Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.28515 | 1.61584 | 0.807922 | − | 0.589290i | \(-0.200592\pi\) | ||||
0.807922 | + | 0.589290i | \(0.200592\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.22190 | 1.61095 | ||||||||
\(5\) | −1.71471 | −0.766839 | −0.383420 | − | 0.923574i | \(-0.625254\pi\) | ||||
−0.383420 | + | 0.923574i | \(0.625254\pi\) | |||||||
\(6\) | −2.28515 | −0.932907 | ||||||||
\(7\) | −3.41344 | −1.29016 | −0.645079 | − | 0.764116i | \(-0.723175\pi\) | ||||
−0.645079 | + | 0.764116i | \(0.723175\pi\) | |||||||
\(8\) | 2.79222 | 0.987198 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.91835 | −1.23909 | ||||||||
\(11\) | −2.39155 | −0.721080 | −0.360540 | − | 0.932744i | \(-0.617408\pi\) | ||||
−0.360540 | + | 0.932744i | \(0.617408\pi\) | |||||||
\(12\) | −3.22190 | −0.930082 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −7.80020 | −2.08469 | ||||||||
\(15\) | 1.71471 | 0.442735 | ||||||||
\(16\) | −0.0631677 | −0.0157919 | ||||||||
\(17\) | 0.255103 | 0.0618715 | 0.0309358 | − | 0.999521i | \(-0.490151\pi\) | ||||
0.0309358 | + | 0.999521i | \(0.490151\pi\) | |||||||
\(18\) | 2.28515 | 0.538614 | ||||||||
\(19\) | 5.27925 | 1.21114 | 0.605572 | − | 0.795791i | \(-0.292945\pi\) | ||||
0.605572 | + | 0.795791i | \(0.292945\pi\) | |||||||
\(20\) | −5.52461 | −1.23534 | ||||||||
\(21\) | 3.41344 | 0.744873 | ||||||||
\(22\) | −5.46505 | −1.16515 | ||||||||
\(23\) | 8.19358 | 1.70848 | 0.854239 | − | 0.519880i | \(-0.174023\pi\) | ||||
0.854239 | + | 0.519880i | \(0.174023\pi\) | |||||||
\(24\) | −2.79222 | −0.569959 | ||||||||
\(25\) | −2.05979 | −0.411957 | ||||||||
\(26\) | 2.28515 | 0.448154 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −10.9977 | −2.07838 | ||||||||
\(29\) | 4.00188 | 0.743131 | 0.371565 | − | 0.928407i | \(-0.378821\pi\) | ||||
0.371565 | + | 0.928407i | \(0.378821\pi\) | |||||||
\(30\) | 3.91835 | 0.715390 | ||||||||
\(31\) | −1.24439 | −0.223498 | −0.111749 | − | 0.993736i | \(-0.535645\pi\) | ||||
−0.111749 | + | 0.993736i | \(0.535645\pi\) | |||||||
\(32\) | −5.72878 | −1.01272 | ||||||||
\(33\) | 2.39155 | 0.416316 | ||||||||
\(34\) | 0.582947 | 0.0999746 | ||||||||
\(35\) | 5.85304 | 0.989344 | ||||||||
\(36\) | 3.22190 | 0.536983 | ||||||||
\(37\) | 7.34531 | 1.20756 | 0.603781 | − | 0.797150i | \(-0.293660\pi\) | ||||
0.603781 | + | 0.797150i | \(0.293660\pi\) | |||||||
\(38\) | 12.0639 | 1.95702 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −4.78783 | −0.757022 | ||||||||
\(41\) | 2.94604 | 0.460095 | 0.230047 | − | 0.973179i | \(-0.426112\pi\) | ||||
0.230047 | + | 0.973179i | \(0.426112\pi\) | |||||||
\(42\) | 7.80020 | 1.20360 | ||||||||
\(43\) | 3.05454 | 0.465813 | 0.232906 | − | 0.972499i | \(-0.425176\pi\) | ||||
0.232906 | + | 0.972499i | \(0.425176\pi\) | |||||||
\(44\) | −7.70534 | −1.16162 | ||||||||
\(45\) | −1.71471 | −0.255613 | ||||||||
\(46\) | 18.7235 | 2.76063 | ||||||||
\(47\) | −11.6137 | −1.69403 | −0.847016 | − | 0.531567i | \(-0.821603\pi\) | ||||
−0.847016 | + | 0.531567i | \(0.821603\pi\) | |||||||
\(48\) | 0.0631677 | 0.00911748 | ||||||||
\(49\) | 4.65154 | 0.664506 | ||||||||
\(50\) | −4.70691 | −0.665658 | ||||||||
\(51\) | −0.255103 | −0.0357215 | ||||||||
\(52\) | 3.22190 | 0.446797 | ||||||||
\(53\) | 0.884763 | 0.121532 | 0.0607658 | − | 0.998152i | \(-0.480646\pi\) | ||||
0.0607658 | + | 0.998152i | \(0.480646\pi\) | |||||||
\(54\) | −2.28515 | −0.310969 | ||||||||
\(55\) | 4.10081 | 0.552953 | ||||||||
\(56\) | −9.53106 | −1.27364 | ||||||||
\(57\) | −5.27925 | −0.699254 | ||||||||
\(58\) | 9.14489 | 1.20078 | ||||||||
\(59\) | 11.4507 | 1.49075 | 0.745376 | − | 0.666644i | \(-0.232270\pi\) | ||||
0.745376 | + | 0.666644i | \(0.232270\pi\) | |||||||
\(60\) | 5.52461 | 0.713224 | ||||||||
\(61\) | 7.88600 | 1.00970 | 0.504850 | − | 0.863207i | \(-0.331548\pi\) | ||||
0.504850 | + | 0.863207i | \(0.331548\pi\) | |||||||
\(62\) | −2.84360 | −0.361138 | ||||||||
\(63\) | −3.41344 | −0.430052 | ||||||||
\(64\) | −12.9648 | −1.62060 | ||||||||
\(65\) | −1.71471 | −0.212683 | ||||||||
\(66\) | 5.46505 | 0.672701 | ||||||||
\(67\) | 7.71850 | 0.942965 | 0.471482 | − | 0.881875i | \(-0.343719\pi\) | ||||
0.471482 | + | 0.881875i | \(0.343719\pi\) | |||||||
\(68\) | 0.821915 | 0.0996718 | ||||||||
\(69\) | −8.19358 | −0.986391 | ||||||||
\(70\) | 13.3750 | 1.59862 | ||||||||
\(71\) | 10.9975 | 1.30517 | 0.652584 | − | 0.757717i | \(-0.273685\pi\) | ||||
0.652584 | + | 0.757717i | \(0.273685\pi\) | |||||||
\(72\) | 2.79222 | 0.329066 | ||||||||
\(73\) | −8.26216 | −0.967012 | −0.483506 | − | 0.875341i | \(-0.660637\pi\) | ||||
−0.483506 | + | 0.875341i | \(0.660637\pi\) | |||||||
\(74\) | 16.7851 | 1.95123 | ||||||||
\(75\) | 2.05979 | 0.237844 | ||||||||
\(76\) | 17.0092 | 1.95109 | ||||||||
\(77\) | 8.16341 | 0.930307 | ||||||||
\(78\) | −2.28515 | −0.258742 | ||||||||
\(79\) | 5.00055 | 0.562606 | 0.281303 | − | 0.959619i | \(-0.409233\pi\) | ||||
0.281303 | + | 0.959619i | \(0.409233\pi\) | |||||||
\(80\) | 0.108314 | 0.0121099 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.73214 | 0.743441 | ||||||||
\(83\) | 16.0795 | 1.76496 | 0.882479 | − | 0.470351i | \(-0.155873\pi\) | ||||
0.882479 | + | 0.470351i | \(0.155873\pi\) | |||||||
\(84\) | 10.9977 | 1.19995 | ||||||||
\(85\) | −0.437426 | −0.0474455 | ||||||||
\(86\) | 6.98007 | 0.752680 | ||||||||
