956042 | ||||||||
\(7\) | −0.132134 | −0.0499420 | −0.0249710 | − | 0.999688i | \(-0.507949\pi\) | ||||
−0.0249710 | + | 0.999688i | \(0.507949\pi\) | |||||||
\(8\) | −6.33481 | −2.23969 | ||||||||
\(9\) | −2.15462 | −0.718208 | ||||||||
\(10\) | 0.0127063 | 0.00401808 | ||||||||
\(11\) | 5.60667 | 1.69047 | 0.845237 | − | 0.534392i | \(-0.179459\pi\) | ||||
0.845237 | + | 0.534392i | \(0.179459\pi\) | |||||||
\(12\) | −4.12570 | −1.19099 | ||||||||
\(13\) | 4.28134 | 1.18743 | 0.593715 | − | 0.804675i | \(-0.297661\pi\) | ||||
0.593715 | + | 0.804675i | \(0.297661\pi\) | |||||||
\(14\) | 0.336545 | 0.0899454 | ||||||||
\(15\) | 0.00458687 | 0.00118432 | ||||||||
\(16\) | 7.16038 | 1.79009 | ||||||||
\(17\) | −5.76338 | −1.39783 | −0.698913 | − | 0.715207i | \(-0.746332\pi\) | ||||
−0.698913 | + | 0.715207i | \(0.746332\pi\) | |||||||
\(18\) | 5.48781 | 1.29349 | ||||||||
\(19\) | −6.95640 | −1.59591 | −0.797954 | − | 0.602718i | \(-0.794084\pi\) | ||||
−0.797954 | + | 0.602718i | \(0.794084\pi\) | |||||||
\(20\) | −0.0223854 | −0.00500552 | ||||||||
\(21\) | 0.121490 | 0.0265113 | ||||||||
\(22\) | −14.2801 | −3.04454 | ||||||||
\(23\) | 6.39969 | 1.33443 | 0.667214 | − | 0.744866i | \(-0.267487\pi\) | ||||
0.667214 | + | 0.744866i | \(0.267487\pi\) | |||||||
\(24\) | 5.82450 | 1.18892 | ||||||||
\(25\) | −4.99998 | −0.999995 | ||||||||
\(26\) | −10.9045 | −2.13856 | ||||||||
\(27\) | 4.73938 | 0.912095 | ||||||||
\(28\) | −0.592909 | −0.112049 | ||||||||
\(29\) | 1.11344 | 0.206760 | 0.103380 | − | 0.994642i | \(-0.467034\pi\) | ||||
0.103380 | + | 0.994642i | \(0.467034\pi\) | |||||||
\(30\) | −0.0116827 | −0.00213296 | ||||||||
\(31\) | 6.59694 | 1.18485 | 0.592423 | − | 0.805627i | \(-0.298172\pi\) | ||||
0.592423 | + | 0.805627i | \(0.298172\pi\) | |||||||
\(32\) | −5.56780 | −0.984258 | ||||||||
\(33\) | −5.15501 | −0.897372 | ||||||||
\(34\) | 14.6793 | 2.51748 | ||||||||
\(35\) | 0.000659184 0 | 0.000111422 0 | ||||||||
\(36\) | −9.66817 | −1.61136 | ||||||||
\(37\) | 3.65341 | 0.600616 | 0.300308 | − | 0.953842i | \(-0.402911\pi\) | ||||
0.300308 | + | 0.953842i | \(0.402911\pi\) | |||||||
\(38\) | 17.7179 | 2.87423 | ||||||||
\(39\) | −3.93645 | −0.630336 | ||||||||
\(40\) | 0.0316028 | 0.00499683 | ||||||||
\(41\) | −3.61946 | −0.565265 | −0.282632 | − | 0.959228i | \(-0.591208\pi\) | ||||
−0.282632 | + | 0.959228i | \(0.591208\pi\) | |||||||
\(42\) | −0.309434 | −0.0477467 | ||||||||
\(43\) | 1.54973 | 0.236332 | 0.118166 | − | 0.992994i | \(-0.462299\pi\) | ||||
0.118166 | + | 0.992994i | \(0.462299\pi\) | |||||||
\(44\) | 25.1581 | 3.79272 | ||||||||
\(45\) | 0.0107489 | 0.00160235 | ||||||||
\(46\) | −16.3000 | −2.40330 | ||||||||
\(47\) | −0.423887 | −0.0618303 | −0.0309152 | − | 0.999522i | \(-0.509842\pi\) | ||||
−0.0309152 | + | 0.999522i | \(0.509842\pi\) | |||||||
\(48\) | −6.58356 | −0.950255 | ||||||||
\(49\) | −6.98254 | −0.997506 | ||||||||
\(50\) | 12.7349 | 1.80099 | ||||||||
\(51\) | 5.29910 | 0.742023 | ||||||||
\(52\) | 19.2111 | 2.66410 | ||||||||
\(53\) | −0.698466 | −0.0959417 | −0.0479709 | − | 0.998849i | \(-0.515275\pi\) | ||||
−0.0479709 | + | 0.998849i | \(0.515275\pi\) | |||||||
\(54\) | −12.0712 | −1.64268 | ||||||||
\(55\) | −0.0279702 | −0.00377150 | ||||||||
\(56\) | 0.837046 | 0.111855 | ||||||||
\(57\) | 6.39602 | 0.847173 | ||||||||
\(58\) | −2.83592 | −0.372374 | ||||||||
\(59\) | 0.427629 | 0.0556726 | 0.0278363 | − | 0.999612i | \(-0.491138\pi\) | ||||
0.0278363 | + | 0.999612i | \(0.491138\pi\) | |||||||
\(60\) | 0.0205821 | 0.00265713 | ||||||||
\(61\) | −8.82156 | −1.12949 | −0.564743 | − | 0.825267i | \(-0.691025\pi\) | ||||
−0.564743 | + | 0.825267i | \(0.691025\pi\) | |||||||
\(62\) | −16.8024 | −2.13390 | ||||||||
\(63\) | 0.284700 | 0.0358688 | ||||||||
\(64\) | −0.139594 | −0.0174493 | ||||||||
\(65\) | −0.0213585 | −0.00264920 | ||||||||
\(66\) | 13.1298 | 1.61616 | ||||||||
\(67\) | 14.5095 | 1.77262 | 0.886308 | − | 0.463096i | \(-0.153262\pi\) | ||||
0.886308 | + | 0.463096i | \(0.153262\pi\) | |||||||
\(68\) | −25.8613 | −3.13614 | ||||||||
\(69\) | −5.88415 | −0.708368 | ||||||||
\(70\) | −0.00167894 | −0.000200671 0 | ||||||||
\(71\) | 11.4271 | 1.35615 | 0.678073 | − | 0.734994i | \(-0.262815\pi\) | ||||
0.678073 | + | 0.734994i | \(0.262815\pi\) | |||||||
\(72\) | 13.6491 | 1.60857 | ||||||||
\(73\) | −7.78949 | −0.911691 | −0.455846 | − | 0.890059i | \(-0.650663\pi\) | ||||
−0.455846 | + | 0.890059i | \(0.650663\pi\) | |||||||
\(74\) | −9.30520 | −1.08171 | ||||||||
\(75\) | 4.59719 | 0.530838 | ||||||||
\(76\) | −31.2146 | −3.58056 | ||||||||
\(77\) | −0.740833 | −0.0844257 | ||||||||
\(78\) | 10.0261 | 1.13523 | ||||||||
\(79\) | 8.90525 | 1.00192 | 0.500960 | − | 0.865471i | \(-0.332981\pi\) | ||||
0.500960 | + | 0.865471i | \(0.332981\pi\) | |||||||
\(80\) | −0.0357213 | −0.00399376 | ||||||||
\(81\) | 2.10628 | 0.234031 | ||||||||
\(82\) | 9.21874 | 1.01804 | ||||||||
\(83\) | 3.14039 | 0.344702 | 0.172351 | − | 0.985036i | \(-0.444864\pi\) | ||||
0.172351 | + | 0.985036i | \(0.444864\pi\) | |||||||
\(84\) | 0.545146 | 0.0594803 | ||||||||
\(85\) | 0.0287520 | 0.00311860 | ||||||||
\(86\) | −3.94716 | −0.425633 | ||||||||
\(87\) | −1.02374 | −0.109757 | ||||||||
\(88\) | −35.5172 | −3.78615 | ||||||||
\(89\) | 9.35921 | 0.992074 | 0.496037 | − | 0.868301i | \(-0.334788\pi\) | ||||
0.496037 | + | 0.868301i | \(0.334788\pi\) | |||||||
\(90\) | −0.0273773 | −0.00288582 | ||||||||
\(91\) | −0.565712 | −0.0593027 | ||||||||
\(92\) | 28.7165 | 2.99390 | ||||||||
\(93\) | −6.06551 | −0.628964 | ||||||||
\(94\) | 1.07964 | 0.111356 | ||||||||
\(95\) | 0.0347037 | 0.00356053 | ||||||||
\(96\) | 5.11928 | 0.522484 | ||||||||
\(97\) | −8.80504 | −0.894016 | −0.447008 | − | 0.894530i | \(-0.647510\pi\) | ||||
−0.447008 | + | 0.894530i | \(0.647510\pi\) | |||||||
\(98\) | 17.7845 | 1.79650 | ||||||||
\(99\) | −12.0803 | −1.21411 | ||||||||
\(100\) | −22.4358 | −2.24358 | ||||||||
\(101\) | 3.60218 | 0.358431 | 0.179215 | − | 0.983810i | \(-0.442644\pi\) | ||||
0.179215 | + | 0.983810i | \(0.442644\pi\) | |||||||
\(102\) | −13.4968 | −1.33638 | ||||||||
\(103\) | −1.56121 | −0.153830 | −0.0769151 | − | 0.997038i | \(-0.524507\pi\) | ||||
−0.0769151 | + | 0.997038i | \(0.524507\pi\) | |||||||
\(104\) | −27.1215 | −2.65948 | ||||||||
\(105\) | −0.000606082 0 | −5.91476e−5 0 | ||||||||
\(106\) | 1.77899 | 0.172791 | ||||||||
\(107\) | 9.60061 | 0.928126 | 0.464063 | − | 0.885802i | \(-0.346391\pi\) | ||||
0.464063 | + | 0.885802i | \(0.346391\pi\) | |||||||
\(108\) | 21.2664 | 2.04636 | ||||||||
\(109\) | −13.3335 | −1.27712 | −0.638559 | − | 0.769573i | \(-0.720469\pi\) | ||||
−0.638559 | + | 0.769573i | \(0.720469\pi\) | |||||||
\(110\) | 0.0712400 | 0.00679246 | ||||||||
\(111\) | −3.35910 | −0.318832 | ||||||||
\(112\) | −0.946131 | −0.0894010 | ||||||||
\(113\) | 5.39416 | 0.507440 | 0.253720 | − | 0.967278i | \(-0.418346\pi\) | ||||
0.253720 | + | 0.967278i | \(0.418346\pi\) | |||||||
\(114\) | −16.2906 | −1.52576 | ||||||||
\(115\) | −0.0319264 | −0.00297715 | ||||||||
\(116\) | 4.99619 | 0.463884 | ||||||||
\(117\) | −9.22468 | −0.852822 | ||||||||
\(118\) | −1.08917 | −0.100266 | ||||||||
