Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8017,2,Mod(1,8017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8017, 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("8017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8017.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: | \(64.0160673005\) |
Analytic rank: | \(1\) |
Dimension: | \(327\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59947 | −1.83810 | −0.919050 | − | 0.394141i | \(-0.871042\pi\) | ||||
−0.919050 | + | 0.394141i | \(0.871042\pi\) | |||||||
\(3\) | −1.49239 | −0.861632 | −0.430816 | − | 0.902440i | \(-0.641774\pi\) | ||||
−0.430816 | + | 0.902440i | \(0.641774\pi\) | |||||||
\(4\) | 4.75723 | 2.37861 | ||||||||
\(5\) | 4.02767 | 1.80123 | 0.900614 | − | 0.434621i | \(-0.143118\pi\) | ||||
0.900614 | + | 0.434621i | \(0.143118\pi\) | |||||||
\(6\) | 3.87942 | 1.58377 | ||||||||
\(7\) | −3.51002 | −1.32666 | −0.663331 | − | 0.748326i | \(-0.730858\pi\) | ||||
−0.663331 | + | 0.748326i | \(0.730858\pi\) | |||||||
\(8\) | −7.16732 | −2.53403 | ||||||||
\(9\) | −0.772773 | −0.257591 | ||||||||
\(10\) | −10.4698 | −3.31084 | ||||||||
\(11\) | 2.23298 | 0.673269 | 0.336634 | − | 0.941635i | \(-0.390711\pi\) | ||||
0.336634 | + | 0.941635i | \(0.390711\pi\) | |||||||
\(12\) | −7.09964 | −2.04949 | ||||||||
\(13\) | −1.36226 | −0.377823 | −0.188911 | − | 0.981994i | \(-0.560496\pi\) | ||||
−0.188911 | + | 0.981994i | \(0.560496\pi\) | |||||||
\(14\) | 9.12417 | 2.43854 | ||||||||
\(15\) | −6.01085 | −1.55199 | ||||||||
\(16\) | 9.11675 | 2.27919 | ||||||||
\(17\) | −1.29513 | −0.314115 | −0.157058 | − | 0.987589i | \(-0.550201\pi\) | ||||
−0.157058 | + | 0.987589i | \(0.550201\pi\) | |||||||
\(18\) | 2.00880 | 0.473478 | ||||||||
\(19\) | −4.22580 | −0.969464 | −0.484732 | − | 0.874663i | \(-0.661083\pi\) | ||||
−0.484732 | + | 0.874663i | \(0.661083\pi\) | |||||||
\(20\) | 19.1605 | 4.28442 | ||||||||
\(21\) | 5.23831 | 1.14309 | ||||||||
\(22\) | −5.80456 | −1.23754 | ||||||||
\(23\) | −2.14241 | −0.446723 | −0.223361 | − | 0.974736i | \(-0.571703\pi\) | ||||
−0.223361 | + | 0.974736i | \(0.571703\pi\) | |||||||
\(24\) | 10.6964 | 2.18340 | ||||||||
\(25\) | 11.2221 | 2.24442 | ||||||||
\(26\) | 3.54115 | 0.694476 | ||||||||
\(27\) | 5.63045 | 1.08358 | ||||||||
\(28\) | −16.6979 | −3.15561 | ||||||||
\(29\) | −0.353354 | −0.0656163 | −0.0328081 | − | 0.999462i | \(-0.510445\pi\) | ||||
−0.0328081 | + | 0.999462i | \(0.510445\pi\) | |||||||
\(30\) | 15.6250 | 2.85272 | ||||||||
\(31\) | −5.53930 | −0.994888 | −0.497444 | − | 0.867496i | \(-0.665728\pi\) | ||||
−0.497444 | + | 0.867496i | \(0.665728\pi\) | |||||||
\(32\) | −9.36405 | −1.65535 | ||||||||
\(33\) | −3.33248 | −0.580110 | ||||||||
\(34\) | 3.36665 | 0.577376 | ||||||||
\(35\) | −14.1372 | −2.38962 | ||||||||
\(36\) | −3.67626 | −0.612709 | ||||||||
\(37\) | −7.16284 | −1.17756 | −0.588782 | − | 0.808292i | \(-0.700392\pi\) | ||||
−0.588782 | + | 0.808292i | \(0.700392\pi\) | |||||||
\(38\) | 10.9848 | 1.78197 | ||||||||
\(39\) | 2.03302 | 0.325544 | ||||||||
\(40\) | −28.8676 | −4.56436 | ||||||||
\(41\) | 8.23137 | 1.28552 | 0.642762 | − | 0.766066i | \(-0.277788\pi\) | ||||
0.642762 | + | 0.766066i | \(0.277788\pi\) | |||||||
\(42\) | −13.6168 | −2.10112 | ||||||||
\(43\) | −4.26310 | −0.650117 | −0.325058 | − | 0.945694i | \(-0.605384\pi\) | ||||
−0.325058 | + | 0.945694i | \(0.605384\pi\) | |||||||
\(44\) | 10.6228 | 1.60145 | ||||||||
\(45\) | −3.11247 | −0.463980 | ||||||||
\(46\) | 5.56911 | 0.821121 | ||||||||
\(47\) | 4.23999 | 0.618466 | 0.309233 | − | 0.950986i | \(-0.399928\pi\) | ||||
0.309233 | + | 0.950986i | \(0.399928\pi\) | |||||||
\(48\) | −13.6057 | −1.96382 | ||||||||
\(49\) | 5.32022 | 0.760031 | ||||||||
\(50\) | −29.1715 | −4.12547 | ||||||||
\(51\) | 1.93284 | 0.270652 | ||||||||
\(52\) | −6.48058 | −0.898694 | ||||||||
\(53\) | 7.89854 | 1.08495 | 0.542474 | − | 0.840073i | \(-0.317488\pi\) | ||||
0.542474 | + | 0.840073i | \(0.317488\pi\) | |||||||
\(54\) | −14.6362 | −1.99173 | ||||||||
\(55\) | 8.99370 | 1.21271 | ||||||||
\(56\) | 25.1574 | 3.36180 | ||||||||
\(57\) | 6.30654 | 0.835321 | ||||||||
\(58\) | 0.918533 | 0.120609 | ||||||||
\(59\) | −4.73553 | −0.616514 | −0.308257 | − | 0.951303i | \(-0.599746\pi\) | ||||
−0.308257 | + | 0.951303i | \(0.599746\pi\) | |||||||
\(60\) | −28.5950 | −3.69159 | ||||||||
\(61\) | 14.5865 | 1.86761 | 0.933805 | − | 0.357781i | \(-0.116467\pi\) | ||||
0.933805 | + | 0.357781i | \(0.116467\pi\) | |||||||
\(62\) | 14.3992 | 1.82870 | ||||||||
\(63\) | 2.71245 | 0.341736 | ||||||||
\(64\) | 6.10803 | 0.763504 | ||||||||
\(65\) | −5.48673 | −0.680545 | ||||||||
\(66\) | 8.66266 | 1.06630 | ||||||||
\(67\) | −8.06693 | −0.985532 | −0.492766 | − | 0.870162i | \(-0.664014\pi\) | ||||
−0.492766 | + | 0.870162i | \(0.664014\pi\) | |||||||
\(68\) | −6.16123 | −0.747159 | ||||||||
\(69\) | 3.19731 | 0.384910 | ||||||||
\(70\) | 36.7491 | 4.39236 | ||||||||
\(71\) | 15.6313 | 1.85509 | 0.927545 | − | 0.373711i | \(-0.121915\pi\) | ||||
0.927545 | + | 0.373711i | \(0.121915\pi\) | |||||||
\(72\) | 5.53871 | 0.652743 | ||||||||
\(73\) | 3.68245 | 0.430998 | 0.215499 | − | 0.976504i | \(-0.430862\pi\) | ||||
0.215499 | + | 0.976504i | \(0.430862\pi\) | |||||||
\(74\) | 18.6196 | 2.16448 | ||||||||
\(75\) | −16.7477 | −1.93386 | ||||||||
\(76\) | −20.1031 | −2.30598 | ||||||||
\(77\) | −7.83780 | −0.893200 | ||||||||
\(78\) | −5.28477 | −0.598383 | ||||||||
\(79\) | −3.05013 | −0.343167 | −0.171583 | − | 0.985170i | \(-0.554888\pi\) | ||||
−0.171583 | + | 0.985170i | \(0.554888\pi\) | |||||||
\(80\) | 36.7192 | 4.10533 | ||||||||
\(81\) | −6.08450 | −0.676056 | ||||||||
\(82\) | −21.3972 | −2.36292 | ||||||||
\(83\) | 14.3652 | 1.57679 | 0.788393 | − | 0.615171i | \(-0.210913\pi\) | ||||
0.788393 | + | 0.615171i | \(0.210913\pi\) | |||||||
\(84\) | 24.9198 | 2.71898 | ||||||||
\(85\) | −5.21636 | −0.565793 | ||||||||
\(86\) | 11.0818 | 1.19498 | ||||||||
\(87\) | 0.527343 | 0.0565371 | ||||||||
\(88\) | −16.0045 | −1.70608 | ||||||||
\(89\) | 11.4896 | 1.21789 | 0.608947 | − | 0.793211i | \(-0.291592\pi\) | ||||
0.608947 | + | 0.793211i | \(0.291592\pi\) | |||||||
\(90\) | 8.09076 | 0.852842 | ||||||||
\(91\) | 4.78156 | 0.501243 | ||||||||
\(92\) | −10.1919 | −1.06258 | ||||||||
\(93\) | 8.26680 | 0.857227 | ||||||||
\(94\) | −11.0217 | −1.13680 | ||||||||
\(95\) | −17.0201 | −1.74623 | ||||||||
\(96\) | 13.9748 | 1.42630 | ||||||||
\(97\) | 3.50207 | 0.355581 | 0.177791 | − | 0.984068i | \(-0.443105\pi\) | ||||
0.177791 | + | 0.984068i | \(0.443105\pi\) | |||||||
\(98\) | −13.8297 | −1.39701 | ||||||||
\(99\) | −1.72559 | −0.173428 | ||||||||
\(100\) | 53.3860 | 5.33860 | ||||||||
\(101\) | −4.27210 | −0.425090 | −0.212545 | − | 0.977151i | \(-0.568175\pi\) | ||||
−0.212545 | + | 0.977151i | \(0.568175\pi\) | |||||||
\(102\) | −5.02435 | −0.497485 | ||||||||
\(103\) | 4.43274 | 0.436771 | 0.218386 | − | 0.975863i | \(-0.429921\pi\) | ||||
0.218386 | + | 0.975863i | \(0.429921\pi\) | |||||||
\(104\) | 9.76375 | 0.957414 | ||||||||
\(105\) | 21.0982 | 2.05897 | ||||||||
\(106\) | −20.5320 | −1.99424 | ||||||||