\(87\) | −4.00188 | −0.429047 | ||||||||
\(88\) | −6.67773 | −0.711849 | ||||||||
\(89\) | −11.1784 | −1.18490 | −0.592452 | − | 0.805606i | \(-0.701840\pi\) | ||||
−0.592452 | + | 0.805606i | \(0.701840\pi\) | |||||||
\(90\) | −3.91835 | −0.413031 | ||||||||
\(91\) | −3.41344 | −0.357825 | ||||||||
\(92\) | 26.3989 | 2.75227 | ||||||||
\(93\) | 1.24439 | 0.129037 | ||||||||
\(94\) | −26.5390 | −2.73729 | ||||||||
\(95\) | −9.05236 | −0.928753 | ||||||||
\(96\) | 5.72878 | 0.584691 | ||||||||
\(97\) | 16.1374 | 1.63851 | 0.819254 | − | 0.573431i | \(-0.194388\pi\) | ||||
0.819254 | + | 0.573431i | \(0.194388\pi\) | |||||||
\(98\) | 10.6295 | 1.07374 | ||||||||
\(99\) | −2.39155 | −0.240360 | ||||||||
\(100\) | −6.63642 | −0.663642 | ||||||||
\(101\) | 7.78769 | 0.774904 | 0.387452 | − | 0.921890i | \(-0.373355\pi\) | ||||
0.387452 | + | 0.921890i | \(0.373355\pi\) | |||||||
\(102\) | −0.582947 | −0.0577204 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 2.79222 | 0.273799 | ||||||||
\(105\) | −5.85304 | −0.571198 | ||||||||
\(106\) | 2.02181 | 0.196376 | ||||||||
\(107\) | −12.7489 | −1.23248 | −0.616241 | − | 0.787558i | \(-0.711345\pi\) | ||||
−0.616241 | + | 0.787558i | \(0.711345\pi\) | |||||||
\(108\) | −3.22190 | −0.310027 | ||||||||
\(109\) | −4.89646 | −0.468996 | −0.234498 | − | 0.972117i | \(-0.575345\pi\) | ||||
−0.234498 | + | 0.972117i | \(0.575345\pi\) | |||||||
\(110\) | 9.37095 | 0.893485 | ||||||||
\(111\) | −7.34531 | −0.697186 | ||||||||
\(112\) | 0.215619 | 0.0203741 | ||||||||
\(113\) | −6.75655 | −0.635603 | −0.317802 | − | 0.948157i | \(-0.602945\pi\) | ||||
−0.317802 | + | 0.948157i | \(0.602945\pi\) | |||||||
\(114\) | −12.0639 | −1.12988 | ||||||||
\(115\) | −14.0496 | −1.31013 | ||||||||
\(116\) | 12.8937 | 1.19715 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 26.1665 | 2.40882 | ||||||||
\(119\) | −0.870777 | −0.0798240 | ||||||||
\(120\) | 4.78783 | 0.437067 | ||||||||
\(121\) | −5.28048 | −0.480044 | ||||||||
\(122\) | 18.0207 | 1.63152 | ||||||||
\(123\) | −2.94604 | −0.265636 | ||||||||
\(124\) | −4.00928 | −0.360044 | ||||||||
\(125\) | 12.1055 | 1.08274 | ||||||||
\(126\) | −7.80020 | −0.694897 | ||||||||
\(127\) | 11.3175 | 1.00427 | 0.502133 | − | 0.864790i | \(-0.332549\pi\) | ||||
0.502133 | + | 0.864790i | \(0.332549\pi\) | |||||||
\(128\) | −18.1689 | −1.60592 | ||||||||
\(129\) | −3.05454 | −0.268937 | ||||||||
\(130\) | −3.91835 | −0.343662 | ||||||||
\(131\) | 19.1731 | 1.67516 | 0.837580 | − | 0.546314i | \(-0.183969\pi\) | ||||
0.837580 | + | 0.546314i | \(0.183969\pi\) | |||||||
\(132\) | 7.70534 | 0.670663 | ||||||||
\(133\) | −18.0204 | −1.56257 | ||||||||
\(134\) | 17.6379 | 1.52368 | ||||||||
\(135\) | 1.71471 | 0.147578 | ||||||||
\(136\) | 0.712302 | 0.0610794 | ||||||||
\(137\) | 17.2171 | 1.47095 | 0.735476 | − | 0.677550i | \(-0.236958\pi\) | ||||
0.735476 | + | 0.677550i | \(0.236958\pi\) | |||||||
\(138\) | −18.7235 | −1.59385 | ||||||||
\(139\) | −11.2343 | −0.952880 | −0.476440 | − | 0.879207i | \(-0.658073\pi\) | ||||
−0.476440 | + | 0.879207i | \(0.658073\pi\) | |||||||
\(140\) | 18.8579 | 1.59378 | ||||||||
\(141\) | 11.6137 | 0.978050 | ||||||||
\(142\) | 25.1310 | 2.10895 | ||||||||
\(143\) | −2.39155 | −0.199992 | ||||||||
\(144\) | −0.0631677 | −0.00526398 | ||||||||
\(145\) | −6.86205 | −0.569862 | ||||||||
\(146\) | −18.8802 | −1.56254 | ||||||||
\(147\) | −4.65154 | −0.383653 | ||||||||
\(148\) | 23.6658 | 1.94532 | ||||||||
\(149\) | 1.54149 | 0.126284 | 0.0631420 | − | 0.998005i | \(-0.479888\pi\) | ||||
0.0631420 | + | 0.998005i | \(0.479888\pi\) | |||||||
\(150\) | 4.70691 | 0.384318 | ||||||||
\(151\) | 9.37962 | 0.763303 | 0.381651 | − | 0.924306i | \(-0.375356\pi\) | ||||
0.381651 | + | 0.924306i | \(0.375356\pi\) | |||||||
\(152\) | 14.7408 | 1.19564 | ||||||||
\(153\) | 0.255103 | 0.0206238 | ||||||||
\(154\) | 18.6546 | 1.50323 | ||||||||
\(155\) | 2.13375 | 0.171387 | ||||||||
\(156\) | −3.22190 | −0.257958 | ||||||||
\(157\) | −20.7437 | −1.65553 | −0.827764 | − | 0.561077i | \(-0.810387\pi\) | ||||
−0.827764 | + | 0.561077i | \(0.810387\pi\) | |||||||
\(158\) | 11.4270 | 0.909083 | ||||||||
\(159\) | −0.884763 | −0.0701663 | ||||||||
\(160\) | 9.82317 | 0.776590 | ||||||||
\(161\) | −27.9682 | −2.20421 | ||||||||
\(162\) | 2.28515 | 0.179538 | ||||||||
\(163\) | 12.2878 | 0.962453 | 0.481226 | − | 0.876596i | \(-0.340192\pi\) | ||||
0.481226 | + | 0.876596i | \(0.340192\pi\) | |||||||
\(164\) | 9.49185 | 0.741189 | ||||||||
\(165\) | −4.10081 | −0.319247 | ||||||||
\(166\) | 36.7441 | 2.85190 | ||||||||
\(167\) | −25.1607 | −1.94699 | −0.973495 | − | 0.228708i | \(-0.926550\pi\) | ||||
−0.973495 | + | 0.228708i | \(0.926550\pi\) | |||||||
\(168\) | 9.53106 | 0.735337 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.999583 | −0.0766645 | ||||||||
\(171\) | 5.27925 | 0.403714 | ||||||||
\(172\) | 9.84141 | 0.750401 | ||||||||
\(173\) | 2.99711 | 0.227866 | 0.113933 | − | 0.993488i | \(-0.463655\pi\) | ||||
0.113933 | + | 0.993488i | \(0.463655\pi\) | |||||||
\(174\) | −9.14489 | −0.693272 | ||||||||
\(175\) | 7.03095 | 0.531490 | ||||||||
\(176\) | 0.151069 | 0.0113872 | ||||||||
\(177\) | −11.4507 | −0.860686 | ||||||||
\(178\) | −25.5442 | −1.91462 | ||||||||
\(179\) | −19.1346 | −1.43018 | −0.715092 | − | 0.699030i | \(-0.753615\pi\) | ||||
−0.715092 | + | 0.699030i | \(0.753615\pi\) | |||||||