\(119\) | 0.761540 | 0.0698103 | ||||||||
\(120\) | −0.0290569 | −0.00265252 | ||||||||
\(121\) | 20.4347 | 1.85770 | ||||||||
\(122\) | 22.4685 | 2.03420 | ||||||||
\(123\) | 3.32789 | 0.300066 | ||||||||
\(124\) | 29.6016 | 2.65830 | ||||||||
\(125\) | 0.0498873 | 0.00446206 | ||||||||
\(126\) | −0.725128 | −0.0645995 | ||||||||
\(127\) | −16.5934 | −1.47242 | −0.736211 | − | 0.676752i | \(-0.763387\pi\) | ||||
−0.736211 | + | 0.676752i | \(0.763387\pi\) | |||||||
\(128\) | 11.4912 | 1.01568 | ||||||||
\(129\) | −1.42489 | −0.125455 | ||||||||
\(130\) | 0.0544000 | 0.00477119 | ||||||||
\(131\) | −18.2276 | −1.59255 | −0.796275 | − | 0.604934i | \(-0.793199\pi\) | ||||
−0.796275 | + | 0.604934i | \(0.793199\pi\) | |||||||
\(132\) | −23.1314 | −2.01333 | ||||||||
\(133\) | 0.919179 | 0.0797029 | ||||||||
\(134\) | −36.9556 | −3.19247 | ||||||||
\(135\) | −0.0236436 | −0.00203491 | ||||||||
\(136\) | 36.5100 | 3.13070 | ||||||||
\(137\) | 13.6741 | 1.16826 | 0.584131 | − | 0.811660i | \(-0.301436\pi\) | ||||
0.584131 | + | 0.811660i | \(0.301436\pi\) | |||||||
\(138\) | 14.9869 | 1.27577 | ||||||||
\(139\) | 6.72038 | 0.570016 | 0.285008 | − | 0.958525i | \(-0.408004\pi\) | ||||
0.285008 | + | 0.958525i | \(0.408004\pi\) | |||||||
\(140\) | 0.00295787 | 0.000249986 0 | ||||||||
\(141\) | 0.389740 | 0.0328221 | ||||||||
\(142\) | −29.1047 | −2.44241 | ||||||||
\(143\) | 24.0041 | 2.00732 | ||||||||
\(144\) | −15.4279 | −1.28566 | ||||||||
\(145\) | −0.00555466 | −0.000461289 0 | ||||||||
\(146\) | 19.8398 | 1.64195 | ||||||||
\(147\) | 6.42005 | 0.529517 | ||||||||
\(148\) | 16.3935 | 1.34753 | ||||||||
\(149\) | 8.80851 | 0.721621 | 0.360810 | − | 0.932639i | \(-0.382500\pi\) | ||||
0.360810 | + | 0.932639i | \(0.382500\pi\) | |||||||
\(150\) | −11.7090 | −0.956037 | ||||||||
\(151\) | 3.55247 | 0.289096 | 0.144548 | − | 0.989498i | \(-0.453827\pi\) | ||||
0.144548 | + | 0.989498i | \(0.453827\pi\) | |||||||
\(152\) | 44.0675 | 3.57435 | ||||||||
\(153\) | 12.4179 | 1.00393 | ||||||||
\(154\) | 1.88690 | 0.152050 | ||||||||
\(155\) | −0.0329104 | −0.00264343 | ||||||||
\(156\) | −17.6635 | −1.41421 | ||||||||
\(157\) | −9.58055 | −0.764612 | −0.382306 | − | 0.924036i | \(-0.624870\pi\) | ||||
−0.382306 | + | 0.924036i | \(0.624870\pi\) | |||||||
\(158\) | −22.6816 | −1.80445 | ||||||||
\(159\) | 0.642200 | 0.0509298 | ||||||||
\(160\) | 0.0277764 | 0.00219591 | ||||||||
\(161\) | −0.845618 | −0.0666440 | ||||||||
\(162\) | −5.36468 | −0.421489 | ||||||||
\(163\) | 18.8960 | 1.48005 | 0.740024 | − | 0.672580i | \(-0.234814\pi\) | ||||
0.740024 | + | 0.672580i | \(0.234814\pi\) | |||||||
\(164\) | −16.2411 | −1.26822 | ||||||||
\(165\) | 0.0257170 | 0.00200207 | ||||||||
\(166\) | −7.99855 | −0.620808 | ||||||||
\(167\) | −23.5498 | −1.82233 | −0.911167 | − | 0.412037i | \(-0.864818\pi\) | ||||
−0.911167 | + | 0.412037i | \(0.864818\pi\) | |||||||
\(168\) | −0.769616 | −0.0593772 | ||||||||
\(169\) | 5.32988 | 0.409991 | ||||||||
\(170\) | −0.0732312 | −0.00561658 | ||||||||
\(171\) | 14.9884 | 1.14619 | ||||||||
\(172\) | 6.95392 | 0.530231 | ||||||||
\(173\) | 21.1821 | 1.61044 | 0.805221 | − | 0.592974i | \(-0.202046\pi\) | ||||
0.805221 | + | 0.592974i | \(0.202046\pi\) | |||||||
\(174\) | 2.60747 | 0.197671 | ||||||||
\(175\) | 0.660668 | 0.0499418 | ||||||||
\(176\) | 40.1459 | 3.02611 | ||||||||
\(177\) | −0.393181 | −0.0295533 | ||||||||
\(178\) | −23.8378 | −1.78672 | ||||||||
\(179\) | −21.2330 | −1.58703 | −0.793515 | − | 0.608550i | \(-0.791751\pi\) | ||||
−0.793515 | + | 0.608550i | \(0.791751\pi\) | |||||||
\(180\) | 0.0482320 | 0.00359500 | ||||||||
\(181\) | −14.7425 | −1.09580 | −0.547900 | − | 0.836544i | \(-0.684572\pi\) | ||||
−0.547900 | + | 0.836544i | \(0.684572\pi\) | |||||||
\(182\) | 1.44086 | 0.106804 | ||||||||
\(183\) | 8.11092 | 0.599577 | ||||||||
\(184\) | −40.5408 | −2.98871 | ||||||||
\(185\) | −0.0182259 | −0.00134000 | ||||||||
\(186\) | 15.4488 | 1.13276 | ||||||||
\(187\) | −32.3134 | −2.36299 | ||||||||
\(188\) | −1.90206 | −0.138722 | ||||||||
\(189\) | −0.626235 | −0.0455519 | ||||||||
\(190\) | −0.0883901 | −0.00641249 | ||||||||
\(191\) | −8.37038 | −0.605659 | −0.302830 | − | 0.953045i | \(-0.597931\pi\) | ||||
−0.302830 | + | 0.953045i | \(0.597931\pi\) | |||||||
\(192\) | 0.128349 | 0.00926280 | ||||||||
\(193\) | 5.05503 | 0.363869 | 0.181935 | − | 0.983311i | \(-0.441764\pi\) | ||||
0.181935 | + | 0.983311i | \(0.441764\pi\) | |||||||
\(194\) | 22.4264 | 1.61012 | ||||||||
\(195\) | 0.0196379 | 0.00140630 | ||||||||
\(196\) | −31.3319 | −2.23799 | ||||||||
\(197\) | −10.0050 | −0.712829 | −0.356415 | − | 0.934328i | \(-0.616001\pi\) | ||||
−0.356415 | + | 0.934328i | \(0.616001\pi\) | |||||||
\(198\) | 30.7683 | 2.18661 | ||||||||
\(199\) | −1.14529 | −0.0811871 | −0.0405936 | − | 0.999176i | \(-0.512925\pi\) | ||||
−0.0405936 | + | 0.999176i | \(0.512925\pi\) | |||||||
\(200\) | 31.6739 | 2.23968 | ||||||||
\(201\) | −13.3406 | −0.940977 | ||||||||
\(202\) | −9.17474 | −0.645532 | ||||||||
\(203\) | −0.147123 | −0.0103260 | ||||||||
\(204\) | 23.7780 | 1.66479 | ||||||||
\(205\) | 0.0180566 | 0.00126112 | ||||||||
\(206\) | 3.97638 | 0.277047 | ||||||||
\(207\) | −13.7889 | −0.958396 | ||||||||
\(208\) | 30.6560 | 2.12561 | ||||||||
\(209\) | −39.0022 | −2.69784 | ||||||||
\(210\) | 0.00154369 | 0.000106525 0 | ||||||||
\(211\) | −20.8380 | −1.43455 | −0.717275 | − | 0.696791i | \(-0.754611\pi\) | ||||
−0.717275 | + | 0.696791i | \(0.754611\pi\) | |||||||
\(212\) | −3.13414 | −0.215254 | ||||||||
\(213\) | −10.5066 | −0.719898 | ||||||||
\(214\) | −24.4527 | −1.67155 | ||||||||
\(215\) | −0.00773122 | −0.000527265 0 | ||||||||
\(216\) | −30.0231 | −2.04281 | ||||||||
\(217\) | −0.871682 | −0.0591736 | ||||||||
\(218\) | 33.9603 | 2.30008 | ||||||||
\(219\) | 7.16200 | 0.483963 | ||||||||
\(220\) | −0.125507 | −0.00846170 | ||||||||
\(221\) | −24.6750 | −1.65982 | ||||||||
\(222\) | 8.55560 | 0.574214 | ||||||||
\(223\) | 14.8917 | 0.997225 | 0.498612 | − | 0.866825i | \(-0.333843\pi\) | ||||
0.498612 | + | 0.866825i | \(0.333843\pi\) | |||||||
\(224\) | 0.735698 | 0.0491559 | ||||||||
\(225\) | 10.7731 | 0.718204 | ||||||||
\(226\) | −13.7389 | −0.913897 | ||||||||
\(227\) | 16.1586 | 1.07248 | 0.536240 | − | 0.844065i | \(-0.319844\pi\) | ||||
0.536240 | + | 0.844065i | \(0.319844\pi\) | |||||||
\(228\) | 28.7000 | 1.90071 | ||||||||
\(229\) | −4.63145 | −0.306055 | −0.153027 | − | 0.988222i | \(-0.548902\pi\) | ||||
−0.153027 | + | 0.988222i | \(0.548902\pi\) | |||||||
\(230\) | 0.0813163 | 0.00536184 | ||||||||
\(231\) | 0.681154 | 0.0448166 | ||||||||
\(232\) | −7.05342 | −0.463080 | ||||||||
\(233\) | −10.2327 | −0.670368 | −0.335184 | − | 0.942153i | \(-0.608799\pi\) | ||||
−0.335184 | + | 0.942153i | \(0.608799\pi\) | |||||||
\(234\) | 23.4952 | 1.53593 | ||||||||
\(235\) | 0.00211466 | 0.000137946 0 | ||||||||
\(236\) | 1.91885 | 0.124906 | ||||||||
\(237\) | −8.18787 | −0.531860 | ||||||||
\(238\) | −1.93964 | −0.125728 | ||||||||
\(239\) | 21.4387 | 1.38675 | 0.693377 | − | 0.720575i | \(-0.256122\pi\) | ||||
0.693377 | + | 0.720575i | \(0.256122\pi\) | |||||||