\(107\) | −2.47332 | −0.239105 | −0.119552 | − | 0.992828i | \(-0.538146\pi\) | ||||
−0.119552 | + | 0.992828i | \(0.538146\pi\) | |||||||
\(108\) | 26.7853 | 2.57742 | ||||||||
\(109\) | 14.5010 | 1.38895 | 0.694474 | − | 0.719518i | \(-0.255637\pi\) | ||||
0.694474 | + | 0.719518i | \(0.255637\pi\) | |||||||
\(110\) | −23.3788 | −2.22908 | ||||||||
\(111\) | 10.6898 | 1.01463 | ||||||||
\(112\) | −31.9999 | −3.02371 | ||||||||
\(113\) | 7.57853 | 0.712928 | 0.356464 | − | 0.934309i | \(-0.383982\pi\) | ||||
0.356464 | + | 0.934309i | \(0.383982\pi\) | |||||||
\(114\) | −16.3936 | −1.53540 | ||||||||
\(115\) | −8.62890 | −0.804649 | ||||||||
\(116\) | −1.68099 | −0.156076 | ||||||||
\(117\) | 1.05272 | 0.0973238 | ||||||||
\(118\) | 12.3099 | 1.13321 | ||||||||
\(119\) | 4.54593 | 0.416725 | ||||||||
\(120\) | 43.0817 | 3.93280 | ||||||||
\(121\) | −6.01380 | −0.546709 | ||||||||
\(122\) | −37.9171 | −3.43286 | ||||||||
\(123\) | −12.2844 | −1.10765 | ||||||||
\(124\) | −26.3517 | −2.36645 | ||||||||
\(125\) | 25.0605 | 2.24148 | ||||||||
\(126\) | −7.05091 | −0.628145 | ||||||||
\(127\) | −12.6084 | −1.11881 | −0.559405 | − | 0.828894i | \(-0.688970\pi\) | ||||
−0.559405 | + | 0.828894i | \(0.688970\pi\) | |||||||
\(128\) | 2.85048 | 0.251949 | ||||||||
\(129\) | 6.36221 | 0.560161 | ||||||||
\(130\) | 14.2626 | 1.25091 | ||||||||
\(131\) | −0.825251 | −0.0721025 | −0.0360512 | − | 0.999350i | \(-0.511478\pi\) | ||||
−0.0360512 | + | 0.999350i | \(0.511478\pi\) | |||||||
\(132\) | −15.8533 | −1.37986 | ||||||||
\(133\) | 14.8326 | 1.28615 | ||||||||
\(134\) | 20.9697 | 1.81151 | ||||||||
\(135\) | 22.6776 | 1.95177 | ||||||||
\(136\) | 9.28262 | 0.795978 | ||||||||
\(137\) | −18.5960 | −1.58877 | −0.794383 | − | 0.607417i | \(-0.792206\pi\) | ||||
−0.794383 | + | 0.607417i | \(0.792206\pi\) | |||||||
\(138\) | −8.31129 | −0.707504 | ||||||||
\(139\) | 7.24923 | 0.614871 | 0.307436 | − | 0.951569i | \(-0.400529\pi\) | ||||
0.307436 | + | 0.951569i | \(0.400529\pi\) | |||||||
\(140\) | −67.2537 | −5.68398 | ||||||||
\(141\) | −6.32772 | −0.532890 | ||||||||
\(142\) | −40.6330 | −3.40984 | ||||||||
\(143\) | −3.04190 | −0.254376 | ||||||||
\(144\) | −7.04517 | −0.587098 | ||||||||
\(145\) | −1.42319 | −0.118190 | ||||||||
\(146\) | −9.57241 | −0.792218 | ||||||||
\(147\) | −7.93984 | −0.654867 | ||||||||
\(148\) | −34.0753 | −2.80097 | ||||||||
\(149\) | −12.5800 | −1.03059 | −0.515297 | − | 0.857012i | \(-0.672318\pi\) | ||||
−0.515297 | + | 0.857012i | \(0.672318\pi\) | |||||||
\(150\) | 43.5352 | 3.55463 | ||||||||
\(151\) | −18.4981 | −1.50536 | −0.752678 | − | 0.658389i | \(-0.771238\pi\) | ||||
−0.752678 | + | 0.658389i | \(0.771238\pi\) | |||||||
\(152\) | 30.2876 | 2.45665 | ||||||||
\(153\) | 1.00084 | 0.0809133 | ||||||||
\(154\) | 20.3741 | 1.64179 | ||||||||
\(155\) | −22.3105 | −1.79202 | ||||||||
\(156\) | 9.67155 | 0.774344 | ||||||||
\(157\) | −7.46170 | −0.595508 | −0.297754 | − | 0.954643i | \(-0.596238\pi\) | ||||
−0.297754 | + | 0.954643i | \(0.596238\pi\) | |||||||
\(158\) | 7.92872 | 0.630775 | ||||||||
\(159\) | −11.7877 | −0.934826 | ||||||||
\(160\) | −37.7153 | −2.98165 | ||||||||
\(161\) | 7.51988 | 0.592650 | ||||||||
\(162\) | 15.8165 | 1.24266 | ||||||||
\(163\) | −6.22827 | −0.487836 | −0.243918 | − | 0.969796i | \(-0.578433\pi\) | ||||
−0.243918 | + | 0.969796i | \(0.578433\pi\) | |||||||
\(164\) | 39.1585 | 3.05776 | ||||||||
\(165\) | −13.4221 | −1.04491 | ||||||||
\(166\) | −37.3419 | −2.89829 | ||||||||
\(167\) | −1.51025 | −0.116866 | −0.0584332 | − | 0.998291i | \(-0.518610\pi\) | ||||
−0.0584332 | + | 0.998291i | \(0.518610\pi\) | |||||||
\(168\) | −37.5446 | −2.89663 | ||||||||
\(169\) | −11.1442 | −0.857250 | ||||||||
\(170\) | 13.5597 | 1.03998 | ||||||||
\(171\) | 3.26558 | 0.249725 | ||||||||
\(172\) | −20.2805 | −1.54638 | ||||||||
\(173\) | −2.46849 | −0.187676 | −0.0938379 | − | 0.995587i | \(-0.529914\pi\) | ||||
−0.0938379 | + | 0.995587i | \(0.529914\pi\) | |||||||
\(174\) | −1.37081 | −0.103921 | ||||||||
\(175\) | −39.3897 | −2.97759 | ||||||||
\(176\) | 20.3575 | 1.53451 | ||||||||
\(177\) | 7.06726 | 0.531208 | ||||||||
\(178\) | −29.8668 | −2.23861 | ||||||||
\(179\) | 19.4236 | 1.45179 | 0.725895 | − | 0.687805i | \(-0.241426\pi\) | ||||
0.725895 | + | 0.687805i | \(0.241426\pi\) | |||||||
\(180\) | −14.8067 | −1.10363 | ||||||||
\(181\) | 9.18538 | 0.682744 | 0.341372 | − | 0.939928i | \(-0.389108\pi\) | ||||
0.341372 | + | 0.939928i | \(0.389108\pi\) | |||||||
\(182\) | −12.4295 | −0.921335 | ||||||||
\(183\) | −21.7688 | −1.60919 | ||||||||
\(184\) | 15.3553 | 1.13201 | ||||||||
\(185\) | −28.8495 | −2.12106 | ||||||||
\(186\) | −21.4893 | −1.57567 | ||||||||
\(187\) | −2.89200 | −0.211484 | ||||||||
\(188\) | 20.1706 | 1.47109 | ||||||||
\(189\) | −19.7630 | −1.43754 | ||||||||
\(190\) | 44.2432 | 3.20974 | ||||||||
\(191\) | 6.15737 | 0.445531 | 0.222766 | − | 0.974872i | \(-0.428492\pi\) | ||||
0.222766 | + | 0.974872i | \(0.428492\pi\) | |||||||
\(192\) | −9.11556 | −0.657859 | ||||||||
\(193\) | −27.6051 | −1.98706 | −0.993529 | − | 0.113575i | \(-0.963770\pi\) | ||||
−0.993529 | + | 0.113575i | \(0.963770\pi\) | |||||||
\(194\) | −9.10351 | −0.653594 | ||||||||
\(195\) | 8.18834 | 0.586379 | ||||||||
\(196\) | 25.3095 | 1.80782 | ||||||||
\(197\) | −24.0659 | −1.71463 | −0.857313 | − | 0.514796i | \(-0.827868\pi\) | ||||
−0.857313 | + | 0.514796i | \(0.827868\pi\) | |||||||
\(198\) | 4.48560 | 0.318778 | ||||||||
\(199\) | −8.12255 | −0.575792 | −0.287896 | − | 0.957662i | \(-0.592956\pi\) | ||||
−0.287896 | + | 0.957662i | \(0.592956\pi\) | |||||||
\(200\) | −80.4323 | −5.68742 | ||||||||
\(201\) | 12.0390 | 0.849166 | ||||||||
\(202\) | 11.1052 | 0.781359 | ||||||||
\(203\) | 1.24028 | 0.0870506 | ||||||||
\(204\) | 9.19496 | 0.643776 | ||||||||
\(205\) | 33.1532 | 2.31552 | ||||||||
\(206\) | −11.5228 | −0.802829 | ||||||||
\(207\) | 1.65559 | 0.115072 | ||||||||
\(208\) | −12.4194 | −0.861129 | ||||||||
\(209\) | −9.43612 | −0.652710 | ||||||||
\(210\) | −54.8440 | −3.78460 | ||||||||
\(211\) | −4.04696 | −0.278604 | −0.139302 | − | 0.990250i | \(-0.544486\pi\) | ||||
−0.139302 | + | 0.990250i | \(0.544486\pi\) | |||||||
\(212\) | 37.5752 | 2.58067 | ||||||||
\(213\) | −23.3279 | −1.59840 | ||||||||
\(214\) | 6.42932 | 0.439499 | ||||||||
\(215\) | −17.1703 | −1.17101 | ||||||||
\(216\) | −40.3552 | −2.74582 | ||||||||
\(217\) | 19.4430 | 1.31988 | ||||||||
\(218\) | −37.6950 | −2.55303 | ||||||||
\(219\) | −5.49565 | −0.371362 | ||||||||
\(220\) | 42.7851 | 2.88457 | ||||||||
\(221\) | 1.76431 | 0.118680 | ||||||||
\(222\) | −27.7877 | −1.86499 | ||||||||
\(223\) | −3.95288 | −0.264705 | −0.132352 | − | 0.991203i | \(-0.542253\pi\) | ||||
−0.132352 | + | 0.991203i | \(0.542253\pi\) | |||||||
\(224\) | 32.8680 | 2.19608 | ||||||||
\(225\) | −8.67213 | −0.578142 | ||||||||
\(226\) | −19.7001 | −1.31043 | ||||||||
\(227\) | −13.8917 | −0.922024 | −0.461012 | − | 0.887394i | \(-0.652514\pi\) | ||||
−0.461012 | + | 0.887394i | \(0.652514\pi\) | |||||||
\(228\) | 30.0016 | 1.98691 | ||||||||
\(229\) | 25.0062 | 1.65245 | 0.826227 | − | 0.563337i | \(-0.190483\pi\) | ||||