\(180\) | −5.52461 | −0.411780 | ||||||||
\(181\) | −11.5217 | −0.856405 | −0.428202 | − | 0.903683i | \(-0.640853\pi\) | ||||
−0.428202 | + | 0.903683i | \(0.640853\pi\) | |||||||
\(182\) | −7.80020 | −0.578190 | ||||||||
\(183\) | −7.88600 | −0.582950 | ||||||||
\(184\) | 22.8782 | 1.68661 | ||||||||
\(185\) | −12.5950 | −0.926006 | ||||||||
\(186\) | 2.84360 | 0.208503 | ||||||||
\(187\) | −0.610091 | −0.0446143 | ||||||||
\(188\) | −37.4182 | −2.72900 | ||||||||
\(189\) | 3.41344 | 0.248291 | ||||||||
\(190\) | −20.6860 | −1.50072 | ||||||||
\(191\) | −16.4594 | −1.19096 | −0.595480 | − | 0.803370i | \(-0.703038\pi\) | ||||
−0.595480 | + | 0.803370i | \(0.703038\pi\) | |||||||
\(192\) | 12.9648 | 0.935652 | ||||||||
\(193\) | 19.1523 | 1.37861 | 0.689306 | − | 0.724470i | \(-0.257915\pi\) | ||||
0.689306 | + | 0.724470i | \(0.257915\pi\) | |||||||
\(194\) | 36.8764 | 2.64757 | ||||||||
\(195\) | 1.71471 | 0.122793 | ||||||||
\(196\) | 14.9868 | 1.07049 | ||||||||
\(197\) | 23.2375 | 1.65560 | 0.827802 | − | 0.561020i | \(-0.189591\pi\) | ||||
0.827802 | + | 0.561020i | \(0.189591\pi\) | |||||||
\(198\) | −5.46505 | −0.388384 | ||||||||
\(199\) | −16.9857 | −1.20408 | −0.602041 | − | 0.798465i | \(-0.705646\pi\) | ||||
−0.602041 | + | 0.798465i | \(0.705646\pi\) | |||||||
\(200\) | −5.75137 | −0.406683 | ||||||||
\(201\) | −7.71850 | −0.544421 | ||||||||
\(202\) | 17.7960 | 1.25212 | ||||||||
\(203\) | −13.6602 | −0.958756 | ||||||||
\(204\) | −0.821915 | −0.0575456 | ||||||||
\(205\) | −5.05160 | −0.352819 | ||||||||
\(206\) | −2.28515 | −0.159214 | ||||||||
\(207\) | 8.19358 | 0.569493 | ||||||||
\(208\) | −0.0631677 | −0.00437989 | ||||||||
\(209\) | −12.6256 | −0.873331 | ||||||||
\(210\) | −13.3750 | −0.922966 | ||||||||
\(211\) | −7.92265 | −0.545418 | −0.272709 | − | 0.962097i | \(-0.587920\pi\) | ||||
−0.272709 | + | 0.962097i | \(0.587920\pi\) | |||||||
\(212\) | 2.85062 | 0.195781 | ||||||||
\(213\) | −10.9975 | −0.753539 | ||||||||
\(214\) | −29.1331 | −1.99150 | ||||||||
\(215\) | −5.23763 | −0.357204 | ||||||||
\(216\) | −2.79222 | −0.189986 | ||||||||
\(217\) | 4.24763 | 0.288348 | ||||||||
\(218\) | −11.1891 | −0.757824 | ||||||||
\(219\) | 8.26216 | 0.558305 | ||||||||
\(220\) | 13.2124 | 0.890779 | ||||||||
\(221\) | 0.255103 | 0.0171601 | ||||||||
\(222\) | −16.7851 | −1.12654 | ||||||||
\(223\) | 7.13905 | 0.478066 | 0.239033 | − | 0.971011i | \(-0.423170\pi\) | ||||
0.239033 | + | 0.971011i | \(0.423170\pi\) | |||||||
\(224\) | 19.5548 | 1.30656 | ||||||||
\(225\) | −2.05979 | −0.137319 | ||||||||
\(226\) | −15.4397 | −1.02703 | ||||||||
\(227\) | 22.8763 | 1.51836 | 0.759178 | − | 0.650883i | \(-0.225601\pi\) | ||||
0.759178 | + | 0.650883i | \(0.225601\pi\) | |||||||
\(228\) | −17.0092 | −1.12646 | ||||||||
\(229\) | −23.8110 | −1.57347 | −0.786736 | − | 0.617289i | \(-0.788231\pi\) | ||||
−0.786736 | + | 0.617289i | \(0.788231\pi\) | |||||||
\(230\) | −32.1053 | −2.11696 | ||||||||
\(231\) | −8.16341 | −0.537113 | ||||||||
\(232\) | 11.1741 | 0.733617 | ||||||||
\(233\) | −12.3701 | −0.810395 | −0.405198 | − | 0.914229i | \(-0.632797\pi\) | ||||
−0.405198 | + | 0.914229i | \(0.632797\pi\) | |||||||
\(234\) | 2.28515 | 0.149385 | ||||||||
\(235\) | 19.9141 | 1.29905 | ||||||||
\(236\) | 36.8929 | 2.40153 | ||||||||
\(237\) | −5.00055 | −0.324821 | ||||||||
\(238\) | −1.98985 | −0.128983 | ||||||||
\(239\) | 7.04450 | 0.455671 | 0.227835 | − | 0.973700i | \(-0.426835\pi\) | ||||
0.227835 | + | 0.973700i | \(0.426835\pi\) | |||||||
\(240\) | −0.108314 | −0.00699164 | ||||||||
\(241\) | 1.57911 | 0.101719 | 0.0508597 | − | 0.998706i | \(-0.483804\pi\) | ||||
0.0508597 | + | 0.998706i | \(0.483804\pi\) | |||||||
\(242\) | −12.0667 | −0.775675 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 25.4079 | 1.62657 | ||||||||
\(245\) | −7.97602 | −0.509569 | ||||||||
\(246\) | −6.73214 | −0.429226 | ||||||||
\(247\) | 5.27925 | 0.335911 | ||||||||
\(248\) | −3.47460 | −0.220637 | ||||||||
\(249\) | −16.0795 | −1.01900 | ||||||||
\(250\) | 27.6627 | 1.74955 | ||||||||
\(251\) | −9.65990 | −0.609727 | −0.304864 | − | 0.952396i | \(-0.598611\pi\) | ||||
−0.304864 | + | 0.952396i | \(0.598611\pi\) | |||||||
\(252\) | −10.9977 | −0.692793 | ||||||||
\(253\) | −19.5954 | −1.23195 | ||||||||
\(254\) | 25.8622 | 1.62274 | ||||||||
\(255\) | 0.437426 | 0.0273927 | ||||||||
\(256\) | −15.5890 | −0.974311 | ||||||||
\(257\) | −17.5266 | −1.09328 | −0.546639 | − | 0.837369i | \(-0.684093\pi\) | ||||
−0.546639 | + | 0.837369i | \(0.684093\pi\) | |||||||
\(258\) | −6.98007 | −0.434560 | ||||||||
\(259\) | −25.0727 | −1.55794 | ||||||||
\(260\) | −5.52461 | −0.342622 | ||||||||
\(261\) | 4.00188 | 0.247710 | ||||||||
\(262\) | 43.8133 | 2.70680 | ||||||||
\(263\) | 24.8504 | 1.53234 | 0.766170 | − | 0.642638i | \(-0.222160\pi\) | ||||
0.766170 | + | 0.642638i | \(0.222160\pi\) | |||||||
\(264\) | 6.67773 | 0.410986 | ||||||||
\(265\) | −1.51711 | −0.0931952 | ||||||||
\(266\) | −41.1792 | −2.52486 | ||||||||
\(267\) | 11.1784 | 0.684104 | ||||||||
\(268\) | 24.8682 | 1.51907 | ||||||||
\(269\) | 9.71874 | 0.592562 | 0.296281 | − | 0.955101i | \(-0.404253\pi\) | ||||
0.296281 | + | 0.955101i | \(0.404253\pi\) | |||||||
\(270\) | 3.91835 | 0.238463 | ||||||||
\(271\) | −1.14079 | −0.0692982 | −0.0346491 | − | 0.999400i | \(-0.511031\pi\) | ||||