\(240\) | 0.0328437 | 0.00212005 | ||||||||
\(241\) | −4.76917 | −0.307209 | −0.153605 | − | 0.988132i | \(-0.549088\pi\) | ||||
−0.153605 | + | 0.988132i | \(0.549088\pi\) | |||||||
\(242\) | −52.0471 | −3.34571 | ||||||||
\(243\) | −16.1548 | −1.03633 | ||||||||
\(244\) | −39.5839 | −2.53410 | ||||||||
\(245\) | 0.0348341 | 0.00222547 | ||||||||
\(246\) | −8.47611 | −0.540417 | ||||||||
\(247\) | −29.7827 | −1.89503 | ||||||||
\(248\) | −41.7904 | −2.65369 | ||||||||
\(249\) | −2.88741 | −0.182982 | ||||||||
\(250\) | −0.127063 | −0.00803615 | ||||||||
\(251\) | −9.18029 | −0.579455 | −0.289728 | − | 0.957109i | \(-0.593565\pi\) | ||||
−0.289728 | + | 0.957109i | \(0.593565\pi\) | |||||||
\(252\) | 1.27750 | 0.0804747 | ||||||||
\(253\) | 35.8809 | 2.25581 | ||||||||
\(254\) | 42.2631 | 2.65183 | ||||||||
\(255\) | −0.0264359 | −0.00165548 | ||||||||
\(256\) | −28.9887 | −1.81179 | ||||||||
\(257\) | 19.2786 | 1.20257 | 0.601284 | − | 0.799036i | \(-0.294656\pi\) | ||||
0.601284 | + | 0.799036i | \(0.294656\pi\) | |||||||
\(258\) | 3.62919 | 0.225943 | ||||||||
\(259\) | −0.482740 | −0.0299960 | ||||||||
\(260\) | −0.0958393 | −0.00594370 | ||||||||
\(261\) | −2.39904 | −0.148497 | ||||||||
\(262\) | 46.4255 | 2.86818 | ||||||||
\(263\) | 9.27487 | 0.571913 | 0.285957 | − | 0.958243i | \(-0.407689\pi\) | ||||
0.285957 | + | 0.958243i | \(0.407689\pi\) | |||||||
\(264\) | 32.6560 | 2.00984 | ||||||||
\(265\) | 0.00348447 | 0.000214049 0 | ||||||||
\(266\) | −2.34114 | −0.143545 | ||||||||
\(267\) | −8.60526 | −0.526633 | ||||||||
\(268\) | 65.1066 | 3.97702 | ||||||||
\(269\) | 16.6379 | 1.01443 | 0.507215 | − | 0.861820i | \(-0.330675\pi\) | ||||
0.507215 | + | 0.861820i | \(0.330675\pi\) | |||||||
\(270\) | 0.0602200 | 0.00366487 | ||||||||
\(271\) | −7.42833 | −0.451239 | −0.225619 | − | 0.974216i | \(-0.572441\pi\) | ||||
−0.225619 | + | 0.974216i | \(0.572441\pi\) | |||||||
\(272\) | −41.2680 | −2.50224 | ||||||||
\(273\) | 0.520140 | 0.0314803 | ||||||||
\(274\) | −34.8280 | −2.10403 | ||||||||
\(275\) | −28.0332 | −1.69047 | ||||||||
\(276\) | −26.4032 | −1.58929 | ||||||||
\(277\) | 24.5833 | 1.47707 | 0.738534 | − | 0.674216i | \(-0.235518\pi\) | ||||
0.738534 | + | 0.674216i | \(0.235518\pi\) | |||||||
\(278\) | −17.1168 | −1.02660 | ||||||||
\(279\) | −14.2139 | −0.850966 | ||||||||
\(280\) | −0.00417581 | −0.000249552 0 | ||||||||
\(281\) | 3.44674 | 0.205615 | 0.102808 | − | 0.994701i | \(-0.467217\pi\) | ||||
0.102808 | + | 0.994701i | \(0.467217\pi\) | |||||||
\(282\) | −0.992666 | −0.0591124 | ||||||||
\(283\) | −13.1816 | −0.783567 | −0.391784 | − | 0.920057i | \(-0.628142\pi\) | ||||
−0.391784 | + | 0.920057i | \(0.628142\pi\) | |||||||
\(284\) | 51.2754 | 3.04263 | ||||||||
\(285\) | −0.0319081 | −0.00189007 | ||||||||
\(286\) | −61.1382 | −3.61517 | ||||||||
\(287\) | 0.478255 | 0.0282305 | ||||||||
\(288\) | 11.9965 | 0.706902 | ||||||||
\(289\) | 16.2166 | 0.953917 | ||||||||
\(290\) | 0.0141477 | 0.000830780 0 | ||||||||
\(291\) | 8.09573 | 0.474580 | ||||||||
\(292\) | −34.9528 | −2.04546 | ||||||||
\(293\) | 14.2934 | 0.835029 | 0.417514 | − | 0.908670i | \(-0.362901\pi\) | ||||
0.417514 | + | 0.908670i | \(0.362901\pi\) | |||||||
\(294\) | −16.3518 | −0.953658 | ||||||||
\(295\) | −0.00213333 | −0.000124207 0 | ||||||||
\(296\) | −23.1436 | −1.34520 | ||||||||
\(297\) | 26.5722 | 1.54187 | ||||||||
\(298\) | −22.4352 | −1.29964 | ||||||||
\(299\) | 27.3992 | 1.58454 | ||||||||
\(300\) | 20.6284 | 1.19098 | ||||||||
\(301\) | −0.204773 | −0.0118029 | ||||||||
\(302\) | −9.04812 | −0.520661 | ||||||||
\(303\) | −3.31200 | −0.190270 | ||||||||
\(304\) | −49.8105 | −2.85683 | ||||||||
\(305\) | 0.0440085 | 0.00251992 | ||||||||
\(306\) | −31.6284 | −1.80807 | ||||||||
\(307\) | −10.0890 | −0.575807 | −0.287903 | − | 0.957659i | \(-0.592958\pi\) | ||||
−0.287903 | + | 0.957659i | \(0.592958\pi\) | |||||||
\(308\) | −3.32424 | −0.189416 | ||||||||
\(309\) | 1.43544 | 0.0816593 | ||||||||
\(310\) | 0.0838227 | 0.00476081 | ||||||||
\(311\) | −13.3890 | −0.759221 | −0.379611 | − | 0.925146i | \(-0.623942\pi\) | ||||
−0.379611 | + | 0.925146i | \(0.623942\pi\) | |||||||
\(312\) | 24.9367 | 1.41176 | ||||||||
\(313\) | 14.1061 | 0.797323 | 0.398662 | − | 0.917098i | \(-0.369475\pi\) | ||||
0.398662 | + | 0.917098i | \(0.369475\pi\) | |||||||
\(314\) | 24.4016 | 1.37706 | ||||||||
\(315\) | −0.00142029 | −8.00245e−5 0 | ||||||||
\(316\) | 39.9594 | 2.24789 | ||||||||
\(317\) | 15.1958 | 0.853484 | 0.426742 | − | 0.904373i | \(-0.359661\pi\) | ||||
0.426742 | + | 0.904373i | \(0.359661\pi\) | |||||||
\(318\) | −1.63568 | −0.0917243 | ||||||||
\(319\) | 6.24268 | 0.349523 | ||||||||
\(320\) | 0.000696400 0 | 3.89300e−5 0 | ||||||||
\(321\) | −8.82722 | −0.492687 | ||||||||
\(322\) | 2.15378 | 0.120026 | ||||||||
\(323\) | 40.0924 | 2.23080 | ||||||||
\(324\) | 9.45123 | 0.525069 | ||||||||
\(325\) | −21.4066 | −1.18742 | ||||||||
\(326\) | −48.1280 | −2.66556 | ||||||||
\(327\) | 12.2594 | 0.677946 | ||||||||
\(328\) | 22.9286 | 1.26602 | ||||||||
\(329\) | 0.0560100 | 0.00308793 | ||||||||
\(330\) | −0.0655011 | −0.00360572 | ||||||||
\(331\) | 33.0920 | 1.81890 | 0.909451 | − | 0.415811i | \(-0.136502\pi\) | ||||
0.909451 | + | 0.415811i | \(0.136502\pi\) | |||||||
\(332\) | 14.0915 | 0.773370 | ||||||||
\(333\) | −7.87172 | −0.431367 | ||||||||
\(334\) | 59.9810 | 3.28202 | ||||||||
\(335\) | −0.0723841 | −0.00395477 | ||||||||
\(336\) | 0.869914 | 0.0474577 | ||||||||
\(337\) | 9.44809 | 0.514670 | 0.257335 | − | 0.966322i | \(-0.417156\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417156\pi\) | |||||||
\(338\) | −13.5752 | −0.738391 | ||||||||
\(339\) | −4.95962 | −0.269370 | ||||||||
\(340\) | 0.129015 | 0.00699684 | ||||||||
\(341\) | 36.9868 | 2.00295 | ||||||||
\(342\) | −38.1754 | −2.06429 | ||||||||
\(343\) | 1.84757 | 0.0997595 | ||||||||
\(344\) | −9.81727 | −0.529312 | ||||||||
\(345\) | 0.0293545 | 0.00158039 | ||||||||
\(346\) | −53.9506 | −2.90040 | ||||||||
\(347\) | 29.5273 | 1.58511 | 0.792554 | − | 0.609801i | \(-0.208751\pi\) | ||||
0.792554 | + | 0.609801i | \(0.208751\pi\) | |||||||
\(348\) | −4.59371 | −0.246249 | ||||||||
\(349\) | −22.2461 | −1.19081 | −0.595405 | − | 0.803426i | \(-0.703008\pi\) | ||||
−0.595405 | + | 0.803426i | \(0.703008\pi\) | |||||||
\(350\) | −1.68272 | −0.0899450 | ||||||||
\(351\) | 20.2909 | 1.08305 | ||||||||
\(352\) | −31.2168 | −1.66386 | ||||||||
\(353\) | 32.4164 | 1.72535 | 0.862674 | − | 0.505760i | \(-0.168788\pi\) | ||||
0.862674 | + | 0.505760i | \(0.168788\pi\) | |||||||
\(354\) | 1.00143 | 0.0532254 | ||||||||
\(355\) | −0.0570068 | −0.00302561 | ||||||||
\(356\) | 41.9964 | 2.22580 | ||||||||
\(357\) | −0.700193 | −0.0370581 | ||||||||
\(358\) | 54.0804 | 2.85824 | ||||||||
\(359\) | 11.1652 | 0.589276 | 0.294638 | − | 0.955609i | \(-0.404801\pi\) | ||||
0.294638 | + | 0.955609i | \(0.404801\pi\) | |||||||
\(360\) | −0.0680921 | −0.00358877 | ||||||||
\(361\) | 29.3916 | 1.54692 | ||||||||
\(362\) | 37.5490 | 1.97353 | ||||||||
\(363\) | −18.7886 | −0.986144 | ||||||||
\(364\) | −2.53845 | −0.133051 | ||||||||
\(365\) | 0.0388598 | 0.00203401 | ||||||||