0.826227 | + | 0.563337i | \(0.190483\pi\) | |||||||
\(230\) | 22.4305 | 1.47903 | ||||||||
\(231\) | 11.6970 | 0.769609 | ||||||||
\(232\) | 2.53260 | 0.166274 | ||||||||
\(233\) | −10.6103 | −0.695106 | −0.347553 | − | 0.937660i | \(-0.612987\pi\) | ||||
−0.347553 | + | 0.937660i | \(0.612987\pi\) | |||||||
\(234\) | −2.73650 | −0.178891 | ||||||||
\(235\) | 17.0773 | 1.11400 | ||||||||
\(236\) | −22.5280 | −1.46645 | ||||||||
\(237\) | 4.55199 | 0.295683 | ||||||||
\(238\) | −11.8170 | −0.765982 | ||||||||
\(239\) | −12.8261 | −0.829651 | −0.414825 | − | 0.909901i | \(-0.636157\pi\) | ||||
−0.414825 | + | 0.909901i | \(0.636157\pi\) | |||||||
\(240\) | −54.7994 | −3.53728 | ||||||||
\(241\) | 13.7210 | 0.883845 | 0.441922 | − | 0.897053i | \(-0.354297\pi\) | ||||
0.441922 | + | 0.897053i | \(0.354297\pi\) | |||||||
\(242\) | 15.6327 | 1.00491 | ||||||||
\(243\) | −7.81089 | −0.501069 | ||||||||
\(244\) | 69.3913 | 4.44232 | ||||||||
\(245\) | 21.4281 | 1.36899 | ||||||||
\(246\) | 31.9329 | 2.03597 | ||||||||
\(247\) | 5.75663 | 0.366286 | ||||||||
\(248\) | 39.7019 | 2.52107 | ||||||||
\(249\) | −21.4385 | −1.35861 | ||||||||
\(250\) | −65.1440 | −4.12007 | ||||||||
\(251\) | −19.5255 | −1.23244 | −0.616218 | − | 0.787576i | \(-0.711336\pi\) | ||||
−0.616218 | + | 0.787576i | \(0.711336\pi\) | |||||||
\(252\) | 12.9037 | 0.812858 | ||||||||
\(253\) | −4.78395 | −0.300764 | ||||||||
\(254\) | 32.7750 | 2.05649 | ||||||||
\(255\) | 7.78484 | 0.487505 | ||||||||
\(256\) | −19.6258 | −1.22661 | ||||||||
\(257\) | 22.7552 | 1.41943 | 0.709714 | − | 0.704490i | \(-0.248824\pi\) | ||||
0.709714 | + | 0.704490i | \(0.248824\pi\) | |||||||
\(258\) | −16.5383 | −1.02963 | ||||||||
\(259\) | 25.1417 | 1.56223 | ||||||||
\(260\) | −26.1016 | −1.61875 | ||||||||
\(261\) | 0.273063 | 0.0169022 | ||||||||
\(262\) | 2.14521 | 0.132532 | ||||||||
\(263\) | −18.0648 | −1.11392 | −0.556961 | − | 0.830538i | \(-0.688033\pi\) | ||||
−0.556961 | + | 0.830538i | \(0.688033\pi\) | |||||||
\(264\) | 23.8849 | 1.47001 | ||||||||
\(265\) | 31.8127 | 1.95424 | ||||||||
\(266\) | −38.5569 | −2.36407 | ||||||||
\(267\) | −17.1470 | −1.04938 | ||||||||
\(268\) | −38.3762 | −2.34420 | ||||||||
\(269\) | 25.6637 | 1.56474 | 0.782372 | − | 0.622811i | \(-0.214010\pi\) | ||||
0.782372 | + | 0.622811i | \(0.214010\pi\) | |||||||
\(270\) | −58.9496 | −3.58756 | ||||||||
\(271\) | 11.9563 | 0.726293 | 0.363147 | − | 0.931732i | \(-0.381702\pi\) | ||||
0.363147 | + | 0.931732i | \(0.381702\pi\) | |||||||
\(272\) | −11.8074 | −0.715928 | ||||||||
\(273\) | −7.13594 | −0.431887 | ||||||||
\(274\) | 48.3398 | 2.92031 | ||||||||
\(275\) | 25.0587 | 1.51110 | ||||||||
\(276\) | 15.2103 | 0.915553 | ||||||||
\(277\) | −22.1823 | −1.33281 | −0.666404 | − | 0.745591i | \(-0.732167\pi\) | ||||
−0.666404 | + | 0.745591i | \(0.732167\pi\) | |||||||
\(278\) | −18.8441 | −1.13020 | ||||||||
\(279\) | 4.28062 | 0.256274 | ||||||||
\(280\) | 101.326 | 6.05536 | ||||||||
\(281\) | −3.27908 | −0.195614 | −0.0978069 | − | 0.995205i | \(-0.531183\pi\) | ||||
−0.0978069 | + | 0.995205i | \(0.531183\pi\) | |||||||
\(282\) | 16.4487 | 0.979505 | ||||||||
\(283\) | −9.59509 | −0.570369 | −0.285185 | − | 0.958473i | \(-0.592055\pi\) | ||||
−0.285185 | + | 0.958473i | \(0.592055\pi\) | |||||||
\(284\) | 74.3615 | 4.41254 | ||||||||
\(285\) | 25.4006 | 1.50460 | ||||||||
\(286\) | 7.90731 | 0.467569 | ||||||||
\(287\) | −28.8922 | −1.70546 | ||||||||
\(288\) | 7.23628 | 0.426402 | ||||||||
\(289\) | −15.3226 | −0.901331 | ||||||||
\(290\) | 3.69954 | 0.217245 | ||||||||
\(291\) | −5.22645 | −0.306380 | ||||||||
\(292\) | 17.5183 | 1.02518 | ||||||||
\(293\) | 19.8258 | 1.15823 | 0.579117 | − | 0.815244i | \(-0.303397\pi\) | ||||
0.579117 | + | 0.815244i | \(0.303397\pi\) | |||||||
\(294\) | 20.6393 | 1.20371 | ||||||||
\(295\) | −19.0731 | −1.11048 | ||||||||
\(296\) | 51.3384 | 2.98398 | ||||||||
\(297\) | 12.5727 | 0.729541 | ||||||||
\(298\) | 32.7013 | 1.89433 | ||||||||
\(299\) | 2.91851 | 0.168782 | ||||||||
\(300\) | −79.6728 | −4.59991 | ||||||||
\(301\) | 14.9636 | 0.862485 | ||||||||
\(302\) | 48.0853 | 2.76700 | ||||||||
\(303\) | 6.37565 | 0.366271 | ||||||||
\(304\) | −38.5255 | −2.20959 | ||||||||
\(305\) | 58.7496 | 3.36399 | ||||||||
\(306\) | −2.60166 | −0.148727 | ||||||||
\(307\) | 0.426475 | 0.0243402 | 0.0121701 | − | 0.999926i | \(-0.496126\pi\) | ||||
0.0121701 | + | 0.999926i | \(0.496126\pi\) | |||||||
\(308\) | −37.2862 | −2.12458 | ||||||||
\(309\) | −6.61538 | −0.376336 | ||||||||
\(310\) | 57.9953 | 3.29391 | ||||||||
\(311\) | −0.218043 | −0.0123641 | −0.00618204 | − | 0.999981i | \(-0.501968\pi\) | ||||
−0.00618204 | + | 0.999981i | \(0.501968\pi\) | |||||||
\(312\) | −14.5713 | −0.824938 | ||||||||
\(313\) | −8.50023 | −0.480461 | −0.240231 | − | 0.970716i | \(-0.577223\pi\) | ||||
−0.240231 | + | 0.970716i | \(0.577223\pi\) | |||||||
\(314\) | 19.3964 | 1.09460 | ||||||||
\(315\) | 10.9248 | 0.615544 | ||||||||
\(316\) | −14.5102 | −0.816261 | ||||||||
\(317\) | 8.86492 | 0.497904 | 0.248952 | − | 0.968516i | \(-0.419914\pi\) | ||||
0.248952 | + | 0.968516i | \(0.419914\pi\) | |||||||
\(318\) | 30.6417 | 1.71830 | ||||||||
\(319\) | −0.789033 | −0.0441774 | ||||||||
\(320\) | 24.6011 | 1.37524 | ||||||||
\(321\) | 3.69116 | 0.206020 | ||||||||
\(322\) | −19.5477 | −1.08935 | ||||||||
\(323\) | 5.47296 | 0.304524 | ||||||||
\(324\) | −28.9454 | −1.60808 | ||||||||
\(325\) | −15.2874 | −0.847993 | ||||||||
\(326\) | 16.1902 | 0.896691 | ||||||||
\(327\) | −21.6412 | −1.19676 | ||||||||
\(328\) | −58.9968 | −3.25755 | ||||||||
\(329\) | −14.8824 | −0.820495 | ||||||||
\(330\) | 34.8903 | 1.92065 | ||||||||
\(331\) | 18.1989 | 1.00030 | 0.500151 | − | 0.865938i | \(-0.333278\pi\) | ||||
0.500151 | + | 0.865938i | \(0.333278\pi\) | |||||||
\(332\) | 68.3386 | 3.75057 | ||||||||
\(333\) | 5.53525 | 0.303330 | ||||||||
\(334\) | 3.92584 | 0.214812 | ||||||||
\(335\) | −32.4909 | −1.77517 | ||||||||
\(336\) | 47.7564 | 2.60532 | ||||||||
\(337\) | −25.4951 | −1.38881 | −0.694404 | − | 0.719586i | \(-0.744332\pi\) | ||||
−0.694404 | + | 0.719586i | \(0.744332\pi\) | |||||||
\(338\) | 28.9691 | 1.57571 | ||||||||
\(339\) | −11.3101 | −0.614281 | ||||||||
\(340\) | −24.8154 | −1.34580 | ||||||||
\(341\) | −12.3691 | −0.669827 | ||||||||
\(342\) | −8.48877 | −0.459020 | ||||||||
\(343\) | 5.89606 | 0.318357 | ||||||||
\(344\) | 30.5550 | 1.64741 | ||||||||
\(345\) | 12.8777 | 0.693311 | ||||||||
\(346\) | 6.41675 | 0.344967 | ||||||||
\(347\) | −1.89644 | −0.101806 | −0.0509031 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509031 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(348\) | 2.50869 | 0.134480 | ||||||||
\(349\) | −25.8118 | −1.38167 | −0.690836 | − | 0.723012i | \(-0.742757\pi\) | ||||
−0.690836 | + | 0.723012i | \(0.742757\pi\) | |||||||
\(350\) | 102.392 | 5.47310 | ||||||||
\(351\) | −7.67013 | −0.409401 | ||||||||
\(352\) | −20.9097 | −1.11449 | ||||||||
\(353\) | −13.8009 | −0.734550 | −0.367275 | − | 0.930112i | \(-0.619709\pi\) | ||||
−0.367275 | + | 0.930112i | \(0.619709\pi\) | |||||||
\(354\) | −18.3711 | −0.976413 | ||||||||