−0.0346491 | + | 0.999400i | \(0.511031\pi\) | |||||||
\(272\) | −0.0161143 | −0.000977071 0 | ||||||||
\(273\) | 3.41344 | 0.206591 | ||||||||
\(274\) | 39.3435 | 2.37683 | ||||||||
\(275\) | 4.92608 | 0.297054 | ||||||||
\(276\) | −26.3989 | −1.58903 | ||||||||
\(277\) | 10.0010 | 0.600900 | 0.300450 | − | 0.953798i | \(-0.402863\pi\) | ||||
0.300450 | + | 0.953798i | \(0.402863\pi\) | |||||||
\(278\) | −25.6720 | −1.53970 | ||||||||
\(279\) | −1.24439 | −0.0744994 | ||||||||
\(280\) | 16.3429 | 0.976678 | ||||||||
\(281\) | −1.05334 | −0.0628371 | −0.0314185 | − | 0.999506i | \(-0.510002\pi\) | ||||
−0.0314185 | + | 0.999506i | \(0.510002\pi\) | |||||||
\(282\) | 26.5390 | 1.58038 | ||||||||
\(283\) | 33.1797 | 1.97233 | 0.986163 | − | 0.165778i | \(-0.0530135\pi\) | ||||
0.986163 | + | 0.165778i | \(0.0530135\pi\) | |||||||
\(284\) | 35.4329 | 2.10256 | ||||||||
\(285\) | 9.05236 | 0.536216 | ||||||||
\(286\) | −5.46505 | −0.323155 | ||||||||
\(287\) | −10.0561 | −0.593594 | ||||||||
\(288\) | −5.72878 | −0.337572 | ||||||||
\(289\) | −16.9349 | −0.996172 | ||||||||
\(290\) | −15.6808 | −0.920808 | ||||||||
\(291\) | −16.1374 | −0.945993 | ||||||||
\(292\) | −26.6198 | −1.55781 | ||||||||
\(293\) | 3.76067 | 0.219701 | 0.109850 | − | 0.993948i | \(-0.464963\pi\) | ||||
0.109850 | + | 0.993948i | \(0.464963\pi\) | |||||||
\(294\) | −10.6295 | −0.619923 | ||||||||
\(295\) | −19.6345 | −1.14317 | ||||||||
\(296\) | 20.5097 | 1.19210 | ||||||||
\(297\) | 2.39155 | 0.138772 | ||||||||
\(298\) | 3.52254 | 0.204055 | ||||||||
\(299\) | 8.19358 | 0.473847 | ||||||||
\(300\) | 6.63642 | 0.383154 | ||||||||
\(301\) | −10.4265 | −0.600972 | ||||||||
\(302\) | 21.4338 | 1.23338 | ||||||||
\(303\) | −7.78769 | −0.447391 | ||||||||
\(304\) | −0.333478 | −0.0191263 | ||||||||
\(305\) | −13.5222 | −0.774277 | ||||||||
\(306\) | 0.582947 | 0.0333249 | ||||||||
\(307\) | −10.5794 | −0.603796 | −0.301898 | − | 0.953340i | \(-0.597620\pi\) | ||||
−0.301898 | + | 0.953340i | \(0.597620\pi\) | |||||||
\(308\) | 26.3017 | 1.49868 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 4.87594 | 0.276935 | ||||||||
\(311\) | 26.1467 | 1.48265 | 0.741323 | − | 0.671149i | \(-0.234199\pi\) | ||||
0.741323 | + | 0.671149i | \(0.234199\pi\) | |||||||
\(312\) | −2.79222 | −0.158078 | ||||||||
\(313\) | −23.8126 | −1.34597 | −0.672985 | − | 0.739656i | \(-0.734988\pi\) | ||||
−0.672985 | + | 0.739656i | \(0.734988\pi\) | |||||||
\(314\) | −47.4024 | −2.67507 | ||||||||
\(315\) | 5.85304 | 0.329781 | ||||||||
\(316\) | 16.1113 | 0.906330 | ||||||||
\(317\) | −20.7133 | −1.16337 | −0.581686 | − | 0.813413i | \(-0.697607\pi\) | ||||
−0.581686 | + | 0.813413i | \(0.697607\pi\) | |||||||
\(318\) | −2.02181 | −0.113378 | ||||||||
\(319\) | −9.57071 | −0.535857 | ||||||||
\(320\) | 22.2308 | 1.24274 | ||||||||
\(321\) | 12.7489 | 0.711573 | ||||||||
\(322\) | −63.9116 | −3.56165 | ||||||||
\(323\) | 1.34675 | 0.0749353 | ||||||||
\(324\) | 3.22190 | 0.178994 | ||||||||
\(325\) | −2.05979 | −0.114256 | ||||||||
\(326\) | 28.0794 | 1.55517 | ||||||||
\(327\) | 4.89646 | 0.270775 | ||||||||
\(328\) | 8.22599 | 0.454205 | ||||||||
\(329\) | 39.6426 | 2.18557 | ||||||||
\(330\) | −9.37095 | −0.515854 | ||||||||
\(331\) | −7.55226 | −0.415110 | −0.207555 | − | 0.978223i | \(-0.566551\pi\) | ||||
−0.207555 | + | 0.978223i | \(0.566551\pi\) | |||||||
\(332\) | 51.8066 | 2.84326 | ||||||||
\(333\) | 7.34531 | 0.402521 | ||||||||
\(334\) | −57.4958 | −3.14603 | ||||||||
\(335\) | −13.2350 | −0.723103 | ||||||||
\(336\) | −0.215619 | −0.0117630 | ||||||||
\(337\) | 18.4564 | 1.00538 | 0.502692 | − | 0.864466i | \(-0.332343\pi\) | ||||
0.502692 | + | 0.864466i | \(0.332343\pi\) | |||||||
\(338\) | 2.28515 | 0.124296 | ||||||||
\(339\) | 6.75655 | 0.366966 | ||||||||
\(340\) | −1.40934 | −0.0764323 | ||||||||
\(341\) | 2.97601 | 0.161160 | ||||||||
\(342\) | 12.0639 | 0.652339 | ||||||||
\(343\) | 8.01631 | 0.432840 | ||||||||
\(344\) | 8.52894 | 0.459849 | ||||||||
\(345\) | 14.0496 | 0.756403 | ||||||||
\(346\) | 6.84883 | 0.368196 | ||||||||
\(347\) | 34.9200 | 1.87460 | 0.937302 | − | 0.348519i | \(-0.113315\pi\) | ||||
0.937302 | + | 0.348519i | \(0.113315\pi\) | |||||||
\(348\) | −12.8937 | −0.691173 | ||||||||
\(349\) | −18.2434 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(350\) | 16.0667 | 0.858804 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 13.7007 | 0.730249 | ||||||||
\(353\) | 36.3598 | 1.93524 | 0.967619 | − | 0.252416i | \(-0.0812251\pi\) | ||||
0.967619 | + | 0.252416i | \(0.0812251\pi\) | |||||||
\(354\) | −26.1665 | −1.39073 | ||||||||
\(355\) | −18.8575 | −1.00085 | ||||||||
\(356\) | −36.0155 | −1.90882 | ||||||||
\(357\) | 0.870777 | 0.0460864 | ||||||||
\(358\) | −43.7253 | −2.31095 | ||||||||
\(359\) | 2.67100 | 0.140970 | 0.0704850 | − | 0.997513i | \(-0.477545\pi\) | ||||
0.0704850 | + | 0.997513i | \(0.477545\pi\) | |||||||
\(360\) | −4.78783 | −0.252341 | ||||||||
\(361\) | 8.87049 | 0.466868 | ||||||||
\(362\) | −26.3289 | −1.38382 | ||||||||
\(363\) | 5.28048 | 0.277153 | ||||||||
\(364\) | −10.9977 | −0.576438 | ||||||||
\(365\) | 14.1672 | 0.741543 | ||||||||
\(366\) | −18.0207 | −0.941956 | ||||||||
\(367\) | 15.2213 | 0.794547 | 0.397274 | − | 0.917700i | \(-0.369956\pi\) | ||||
0.397274 | + | 0.917700i | \(0.369956\pi\) | |||||||
\(368\) | −0.517570 | −0.0269802 | ||||||||