\(366\) | −20.6585 | −1.07984 | ||||||||
\(367\) | 4.41283 | 0.230348 | 0.115174 | − | 0.993345i | \(-0.463258\pi\) | ||||
0.115174 | + | 0.993345i | \(0.463258\pi\) | |||||||
\(368\) | 45.8242 | 2.38875 | ||||||||
\(369\) | 7.79858 | 0.405978 | ||||||||
\(370\) | 0.0464213 | 0.00241333 | ||||||||
\(371\) | 0.0922913 | 0.00479153 | ||||||||
\(372\) | −27.2170 | −1.41114 | ||||||||
\(373\) | −30.0648 | −1.55670 | −0.778348 | − | 0.627833i | \(-0.783942\pi\) | ||||
−0.778348 | + | 0.627833i | \(0.783942\pi\) | |||||||
\(374\) | 82.3019 | 4.25573 | ||||||||
\(375\) | −0.0458685 | −0.00236864 | ||||||||
\(376\) | 2.68525 | 0.138481 | ||||||||
\(377\) | 4.76701 | 0.245513 | ||||||||
\(378\) | 1.59502 | 0.0820388 | ||||||||
\(379\) | 2.03871 | 0.104721 | 0.0523607 | − | 0.998628i | \(-0.483325\pi\) | ||||
0.0523607 | + | 0.998628i | \(0.483325\pi\) | |||||||
\(380\) | 0.155722 | 0.00798835 | ||||||||
\(381\) | 15.2566 | 0.781622 | ||||||||
\(382\) | 21.3193 | 1.09079 | ||||||||
\(383\) | 10.9931 | 0.561720 | 0.280860 | − | 0.959749i | \(-0.409380\pi\) | ||||
0.280860 | + | 0.959749i | \(0.409380\pi\) | |||||||
\(384\) | −10.5655 | −0.539167 | ||||||||
\(385\) | 0.00369582 | 0.000188357 0 | ||||||||
\(386\) | −12.8751 | −0.655327 | ||||||||
\(387\) | −3.33909 | −0.169736 | ||||||||
\(388\) | −39.5097 | −2.00580 | ||||||||
\(389\) | 33.0476 | 1.67558 | 0.837789 | − | 0.545994i | \(-0.183848\pi\) | ||||
0.837789 | + | 0.545994i | \(0.183848\pi\) | |||||||
\(390\) | −0.0500177 | −0.00253274 | ||||||||
\(391\) | −36.8839 | −1.86530 | ||||||||
\(392\) | 44.2331 | 2.23411 | ||||||||
\(393\) | 16.7592 | 0.845391 | ||||||||
\(394\) | 25.4828 | 1.28380 | ||||||||
\(395\) | −0.0444260 | −0.00223532 | ||||||||
\(396\) | −54.2062 | −2.72397 | ||||||||
\(397\) | −30.4586 | −1.52867 | −0.764337 | − | 0.644818i | \(-0.776933\pi\) | ||||
−0.764337 | + | 0.644818i | \(0.776933\pi\) | |||||||
\(398\) | 2.91703 | 0.146218 | ||||||||
\(399\) | −0.845133 | −0.0423096 | ||||||||
\(400\) | −35.8017 | −1.79009 | ||||||||
\(401\) | −9.58603 | −0.478704 | −0.239352 | − | 0.970933i | \(-0.576935\pi\) | ||||
−0.239352 | + | 0.970933i | \(0.576935\pi\) | |||||||
\(402\) | 33.9785 | 1.69470 | ||||||||
\(403\) | 28.2437 | 1.40692 | ||||||||
\(404\) | 16.1636 | 0.804170 | ||||||||
\(405\) | −0.0105077 | −0.000522131 0 | ||||||||
\(406\) | 0.374722 | 0.0185971 | ||||||||
\(407\) | 20.4834 | 1.01533 | ||||||||
\(408\) | −33.5688 | −1.66190 | ||||||||
\(409\) | 8.78053 | 0.434169 | 0.217085 | − | 0.976153i | \(-0.430345\pi\) | ||||
0.217085 | + | 0.976153i | \(0.430345\pi\) | |||||||
\(410\) | −0.0459899 | −0.00227128 | ||||||||
\(411\) | −12.5726 | −0.620161 | ||||||||
\(412\) | −7.00540 | −0.345131 | ||||||||
\(413\) | −0.0565045 | −0.00278040 | ||||||||
\(414\) | 35.1203 | 1.72607 | ||||||||
\(415\) | −0.0156666 | −0.000769043 0 | ||||||||
\(416\) | −23.8377 | −1.16874 | ||||||||
\(417\) | −6.17901 | −0.302587 | ||||||||
\(418\) | 99.3384 | 4.85880 | ||||||||
\(419\) | 5.01986 | 0.245236 | 0.122618 | − | 0.992454i | \(-0.460871\pi\) | ||||
0.122618 | + | 0.992454i | \(0.460871\pi\) | |||||||
\(420\) | −0.00271960 | −0.000132703 0 | ||||||||
\(421\) | −7.15490 | −0.348708 | −0.174354 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174354 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(422\) | 53.0743 | 2.58362 | ||||||||
\(423\) | 0.913318 | 0.0444070 | ||||||||
\(424\) | 4.42465 | 0.214880 | ||||||||
\(425\) | 28.8168 | 1.39782 | ||||||||
\(426\) | 26.7601 | 1.29653 | ||||||||
\(427\) | 1.16563 | 0.0564088 | ||||||||
\(428\) | 43.0796 | 2.08233 | ||||||||
\(429\) | −22.0704 | −1.06557 | ||||||||
\(430\) | 0.0196914 | 0.000949602 0 | ||||||||
\(431\) | 15.2131 | 0.732791 | 0.366395 | − | 0.930459i | \(-0.380592\pi\) | ||||
0.366395 | + | 0.930459i | \(0.380592\pi\) | |||||||
\(432\) | 33.9358 | 1.63274 | ||||||||
\(433\) | 37.7158 | 1.81251 | 0.906254 | − | 0.422734i | \(-0.138930\pi\) | ||||
0.906254 | + | 0.422734i | \(0.138930\pi\) | |||||||
\(434\) | 2.22017 | 0.106571 | ||||||||
\(435\) | 0.00510719 | 0.000244871 0 | ||||||||
\(436\) | −59.8297 | −2.86532 | ||||||||
\(437\) | −44.5188 | −2.12962 | ||||||||
\(438\) | −18.2416 | −0.871615 | ||||||||
\(439\) | −6.55294 | −0.312755 | −0.156377 | − | 0.987697i | \(-0.549982\pi\) | ||||
−0.156377 | + | 0.987697i | \(0.549982\pi\) | |||||||
\(440\) | 0.177186 | 0.00844702 | ||||||||
\(441\) | 15.0448 | 0.716417 | ||||||||
\(442\) | 62.8471 | 2.98933 | ||||||||
\(443\) | 37.4385 | 1.77876 | 0.889379 | − | 0.457171i | \(-0.151137\pi\) | ||||
0.889379 | + | 0.457171i | \(0.151137\pi\) | |||||||
\(444\) | −15.0729 | −0.715326 | ||||||||
\(445\) | −0.0466907 | −0.00221335 | ||||||||
\(446\) | −37.9292 | −1.79600 | ||||||||
\(447\) | −8.09892 | −0.383066 | ||||||||
\(448\) | 0.0184452 | 0.000871454 0 | ||||||||
\(449\) | 0.596286 | 0.0281405 | 0.0140702 | − | 0.999901i | \(-0.495521\pi\) | ||||
0.0140702 | + | 0.999901i | \(0.495521\pi\) | |||||||
\(450\) | −27.4389 | −1.29348 | ||||||||
\(451\) | −20.2931 | −0.955565 | ||||||||
\(452\) | 24.2045 | 1.13849 | ||||||||
\(453\) | −3.26630 | −0.153464 | ||||||||
\(454\) | −41.1557 | −1.93153 | ||||||||
\(455\) | 0.00282219 | 0.000132306 0 | ||||||||
\(456\) | −40.5176 | −1.89741 | ||||||||
\(457\) | 36.3978 | 1.70262 | 0.851309 | − | 0.524664i | \(-0.175809\pi\) | ||||
0.851309 | + | 0.524664i | \(0.175809\pi\) | |||||||
\(458\) | 11.7963 | 0.551203 | ||||||||
\(459\) | −27.3149 | −1.27495 | ||||||||
\(460\) | −0.143259 | −0.00667950 | ||||||||
\(461\) | −36.4399 | −1.69718 | −0.848589 | − | 0.529053i | \(-0.822547\pi\) | ||||
−0.848589 | + | 0.529053i | \(0.822547\pi\) | |||||||
\(462\) | −1.73489 | −0.0807145 | ||||||||
\(463\) | 38.0092 | 1.76644 | 0.883218 | − | 0.468962i | \(-0.155372\pi\) | ||||
0.883218 | + | 0.468962i | \(0.155372\pi\) | |||||||
\(464\) | 7.97263 | 0.370120 | ||||||||
\(465\) | 0.0302593 | 0.00140324 | ||||||||
\(466\) | 26.0627 | 1.20733 | ||||||||
\(467\) | 12.9150 | 0.597633 | 0.298816 | − | 0.954311i | \(-0.403408\pi\) | ||||
0.298816 | + | 0.954311i | \(0.403408\pi\) | |||||||
\(468\) | −41.3927 | −1.91338 | ||||||||
\(469\) | −1.91720 | −0.0885281 | ||||||||
\(470\) | −0.00538604 | −0.000248439 0 | ||||||||
\(471\) | 8.80878 | 0.405887 | ||||||||
\(472\) | −2.70895 | −0.124690 | ||||||||
\(473\) | 8.68884 | 0.399513 | ||||||||
\(474\) | 20.8545 | 0.957877 | ||||||||
\(475\) | 34.7818 | 1.59590 | ||||||||
\(476\) | 3.41716 | 0.156625 | ||||||||
\(477\) | 1.50493 | 0.0689061 | ||||||||
\(478\) | −54.6042 | −2.49754 | ||||||||
\(479\) | 21.7375 | 0.993211 | 0.496606 | − | 0.867976i | \(-0.334580\pi\) | ||||
0.496606 | + | 0.867976i | \(0.334580\pi\) | |||||||
\(480\) | −0.0255388 | −0.00116568 | ||||||||
\(481\) | 15.6415 | 0.713190 | ||||||||
\(482\) | 12.1471 | 0.553283 | ||||||||
\(483\) | 0.777498 | 0.0353774 | ||||||||
\(484\) | 91.6941 | 4.16791 | ||||||||
\(485\) | 0.0439261 | 0.00199458 | ||||||||
\(486\) | 41.1460 | 1.86642 | ||||||||
\(487\) | 33.8375 | 1.53332 | 0.766661 | − | 0.642052i | \(-0.221917\pi\) | ||||
0.766661 | + | 0.642052i | \(0.221917\pi\) | |||||||
\(488\) | 55.8829 | 2.52970 | ||||||||
\(489\) | −17.3738 | −0.785670 | ||||||||