\(355\) | 62.9575 | 3.34144 | ||||||||
\(356\) | 54.6586 | 2.89690 | ||||||||
\(357\) | −6.78430 | −0.359063 | ||||||||
\(358\) | −50.4911 | −2.66854 | ||||||||
\(359\) | −15.7467 | −0.831081 | −0.415541 | − | 0.909575i | \(-0.636408\pi\) | ||||
−0.415541 | + | 0.909575i | \(0.636408\pi\) | |||||||
\(360\) | 22.3081 | 1.17574 | ||||||||
\(361\) | −1.14264 | −0.0601390 | ||||||||
\(362\) | −23.8771 | −1.25495 | ||||||||
\(363\) | 8.97493 | 0.471062 | ||||||||
\(364\) | 22.7469 | 1.19226 | ||||||||
\(365\) | 14.8317 | 0.776326 | ||||||||
\(366\) | 56.5871 | 2.95786 | ||||||||
\(367\) | 17.9908 | 0.939111 | 0.469556 | − | 0.882903i | \(-0.344414\pi\) | ||||
0.469556 | + | 0.882903i | \(0.344414\pi\) | |||||||
\(368\) | −19.5318 | −1.01816 | ||||||||
\(369\) | −6.36098 | −0.331139 | ||||||||
\(370\) | 74.9934 | 3.89872 | ||||||||
\(371\) | −27.7240 | −1.43936 | ||||||||
\(372\) | 39.3270 | 2.03901 | ||||||||
\(373\) | −10.5044 | −0.543900 | −0.271950 | − | 0.962311i | \(-0.587668\pi\) | ||||
−0.271950 | + | 0.962311i | \(0.587668\pi\) | |||||||
\(374\) | 7.51766 | 0.388729 | ||||||||
\(375\) | −37.4001 | −1.93133 | ||||||||
\(376\) | −30.3893 | −1.56721 | ||||||||
\(377\) | 0.481361 | 0.0247913 | ||||||||
\(378\) | 51.3732 | 2.64235 | ||||||||
\(379\) | −38.5594 | −1.98066 | −0.990332 | − | 0.138720i | \(-0.955701\pi\) | ||||
−0.990332 | + | 0.138720i | \(0.955701\pi\) | |||||||
\(380\) | −80.9685 | −4.15359 | ||||||||
\(381\) | 18.8166 | 0.964002 | ||||||||
\(382\) | −16.0059 | −0.818931 | ||||||||
\(383\) | 15.4110 | 0.787465 | 0.393732 | − | 0.919225i | \(-0.371184\pi\) | ||||
0.393732 | + | 0.919225i | \(0.371184\pi\) | |||||||
\(384\) | −4.25402 | −0.217087 | ||||||||
\(385\) | −31.5680 | −1.60886 | ||||||||
\(386\) | 71.7585 | 3.65241 | ||||||||
\(387\) | 3.29441 | 0.167464 | ||||||||
\(388\) | 16.6601 | 0.845790 | ||||||||
\(389\) | 15.3831 | 0.779955 | 0.389977 | − | 0.920824i | \(-0.372483\pi\) | ||||
0.389977 | + | 0.920824i | \(0.372483\pi\) | |||||||
\(390\) | −21.2853 | −1.07782 | ||||||||
\(391\) | 2.77470 | 0.140323 | ||||||||
\(392\) | −38.1317 | −1.92594 | ||||||||
\(393\) | 1.23160 | 0.0621258 | ||||||||
\(394\) | 62.5585 | 3.15165 | ||||||||
\(395\) | −12.2849 | −0.618122 | ||||||||
\(396\) | −8.20900 | −0.412518 | ||||||||
\(397\) | 2.06198 | 0.103488 | 0.0517439 | − | 0.998660i | \(-0.483522\pi\) | ||||
0.0517439 | + | 0.998660i | \(0.483522\pi\) | |||||||
\(398\) | 21.1143 | 1.05836 | ||||||||
\(399\) | −22.1360 | −1.10819 | ||||||||
\(400\) | 102.309 | 5.11545 | ||||||||
\(401\) | −35.8697 | −1.79125 | −0.895625 | − | 0.444810i | \(-0.853271\pi\) | ||||
−0.895625 | + | 0.444810i | \(0.853271\pi\) | |||||||
\(402\) | −31.2950 | −1.56085 | ||||||||
\(403\) | 7.54597 | 0.375891 | ||||||||
\(404\) | −20.3234 | −1.01113 | ||||||||
\(405\) | −24.5064 | −1.21773 | ||||||||
\(406\) | −3.22407 | −0.160008 | ||||||||
\(407\) | −15.9945 | −0.792817 | ||||||||
\(408\) | −13.8533 | −0.685840 | ||||||||
\(409\) | −8.67264 | −0.428835 | −0.214417 | − | 0.976742i | \(-0.568785\pi\) | ||||
−0.214417 | + | 0.976742i | \(0.568785\pi\) | |||||||
\(410\) | −86.1807 | −4.25616 | ||||||||
\(411\) | 27.7525 | 1.36893 | ||||||||
\(412\) | 21.0876 | 1.03891 | ||||||||
\(413\) | 16.6218 | 0.817905 | ||||||||
\(414\) | −4.30366 | −0.211513 | ||||||||
\(415\) | 57.8583 | 2.84015 | ||||||||
\(416\) | 12.7563 | 0.625427 | ||||||||
\(417\) | −10.8187 | −0.529793 | ||||||||
\(418\) | 24.5289 | 1.19975 | ||||||||
\(419\) | −25.2913 | −1.23556 | −0.617779 | − | 0.786351i | \(-0.711968\pi\) | ||||
−0.617779 | + | 0.786351i | \(0.711968\pi\) | |||||||
\(420\) | 100.369 | 4.89750 | ||||||||
\(421\) | −2.61582 | −0.127487 | −0.0637437 | − | 0.997966i | \(-0.520304\pi\) | ||||
−0.0637437 | + | 0.997966i | \(0.520304\pi\) | |||||||
\(422\) | 10.5199 | 0.512102 | ||||||||
\(423\) | −3.27655 | −0.159311 | ||||||||
\(424\) | −56.6114 | −2.74929 | ||||||||
\(425\) | −14.5341 | −0.705007 | ||||||||
\(426\) | 60.6402 | 2.93803 | ||||||||
\(427\) | −51.1989 | −2.47769 | ||||||||
\(428\) | −11.7661 | −0.568738 | ||||||||
\(429\) | 4.53970 | 0.219179 | ||||||||
\(430\) | 44.6337 | 2.15243 | ||||||||
\(431\) | −14.0539 | −0.676951 | −0.338475 | − | 0.940975i | \(-0.609911\pi\) | ||||
−0.338475 | + | 0.940975i | \(0.609911\pi\) | |||||||
\(432\) | 51.3314 | 2.46968 | ||||||||
\(433\) | 33.6468 | 1.61696 | 0.808482 | − | 0.588521i | \(-0.200290\pi\) | ||||
0.808482 | + | 0.588521i | \(0.200290\pi\) | |||||||
\(434\) | −50.5415 | −2.42607 | ||||||||
\(435\) | 2.12396 | 0.101836 | ||||||||
\(436\) | 68.9847 | 3.30377 | ||||||||
\(437\) | 9.05337 | 0.433082 | ||||||||
\(438\) | 14.2858 | 0.682600 | ||||||||
\(439\) | 20.0222 | 0.955609 | 0.477804 | − | 0.878466i | \(-0.341433\pi\) | ||||
0.477804 | + | 0.878466i | \(0.341433\pi\) | |||||||
\(440\) | −64.4607 | −3.07304 | ||||||||
\(441\) | −4.11132 | −0.195777 | ||||||||
\(442\) | −4.58625 | −0.218146 | ||||||||
\(443\) | 5.44302 | 0.258606 | 0.129303 | − | 0.991605i | \(-0.458726\pi\) | ||||
0.129303 | + | 0.991605i | \(0.458726\pi\) | |||||||
\(444\) | 50.8536 | 2.41340 | ||||||||
\(445\) | 46.2763 | 2.19370 | ||||||||
\(446\) | 10.2754 | 0.486554 | ||||||||
\(447\) | 18.7743 | 0.887992 | ||||||||
\(448\) | −21.4393 | −1.01291 | ||||||||
\(449\) | −11.7769 | −0.555784 | −0.277892 | − | 0.960612i | \(-0.589636\pi\) | ||||
−0.277892 | + | 0.960612i | \(0.589636\pi\) | |||||||
\(450\) | 22.5429 | 1.06268 | ||||||||
\(451\) | 18.3805 | 0.865503 | ||||||||
\(452\) | 36.0528 | 1.69578 | ||||||||
\(453\) | 27.6064 | 1.29706 | ||||||||
\(454\) | 36.1110 | 1.69477 | ||||||||
\(455\) | 19.2585 | 0.902853 | ||||||||
\(456\) | −45.2009 | −2.11673 | ||||||||
\(457\) | −6.35760 | −0.297396 | −0.148698 | − | 0.988883i | \(-0.547508\pi\) | ||||
−0.148698 | + | 0.988883i | \(0.547508\pi\) | |||||||
\(458\) | −65.0027 | −3.03738 | ||||||||
\(459\) | −7.29217 | −0.340369 | ||||||||
\(460\) | −41.0496 | −1.91395 | ||||||||
\(461\) | 11.7091 | 0.545349 | 0.272674 | − | 0.962106i | \(-0.412092\pi\) | ||||
0.272674 | + | 0.962106i | \(0.412092\pi\) | |||||||
\(462\) | −30.4061 | −1.41462 | ||||||||
\(463\) | 16.8431 | 0.782767 | 0.391384 | − | 0.920228i | \(-0.371997\pi\) | ||||
0.391384 | + | 0.920228i | \(0.371997\pi\) | |||||||
\(464\) | −3.22144 | −0.149552 | ||||||||
\(465\) | 33.2959 | 1.54406 | ||||||||
\(466\) | 27.5812 | 1.27767 | ||||||||
\(467\) | −33.0153 | −1.52777 | −0.763883 | − | 0.645355i | \(-0.776709\pi\) | ||||
−0.763883 | + | 0.645355i | \(0.776709\pi\) | |||||||
\(468\) | 5.00801 | 0.231496 | ||||||||
\(469\) | 28.3151 | 1.30747 | ||||||||
\(470\) | −44.3918 | −2.04764 | ||||||||
\(471\) | 11.1358 | 0.513109 | ||||||||
\(472\) | 33.9410 | 1.56226 | ||||||||
\(473\) | −9.51942 | −0.437703 | ||||||||
\(474\) | −11.8327 | −0.543496 | ||||||||
\(475\) | −47.4223 | −2.17588 | ||||||||
\(476\) | 21.6260 | 0.991227 | ||||||||
\(477\) | −6.10378 | −0.279473 | ||||||||
\(478\) | 33.3410 | 1.52498 | ||||||||
\(479\) | 20.0977 | 0.918287 | 0.459143 | − | 0.888362i | \(-0.348156\pi\) | ||||
0.459143 | + | 0.888362i | \(0.348156\pi\) | |||||||
\(480\) | 56.2859 | 2.56909 | ||||||||