\(369\) | 2.94604 | 0.153365 | ||||||||
\(370\) | −28.7815 | −1.49628 | ||||||||
\(371\) | −3.02008 | −0.156795 | ||||||||
\(372\) | 4.00928 | 0.207872 | ||||||||
\(373\) | −0.625827 | −0.0324041 | −0.0162021 | − | 0.999869i | \(-0.505157\pi\) | ||||
−0.0162021 | + | 0.999869i | \(0.505157\pi\) | |||||||
\(374\) | −1.39415 | −0.0720897 | ||||||||
\(375\) | −12.1055 | −0.625123 | ||||||||
\(376\) | −32.4280 | −1.67235 | ||||||||
\(377\) | 4.00188 | 0.206107 | ||||||||
\(378\) | 7.80020 | 0.401199 | ||||||||
\(379\) | 26.0071 | 1.33589 | 0.667946 | − | 0.744209i | \(-0.267174\pi\) | ||||
0.667946 | + | 0.744209i | \(0.267174\pi\) | |||||||
\(380\) | −29.1658 | −1.49617 | ||||||||
\(381\) | −11.3175 | −0.579813 | ||||||||
\(382\) | −37.6121 | −1.92440 | ||||||||
\(383\) | −9.03498 | −0.461666 | −0.230833 | − | 0.972993i | \(-0.574145\pi\) | ||||
−0.230833 | + | 0.972993i | \(0.574145\pi\) | |||||||
\(384\) | 18.1689 | 0.927176 | ||||||||
\(385\) | −13.9978 | −0.713396 | ||||||||
\(386\) | 43.7658 | 2.22762 | ||||||||
\(387\) | 3.05454 | 0.155271 | ||||||||
\(388\) | 51.9931 | 2.63955 | ||||||||
\(389\) | 16.7774 | 0.850646 | 0.425323 | − | 0.905042i | \(-0.360160\pi\) | ||||
0.425323 | + | 0.905042i | \(0.360160\pi\) | |||||||
\(390\) | 3.91835 | 0.198414 | ||||||||
\(391\) | 2.09020 | 0.105706 | ||||||||
\(392\) | 12.9881 | 0.655999 | ||||||||
\(393\) | −19.1731 | −0.967155 | ||||||||
\(394\) | 53.1011 | 2.67520 | ||||||||
\(395\) | −8.57447 | −0.431429 | ||||||||
\(396\) | −7.70534 | −0.387208 | ||||||||
\(397\) | −2.34156 | −0.117519 | −0.0587597 | − | 0.998272i | \(-0.518715\pi\) | ||||
−0.0587597 | + | 0.998272i | \(0.518715\pi\) | |||||||
\(398\) | −38.8148 | −1.94561 | ||||||||
\(399\) | 18.0204 | 0.902148 | ||||||||
\(400\) | 0.130112 | 0.00650560 | ||||||||
\(401\) | 22.7341 | 1.13529 | 0.567644 | − | 0.823274i | \(-0.307855\pi\) | ||||
0.567644 | + | 0.823274i | \(0.307855\pi\) | |||||||
\(402\) | −17.6379 | −0.879699 | ||||||||
\(403\) | −1.24439 | −0.0619873 | ||||||||
\(404\) | 25.0912 | 1.24833 | ||||||||
\(405\) | −1.71471 | −0.0852044 | ||||||||
\(406\) | −31.2155 | −1.54920 | ||||||||
\(407\) | −17.5667 | −0.870748 | ||||||||
\(408\) | −0.712302 | −0.0352642 | ||||||||
\(409\) | −28.2430 | −1.39653 | −0.698264 | − | 0.715841i | \(-0.746044\pi\) | ||||
−0.698264 | + | 0.715841i | \(0.746044\pi\) | |||||||
\(410\) | −11.5436 | −0.570100 | ||||||||
\(411\) | −17.2171 | −0.849255 | ||||||||
\(412\) | −3.22190 | −0.158732 | ||||||||
\(413\) | −39.0862 | −1.92330 | ||||||||
\(414\) | 18.7235 | 0.920211 | ||||||||
\(415\) | −27.5717 | −1.35344 | ||||||||
\(416\) | −5.72878 | −0.280877 | ||||||||
\(417\) | 11.2343 | 0.550145 | ||||||||
\(418\) | −28.8514 | −1.41117 | ||||||||
\(419\) | −31.9451 | −1.56062 | −0.780310 | − | 0.625392i | \(-0.784939\pi\) | ||||
−0.780310 | + | 0.625392i | \(0.784939\pi\) | |||||||
\(420\) | −18.8579 | −0.920171 | ||||||||
\(421\) | 12.3594 | 0.602358 | 0.301179 | − | 0.953568i | \(-0.402620\pi\) | ||||
0.301179 | + | 0.953568i | \(0.402620\pi\) | |||||||
\(422\) | −18.1044 | −0.881309 | ||||||||
\(423\) | −11.6137 | −0.564677 | ||||||||
\(424\) | 2.47045 | 0.119976 | ||||||||
\(425\) | −0.525457 | −0.0254884 | ||||||||
\(426\) | −25.1310 | −1.21760 | ||||||||
\(427\) | −26.9184 | −1.30267 | ||||||||
\(428\) | −41.0756 | −1.98546 | ||||||||
\(429\) | 2.39155 | 0.115465 | ||||||||
\(430\) | −11.9688 | −0.577185 | ||||||||
\(431\) | 16.7482 | 0.806734 | 0.403367 | − | 0.915038i | \(-0.367840\pi\) | ||||
0.403367 | + | 0.915038i | \(0.367840\pi\) | |||||||
\(432\) | 0.0631677 | 0.00303916 | ||||||||
\(433\) | −28.9389 | −1.39072 | −0.695359 | − | 0.718663i | \(-0.744754\pi\) | ||||
−0.695359 | + | 0.718663i | \(0.744754\pi\) | |||||||
\(434\) | 9.70646 | 0.465925 | ||||||||
\(435\) | 6.86205 | 0.329010 | ||||||||
\(436\) | −15.7759 | −0.755529 | ||||||||
\(437\) | 43.2559 | 2.06921 | ||||||||
\(438\) | 18.8802 | 0.902133 | ||||||||
\(439\) | 7.25628 | 0.346323 | 0.173162 | − | 0.984893i | \(-0.444602\pi\) | ||||
0.173162 | + | 0.984893i | \(0.444602\pi\) | |||||||
\(440\) | 11.4503 | 0.545874 | ||||||||
\(441\) | 4.65154 | 0.221502 | ||||||||
\(442\) | 0.582947 | 0.0277280 | ||||||||
\(443\) | 14.8478 | 0.705441 | 0.352721 | − | 0.935729i | \(-0.385257\pi\) | ||||
0.352721 | + | 0.935729i | \(0.385257\pi\) | |||||||
\(444\) | −23.6658 | −1.12313 | ||||||||
\(445\) | 19.1676 | 0.908631 | ||||||||
\(446\) | 16.3138 | 0.772480 | ||||||||
\(447\) | −1.54149 | −0.0729102 | ||||||||
\(448\) | 44.2544 | 2.09083 | ||||||||
\(449\) | −20.2016 | −0.953375 | −0.476687 | − | 0.879073i | \(-0.658163\pi\) | ||||
−0.476687 | + | 0.879073i | \(0.658163\pi\) | |||||||
\(450\) | −4.70691 | −0.221886 | ||||||||
\(451\) | −7.04561 | −0.331765 | ||||||||
\(452\) | −21.7689 | −1.02392 | ||||||||
\(453\) | −9.37962 | −0.440693 | ||||||||
\(454\) | 52.2758 | 2.45343 | ||||||||
\(455\) | 5.85304 | 0.274395 | ||||||||
\(456\) | −14.7408 | −0.690302 | ||||||||
\(457\) | −18.7638 | −0.877733 | −0.438867 | − | 0.898552i | \(-0.644620\pi\) | ||||
−0.438867 | + | 0.898552i | \(0.644620\pi\) | |||||||
\(458\) | −54.4116 | −2.54248 | ||||||||
\(459\) | −0.255103 | −0.0119072 | ||||||||
\(460\) | −45.2663 | −2.11055 | ||||||||
\(461\) | 33.5705 | 1.56353 | 0.781767 | − | 0.623571i | \(-0.214319\pi\) | ||||
0.781767 | + | 0.623571i | \(0.214319\pi\) | |||||||
\(462\) | −18.6546 | −0.867890 | ||||||||