\(490\) | −0.0887222 | −0.00400806 | ||||||||
\(491\) | −2.50531 | −0.113063 | −0.0565315 | − | 0.998401i | \(-0.518004\pi\) | ||||
−0.0565315 | + | 0.998401i | \(0.518004\pi\) | |||||||
\(492\) | 14.9328 | 0.673223 | ||||||||
\(493\) | −6.41717 | −0.289015 | ||||||||
\(494\) | 75.8564 | 3.41294 | ||||||||
\(495\) | 0.0602653 | 0.00270872 | ||||||||
\(496\) | 47.2366 | 2.12099 | ||||||||
\(497\) | −1.50991 | −0.0677287 | ||||||||
\(498\) | 7.35421 | 0.329550 | ||||||||
\(499\) | 18.9020 | 0.846169 | 0.423084 | − | 0.906090i | \(-0.360947\pi\) | ||||
0.423084 | + | 0.906090i | \(0.360947\pi\) | |||||||
\(500\) | 0.223853 | 0.0100110 | ||||||||
\(501\) | 21.6527 | 0.967369 | ||||||||
\(502\) | 23.3821 | 1.04360 | ||||||||
\(503\) | 11.4790 | 0.511824 | 0.255912 | − | 0.966700i | \(-0.417624\pi\) | ||||
0.255912 | + | 0.966700i | \(0.417624\pi\) | |||||||
\(504\) | −1.80352 | −0.0803351 | ||||||||
\(505\) | −0.0179704 | −0.000799671 0 | ||||||||
\(506\) | −91.3885 | −4.06271 | ||||||||
\(507\) | −4.90052 | −0.217640 | ||||||||
\(508\) | −74.4572 | −3.30351 | ||||||||
\(509\) | −3.17455 | −0.140709 | −0.0703547 | − | 0.997522i | \(-0.522413\pi\) | ||||
−0.0703547 | + | 0.997522i | \(0.522413\pi\) | |||||||
\(510\) | 0.0673320 | 0.00298151 | ||||||||
\(511\) | 1.02926 | 0.0455317 | ||||||||
\(512\) | 50.8517 | 2.24735 | ||||||||
\(513\) | −32.9691 | −1.45562 | ||||||||
\(514\) | −49.1025 | −2.16582 | ||||||||
\(515\) | 0.00778845 | 0.000343200 0 | ||||||||
\(516\) | −6.39373 | −0.281468 | ||||||||
\(517\) | −2.37659 | −0.104523 | ||||||||
\(518\) | 1.22954 | 0.0540227 | ||||||||
\(519\) | −19.4757 | −0.854889 | ||||||||
\(520\) | 0.135302 | 0.00593339 | ||||||||
\(521\) | 9.39862 | 0.411761 | 0.205880 | − | 0.978577i | \(-0.433994\pi\) | ||||
0.205880 | + | 0.978577i | \(0.433994\pi\) | |||||||
\(522\) | 6.11034 | 0.267442 | ||||||||
\(523\) | 19.3112 | 0.844421 | 0.422211 | − | 0.906498i | \(-0.361254\pi\) | ||||
0.422211 | + | 0.906498i | \(0.361254\pi\) | |||||||
\(524\) | −81.7903 | −3.57303 | ||||||||
\(525\) | −0.607447 | −0.0265111 | ||||||||
\(526\) | −23.6230 | −1.03001 | ||||||||
\(527\) | −38.0207 | −1.65621 | ||||||||
\(528\) | −36.9118 | −1.60638 | ||||||||
\(529\) | 17.9560 | 0.780696 | ||||||||
\(530\) | −0.00887492 | −0.000385502 0 | ||||||||
\(531\) | −0.921381 | −0.0399845 | ||||||||
\(532\) | 4.12452 | 0.178820 | ||||||||
\(533\) | −15.4961 | −0.671212 | ||||||||
\(534\) | 21.9175 | 0.948465 | ||||||||
\(535\) | −0.0478950 | −0.00207068 | ||||||||
\(536\) | −91.9149 | −3.97012 | ||||||||
\(537\) | 19.5226 | 0.842461 | ||||||||
\(538\) | −42.3766 | −1.82698 | ||||||||
\(539\) | −39.1488 | −1.68626 | ||||||||
\(540\) | −0.106093 | −0.00456551 | ||||||||
\(541\) | −3.83761 | −0.164992 | −0.0824959 | − | 0.996591i | \(-0.526289\pi\) | ||||
−0.0824959 | + | 0.996591i | \(0.526289\pi\) | |||||||
\(542\) | 18.9199 | 0.812679 | ||||||||
\(543\) | 13.5549 | 0.581695 | ||||||||
\(544\) | 32.0894 | 1.37582 | ||||||||
\(545\) | 0.0665174 | 0.00284929 | ||||||||
\(546\) | −1.32479 | −0.0566959 | ||||||||
\(547\) | −33.3107 | −1.42426 | −0.712131 | − | 0.702047i | \(-0.752270\pi\) | ||||
−0.712131 | + | 0.702047i | \(0.752270\pi\) | |||||||
\(548\) | 61.3583 | 2.62110 | ||||||||
\(549\) | 19.0071 | 0.811205 | ||||||||
\(550\) | 71.4004 | 3.04452 | ||||||||
\(551\) | −7.74552 | −0.329970 | ||||||||
\(552\) | 37.2750 | 1.58653 | ||||||||
\(553\) | −1.17669 | −0.0500379 | ||||||||
\(554\) | −62.6135 | −2.66019 | ||||||||
\(555\) | 0.0167577 | 0.000711324 0 | ||||||||
\(556\) | 30.1555 | 1.27888 | ||||||||
\(557\) | −10.9936 | −0.465813 | −0.232907 | − | 0.972499i | \(-0.574824\pi\) | ||||
−0.232907 | + | 0.972499i | \(0.574824\pi\) | |||||||
\(558\) | 36.2028 | 1.53259 | ||||||||
\(559\) | 6.63493 | 0.280628 | ||||||||
\(560\) | 0.00472000 | 0.000199457 0 | ||||||||
\(561\) | 29.7103 | 1.25437 | ||||||||
\(562\) | −8.77883 | −0.370313 | ||||||||
\(563\) | 26.2323 | 1.10556 | 0.552779 | − | 0.833328i | \(-0.313567\pi\) | ||||
0.552779 | + | 0.833328i | \(0.313567\pi\) | |||||||
\(564\) | 1.74883 | 0.0736391 | ||||||||
\(565\) | −0.0269101 | −0.00113212 | ||||||||
\(566\) | 33.5735 | 1.41120 | ||||||||
\(567\) | −0.278311 | −0.0116880 | ||||||||
\(568\) | −72.3885 | −3.03735 | ||||||||
\(569\) | 1.61722 | 0.0677972 | 0.0338986 | − | 0.999425i | \(-0.489208\pi\) | ||||
0.0338986 | + | 0.999425i | \(0.489208\pi\) | |||||||
\(570\) | 0.0812697 | 0.00340401 | ||||||||
\(571\) | 31.1273 | 1.30264 | 0.651318 | − | 0.758805i | \(-0.274216\pi\) | ||||
0.651318 | + | 0.758805i | \(0.274216\pi\) | |||||||
\(572\) | 107.710 | 4.50360 | ||||||||
\(573\) | 7.69609 | 0.321509 | ||||||||
\(574\) | −1.21811 | −0.0508430 | ||||||||
\(575\) | −31.9983 | −1.33442 | ||||||||
\(576\) | 0.300773 | 0.0125322 | ||||||||
\(577\) | −29.8247 | −1.24162 | −0.620808 | − | 0.783962i | \(-0.713195\pi\) | ||||
−0.620808 | + | 0.783962i | \(0.713195\pi\) | |||||||
\(578\) | −41.3035 | −1.71800 | ||||||||
\(579\) | −4.64781 | −0.193157 | ||||||||
\(580\) | −0.0249247 | −0.00103494 | ||||||||
\(581\) | −0.414953 | −0.0172151 | ||||||||
\(582\) | −20.6198 | −0.854717 | ||||||||
\(583\) | −3.91607 | −0.162187 | ||||||||
\(584\) | 49.3450 | 2.04191 | ||||||||
\(585\) | 0.0460196 | 0.00190267 | ||||||||
\(586\) | −36.4052 | −1.50388 | ||||||||
\(587\) | −7.69834 | −0.317745 | −0.158872 | − | 0.987299i | \(-0.550786\pi\) | ||||
−0.158872 | + | 0.987299i | \(0.550786\pi\) | |||||||
\(588\) | 28.8079 | 1.18802 | ||||||||
\(589\) | −45.8910 | −1.89091 | ||||||||
\(590\) | 0.00543359 | 0.000223697 0 | ||||||||
\(591\) | 9.19906 | 0.378399 | ||||||||
\(592\) | 26.1598 | 1.07516 | ||||||||
\(593\) | 15.4321 | 0.633722 | 0.316861 | − | 0.948472i | \(-0.397371\pi\) | ||||
0.316861 | + | 0.948472i | \(0.397371\pi\) | |||||||
\(594\) | −67.6791 | −2.77691 | ||||||||
\(595\) | −0.00379913 | −0.000155749 0 | ||||||||
\(596\) | 39.5253 | 1.61902 | ||||||||
\(597\) | 1.05303 | 0.0430974 | ||||||||
\(598\) | −69.7857 | −2.85375 | ||||||||
\(599\) | −19.0519 | −0.778441 | −0.389221 | − | 0.921145i | \(-0.627256\pi\) | ||||
−0.389221 | + | 0.921145i | \(0.627256\pi\) | |||||||
\(600\) | −29.1224 | −1.18892 | ||||||||
\(601\) | 34.9430 | 1.42536 | 0.712678 | − | 0.701492i | \(-0.247482\pi\) | ||||
0.712678 | + | 0.701492i | \(0.247482\pi\) | |||||||
\(602\) | 0.521555 | 0.0212570 | ||||||||
\(603\) | −31.2625 | −1.27311 | ||||||||
\(604\) | 15.9406 | 0.648612 | ||||||||
\(605\) | −0.101944 | −0.00414460 | ||||||||
\(606\) | 8.43565 | 0.342675 | ||||||||
\(607\) | −6.67583 | −0.270963 | −0.135482 | − | 0.990780i | \(-0.543258\pi\) | ||||
−0.135482 | + | 0.990780i | \(0.543258\pi\) | |||||||
\(608\) | 38.7319 | 1.57079 | ||||||||
\(609\) | 0.135271 | 0.00548148 | ||||||||
\(610\) | −0.112089 | −0.00453837 | ||||||||
\(611\) | −1.81481 | −0.0734192 | ||||||||
\(612\) | 55.7214 | 2.25240 | ||||||||
\(613\) | 16.2939 | 0.658105 | 0.329052 | − | 0.944312i | \(-0.393271\pi\) | ||||
0.329052 | + | 0.944312i | \(0.393271\pi\) | |||||||
\(614\) | 25.6965 | 1.03703 | ||||||||
\(615\) | −0.0166020 | −0.000669457 0 | ||||||||
\(616\) | 4.69304 | 0.189088 | ||||||||