\(481\) | 9.75766 | 0.444911 | ||||||||
\(482\) | −35.6672 | −1.62460 | ||||||||
\(483\) | −11.2226 | −0.510646 | ||||||||
\(484\) | −28.6090 | −1.30041 | ||||||||
\(485\) | 14.1052 | 0.640482 | ||||||||
\(486\) | 20.3042 | 0.921015 | ||||||||
\(487\) | −8.41434 | −0.381290 | −0.190645 | − | 0.981659i | \(-0.561058\pi\) | ||||
−0.190645 | + | 0.981659i | \(0.561058\pi\) | |||||||
\(488\) | −104.546 | −4.73258 | ||||||||
\(489\) | 9.29501 | 0.420335 | ||||||||
\(490\) | −55.7015 | −2.51634 | ||||||||
\(491\) | −27.8242 | −1.25569 | −0.627845 | − | 0.778338i | \(-0.716063\pi\) | ||||
−0.627845 | + | 0.778338i | \(0.716063\pi\) | |||||||
\(492\) | −58.4397 | −2.63467 | ||||||||
\(493\) | 0.457640 | 0.0206111 | ||||||||
\(494\) | −14.9642 | −0.673270 | ||||||||
\(495\) | −6.95009 | −0.312383 | ||||||||
\(496\) | −50.5004 | −2.26754 | ||||||||
\(497\) | −54.8660 | −2.46108 | ||||||||
\(498\) | 55.7286 | 2.49726 | ||||||||
\(499\) | 0.537870 | 0.0240784 | 0.0120392 | − | 0.999928i | \(-0.496168\pi\) | ||||
0.0120392 | + | 0.999928i | \(0.496168\pi\) | |||||||
\(500\) | 119.219 | 5.33162 | ||||||||
\(501\) | 2.25388 | 0.100696 | ||||||||
\(502\) | 50.7558 | 2.26534 | ||||||||
\(503\) | −13.1843 | −0.587861 | −0.293930 | − | 0.955827i | \(-0.594963\pi\) | ||||
−0.293930 | + | 0.955827i | \(0.594963\pi\) | |||||||
\(504\) | −19.4410 | −0.865969 | ||||||||
\(505\) | −17.2066 | −0.765684 | ||||||||
\(506\) | 12.4357 | 0.552835 | ||||||||
\(507\) | 16.6316 | 0.738634 | ||||||||
\(508\) | −59.9808 | −2.66122 | ||||||||
\(509\) | 29.4147 | 1.30378 | 0.651891 | − | 0.758313i | \(-0.273976\pi\) | ||||
0.651891 | + | 0.758313i | \(0.273976\pi\) | |||||||
\(510\) | −20.2364 | −0.896084 | ||||||||
\(511\) | −12.9255 | −0.571789 | ||||||||
\(512\) | 45.3156 | 2.00269 | ||||||||
\(513\) | −23.7931 | −1.05049 | ||||||||
\(514\) | −59.1513 | −2.60905 | ||||||||
\(515\) | 17.8536 | 0.786724 | ||||||||
\(516\) | 30.2665 | 1.33241 | ||||||||
\(517\) | 9.46781 | 0.416394 | ||||||||
\(518\) | −65.3550 | −2.87153 | ||||||||
\(519\) | 3.68395 | 0.161707 | ||||||||
\(520\) | 39.3251 | 1.72452 | ||||||||
\(521\) | 25.9814 | 1.13827 | 0.569134 | − | 0.822245i | \(-0.307279\pi\) | ||||
0.569134 | + | 0.822245i | \(0.307279\pi\) | |||||||
\(522\) | −0.709817 | −0.0310679 | ||||||||
\(523\) | −16.8680 | −0.737584 | −0.368792 | − | 0.929512i | \(-0.620229\pi\) | ||||
−0.368792 | + | 0.929512i | \(0.620229\pi\) | |||||||
\(524\) | −3.92590 | −0.171504 | ||||||||
\(525\) | 58.7849 | 2.56558 | ||||||||
\(526\) | 46.9588 | 2.04750 | ||||||||
\(527\) | 7.17412 | 0.312510 | ||||||||
\(528\) | −30.3813 | −1.32218 | ||||||||
\(529\) | −18.4101 | −0.800439 | ||||||||
\(530\) | −82.6960 | −3.59209 | ||||||||
\(531\) | 3.65949 | 0.158808 | ||||||||
\(532\) | 70.5621 | 3.05926 | ||||||||
\(533\) | −11.2133 | −0.485700 | ||||||||
\(534\) | 44.5729 | 1.92886 | ||||||||
\(535\) | −9.96171 | −0.430682 | ||||||||
\(536\) | 57.8182 | 2.49737 | ||||||||
\(537\) | −28.9876 | −1.25091 | ||||||||
\(538\) | −66.7120 | −2.87616 | ||||||||
\(539\) | 11.8799 | 0.511705 | ||||||||
\(540\) | 107.882 | 4.64251 | ||||||||
\(541\) | −4.42766 | −0.190360 | −0.0951799 | − | 0.995460i | \(-0.530343\pi\) | ||||
−0.0951799 | + | 0.995460i | \(0.530343\pi\) | |||||||
\(542\) | −31.0800 | −1.33500 | ||||||||
\(543\) | −13.7082 | −0.588274 | ||||||||
\(544\) | 12.1277 | 0.519970 | ||||||||
\(545\) | 58.4053 | 2.50181 | ||||||||
\(546\) | 18.5496 | 0.793852 | ||||||||
\(547\) | 3.77903 | 0.161579 | 0.0807897 | − | 0.996731i | \(-0.474256\pi\) | ||||
0.0807897 | + | 0.996731i | \(0.474256\pi\) | |||||||
\(548\) | −88.4655 | −3.77906 | ||||||||
\(549\) | −11.2721 | −0.481080 | ||||||||
\(550\) | −65.1393 | −2.77755 | ||||||||
\(551\) | 1.49320 | 0.0636126 | ||||||||
\(552\) | −22.9161 | −0.975374 | ||||||||
\(553\) | 10.7060 | 0.455266 | ||||||||
\(554\) | 57.6623 | 2.44983 | ||||||||
\(555\) | 43.0548 | 1.82757 | ||||||||
\(556\) | 34.4862 | 1.46254 | ||||||||
\(557\) | 21.4370 | 0.908314 | 0.454157 | − | 0.890922i | \(-0.349940\pi\) | ||||
0.454157 | + | 0.890922i | \(0.349940\pi\) | |||||||
\(558\) | −11.1273 | −0.471058 | ||||||||
\(559\) | 5.80745 | 0.245629 | ||||||||
\(560\) | −128.885 | −5.44639 | ||||||||
\(561\) | 4.31599 | 0.182221 | ||||||||
\(562\) | 8.52387 | 0.359558 | ||||||||
\(563\) | −41.0285 | −1.72914 | −0.864572 | − | 0.502509i | \(-0.832410\pi\) | ||||
−0.864572 | + | 0.502509i | \(0.832410\pi\) | |||||||
\(564\) | −30.1024 | −1.26754 | ||||||||
\(565\) | 30.5238 | 1.28415 | ||||||||
\(566\) | 24.9421 | 1.04840 | ||||||||
\(567\) | 21.3567 | 0.896898 | ||||||||
\(568\) | −112.034 | −4.70085 | ||||||||
\(569\) | 39.8989 | 1.67265 | 0.836325 | − | 0.548234i | \(-0.184700\pi\) | ||||
0.836325 | + | 0.548234i | \(0.184700\pi\) | |||||||
\(570\) | −66.0281 | −2.76561 | ||||||||
\(571\) | 41.6885 | 1.74461 | 0.872304 | − | 0.488964i | \(-0.162625\pi\) | ||||
0.872304 | + | 0.488964i | \(0.162625\pi\) | |||||||
\(572\) | −14.4710 | −0.605063 | ||||||||
\(573\) | −9.18919 | −0.383884 | ||||||||
\(574\) | 75.1044 | 3.13480 | ||||||||
\(575\) | −24.0423 | −1.00263 | ||||||||
\(576\) | −4.72012 | −0.196672 | ||||||||
\(577\) | −10.2985 | −0.428732 | −0.214366 | − | 0.976753i | \(-0.568769\pi\) | ||||
−0.214366 | + | 0.976753i | \(0.568769\pi\) | |||||||
\(578\) | 39.8307 | 1.65674 | ||||||||
\(579\) | 41.1976 | 1.71211 | ||||||||
\(580\) | −6.77045 | −0.281128 | ||||||||
\(581\) | −50.4221 | −2.09186 | ||||||||
\(582\) | 13.5860 | 0.563157 | ||||||||
\(583\) | 17.6373 | 0.730462 | ||||||||
\(584\) | −26.3933 | −1.09216 | ||||||||
\(585\) | 4.23999 | 0.175302 | ||||||||
\(586\) | −51.5364 | −2.12895 | ||||||||
\(587\) | −24.4774 | −1.01029 | −0.505146 | − | 0.863034i | \(-0.668561\pi\) | ||||
−0.505146 | + | 0.863034i | \(0.668561\pi\) | |||||||
\(588\) | −37.7716 | −1.55768 | ||||||||
\(589\) | 23.4080 | 0.964508 | ||||||||
\(590\) | 49.5800 | 2.04118 | ||||||||
\(591\) | 35.9157 | 1.47738 | ||||||||
\(592\) | −65.3018 | −2.68389 | ||||||||
\(593\) | −24.5084 | −1.00644 | −0.503219 | − | 0.864159i | \(-0.667851\pi\) | ||||
−0.503219 | + | 0.864159i | \(0.667851\pi\) | |||||||
\(594\) | −32.6823 | −1.34097 | ||||||||
\(595\) | 18.3095 | 0.750616 | ||||||||
\(596\) | −59.8459 | −2.45138 | ||||||||
\(597\) | 12.1220 | 0.496121 | ||||||||
\(598\) | −7.58658 | −0.310238 | ||||||||
\(599\) | −47.1516 | −1.92656 | −0.963282 | − | 0.268492i | \(-0.913475\pi\) | ||||
−0.963282 | + | 0.268492i | \(0.913475\pi\) | |||||||
\(600\) | 120.036 | 4.90046 | ||||||||
\(601\) | 13.5494 | 0.552690 | 0.276345 | − | 0.961059i | \(-0.410877\pi\) | ||||
0.276345 | + | 0.961059i | \(0.410877\pi\) | |||||||
\(602\) | −38.8972 | −1.58533 | ||||||||
\(603\) | 6.23390 | 0.253864 | ||||||||
\(604\) | −87.9998 | −3.58066 | ||||||||
\(605\) | −24.2216 | −0.984747 | ||||||||
\(606\) | −16.5733 | −0.673243 | ||||||||
\(607\) | 0.385009 | 0.0156270 | 0.00781351 | − | 0.999969i | \(-0.497513\pi\) | ||||
0.00781351 | + | 0.999969i | \(0.497513\pi\) | |||||||
\(608\) | 39.5706 | 1.60480 | ||||||||
\(609\) | −1.85098 | −0.0750055 | ||||||||
\(610\) | −152.718 | −6.18335 | ||||||||
\(611\) | −5.77597 | −0.233671 | ||||||||