\(463\) | 33.6119 | 1.56208 | 0.781038 | − | 0.624483i | \(-0.214690\pi\) | ||||
0.781038 | + | 0.624483i | \(0.214690\pi\) | |||||||
\(464\) | −0.252790 | −0.0117355 | ||||||||
\(465\) | −2.13375 | −0.0989505 | ||||||||
\(466\) | −28.2676 | −1.30947 | ||||||||
\(467\) | −28.2426 | −1.30691 | −0.653455 | − | 0.756965i | \(-0.726681\pi\) | ||||
−0.653455 | + | 0.756965i | \(0.726681\pi\) | |||||||
\(468\) | 3.22190 | 0.148932 | ||||||||
\(469\) | −26.3466 | −1.21657 | ||||||||
\(470\) | 45.5066 | 2.09906 | ||||||||
\(471\) | 20.7437 | 0.955819 | ||||||||
\(472\) | 31.9728 | 1.47167 | ||||||||
\(473\) | −7.30509 | −0.335888 | ||||||||
\(474\) | −11.4270 | −0.524860 | ||||||||
\(475\) | −10.8741 | −0.498939 | ||||||||
\(476\) | −2.80555 | −0.128592 | ||||||||
\(477\) | 0.884763 | 0.0405105 | ||||||||
\(478\) | 16.0977 | 0.736293 | ||||||||
\(479\) | 18.0801 | 0.826101 | 0.413051 | − | 0.910708i | \(-0.364463\pi\) | ||||
0.413051 | + | 0.910708i | \(0.364463\pi\) | |||||||
\(480\) | −9.82317 | −0.448365 | ||||||||
\(481\) | 7.34531 | 0.334917 | ||||||||
\(482\) | 3.60850 | 0.164363 | ||||||||
\(483\) | 27.9682 | 1.27260 | ||||||||
\(484\) | −17.0132 | −0.773326 | ||||||||
\(485\) | −27.6709 | −1.25647 | ||||||||
\(486\) | −2.28515 | −0.103656 | ||||||||
\(487\) | 11.3088 | 0.512449 | 0.256225 | − | 0.966617i | \(-0.417521\pi\) | ||||
0.256225 | + | 0.966617i | \(0.417521\pi\) | |||||||
\(488\) | 22.0194 | 0.996773 | ||||||||
\(489\) | −12.2878 | −0.555672 | ||||||||
\(490\) | −18.2264 | −0.823384 | ||||||||
\(491\) | −11.1297 | −0.502278 | −0.251139 | − | 0.967951i | \(-0.580805\pi\) | ||||
−0.251139 | + | 0.967951i | \(0.580805\pi\) | |||||||
\(492\) | −9.49185 | −0.427926 | ||||||||
\(493\) | 1.02089 | 0.0459786 | ||||||||
\(494\) | 12.0639 | 0.542779 | ||||||||
\(495\) | 4.10081 | 0.184318 | ||||||||
\(496\) | 0.0786050 | 0.00352947 | ||||||||
\(497\) | −37.5394 | −1.68387 | ||||||||
\(498\) | −36.7441 | −1.64654 | ||||||||
\(499\) | −33.5896 | −1.50368 | −0.751838 | − | 0.659348i | \(-0.770833\pi\) | ||||
−0.751838 | + | 0.659348i | \(0.770833\pi\) | |||||||
\(500\) | 39.0025 | 1.74425 | ||||||||
\(501\) | 25.1607 | 1.12410 | ||||||||
\(502\) | −22.0743 | −0.985224 | ||||||||
\(503\) | −29.6226 | −1.32080 | −0.660402 | − | 0.750912i | \(-0.729614\pi\) | ||||
−0.660402 | + | 0.750912i | \(0.729614\pi\) | |||||||
\(504\) | −9.53106 | −0.424547 | ||||||||
\(505\) | −13.3536 | −0.594227 | ||||||||
\(506\) | −44.7783 | −1.99064 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 36.4638 | 1.61782 | ||||||||
\(509\) | −6.23103 | −0.276185 | −0.138093 | − | 0.990419i | \(-0.544097\pi\) | ||||
−0.138093 | + | 0.990419i | \(0.544097\pi\) | |||||||
\(510\) | 0.999583 | 0.0442623 | ||||||||
\(511\) | 28.2023 | 1.24760 | ||||||||
\(512\) | 0.714630 | 0.0315825 | ||||||||
\(513\) | −5.27925 | −0.233085 | ||||||||
\(514\) | −40.0508 | −1.76657 | ||||||||
\(515\) | 1.71471 | 0.0755589 | ||||||||
\(516\) | −9.84141 | −0.433244 | ||||||||
\(517\) | 27.7748 | 1.22153 | ||||||||
\(518\) | −57.2949 | −2.51739 | ||||||||
\(519\) | −2.99711 | −0.131558 | ||||||||
\(520\) | −4.78783 | −0.209960 | ||||||||
\(521\) | −36.8476 | −1.61432 | −0.807161 | − | 0.590332i | \(-0.798997\pi\) | ||||
−0.807161 | + | 0.590332i | \(0.798997\pi\) | |||||||
\(522\) | 9.14489 | 0.400261 | ||||||||
\(523\) | −4.70510 | −0.205740 | −0.102870 | − | 0.994695i | \(-0.532802\pi\) | ||||
−0.102870 | + | 0.994695i | \(0.532802\pi\) | |||||||
\(524\) | 61.7738 | 2.69860 | ||||||||
\(525\) | −7.03095 | −0.306856 | ||||||||
\(526\) | 56.7868 | 2.47602 | ||||||||
\(527\) | −0.317446 | −0.0138282 | ||||||||
\(528\) | −0.151069 | −0.00657443 | ||||||||
\(529\) | 44.1347 | 1.91890 | ||||||||
\(530\) | −3.46682 | −0.150589 | ||||||||
\(531\) | 11.4507 | 0.496917 | ||||||||
\(532\) | −58.0598 | −2.51721 | ||||||||
\(533\) | 2.94604 | 0.127607 | ||||||||
\(534\) | 25.5442 | 1.10541 | ||||||||
\(535\) | 21.8606 | 0.945115 | ||||||||
\(536\) | 21.5517 | 0.930893 | ||||||||
\(537\) | 19.1346 | 0.825718 | ||||||||
\(538\) | 22.2088 | 0.957488 | ||||||||
\(539\) | −11.1244 | −0.479162 | ||||||||
\(540\) | 5.52461 | 0.237741 | ||||||||
\(541\) | 18.2189 | 0.783294 | 0.391647 | − | 0.920116i | \(-0.371906\pi\) | ||||
0.391647 | + | 0.920116i | \(0.371906\pi\) | |||||||
\(542\) | −2.60688 | −0.111975 | ||||||||
\(543\) | 11.5217 | 0.494446 | ||||||||
\(544\) | −1.46143 | −0.0626582 | ||||||||
\(545\) | 8.39599 | 0.359645 | ||||||||
\(546\) | 7.80020 | 0.333818 | ||||||||
\(547\) | −4.53208 | −0.193778 | −0.0968889 | − | 0.995295i | \(-0.530889\pi\) | ||||
−0.0968889 | + | 0.995295i | \(0.530889\pi\) | |||||||
\(548\) | 55.4716 | 2.36963 | ||||||||
\(549\) | 7.88600 | 0.336566 | ||||||||
\(550\) | 11.2568 | 0.479993 | ||||||||
\(551\) | 21.1269 | 0.900038 | ||||||||
\(552\) | −22.8782 | −0.973763 | ||||||||
\(553\) | −17.0691 | −0.725850 | ||||||||
\(554\) | 22.8537 | 0.970959 | ||||||||
\(555\) | 12.5950 | 0.534630 | ||||||||
\(556\) | −36.1957 | −1.53504 | ||||||||
\(557\) | −42.3256 | −1.79339 | −0.896697 | − | 0.442645i | \(-0.854040\pi\) | ||||
−0.896697 | + | 0.442645i | \(0.854040\pi\) | |||||||
\(558\) | −2.84360 | −0.120379 | ||||||||
\(559\) | 3.05454 | 0.129193 | ||||||||
\(560\) | −0.369723 | −0.0156236 | ||||||||
\(561\) | 0.610091 | 0.0257581 | ||||||||
\(562\) | −2.40704 | −0.101535 | ||||||||