\(617\) | −41.7478 | −1.68070 | −0.840352 | − | 0.542040i | \(-0.817652\pi\) | ||||
−0.840352 | + | 0.542040i | \(0.817652\pi\) | |||||||
\(618\) | −3.65605 | −0.147068 | ||||||||
\(619\) | 9.76112 | 0.392333 | 0.196166 | − | 0.980571i | \(-0.437151\pi\) | ||||
0.196166 | + | 0.980571i | \(0.437151\pi\) | |||||||
\(620\) | −0.147675 | −0.00593077 | ||||||||
\(621\) | 30.3306 | 1.21712 | ||||||||
\(622\) | 34.1017 | 1.36735 | ||||||||
\(623\) | −1.23667 | −0.0495462 | ||||||||
\(624\) | −28.1865 | −1.12836 | ||||||||
\(625\) | 24.9996 | 0.999985 | ||||||||
\(626\) | −35.9281 | −1.43598 | ||||||||
\(627\) | 35.8603 | 1.43212 | ||||||||
\(628\) | −42.9896 | −1.71547 | ||||||||
\(629\) | −21.0560 | −0.839557 | ||||||||
\(630\) | 0.00361748 | 0.000144124 0 | ||||||||
\(631\) | −6.55693 | −0.261027 | −0.130514 | − | 0.991447i | \(-0.541663\pi\) | ||||
−0.130514 | + | 0.991447i | \(0.541663\pi\) | |||||||
\(632\) | −56.4131 | −2.24399 | ||||||||
\(633\) | 19.1594 | 0.761517 | ||||||||
\(634\) | −38.7037 | −1.53712 | ||||||||
\(635\) | 0.0827800 | 0.00328502 | ||||||||
\(636\) | 2.88166 | 0.114265 | ||||||||
\(637\) | −29.8946 | −1.18447 | ||||||||
\(638\) | −15.9001 | −0.629489 | ||||||||
\(639\) | −24.6211 | −0.973995 | ||||||||
\(640\) | −0.0573264 | −0.00226603 | ||||||||
\(641\) | 34.3272 | 1.35584 | 0.677922 | − | 0.735134i | \(-0.262881\pi\) | ||||
0.677922 | + | 0.735134i | \(0.262881\pi\) | |||||||
\(642\) | 22.4829 | 0.887328 | ||||||||
\(643\) | −2.32588 | −0.0917238 | −0.0458619 | − | 0.998948i | \(-0.514603\pi\) | ||||
−0.0458619 | + | 0.998948i | \(0.514603\pi\) | |||||||
\(644\) | −3.79443 | −0.149522 | ||||||||
\(645\) | 0.00710842 | 0.000279894 0 | ||||||||
\(646\) | −102.115 | −4.01767 | ||||||||
\(647\) | −17.8101 | −0.700186 | −0.350093 | − | 0.936715i | \(-0.613850\pi\) | ||||
−0.350093 | + | 0.936715i | \(0.613850\pi\) | |||||||
\(648\) | −13.3429 | −0.524158 | ||||||||
\(649\) | 2.39758 | 0.0941131 | ||||||||
\(650\) | 54.5225 | 2.13855 | ||||||||
\(651\) | 0.801462 | 0.0314118 | ||||||||
\(652\) | 84.7896 | 3.32062 | ||||||||
\(653\) | −37.2591 | −1.45806 | −0.729031 | − | 0.684480i | \(-0.760029\pi\) | ||||
−0.729031 | + | 0.684480i | \(0.760029\pi\) | |||||||
\(654\) | −31.2246 | −1.22098 | ||||||||
\(655\) | 0.0909327 | 0.00355303 | ||||||||
\(656\) | −25.9167 | −1.01188 | ||||||||
\(657\) | 16.7834 | 0.654784 | ||||||||
\(658\) | −0.142657 | −0.00556135 | ||||||||
\(659\) | −27.8300 | −1.08410 | −0.542052 | − | 0.840345i | \(-0.682352\pi\) | ||||
−0.542052 | + | 0.840345i | \(0.682352\pi\) | |||||||
\(660\) | 0.115397 | 0.00449181 | ||||||||
\(661\) | 22.0184 | 0.856417 | 0.428208 | − | 0.903680i | \(-0.359145\pi\) | ||||
0.428208 | + | 0.903680i | \(0.359145\pi\) | |||||||
\(662\) | −84.2851 | −3.27583 | ||||||||
\(663\) | 22.6873 | 0.881100 | ||||||||
\(664\) | −19.8938 | −0.772028 | ||||||||
\(665\) | −0.00458555 | −0.000177820 0 | ||||||||
\(666\) | 20.0492 | 0.776891 | ||||||||
\(667\) | 7.12566 | 0.275906 | ||||||||
\(668\) | −105.672 | −4.08857 | ||||||||
\(669\) | −13.6921 | −0.529368 | ||||||||
\(670\) | 0.184362 | 0.00712252 | ||||||||
\(671\) | −49.4596 | −1.90937 | ||||||||
\(672\) | −0.676432 | −0.0260939 | ||||||||
\(673\) | 12.9910 | 0.500765 | 0.250383 | − | 0.968147i | \(-0.419444\pi\) | ||||
0.250383 | + | 0.968147i | \(0.419444\pi\) | |||||||
\(674\) | −24.0642 | −0.926919 | ||||||||
\(675\) | −23.6968 | −0.912090 | ||||||||
\(676\) | 23.9161 | 0.919849 | ||||||||
\(677\) | 19.2858 | 0.741214 | 0.370607 | − | 0.928790i | \(-0.379150\pi\) | ||||
0.370607 | + | 0.928790i | \(0.379150\pi\) | |||||||
\(678\) | 12.6321 | 0.485134 | ||||||||
\(679\) | 1.16345 | 0.0446490 | ||||||||
\(680\) | −0.182139 | −0.00698470 | ||||||||
\(681\) | −14.8569 | −0.569316 | ||||||||
\(682\) | −94.2052 | −3.60731 | ||||||||
\(683\) | 3.84053 | 0.146954 | 0.0734769 | − | 0.997297i | \(-0.476590\pi\) | ||||
0.0734769 | + | 0.997297i | \(0.476590\pi\) | |||||||
\(684\) | 67.2557 | 2.57159 | ||||||||
\(685\) | −0.0682168 | −0.00260643 | ||||||||
\(686\) | −4.70575 | −0.179667 | ||||||||
\(687\) | 4.25835 | 0.162466 | ||||||||
\(688\) | 11.0967 | 0.423057 | ||||||||
\(689\) | −2.99037 | −0.113924 | ||||||||
\(690\) | −0.0747657 | −0.00284628 | ||||||||
\(691\) | −4.53712 | −0.172600 | −0.0863001 | − | 0.996269i | \(-0.527504\pi\) | ||||
−0.0863001 | + | 0.996269i | \(0.527504\pi\) | |||||||
\(692\) | 95.0476 | 3.61317 | ||||||||
\(693\) | 1.59622 | 0.0606352 | ||||||||
\(694\) | −75.2058 | −2.85477 | ||||||||
\(695\) | −0.0335263 | −0.00127172 | ||||||||
\(696\) | 6.48522 | 0.245822 | ||||||||
\(697\) | 20.8603 | 0.790142 | ||||||||
\(698\) | 56.6608 | 2.14464 | ||||||||
\(699\) | 9.40841 | 0.355859 | ||||||||
\(700\) | 2.96453 | 0.112049 | ||||||||
\(701\) | 16.3276 | 0.616686 | 0.308343 | − | 0.951275i | \(-0.400226\pi\) | ||||
0.308343 | + | 0.951275i | \(0.400226\pi\) | |||||||
\(702\) | −51.6808 | −1.95057 | ||||||||
\(703\) | −25.4146 | −0.958529 | ||||||||
\(704\) | −0.782659 | −0.0294976 | ||||||||
\(705\) | −0.00194431 | −7.32271e−5 0 | ||||||||
\(706\) | −82.5642 | −3.10735 | ||||||||
\(707\) | −0.475972 | −0.0179008 | ||||||||
\(708\) | −1.76427 | −0.0663054 | ||||||||
\(709\) | 1.04251 | 0.0391523 | 0.0195761 | − | 0.999808i | \(-0.493768\pi\) | ||||
0.0195761 | + | 0.999808i | \(0.493768\pi\) | |||||||
\(710\) | 0.145196 | 0.00544911 | ||||||||
\(711\) | −19.1875 | −0.719586 | ||||||||
\(712\) | −59.2888 | −2.22194 | ||||||||
\(713\) | 42.2184 | 1.58109 | ||||||||
\(714\) | 1.78339 | 0.0667416 | ||||||||
\(715\) | −0.119750 | −0.00447840 | ||||||||
\(716\) | −95.2763 | −3.56064 | ||||||||
\(717\) | −19.7117 | −0.736145 | ||||||||
\(718\) | −28.4376 | −1.06128 | ||||||||
\(719\) | 21.2837 | 0.793749 | 0.396875 | − | 0.917873i | \(-0.370095\pi\) | ||||
0.396875 | + | 0.917873i | \(0.370095\pi\) | |||||||
\(720\) | 0.0769659 | 0.00286835 | ||||||||
\(721\) | 0.206289 | 0.00768259 | ||||||||
\(722\) | −74.8601 | −2.78600 | ||||||||
\(723\) | 4.38498 | 0.163079 | ||||||||
\(724\) | −66.1520 | −2.45852 | ||||||||
\(725\) | −5.56716 | −0.206759 | ||||||||
\(726\) | 47.8543 | 1.77604 | ||||||||
\(727\) | 10.6453 | 0.394813 | 0.197406 | − | 0.980322i | \(-0.436748\pi\) | ||||
0.197406 | + | 0.980322i | \(0.436748\pi\) | |||||||
\(728\) | 3.58368 | 0.132820 | ||||||||
\(729\) | 8.53455 | 0.316094 | ||||||||
\(730\) | −0.0989756 | −0.00366325 | ||||||||
\(731\) | −8.93170 | −0.330351 | ||||||||
\(732\) | 36.3951 | 1.34520 | ||||||||
\(733\) | 49.2118 | 1.81768 | 0.908840 | − | 0.417145i | \(-0.136969\pi\) | ||||
0.908840 | + | 0.417145i | \(0.136969\pi\) | |||||||
\(734\) | −11.2394 | −0.414855 | ||||||||
\(735\) | −0.0320280 | −0.00118137 | ||||||||
\(736\) | −35.6322 | −1.31342 | ||||||||
\(737\) | 81.3499 | 2.99656 | ||||||||
\(738\) | −19.8629 | −0.731164 | ||||||||
\(739\) | 11.3132 | 0.416164 | 0.208082 | − | 0.978111i | \(-0.433278\pi\) | ||||
0.208082 | + | 0.978111i | \(0.433278\pi\) | |||||||
\(740\) | −0.0817828 | −0.00300640 | ||||||||
\(741\) | 27.3835 | 1.00596 | ||||||||
\(742\) | −0.235065 | −0.00862952 | ||||||||
\(743\) | 30.3159 | 1.11218 | 0.556091 | − | 0.831122i | \(-0.312301\pi\) | ||||
0.556091 | + | 0.831122i | \(0.312301\pi\) | |||||||