\(612\) | 4.76123 | 0.192461 | ||||||||
\(613\) | −18.5161 | −0.747859 | −0.373930 | − | 0.927457i | \(-0.621990\pi\) | ||||
−0.373930 | + | 0.927457i | \(0.621990\pi\) | |||||||
\(614\) | −1.10861 | −0.0447398 | ||||||||
\(615\) | −49.4775 | −1.99513 | ||||||||
\(616\) | 56.1760 | 2.26339 | ||||||||
\(617\) | 27.4384 | 1.10463 | 0.552313 | − | 0.833637i | \(-0.313745\pi\) | ||||
0.552313 | + | 0.833637i | \(0.313745\pi\) | |||||||
\(618\) | 17.1965 | 0.691743 | ||||||||
\(619\) | 47.6959 | 1.91706 | 0.958531 | − | 0.284989i | \(-0.0919900\pi\) | ||||
0.958531 | + | 0.284989i | \(0.0919900\pi\) | |||||||
\(620\) | −106.136 | −4.26252 | ||||||||
\(621\) | −12.0627 | −0.484060 | ||||||||
\(622\) | 0.566795 | 0.0227264 | ||||||||
\(623\) | −40.3287 | −1.61573 | ||||||||
\(624\) | 18.5346 | 0.741976 | ||||||||
\(625\) | 44.8250 | 1.79300 | ||||||||
\(626\) | 22.0961 | 0.883136 | ||||||||
\(627\) | 14.0824 | 0.562396 | ||||||||
\(628\) | −35.4970 | −1.41648 | ||||||||
\(629\) | 9.27682 | 0.369891 | ||||||||
\(630\) | −28.3987 | −1.13143 | ||||||||
\(631\) | −27.1429 | −1.08054 | −0.540270 | − | 0.841492i | \(-0.681678\pi\) | ||||
−0.540270 | + | 0.841492i | \(0.681678\pi\) | |||||||
\(632\) | 21.8613 | 0.869595 | ||||||||
\(633\) | 6.03964 | 0.240054 | ||||||||
\(634\) | −23.0441 | −0.915197 | ||||||||
\(635\) | −50.7822 | −2.01523 | ||||||||
\(636\) | −56.0768 | −2.22359 | ||||||||
\(637\) | −7.24752 | −0.287157 | ||||||||
\(638\) | 2.05107 | 0.0812025 | ||||||||
\(639\) | −12.0794 | −0.477855 | ||||||||
\(640\) | 11.4808 | 0.453817 | ||||||||
\(641\) | 21.9832 | 0.868286 | 0.434143 | − | 0.900844i | \(-0.357051\pi\) | ||||
0.434143 | + | 0.900844i | \(0.357051\pi\) | |||||||
\(642\) | −9.59504 | −0.378686 | ||||||||
\(643\) | 42.0389 | 1.65785 | 0.828925 | − | 0.559359i | \(-0.188953\pi\) | ||||
0.828925 | + | 0.559359i | \(0.188953\pi\) | |||||||
\(644\) | 35.7738 | 1.40968 | ||||||||
\(645\) | 25.6248 | 1.00898 | ||||||||
\(646\) | −14.2268 | −0.559745 | ||||||||
\(647\) | −25.3347 | −0.996009 | −0.498005 | − | 0.867174i | \(-0.665934\pi\) | ||||
−0.498005 | + | 0.867174i | \(0.665934\pi\) | |||||||
\(648\) | 43.6096 | 1.71315 | ||||||||
\(649\) | −10.5743 | −0.415079 | ||||||||
\(650\) | 39.7391 | 1.55870 | ||||||||
\(651\) | −29.0166 | −1.13725 | ||||||||
\(652\) | −29.6293 | −1.16037 | ||||||||
\(653\) | −40.1446 | −1.57098 | −0.785490 | − | 0.618875i | \(-0.787589\pi\) | ||||
−0.785490 | + | 0.618875i | \(0.787589\pi\) | |||||||
\(654\) | 56.2556 | 2.19977 | ||||||||
\(655\) | −3.32383 | −0.129873 | ||||||||
\(656\) | 75.0433 | 2.92995 | ||||||||
\(657\) | −2.84570 | −0.111021 | ||||||||
\(658\) | 38.6864 | 1.50815 | ||||||||
\(659\) | −24.3984 | −0.950426 | −0.475213 | − | 0.879871i | \(-0.657629\pi\) | ||||
−0.475213 | + | 0.879871i | \(0.657629\pi\) | |||||||
\(660\) | −63.8520 | −2.48543 | ||||||||
\(661\) | −26.1812 | −1.01833 | −0.509165 | − | 0.860669i | \(-0.670046\pi\) | ||||
−0.509165 | + | 0.860669i | \(0.670046\pi\) | |||||||
\(662\) | −47.3074 | −1.83866 | ||||||||
\(663\) | −2.63303 | −0.102258 | ||||||||
\(664\) | −102.960 | −3.99562 | ||||||||
\(665\) | 59.7408 | 2.31665 | ||||||||
\(666\) | −14.3887 | −0.557551 | ||||||||
\(667\) | 0.757029 | 0.0293123 | ||||||||
\(668\) | −7.18459 | −0.277980 | ||||||||
\(669\) | 5.89924 | 0.228078 | ||||||||
\(670\) | 84.4590 | 3.26294 | ||||||||
\(671\) | 32.5714 | 1.25740 | ||||||||
\(672\) | −49.0518 | −1.89221 | ||||||||
\(673\) | 33.6298 | 1.29634 | 0.648168 | − | 0.761498i | \(-0.275536\pi\) | ||||
0.648168 | + | 0.761498i | \(0.275536\pi\) | |||||||
\(674\) | 66.2737 | 2.55277 | ||||||||
\(675\) | 63.1854 | 2.43201 | ||||||||
\(676\) | −53.0157 | −2.03907 | ||||||||
\(677\) | −25.9059 | −0.995646 | −0.497823 | − | 0.867279i | \(-0.665867\pi\) | ||||
−0.497823 | + | 0.867279i | \(0.665867\pi\) | |||||||
\(678\) | 29.4003 | 1.12911 | ||||||||
\(679\) | −12.2923 | −0.471736 | ||||||||
\(680\) | 37.3873 | 1.43374 | ||||||||
\(681\) | 20.7318 | 0.794445 | ||||||||
\(682\) | 32.1532 | 1.23121 | ||||||||
\(683\) | 3.72372 | 0.142484 | 0.0712422 | − | 0.997459i | \(-0.477304\pi\) | ||||
0.0712422 | + | 0.997459i | \(0.477304\pi\) | |||||||
\(684\) | 15.5351 | 0.594000 | ||||||||
\(685\) | −74.8986 | −2.86173 | ||||||||
\(686\) | −15.3266 | −0.585173 | ||||||||
\(687\) | −37.3189 | −1.42381 | ||||||||
\(688\) | −38.8656 | −1.48174 | ||||||||
\(689\) | −10.7599 | −0.409918 | ||||||||
\(690\) | −33.4751 | −1.27438 | ||||||||
\(691\) | −21.2141 | −0.807022 | −0.403511 | − | 0.914975i | \(-0.632210\pi\) | ||||
−0.403511 | + | 0.914975i | \(0.632210\pi\) | |||||||
\(692\) | −11.7432 | −0.446408 | ||||||||
\(693\) | 6.05684 | 0.230080 | ||||||||
\(694\) | 4.92973 | 0.187130 | ||||||||
\(695\) | 29.1975 | 1.10752 | ||||||||
\(696\) | −3.77963 | −0.143267 | ||||||||
\(697\) | −10.6607 | −0.403803 | ||||||||
\(698\) | 67.0968 | 2.53965 | ||||||||
\(699\) | 15.8347 | 0.598925 | ||||||||
\(700\) | −187.386 | −7.08252 | ||||||||
\(701\) | −26.2422 | −0.991153 | −0.495576 | − | 0.868564i | \(-0.665043\pi\) | ||||
−0.495576 | + | 0.868564i | \(0.665043\pi\) | |||||||
\(702\) | 19.9383 | 0.752521 | ||||||||
\(703\) | 30.2687 | 1.14161 | ||||||||
\(704\) | 13.6391 | 0.514043 | ||||||||
\(705\) | −25.4859 | −0.959856 | ||||||||
\(706\) | 35.8751 | 1.35018 | ||||||||
\(707\) | 14.9952 | 0.563951 | ||||||||
\(708\) | 33.6205 | 1.26354 | ||||||||
\(709\) | 25.2961 | 0.950015 | 0.475007 | − | 0.879982i | \(-0.342445\pi\) | ||||
0.475007 | + | 0.879982i | \(0.342445\pi\) | |||||||
\(710\) | −163.656 | −6.14190 | ||||||||
\(711\) | 2.35706 | 0.0883967 | ||||||||
\(712\) | −82.3496 | −3.08618 | ||||||||
\(713\) | 11.8674 | 0.444439 | ||||||||
\(714\) | 17.6356 | 0.659995 | ||||||||
\(715\) | −12.2518 | −0.458190 | ||||||||
\(716\) | 92.4026 | 3.45325 | ||||||||
\(717\) | 19.1415 | 0.714853 | ||||||||
\(718\) | 40.9331 | 1.52761 | ||||||||
\(719\) | 32.4592 | 1.21052 | 0.605262 | − | 0.796027i | \(-0.293069\pi\) | ||||
0.605262 | + | 0.796027i | \(0.293069\pi\) | |||||||
\(720\) | −28.3756 | −1.05750 | ||||||||
\(721\) | −15.5590 | −0.579447 | ||||||||
\(722\) | 2.97026 | 0.110542 | ||||||||
\(723\) | −20.4770 | −0.761548 | ||||||||
\(724\) | 43.6969 | 1.62398 | ||||||||
\(725\) | −3.96538 | −0.147270 | ||||||||
\(726\) | −23.3300 | −0.865859 | ||||||||
\(727\) | −3.20301 | −0.118793 | −0.0593966 | − | 0.998234i | \(-0.518918\pi\) | ||||
−0.0593966 | + | 0.998234i | \(0.518918\pi\) | |||||||
\(728\) | −34.2709 | −1.27016 | ||||||||
\(729\) | 29.9104 | 1.10779 | ||||||||
\(730\) | −38.5545 | −1.42697 | ||||||||
\(731\) | 5.52127 | 0.204212 | ||||||||
\(732\) | −103.559 | −3.82765 | ||||||||
\(733\) | 23.0781 | 0.852408 | 0.426204 | − | 0.904627i | \(-0.359851\pi\) | ||||
0.426204 | + | 0.904627i | \(0.359851\pi\) | |||||||
\(734\) | −46.7664 | −1.72618 | ||||||||
\(735\) | −31.9790 | −1.17956 | ||||||||
\(736\) | 20.0616 | 0.739480 | ||||||||
\(737\) | −18.0133 | −0.663528 | ||||||||
\(738\) | 16.5352 | 0.608667 | ||||||||
\(739\) | −44.9883 | −1.65492 | −0.827460 | − | 0.561525i | \(-0.810215\pi\) | ||||
−0.827460 | + | 0.561525i | \(0.810215\pi\) | |||||||
\(740\) | −137.244 | −5.04518 | ||||||||