\(563\) | 0.157148 | 0.00662302 | 0.00331151 | − | 0.999995i | \(-0.498946\pi\) | ||||
0.00331151 | + | 0.999995i | \(0.498946\pi\) | |||||||
\(564\) | 37.4182 | 1.57559 | ||||||||
\(565\) | 11.5855 | 0.487405 | ||||||||
\(566\) | 75.8204 | 3.18697 | ||||||||
\(567\) | −3.41344 | −0.143351 | ||||||||
\(568\) | 30.7075 | 1.28846 | ||||||||
\(569\) | −4.28598 | −0.179677 | −0.0898387 | − | 0.995956i | \(-0.528635\pi\) | ||||
−0.0898387 | + | 0.995956i | \(0.528635\pi\) | |||||||
\(570\) | 20.6860 | 0.866440 | ||||||||
\(571\) | 38.8367 | 1.62527 | 0.812633 | − | 0.582776i | \(-0.198033\pi\) | ||||
0.812633 | + | 0.582776i | \(0.198033\pi\) | |||||||
\(572\) | −7.70534 | −0.322176 | ||||||||
\(573\) | 16.4594 | 0.687601 | ||||||||
\(574\) | −22.9797 | −0.959156 | ||||||||
\(575\) | −16.8770 | −0.703820 | ||||||||
\(576\) | −12.9648 | −0.540199 | ||||||||
\(577\) | 37.4133 | 1.55754 | 0.778769 | − | 0.627311i | \(-0.215844\pi\) | ||||
0.778769 | + | 0.627311i | \(0.215844\pi\) | |||||||
\(578\) | −38.6988 | −1.60966 | ||||||||
\(579\) | −19.1523 | −0.795943 | ||||||||
\(580\) | −22.1088 | −0.918019 | ||||||||
\(581\) | −54.8865 | −2.27707 | ||||||||
\(582\) | −36.8764 | −1.52858 | ||||||||
\(583\) | −2.11596 | −0.0876340 | ||||||||
\(584\) | −23.0697 | −0.954633 | ||||||||
\(585\) | −1.71471 | −0.0708943 | ||||||||
\(586\) | 8.59368 | 0.355002 | ||||||||
\(587\) | 40.4137 | 1.66805 | 0.834026 | − | 0.551724i | \(-0.186030\pi\) | ||||
0.834026 | + | 0.551724i | \(0.186030\pi\) | |||||||
\(588\) | −14.9868 | −0.618045 | ||||||||
\(589\) | −6.56942 | −0.270688 | ||||||||
\(590\) | −44.8678 | −1.84718 | ||||||||
\(591\) | −23.2375 | −0.955864 | ||||||||
\(592\) | −0.463987 | −0.0190697 | ||||||||
\(593\) | 0.923076 | 0.0379062 | 0.0189531 | − | 0.999820i | \(-0.493967\pi\) | ||||
0.0189531 | + | 0.999820i | \(0.493967\pi\) | |||||||
\(594\) | 5.46505 | 0.224234 | ||||||||
\(595\) | 1.49313 | 0.0612122 | ||||||||
\(596\) | 4.96654 | 0.203437 | ||||||||
\(597\) | 16.9857 | 0.695177 | ||||||||
\(598\) | 18.7235 | 0.765662 | ||||||||
\(599\) | 8.63432 | 0.352789 | 0.176394 | − | 0.984320i | \(-0.443557\pi\) | ||||
0.176394 | + | 0.984320i | \(0.443557\pi\) | |||||||
\(600\) | 5.75137 | 0.234799 | ||||||||
\(601\) | −30.3188 | −1.23673 | −0.618364 | − | 0.785892i | \(-0.712204\pi\) | ||||
−0.618364 | + | 0.785892i | \(0.712204\pi\) | |||||||
\(602\) | −23.8260 | −0.971076 | ||||||||
\(603\) | 7.71850 | 0.314322 | ||||||||
\(604\) | 30.2202 | 1.22964 | ||||||||
\(605\) | 9.05447 | 0.368116 | ||||||||
\(606\) | −17.7960 | −0.722914 | ||||||||
\(607\) | −2.17453 | −0.0882613 | −0.0441307 | − | 0.999026i | \(-0.514052\pi\) | ||||
−0.0441307 | + | 0.999026i | \(0.514052\pi\) | |||||||
\(608\) | −30.2437 | −1.22654 | ||||||||
\(609\) | 13.6602 | 0.553538 | ||||||||
\(610\) | −30.9001 | −1.25111 | ||||||||
\(611\) | −11.6137 | −0.469840 | ||||||||
\(612\) | 0.821915 | 0.0332239 | ||||||||
\(613\) | 29.7489 | 1.20155 | 0.600774 | − | 0.799419i | \(-0.294859\pi\) | ||||
0.600774 | + | 0.799419i | \(0.294859\pi\) | |||||||
\(614\) | −24.1754 | −0.975640 | ||||||||
\(615\) | 5.05160 | 0.203700 | ||||||||
\(616\) | 22.7940 | 0.918397 | ||||||||
\(617\) | 11.2602 | 0.453319 | 0.226659 | − | 0.973974i | \(-0.427220\pi\) | ||||
0.226659 | + | 0.973974i | \(0.427220\pi\) | |||||||
\(618\) | 2.28515 | 0.0919221 | ||||||||
\(619\) | 44.5760 | 1.79166 | 0.895829 | − | 0.444398i | \(-0.146582\pi\) | ||||
0.895829 | + | 0.444398i | \(0.146582\pi\) | |||||||
\(620\) | 6.87474 | 0.276096 | ||||||||
\(621\) | −8.19358 | −0.328797 | ||||||||
\(622\) | 59.7491 | 2.39572 | ||||||||
\(623\) | 38.1566 | 1.52871 | ||||||||
\(624\) | 0.0631677 | 0.00252873 | ||||||||
\(625\) | −10.4584 | −0.418334 | ||||||||
\(626\) | −54.4154 | −2.17488 | ||||||||
\(627\) | 12.6256 | 0.504218 | ||||||||
\(628\) | −66.8341 | −2.66697 | ||||||||
\(629\) | 1.87381 | 0.0747136 | ||||||||
\(630\) | 13.3750 | 0.532875 | ||||||||
\(631\) | −17.9206 | −0.713408 | −0.356704 | − | 0.934217i | \(-0.616100\pi\) | ||||
−0.356704 | + | 0.934217i | \(0.616100\pi\) | |||||||
\(632\) | 13.9626 | 0.555404 | ||||||||
\(633\) | 7.92265 | 0.314897 | ||||||||
\(634\) | −47.3328 | −1.87983 | ||||||||
\(635\) | −19.4062 | −0.770111 | ||||||||
\(636\) | −2.85062 | −0.113034 | ||||||||
\(637\) | 4.65154 | 0.184301 | ||||||||
\(638\) | −21.8705 | −0.865860 | ||||||||
\(639\) | 10.9975 | 0.435056 | ||||||||
\(640\) | 31.1542 | 1.23148 | ||||||||
\(641\) | 16.8217 | 0.664417 | 0.332209 | − | 0.943206i | \(-0.392206\pi\) | ||||
0.332209 | + | 0.943206i | \(0.392206\pi\) | |||||||
\(642\) | 29.1331 | 1.14979 | ||||||||
\(643\) | −38.0452 | −1.50036 | −0.750178 | − | 0.661236i | \(-0.770032\pi\) | ||||
−0.750178 | + | 0.661236i | \(0.770032\pi\) | |||||||
\(644\) | −90.1108 | −3.55086 | ||||||||
\(645\) | 5.23763 | 0.206232 | ||||||||
\(646\) | 3.07753 | 0.121084 | ||||||||
\(647\) | −16.3953 | −0.644567 | −0.322283 | − | 0.946643i | \(-0.604450\pi\) | ||||
−0.322283 | + | 0.946643i | \(0.604450\pi\) | |||||||
\(648\) | 2.79222 | 0.109689 | ||||||||
\(649\) | −27.3849 | −1.07495 | ||||||||
\(650\) | −4.70691 | −0.184620 | ||||||||
\(651\) | −4.24763 | −0.166478 | ||||||||
\(652\) | 39.5900 | 1.55046 | ||||||||
\(653\) | 14.4785 | 0.566588 | 0.283294 | − | 0.959033i | \(-0.408573\pi\) | ||||
0.283294 | + | 0.959033i | \(0.408573\pi\) | |||||||
\(654\) | 11.1891 | 0.437530 | ||||||||