\(744\) | 38.4239 | 1.40869 | ||||||||
\(745\) | −0.0439434 | −0.00160996 | ||||||||
\(746\) | 76.5748 | 2.80360 | ||||||||
\(747\) | −6.76636 | −0.247568 | ||||||||
\(748\) | −144.996 | −5.30157 | ||||||||
\(749\) | −1.26857 | −0.0463525 | ||||||||
\(750\) | 0.116827 | 0.00426591 | ||||||||
\(751\) | 33.8317 | 1.23454 | 0.617269 | − | 0.786752i | \(-0.288239\pi\) | ||||
0.617269 | + | 0.786752i | \(0.288239\pi\) | |||||||
\(752\) | −3.03519 | −0.110682 | ||||||||
\(753\) | 8.44076 | 0.307598 | ||||||||
\(754\) | −12.1415 | −0.442169 | ||||||||
\(755\) | −0.0177224 | −0.000644983 0 | ||||||||
\(756\) | −2.81002 | −0.102200 | ||||||||
\(757\) | −32.9599 | −1.19795 | −0.598975 | − | 0.800768i | \(-0.704425\pi\) | ||||
−0.598975 | + | 0.800768i | \(0.704425\pi\) | |||||||
\(758\) | −5.19257 | −0.188603 | ||||||||
\(759\) | −32.9905 | −1.19748 | ||||||||
\(760\) | −0.219842 | −0.00797449 | ||||||||
\(761\) | 37.8923 | 1.37359 | 0.686797 | − | 0.726849i | \(-0.259016\pi\) | ||||
0.686797 | + | 0.726849i | \(0.259016\pi\) | |||||||
\(762\) | −38.8586 | −1.40770 | ||||||||
\(763\) | 1.76181 | 0.0637819 | ||||||||
\(764\) | −37.5593 | −1.35885 | ||||||||
\(765\) | −0.0619498 | −0.00223980 | ||||||||
\(766\) | −27.9993 | −1.01165 | ||||||||
\(767\) | 1.83083 | 0.0661073 | ||||||||
\(768\) | 26.6535 | 0.961774 | ||||||||
\(769\) | −13.6451 | −0.492057 | −0.246028 | − | 0.969263i | \(-0.579126\pi\) | ||||
−0.246028 | + | 0.969263i | \(0.579126\pi\) | |||||||
\(770\) | −0.00941324 | −0.000339230 0 | ||||||||
\(771\) | −17.7256 | −0.638372 | ||||||||
\(772\) | 22.6828 | 0.816372 | ||||||||
\(773\) | 16.3568 | 0.588312 | 0.294156 | − | 0.955757i | \(-0.404961\pi\) | ||||
0.294156 | + | 0.955757i | \(0.404961\pi\) | |||||||
\(774\) | 8.50464 | 0.305693 | ||||||||
\(775\) | −32.9845 | −1.18484 | ||||||||
\(776\) | 55.7783 | 2.00232 | ||||||||
\(777\) | 0.443852 | 0.0159231 | ||||||||
\(778\) | −84.1719 | −3.01771 | ||||||||
\(779\) | 25.1784 | 0.902111 | ||||||||
\(780\) | 0.0881188 | 0.00315516 | ||||||||
\(781\) | 64.0679 | 2.29253 | ||||||||
\(782\) | 93.9429 | 3.35939 | ||||||||
\(783\) | 5.27701 | 0.188585 | ||||||||
\(784\) | −49.9976 | −1.78563 | ||||||||
\(785\) | 0.0477949 | 0.00170587 | ||||||||
\(786\) | −42.6856 | −1.52255 | ||||||||
\(787\) | 43.2127 | 1.54037 | 0.770183 | − | 0.637823i | \(-0.220165\pi\) | ||||
0.770183 | + | 0.637823i | \(0.220165\pi\) | |||||||
\(788\) | −44.8943 | −1.59929 | ||||||||
\(789\) | −8.52772 | −0.303595 | ||||||||
\(790\) | 0.113153 | 0.00402579 | ||||||||
\(791\) | −0.712753 | −0.0253426 | ||||||||
\(792\) | 76.5262 | 2.71924 | ||||||||
\(793\) | −37.7681 | −1.34118 | ||||||||
\(794\) | 77.5778 | 2.75313 | ||||||||
\(795\) | −0.00320377 | −0.000113626 0 | ||||||||
\(796\) | −5.13910 | −0.182150 | ||||||||
\(797\) | −41.2363 | −1.46067 | −0.730333 | − | 0.683091i | \(-0.760635\pi\) | ||||
−0.730333 | + | 0.683091i | \(0.760635\pi\) | |||||||
\(798\) | 2.15255 | 0.0761994 | ||||||||
\(799\) | 2.44302 | 0.0864280 | ||||||||
\(800\) | 27.8389 | 0.984253 | ||||||||
\(801\) | −20.1656 | −0.712516 | ||||||||
\(802\) | 24.4156 | 0.862143 | ||||||||
\(803\) | −43.6731 | −1.54119 | ||||||||
\(804\) | −59.8618 | −2.11116 | ||||||||
\(805\) | 0.00421857 | 0.000148685 0 | ||||||||
\(806\) | −71.9366 | −2.53386 | ||||||||
\(807\) | −15.2976 | −0.538500 | ||||||||
\(808\) | −22.8192 | −0.802775 | ||||||||
\(809\) | 8.31538 | 0.292353 | 0.146177 | − | 0.989259i | \(-0.453303\pi\) | ||||
0.146177 | + | 0.989259i | \(0.453303\pi\) | |||||||
\(810\) | 0.0267630 | 0.000940356 0 | ||||||||
\(811\) | 25.4116 | 0.892321 | 0.446160 | − | 0.894953i | \(-0.352791\pi\) | ||||
0.446160 | + | 0.894953i | \(0.352791\pi\) | |||||||
\(812\) | −0.660168 | −0.0231673 | ||||||||
\(813\) | 6.82993 | 0.239536 | ||||||||
\(814\) | −52.1712 | −1.82860 | ||||||||
\(815\) | −0.0942673 | −0.00330204 | ||||||||
\(816\) | 37.9436 | 1.32829 | ||||||||
\(817\) | −10.7806 | −0.377164 | ||||||||
\(818\) | −22.3639 | −0.781937 | ||||||||
\(819\) | 1.21890 | 0.0425917 | ||||||||
\(820\) | 0.0810229 | 0.00282944 | ||||||||
\(821\) | −0.188389 | −0.00657482 | −0.00328741 | − | 0.999995i | \(-0.501046\pi\) | ||||
−0.00328741 | + | 0.999995i | \(0.501046\pi\) | |||||||
\(822\) | 32.0223 | 1.11691 | ||||||||
\(823\) | 2.93960 | 0.102468 | 0.0512340 | − | 0.998687i | \(-0.483685\pi\) | ||||
0.0512340 | + | 0.998687i | \(0.483685\pi\) | |||||||
\(824\) | 9.88994 | 0.344533 | ||||||||
\(825\) | 25.7749 | 0.897368 | ||||||||
\(826\) | 0.143917 | 0.00500750 | ||||||||
\(827\) | 5.22540 | 0.181705 | 0.0908526 | − | 0.995864i | \(-0.471041\pi\) | ||||
0.0908526 | + | 0.995864i | \(0.471041\pi\) | |||||||
\(828\) | −61.8733 | −2.15025 | ||||||||
\(829\) | 12.2304 | 0.424779 | 0.212389 | − | 0.977185i | \(-0.431875\pi\) | ||||
0.212389 | + | 0.977185i | \(0.431875\pi\) | |||||||
\(830\) | 0.0399027 | 0.00138504 | ||||||||
\(831\) | −22.6030 | −0.784088 | ||||||||
\(832\) | −0.597651 | −0.0207198 | ||||||||
\(833\) | 40.2431 | 1.39434 | ||||||||
\(834\) | 15.7379 | 0.544959 | ||||||||
\(835\) | 0.117484 | 0.00406569 | ||||||||
\(836\) | −175.010 | −6.05284 | ||||||||
\(837\) | 31.2654 | 1.08069 | ||||||||
\(838\) | −12.7856 | −0.441670 | ||||||||
\(839\) | −34.6254 | −1.19540 | −0.597700 | − | 0.801720i | \(-0.703919\pi\) | ||||
−0.597700 | + | 0.801720i | \(0.703919\pi\) | |||||||
\(840\) | 0.00383942 | 0.000132472 0 | ||||||||
\(841\) | −27.7603 | −0.957250 | ||||||||
\(842\) | 18.2235 | 0.628022 | ||||||||
\(843\) | −3.16908 | −0.109149 | ||||||||
\(844\) | −93.5039 | −3.21854 | ||||||||
\(845\) | −0.0265894 | −0.000914703 0 | ||||||||
\(846\) | −2.32621 | −0.0799769 | ||||||||
\(847\) | −2.70013 | −0.0927774 | ||||||||
\(848\) | −5.00128 | −0.171745 | ||||||||
\(849\) | 12.1198 | 0.415949 | ||||||||
\(850\) | −73.3961 | −2.51747 | ||||||||
\(851\) | 23.3807 | 0.801479 | ||||||||
\(852\) | −47.1448 | −1.61515 | ||||||||
\(853\) | −41.2028 | −1.41076 | −0.705379 | − | 0.708830i | \(-0.749223\pi\) | ||||
−0.705379 | + | 0.708830i | \(0.749223\pi\) | |||||||
\(854\) | −2.96885 | −0.101592 | ||||||||
\(855\) | −0.0747735 | −0.00255720 | ||||||||
\(856\) | −60.8181 | −2.07872 | ||||||||
\(857\) | −42.5430 | −1.45324 | −0.726620 | − | 0.687040i | \(-0.758910\pi\) | ||||
−0.726620 | + | 0.687040i | \(0.758910\pi\) | |||||||
\(858\) | 56.2131 | 1.91908 | ||||||||
\(859\) | −11.8359 | −0.403835 | −0.201917 | − | 0.979403i | \(-0.564717\pi\) | ||||
−0.201917 | + | 0.979403i | \(0.564717\pi\) | |||||||
\(860\) | −0.0346913 | −0.00118296 | ||||||||
\(861\) | −0.439728 | −0.0149859 | ||||||||
\(862\) | −38.7477 | −1.31975 | ||||||||
\(863\) | −23.3851 | −0.796037 | −0.398019 | − | 0.917377i | \(-0.630302\pi\) | ||||
−0.398019 | + | 0.917377i | \(0.630302\pi\) | |||||||
\(864\) | −26.3880 | −0.897737 | ||||||||
\(865\) | −0.105672 | −0.00359295 | ||||||||
\(866\) | −96.0620 | −3.26432 | ||||||||
\(867\) | −14.9102 | −0.506378 | ||||||||
\(868\) | −3.91139 | −0.132761 | ||||||||
\(869\) | 49.9288 | 1.69372 | ||||||||
\(870\) | −0.0130080 | −0.000441012 0 | ||||||||
\(871\) | 62.1200 | 2.10486 | ||||||||
\(872\) | 84.4652 | 2.86035 | ||||||||
\(873\) | 18.9715 | 0.642090 | ||||||||