\(741\) | −8.59114 | −0.315603 | ||||||||
\(742\) | 72.0677 | 2.64569 | ||||||||
\(743\) | 20.2450 | 0.742718 | 0.371359 | − | 0.928489i | \(-0.378892\pi\) | ||||
0.371359 | + | 0.928489i | \(0.378892\pi\) | |||||||
\(744\) | −59.2507 | −2.17224 | ||||||||
\(745\) | −50.6680 | −1.85633 | ||||||||
\(746\) | 27.3060 | 0.999742 | ||||||||
\(747\) | −11.1010 | −0.406166 | ||||||||
\(748\) | −13.7579 | −0.503039 | ||||||||
\(749\) | 8.68140 | 0.317211 | ||||||||
\(750\) | 97.2202 | 3.54998 | ||||||||
\(751\) | −23.0639 | −0.841615 | −0.420808 | − | 0.907150i | \(-0.638253\pi\) | ||||
−0.420808 | + | 0.907150i | \(0.638253\pi\) | |||||||
\(752\) | 38.6549 | 1.40960 | ||||||||
\(753\) | 29.1396 | 1.06191 | ||||||||
\(754\) | −1.25128 | −0.0455690 | ||||||||
\(755\) | −74.5043 | −2.71149 | ||||||||
\(756\) | −94.0169 | −3.41936 | ||||||||
\(757\) | 39.0657 | 1.41987 | 0.709933 | − | 0.704269i | \(-0.248725\pi\) | ||||
0.709933 | + | 0.704269i | \(0.248725\pi\) | |||||||
\(758\) | 100.234 | 3.64066 | ||||||||
\(759\) | 7.13952 | 0.259148 | ||||||||
\(760\) | 121.988 | 4.42499 | ||||||||
\(761\) | 7.94331 | 0.287945 | 0.143972 | − | 0.989582i | \(-0.454012\pi\) | ||||
0.143972 | + | 0.989582i | \(0.454012\pi\) | |||||||
\(762\) | −48.9131 | −1.77193 | ||||||||
\(763\) | −50.8989 | −1.84266 | ||||||||
\(764\) | 29.2920 | 1.05975 | ||||||||
\(765\) | 4.03106 | 0.145743 | ||||||||
\(766\) | −40.0603 | −1.44744 | ||||||||
\(767\) | 6.45102 | 0.232933 | ||||||||
\(768\) | 29.2893 | 1.05689 | ||||||||
\(769\) | −4.36395 | −0.157368 | −0.0786840 | − | 0.996900i | \(-0.525072\pi\) | ||||
−0.0786840 | + | 0.996900i | \(0.525072\pi\) | |||||||
\(770\) | 82.0600 | 2.95724 | ||||||||
\(771\) | −33.9596 | −1.22302 | ||||||||
\(772\) | −131.324 | −4.72644 | ||||||||
\(773\) | −0.811750 | −0.0291966 | −0.0145983 | − | 0.999893i | \(-0.504647\pi\) | ||||
−0.0145983 | + | 0.999893i | \(0.504647\pi\) | |||||||
\(774\) | −8.56370 | −0.307816 | ||||||||
\(775\) | −62.1626 | −2.23295 | ||||||||
\(776\) | −25.1004 | −0.901053 | ||||||||
\(777\) | −37.5212 | −1.34607 | ||||||||
\(778\) | −39.9879 | −1.43363 | ||||||||
\(779\) | −34.7841 | −1.24627 | ||||||||
\(780\) | 38.9538 | 1.39477 | ||||||||
\(781\) | 34.9043 | 1.24897 | ||||||||
\(782\) | −7.21273 | −0.257927 | ||||||||
\(783\) | −1.98954 | −0.0711005 | ||||||||
\(784\) | 48.5031 | 1.73225 | ||||||||
\(785\) | −30.0532 | −1.07265 | ||||||||
\(786\) | −3.20149 | −0.114193 | ||||||||
\(787\) | 13.4356 | 0.478926 | 0.239463 | − | 0.970906i | \(-0.423029\pi\) | ||||
0.239463 | + | 0.970906i | \(0.423029\pi\) | |||||||
\(788\) | −114.487 | −4.07843 | ||||||||
\(789\) | 26.9597 | 0.959791 | ||||||||
\(790\) | 31.9342 | 1.13617 | ||||||||
\(791\) | −26.6008 | −0.945815 | ||||||||
\(792\) | 12.3678 | 0.439471 | ||||||||
\(793\) | −19.8706 | −0.705626 | ||||||||
\(794\) | −5.36005 | −0.190221 | ||||||||
\(795\) | −47.4769 | −1.68383 | ||||||||
\(796\) | −38.6408 | −1.36959 | ||||||||
\(797\) | −0.792719 | −0.0280796 | −0.0140398 | − | 0.999901i | \(-0.504469\pi\) | ||||
−0.0140398 | + | 0.999901i | \(0.504469\pi\) | |||||||
\(798\) | 57.5419 | 2.03696 | ||||||||
\(799\) | −5.49134 | −0.194270 | ||||||||
\(800\) | −105.084 | −3.71529 | ||||||||
\(801\) | −8.87885 | −0.313719 | ||||||||
\(802\) | 93.2422 | 3.29250 | ||||||||
\(803\) | 8.22284 | 0.290178 | ||||||||
\(804\) | 57.2722 | 2.01984 | ||||||||
\(805\) | 30.2876 | 1.06750 | ||||||||
\(806\) | −19.6155 | −0.690926 | ||||||||
\(807\) | −38.3003 | −1.34823 | ||||||||
\(808\) | 30.6195 | 1.07719 | ||||||||
\(809\) | −26.9593 | −0.947838 | −0.473919 | − | 0.880569i | \(-0.657161\pi\) | ||||
−0.473919 | + | 0.880569i | \(0.657161\pi\) | |||||||
\(810\) | 63.7034 | 2.23831 | ||||||||
\(811\) | −44.1083 | −1.54885 | −0.774425 | − | 0.632666i | \(-0.781961\pi\) | ||||
−0.774425 | + | 0.632666i | \(0.781961\pi\) | |||||||
\(812\) | 5.90029 | 0.207060 | ||||||||
\(813\) | −17.8435 | −0.625797 | ||||||||
\(814\) | 41.5771 | 1.45728 | ||||||||
\(815\) | −25.0854 | −0.878703 | ||||||||
\(816\) | 17.6212 | 0.616866 | ||||||||
\(817\) | 18.0150 | 0.630265 | ||||||||
\(818\) | 22.5442 | 0.788241 | ||||||||
\(819\) | −3.69506 | −0.129116 | ||||||||
\(820\) | 157.717 | 5.50773 | ||||||||
\(821\) | −26.7055 | −0.932028 | −0.466014 | − | 0.884777i | \(-0.654310\pi\) | ||||
−0.466014 | + | 0.884777i | \(0.654310\pi\) | |||||||
\(822\) | −72.1418 | −2.51623 | ||||||||
\(823\) | −4.04766 | −0.141092 | −0.0705462 | − | 0.997509i | \(-0.522474\pi\) | ||||
−0.0705462 | + | 0.997509i | \(0.522474\pi\) | |||||||
\(824\) | −31.7709 | −1.10679 | ||||||||
\(825\) | −37.3974 | −1.30201 | ||||||||
\(826\) | −43.2078 | −1.50339 | ||||||||
\(827\) | 6.87816 | 0.239177 | 0.119589 | − | 0.992824i | \(-0.461842\pi\) | ||||
0.119589 | + | 0.992824i | \(0.461842\pi\) | |||||||
\(828\) | 7.87603 | 0.273711 | ||||||||
\(829\) | −0.319932 | −0.0111117 | −0.00555586 | − | 0.999985i | \(-0.501768\pi\) | ||||
−0.00555586 | + | 0.999985i | \(0.501768\pi\) | |||||||
\(830\) | −150.401 | −5.22048 | ||||||||
\(831\) | 33.1047 | 1.14839 | ||||||||
\(832\) | −8.32072 | −0.288469 | ||||||||
\(833\) | −6.89038 | −0.238738 | ||||||||
\(834\) | 28.1228 | 0.973812 | ||||||||
\(835\) | −6.08277 | −0.210503 | ||||||||
\(836\) | −44.8898 | −1.55254 | ||||||||
\(837\) | −31.1887 | −1.07804 | ||||||||
\(838\) | 65.7438 | 2.27108 | ||||||||
\(839\) | −10.5949 | −0.365778 | −0.182889 | − | 0.983134i | \(-0.558545\pi\) | ||||
−0.182889 | + | 0.983134i | \(0.558545\pi\) | |||||||
\(840\) | −151.217 | −5.21749 | ||||||||
\(841\) | −28.8751 | −0.995695 | ||||||||
\(842\) | 6.79974 | 0.234335 | ||||||||
\(843\) | 4.89367 | 0.168547 | ||||||||
\(844\) | −19.2523 | −0.662691 | ||||||||
\(845\) | −44.8853 | −1.54410 | ||||||||
\(846\) | 8.51728 | 0.292830 | ||||||||
\(847\) | 21.1085 | 0.725298 | ||||||||
\(848\) | 72.0090 | 2.47280 | ||||||||
\(849\) | 14.3196 | 0.491448 | ||||||||
\(850\) | 37.7809 | 1.29587 | ||||||||
\(851\) | 15.3457 | 0.526045 | ||||||||
\(852\) | −110.976 | −3.80199 | ||||||||
\(853\) | −12.0349 | −0.412066 | −0.206033 | − | 0.978545i | \(-0.566055\pi\) | ||||
−0.206033 | + | 0.978545i | \(0.566055\pi\) | |||||||
\(854\) | 133.090 | 4.55424 | ||||||||
\(855\) | 13.1527 | 0.449812 | ||||||||
\(856\) | 17.7271 | 0.605899 | ||||||||
\(857\) | −19.6152 | −0.670044 | −0.335022 | − | 0.942210i | \(-0.608744\pi\) | ||||
−0.335022 | + | 0.942210i | \(0.608744\pi\) | |||||||
\(858\) | −11.8008 | −0.402872 | ||||||||
\(859\) | 35.0648 | 1.19640 | 0.598198 | − | 0.801348i | \(-0.295884\pi\) | ||||
0.598198 | + | 0.801348i | \(0.295884\pi\) | |||||||
\(860\) | −81.6832 | −2.78537 | ||||||||
\(861\) | 43.1185 | 1.46947 | ||||||||
\(862\) | 36.5326 | 1.24430 | ||||||||
\(863\) | −21.1499 | −0.719950 | −0.359975 | − | 0.932962i | \(-0.617215\pi\) | ||||
−0.359975 | + | 0.932962i | \(0.617215\pi\) | |||||||
\(864\) | −52.7238 | −1.79370 | ||||||||
\(865\) | −9.94225 | −0.338047 | ||||||||
\(866\) | −87.4638 | −2.97214 | ||||||||
\(867\) | 22.8673 | 0.776616 | ||||||||
\(868\) | 92.4949 | 3.13948 | ||||||||
\(869\) | −6.81089 | −0.231044 | ||||||||
\(870\) | −5.52116 | −0.187185 | ||||||||
\(871\) | 10.9893 | 0.372357 | ||||||||