\(874\) | 113.389 | 3.83544 | ||||||||
\(875\) | −0.00659182 | −0.000222844 0 | ||||||||
\(876\) | 32.1371 | 1.08581 | ||||||||
\(877\) | 3.34805 | 0.113056 | 0.0565278 | − | 0.998401i | \(-0.481997\pi\) | ||||
0.0565278 | + | 0.998401i | \(0.481997\pi\) | |||||||
\(878\) | 16.6903 | 0.563270 | ||||||||
\(879\) | −13.1420 | −0.443267 | ||||||||
\(880\) | −0.200277 | −0.00675135 | ||||||||
\(881\) | −20.3096 | −0.684248 | −0.342124 | − | 0.939655i | \(-0.611146\pi\) | ||||
−0.342124 | + | 0.939655i | \(0.611146\pi\) | |||||||
\(882\) | −38.3189 | −1.29026 | ||||||||
\(883\) | −53.3092 | −1.79400 | −0.896999 | − | 0.442033i | \(-0.854257\pi\) | ||||
−0.896999 | + | 0.442033i | \(0.854257\pi\) | |||||||
\(884\) | −110.721 | −3.72395 | ||||||||
\(885\) | 0.00196148 | 6.59344e−5 0 | ||||||||
\(886\) | −95.3556 | −3.20354 | ||||||||
\(887\) | 28.4212 | 0.954290 | 0.477145 | − | 0.878825i | \(-0.341672\pi\) | ||||
0.477145 | + | 0.878825i | \(0.341672\pi\) | |||||||
\(888\) | 21.2793 | 0.714085 | ||||||||
\(889\) | 2.19255 | 0.0735358 | ||||||||
\(890\) | 0.118921 | 0.00398624 | ||||||||
\(891\) | 11.8092 | 0.395623 | ||||||||
\(892\) | 66.8218 | 2.23736 | ||||||||
\(893\) | 2.94873 | 0.0986755 | ||||||||
\(894\) | 20.6279 | 0.689900 | ||||||||
\(895\) | 0.105926 | 0.00354072 | ||||||||
\(896\) | −1.51838 | −0.0507254 | ||||||||
\(897\) | −25.1920 | −0.841138 | ||||||||
\(898\) | −1.51874 | −0.0506809 | ||||||||
\(899\) | 7.34528 | 0.244979 | ||||||||
\(900\) | 48.3406 | 1.61135 | ||||||||
\(901\) | 4.02553 | 0.134110 | ||||||||
\(902\) | 51.6864 | 1.72097 | ||||||||
\(903\) | 0.188277 | 0.00626546 | ||||||||
\(904\) | −34.1710 | −1.13651 | ||||||||
\(905\) | 0.0735464 | 0.00244477 | ||||||||
\(906\) | 8.31924 | 0.276388 | ||||||||
\(907\) | −25.8031 | −0.856778 | −0.428389 | − | 0.903594i | \(-0.640919\pi\) | ||||
−0.428389 | + | 0.903594i | \(0.640919\pi\) | |||||||
\(908\) | 72.5062 | 2.40620 | ||||||||
\(909\) | −7.76135 | −0.257428 | ||||||||
\(910\) | −0.00718810 | −0.000238283 0 | ||||||||
\(911\) | 4.69496 | 0.155551 | 0.0777755 | − | 0.996971i | \(-0.475218\pi\) | ||||
0.0777755 | + | 0.996971i | \(0.475218\pi\) | |||||||
\(912\) | 45.7979 | 1.51652 | ||||||||
\(913\) | 17.6071 | 0.582710 | ||||||||
\(914\) | −92.7050 | −3.06641 | ||||||||
\(915\) | −0.0404633 | −0.00133768 | ||||||||
\(916\) | −20.7821 | −0.686660 | ||||||||
\(917\) | 2.40849 | 0.0795352 | ||||||||
\(918\) | 69.5708 | 2.29618 | ||||||||
\(919\) | 0.415191 | 0.0136959 | 0.00684794 | − | 0.999977i | \(-0.497820\pi\) | ||||
0.00684794 | + | 0.999977i | \(0.497820\pi\) | |||||||
\(920\) | 0.202248 | 0.00666791 | ||||||||
\(921\) | 9.27622 | 0.305662 | ||||||||
\(922\) | 92.8123 | 3.05661 | ||||||||
\(923\) | 48.9233 | 1.61033 | ||||||||
\(924\) | 3.05645 | 0.100550 | ||||||||
\(925\) | −18.2669 | −0.600613 | ||||||||
\(926\) | −96.8091 | −3.18134 | ||||||||
\(927\) | 3.36381 | 0.110482 | ||||||||
\(928\) | −6.19940 | −0.203505 | ||||||||
\(929\) | 27.8702 | 0.914392 | 0.457196 | − | 0.889366i | \(-0.348854\pi\) | ||||
0.457196 | + | 0.889366i | \(0.348854\pi\) | |||||||
\(930\) | −0.0770702 | −0.00252723 | ||||||||
\(931\) | 48.5734 | 1.59193 | ||||||||
\(932\) | −45.9160 | −1.50403 | ||||||||
\(933\) | 12.3104 | 0.403026 | ||||||||
\(934\) | −32.8943 | −1.07633 | ||||||||
\(935\) | 0.161203 | 0.00527191 | ||||||||
\(936\) | 58.4366 | 1.91006 | ||||||||
\(937\) | 5.72390 | 0.186992 | 0.0934959 | − | 0.995620i | \(-0.470196\pi\) | ||||
0.0934959 | + | 0.995620i | \(0.470196\pi\) | |||||||
\(938\) | 4.88309 | 0.159439 | ||||||||
\(939\) | −12.9697 | −0.423252 | ||||||||
\(940\) | 0.00948887 | 0.000309493 0 | ||||||||
\(941\) | 14.9870 | 0.488561 | 0.244281 | − | 0.969705i | \(-0.421448\pi\) | ||||
0.244281 | + | 0.969705i | \(0.421448\pi\) | |||||||
\(942\) | −22.4359 | −0.731001 | ||||||||
\(943\) | −23.1634 | −0.754305 | ||||||||
\(944\) | 3.06199 | 0.0996592 | ||||||||
\(945\) | 0.00312413 | 0.000101628 0 | ||||||||
\(946\) | −22.1304 | −0.719521 | ||||||||
\(947\) | 17.2751 | 0.561366 | 0.280683 | − | 0.959801i | \(-0.409439\pi\) | ||||
0.280683 | + | 0.959801i | \(0.409439\pi\) | |||||||
\(948\) | −36.7404 | −1.19327 | ||||||||
\(949\) | −33.3495 | −1.08257 | ||||||||
\(950\) | −88.5891 | −2.87421 | ||||||||
\(951\) | −13.9717 | −0.453064 | ||||||||
\(952\) | −4.82421 | −0.156354 | ||||||||
\(953\) | −21.2276 | −0.687631 | −0.343815 | − | 0.939037i | \(-0.611719\pi\) | ||||
−0.343815 | + | 0.939037i | \(0.611719\pi\) | |||||||
\(954\) | −3.83305 | −0.124100 | ||||||||
\(955\) | 0.0417577 | 0.00135125 | ||||||||
\(956\) | 96.1991 | 3.11130 | ||||||||
\(957\) | −5.73979 | −0.185541 | ||||||||
\(958\) | −55.3652 | −1.78877 | ||||||||
\(959\) | −1.80682 | −0.0583454 | ||||||||
\(960\) | −0.000640301 0 | −2.06656e−5 0 | ||||||||
\(961\) | 12.5196 | 0.403859 | ||||||||
\(962\) | −39.8387 | −1.28445 | ||||||||
\(963\) | −20.6857 | −0.666588 | ||||||||
\(964\) | −21.4001 | −0.689251 | ||||||||
\(965\) | −0.0252183 | −0.000811804 0 | ||||||||
\(966\) | −1.98028 | −0.0637145 | ||||||||
\(967\) | 17.7383 | 0.570426 | 0.285213 | − | 0.958464i | \(-0.407936\pi\) | ||||
0.285213 | + | 0.958464i | \(0.407936\pi\) | |||||||
\(968\) | −129.450 | −4.16068 | ||||||||
\(969\) | −36.8627 | −1.18420 | ||||||||
\(970\) | −0.111879 | −0.00359223 | ||||||||
\(971\) | −56.1507 | −1.80196 | −0.900980 | − | 0.433860i | \(-0.857151\pi\) | ||||
−0.900980 | + | 0.433860i | \(0.857151\pi\) | |||||||
\(972\) | −72.4892 | −2.32509 | ||||||||
\(973\) | −0.887993 | −0.0284677 | ||||||||
\(974\) | −86.1838 | −2.76151 | ||||||||
\(975\) | 19.6821 | 0.630333 | ||||||||
\(976\) | −63.1657 | −2.02188 | ||||||||
\(977\) | −17.3861 | −0.556230 | −0.278115 | − | 0.960548i | \(-0.589710\pi\) | ||||
−0.278115 | + | 0.960548i | \(0.589710\pi\) | |||||||
\(978\) | 44.2509 | 1.41499 | ||||||||
\(979\) | 52.4740 | 1.67708 | ||||||||
\(980\) | 0.156307 | 0.00499303 | ||||||||
\(981\) | 28.7287 | 0.917236 | ||||||||
\(982\) | 6.38101 | 0.203626 | ||||||||
\(983\) | 42.6594 | 1.36062 | 0.680311 | − | 0.732924i | \(-0.261845\pi\) | ||||
0.680311 | + | 0.732924i | \(0.261845\pi\) | |||||||
\(984\) | −21.0816 | −0.672055 | ||||||||
\(985\) | 0.0499126 | 0.00159035 | ||||||||
\(986\) | 16.3445 | 0.520514 | ||||||||
\(987\) | −0.0514980 | −0.00163920 | ||||||||
\(988\) | −133.640 | −4.25166 | ||||||||
\(989\) | 9.91781 | 0.315368 | ||||||||
\(990\) | −0.153495 | −0.00487840 | ||||||||
\(991\) | 3.73568 | 0.118668 | 0.0593340 | − | 0.998238i | \(-0.481102\pi\) | ||||
0.0593340 | + | 0.998238i | \(0.481102\pi\) | |||||||
\(992\) | −36.7305 | −1.16619 | ||||||||
\(993\) | −30.4262 | −0.965547 | ||||||||
\(994\) | 3.84573 | 0.121979 | ||||||||
\(995\) | 0.00571354 | 0.000181131 0 | ||||||||
\(996\) | −12.9563 | −0.410536 | ||||||||
\(997\) | 43.5670 | 1.37978 | 0.689890 | − | 0.723914i | \(-0.257659\pi\) | ||||
0.689890 | + | 0.723914i | \(0.257659\pi\) | |||||||
\(998\) | −48.1432 | −1.52395 | ||||||||
\(999\) | 17.3149 | 0.547819 |
(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 | 4003.2.a.c.1.10 | ✓ | 179 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.c.1.10 | ✓ | 179 | 1.1 | even | 1 | trivial |