\(872\) | −103.934 | −3.51963 | ||||||||
\(873\) | −2.70630 | −0.0915945 | ||||||||
\(874\) | −23.5339 | −0.796048 | ||||||||
\(875\) | −87.9629 | −2.97369 | ||||||||
\(876\) | −26.1441 | −0.883326 | ||||||||
\(877\) | −2.93266 | −0.0990288 | −0.0495144 | − | 0.998773i | \(-0.515767\pi\) | ||||
−0.0495144 | + | 0.998773i | \(0.515767\pi\) | |||||||
\(878\) | −52.0471 | −1.75651 | ||||||||
\(879\) | −29.5878 | −0.997971 | ||||||||
\(880\) | 81.9933 | 2.76399 | ||||||||
\(881\) | 40.0242 | 1.34845 | 0.674225 | − | 0.738526i | \(-0.264478\pi\) | ||||
0.674225 | + | 0.738526i | \(0.264478\pi\) | |||||||
\(882\) | 10.6872 | 0.359858 | ||||||||
\(883\) | 22.6408 | 0.761922 | 0.380961 | − | 0.924591i | \(-0.375593\pi\) | ||||
0.380961 | + | 0.924591i | \(0.375593\pi\) | |||||||
\(884\) | 8.39320 | 0.282294 | ||||||||
\(885\) | 28.4646 | 0.956826 | ||||||||
\(886\) | −14.1490 | −0.475344 | ||||||||
\(887\) | −4.89817 | −0.164464 | −0.0822322 | − | 0.996613i | \(-0.526205\pi\) | ||||
−0.0822322 | + | 0.996613i | \(0.526205\pi\) | |||||||
\(888\) | −76.6169 | −2.57109 | ||||||||
\(889\) | 44.2555 | 1.48428 | ||||||||
\(890\) | −120.294 | −4.03225 | ||||||||
\(891\) | −13.5866 | −0.455167 | ||||||||
\(892\) | −18.8048 | −0.629630 | ||||||||
\(893\) | −17.9173 | −0.599581 | ||||||||
\(894\) | −48.8030 | −1.63222 | ||||||||
\(895\) | 78.2319 | 2.61500 | ||||||||
\(896\) | −10.0052 | −0.334251 | ||||||||
\(897\) | −4.35556 | −0.145428 | ||||||||
\(898\) | 30.6135 | 1.02159 | ||||||||
\(899\) | 1.95734 | 0.0652808 | ||||||||
\(900\) | −41.2553 | −1.37518 | ||||||||
\(901\) | −10.2296 | −0.340799 | ||||||||
\(902\) | −47.7795 | −1.59088 | ||||||||
\(903\) | −22.3315 | −0.743144 | ||||||||
\(904\) | −54.3177 | −1.80658 | ||||||||
\(905\) | 36.9956 | 1.22978 | ||||||||
\(906\) | −71.7619 | −2.38413 | ||||||||
\(907\) | −22.6748 | −0.752905 | −0.376452 | − | 0.926436i | \(-0.622856\pi\) | ||||
−0.376452 | + | 0.926436i | \(0.622856\pi\) | |||||||
\(908\) | −66.0859 | −2.19314 | ||||||||
\(909\) | 3.30137 | 0.109499 | ||||||||
\(910\) | −50.0618 | −1.65953 | ||||||||
\(911\) | −23.5333 | −0.779692 | −0.389846 | − | 0.920880i | \(-0.627472\pi\) | ||||
−0.389846 | + | 0.920880i | \(0.627472\pi\) | |||||||
\(912\) | 57.4951 | 1.90385 | ||||||||
\(913\) | 32.0772 | 1.06160 | ||||||||
\(914\) | 16.5264 | 0.546644 | ||||||||
\(915\) | −87.6773 | −2.89852 | ||||||||
\(916\) | 118.960 | 3.93055 | ||||||||
\(917\) | 2.89664 | 0.0956556 | ||||||||
\(918\) | 18.9557 | 0.625633 | ||||||||
\(919\) | −16.3232 | −0.538453 | −0.269227 | − | 0.963077i | \(-0.586768\pi\) | ||||
−0.269227 | + | 0.963077i | \(0.586768\pi\) | |||||||
\(920\) | 61.8460 | 2.03900 | ||||||||
\(921\) | −0.636467 | −0.0209723 | ||||||||
\(922\) | −30.4375 | −1.00241 | ||||||||
\(923\) | −21.2939 | −0.700896 | ||||||||
\(924\) | 55.6455 | 1.83060 | ||||||||
\(925\) | −80.3821 | −2.64295 | ||||||||
\(926\) | −43.7832 | −1.43881 | ||||||||
\(927\) | −3.42550 | −0.112508 | ||||||||
\(928\) | 3.30883 | 0.108618 | ||||||||
\(929\) | −52.5136 | −1.72292 | −0.861458 | − | 0.507829i | \(-0.830448\pi\) | ||||
−0.861458 | + | 0.507829i | \(0.830448\pi\) | |||||||
\(930\) | −86.5516 | −2.83814 | ||||||||
\(931\) | −22.4822 | −0.736823 | ||||||||
\(932\) | −50.4757 | −1.65339 | ||||||||
\(933\) | 0.325405 | 0.0106533 | ||||||||
\(934\) | 85.8221 | 2.80819 | ||||||||
\(935\) | −11.6480 | −0.380931 | ||||||||
\(936\) | −7.54516 | −0.246621 | ||||||||
\(937\) | −28.6251 | −0.935142 | −0.467571 | − | 0.883956i | \(-0.654871\pi\) | ||||
−0.467571 | + | 0.883956i | \(0.654871\pi\) | |||||||
\(938\) | −73.6040 | −2.40326 | ||||||||
\(939\) | 12.6857 | 0.413981 | ||||||||
\(940\) | 81.2404 | 2.64977 | ||||||||
\(941\) | 4.68441 | 0.152707 | 0.0763536 | − | 0.997081i | \(-0.475672\pi\) | ||||
0.0763536 | + | 0.997081i | \(0.475672\pi\) | |||||||
\(942\) | −28.9470 | −0.943145 | ||||||||
\(943\) | −17.6349 | −0.574273 | ||||||||
\(944\) | −43.1726 | −1.40515 | ||||||||
\(945\) | −79.5986 | −2.58934 | ||||||||
\(946\) | 24.7454 | 0.804542 | ||||||||
\(947\) | 30.7789 | 1.00018 | 0.500090 | − | 0.865973i | \(-0.333300\pi\) | ||||
0.500090 | + | 0.865973i | \(0.333300\pi\) | |||||||
\(948\) | 21.6548 | 0.703316 | ||||||||
\(949\) | −5.01646 | −0.162841 | ||||||||
\(950\) | 123.273 | 3.99949 | ||||||||
\(951\) | −13.2299 | −0.429009 | ||||||||
\(952\) | −32.5821 | −1.05599 | ||||||||
\(953\) | −3.12000 | −0.101067 | −0.0505334 | − | 0.998722i | \(-0.516092\pi\) | ||||
−0.0505334 | + | 0.998722i | \(0.516092\pi\) | |||||||
\(954\) | 15.8666 | 0.513699 | ||||||||
\(955\) | 24.7998 | 0.802503 | ||||||||
\(956\) | −61.0166 | −1.97342 | ||||||||
\(957\) | 1.17755 | 0.0380646 | ||||||||
\(958\) | −52.2433 | −1.68790 | ||||||||
\(959\) | 65.2724 | 2.10776 | ||||||||
\(960\) | −36.7144 | −1.18495 | ||||||||
\(961\) | −0.316139 | −0.0101980 | ||||||||
\(962\) | −25.3647 | −0.817791 | ||||||||
\(963\) | 1.91132 | 0.0615913 | ||||||||
\(964\) | 65.2737 | 2.10232 | ||||||||
\(965\) | −111.184 | −3.57914 | ||||||||
\(966\) | 29.1728 | 0.938618 | ||||||||
\(967\) | 36.7361 | 1.18135 | 0.590676 | − | 0.806909i | \(-0.298861\pi\) | ||||
0.590676 | + | 0.806909i | \(0.298861\pi\) | |||||||
\(968\) | 43.1028 | 1.38538 | ||||||||
\(969\) | −8.16779 | −0.262387 | ||||||||
\(970\) | −36.6659 | −1.17727 | ||||||||
\(971\) | −14.8858 | −0.477709 | −0.238855 | − | 0.971055i | \(-0.576772\pi\) | ||||
−0.238855 | + | 0.971055i | \(0.576772\pi\) | |||||||
\(972\) | −37.1582 | −1.19185 | ||||||||
\(973\) | −25.4449 | −0.815726 | ||||||||
\(974\) | 21.8728 | 0.700850 | ||||||||
\(975\) | 22.8148 | 0.730658 | ||||||||
\(976\) | 132.981 | 4.25663 | ||||||||
\(977\) | −26.2048 | −0.838367 | −0.419184 | − | 0.907902i | \(-0.637684\pi\) | ||||
−0.419184 | + | 0.907902i | \(0.637684\pi\) | |||||||
\(978\) | −24.1621 | −0.772618 | ||||||||
\(979\) | 25.6560 | 0.819970 | ||||||||
\(980\) | 101.938 | 3.25630 | ||||||||
\(981\) | −11.2060 | −0.357780 | ||||||||
\(982\) | 72.3282 | 2.30808 | ||||||||
\(983\) | 17.9934 | 0.573900 | 0.286950 | − | 0.957946i | \(-0.407359\pi\) | ||||
0.286950 | + | 0.957946i | \(0.407359\pi\) | |||||||
\(984\) | 88.0463 | 2.80681 | ||||||||
\(985\) | −96.9295 | −3.08843 | ||||||||
\(986\) | −1.18962 | −0.0378852 | ||||||||
\(987\) | 22.2104 | 0.706964 | ||||||||
\(988\) | 27.3856 | 0.871252 | ||||||||
\(989\) | 9.13329 | 0.290422 | ||||||||
\(990\) | 18.0665 | 0.574192 | ||||||||
\(991\) | 15.8588 | 0.503772 | 0.251886 | − | 0.967757i | \(-0.418949\pi\) | ||||
0.251886 | + | 0.967757i | \(0.418949\pi\) | |||||||
\(992\) | 51.8703 | 1.64688 | ||||||||
\(993\) | −27.1599 | −0.861892 | ||||||||
\(994\) | 142.622 | 4.52371 | ||||||||
\(995\) | −32.7149 | −1.03713 | ||||||||
\(996\) | −101.988 | −3.23161 | ||||||||
\(997\) | 9.67200 | 0.306315 | 0.153158 | − | 0.988202i | \(-0.451056\pi\) | ||||
0.153158 | + | 0.988202i | \(0.451056\pi\) | |||||||
\(998\) | −1.39817 | −0.0442585 | ||||||||
\(999\) | −40.3300 | −1.27599 |
(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 | 8017.2.a.a.1.17 | ✓ | 327 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8017.2.a.a.1.17 | ✓ | 327 | 1.1 | even | 1 | trivial |