\(655\) | −32.8762 | −1.28458 | ||||||||
\(656\) | −0.186095 | −0.00726578 | ||||||||
\(657\) | −8.26216 | −0.322337 | ||||||||
\(658\) | 90.5892 | 3.53154 | ||||||||
\(659\) | 12.9251 | 0.503489 | 0.251745 | − | 0.967794i | \(-0.418996\pi\) | ||||
0.251745 | + | 0.967794i | \(0.418996\pi\) | |||||||
\(660\) | −13.2124 | −0.514291 | ||||||||
\(661\) | −43.1292 | −1.67753 | −0.838766 | − | 0.544491i | \(-0.816723\pi\) | ||||
−0.838766 | + | 0.544491i | \(0.816723\pi\) | |||||||
\(662\) | −17.2580 | −0.670753 | ||||||||
\(663\) | −0.255103 | −0.00990737 | ||||||||
\(664\) | 44.8976 | 1.74236 | ||||||||
\(665\) | 30.8996 | 1.19824 | ||||||||
\(666\) | 16.7851 | 0.650410 | ||||||||
\(667\) | 32.7897 | 1.26962 | ||||||||
\(668\) | −81.0651 | −3.13650 | ||||||||
\(669\) | −7.13905 | −0.276012 | ||||||||
\(670\) | −30.2438 | −1.16842 | ||||||||
\(671\) | −18.8598 | −0.728074 | ||||||||
\(672\) | −19.5548 | −0.754344 | ||||||||
\(673\) | 41.2697 | 1.59083 | 0.795414 | − | 0.606066i | \(-0.207253\pi\) | ||||
0.795414 | + | 0.606066i | \(0.207253\pi\) | |||||||
\(674\) | 42.1756 | 1.62454 | ||||||||
\(675\) | 2.05979 | 0.0792812 | ||||||||
\(676\) | 3.22190 | 0.123919 | ||||||||
\(677\) | 12.2927 | 0.472445 | 0.236223 | − | 0.971699i | \(-0.424091\pi\) | ||||
0.236223 | + | 0.971699i | \(0.424091\pi\) | |||||||
\(678\) | 15.4397 | 0.592959 | ||||||||
\(679\) | −55.0841 | −2.11393 | ||||||||
\(680\) | −1.22139 | −0.0468381 | ||||||||
\(681\) | −22.8763 | −0.876623 | ||||||||
\(682\) | 6.80063 | 0.260409 | ||||||||
\(683\) | 26.7405 | 1.02320 | 0.511599 | − | 0.859224i | \(-0.329053\pi\) | ||||
0.511599 | + | 0.859224i | \(0.329053\pi\) | |||||||
\(684\) | 17.0092 | 0.650363 | ||||||||
\(685\) | −29.5222 | −1.12798 | ||||||||
\(686\) | 18.3185 | 0.699402 | ||||||||
\(687\) | 23.8110 | 0.908445 | ||||||||
\(688\) | −0.192948 | −0.00735609 | ||||||||
\(689\) | 0.884763 | 0.0337068 | ||||||||
\(690\) | 32.1053 | 1.22223 | ||||||||
\(691\) | −10.3840 | −0.395027 | −0.197514 | − | 0.980300i | \(-0.563287\pi\) | ||||
−0.197514 | + | 0.980300i | \(0.563287\pi\) | |||||||
\(692\) | 9.65638 | 0.367080 | ||||||||
\(693\) | 8.16341 | 0.310102 | ||||||||
\(694\) | 79.7973 | 3.02907 | ||||||||
\(695\) | 19.2635 | 0.730706 | ||||||||
\(696\) | −11.1741 | −0.423554 | ||||||||
\(697\) | 0.751544 | 0.0284667 | ||||||||
\(698\) | −41.6888 | −1.57795 | ||||||||
\(699\) | 12.3701 | 0.467882 | ||||||||
\(700\) | 22.6530 | 0.856203 | ||||||||
\(701\) | −1.89474 | −0.0715634 | −0.0357817 | − | 0.999360i | \(-0.511392\pi\) | ||||
−0.0357817 | + | 0.999360i | \(0.511392\pi\) | |||||||
\(702\) | −2.28515 | −0.0862473 | ||||||||
\(703\) | 38.7777 | 1.46253 | ||||||||
\(704\) | 31.0059 | 1.16858 | ||||||||
\(705\) | −19.9141 | −0.750007 | ||||||||
\(706\) | 83.0875 | 3.12704 | ||||||||
\(707\) | −26.5828 | −0.999749 | ||||||||
\(708\) | −36.8929 | −1.38652 | ||||||||
\(709\) | 1.58262 | 0.0594365 | 0.0297182 | − | 0.999558i | \(-0.490539\pi\) | ||||
0.0297182 | + | 0.999558i | \(0.490539\pi\) | |||||||
\(710\) | −43.0922 | −1.61722 | ||||||||
\(711\) | 5.00055 | 0.187535 | ||||||||
\(712\) | −31.2124 | −1.16973 | ||||||||
\(713\) | −10.1960 | −0.381842 | ||||||||
\(714\) | 1.98985 | 0.0744684 | ||||||||
\(715\) | 4.10081 | 0.153361 | ||||||||
\(716\) | −61.6496 | −2.30395 | ||||||||
\(717\) | −7.04450 | −0.263082 | ||||||||
\(718\) | 6.10362 | 0.227785 | ||||||||
\(719\) | 37.4439 | 1.39642 | 0.698211 | − | 0.715892i | \(-0.253980\pi\) | ||||
0.698211 | + | 0.715892i | \(0.253980\pi\) | |||||||
\(720\) | 0.108314 | 0.00403663 | ||||||||
\(721\) | 3.41344 | 0.127123 | ||||||||
\(722\) | 20.2704 | 0.754386 | ||||||||
\(723\) | −1.57911 | −0.0587277 | ||||||||
\(724\) | −37.1219 | −1.37962 | ||||||||
\(725\) | −8.24302 | −0.306138 | ||||||||
\(726\) | 12.0667 | 0.447836 | ||||||||
\(727\) | −37.5084 | −1.39111 | −0.695555 | − | 0.718473i | \(-0.744842\pi\) | ||||
−0.695555 | + | 0.718473i | \(0.744842\pi\) | |||||||
\(728\) | −9.53106 | −0.353244 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 32.3741 | 1.19822 | ||||||||
\(731\) | 0.779221 | 0.0288205 | ||||||||
\(732\) | −25.4079 | −0.939103 | ||||||||
\(733\) | −10.9898 | −0.405916 | −0.202958 | − | 0.979187i | \(-0.565055\pi\) | ||||
−0.202958 | + | 0.979187i | \(0.565055\pi\) | |||||||
\(734\) | 34.7830 | 1.28386 | ||||||||
\(735\) | 7.97602 | 0.294200 | ||||||||
\(736\) | −46.9392 | −1.73020 | ||||||||
\(737\) | −18.4592 | −0.679953 | ||||||||
\(738\) | 6.73214 | 0.247814 | ||||||||
\(739\) | 1.70284 | 0.0626401 | 0.0313201 | − | 0.999509i | \(-0.490029\pi\) | ||||
0.0313201 | + | 0.999509i | \(0.490029\pi\) | |||||||
\(740\) | −40.5799 | −1.49175 | ||||||||
\(741\) | −5.27925 | −0.193938 | ||||||||
\(742\) | −6.90133 | −0.253356 | ||||||||
\(743\) | 27.3427 | 1.00311 | 0.501554 | − | 0.865126i | \(-0.332762\pi\) | ||||
0.501554 | + | 0.865126i | \(0.332762\pi\) | |||||||
\(744\) | 3.47460 | 0.127385 | ||||||||
\(745\) | −2.64321 | −0.0968396 | ||||||||
\(746\) | −1.43011 | −0.0523600 | ||||||||
\(747\) | 16.0795 | 0.588320 | ||||||||
\(748\) | −1.96565 | −0.0718714 | ||||||||
\(749\) | 43.5175 | 1.59009 | ||||||||
\(750\) | −27.6627 | −1.01010 | ||||||||
\(751\) | 18.7547 | 0.684368 | 0.342184 | − | 0.939633i | \(-0.388833\pi\) | ||||
0.342184 | + | 0.939633i | \(0.388833\pi\) | |||||||
\(752\) | 0.733611 | 0.0267520 | ||||||||
\(753\) | 9.65990 | 0.352026 | ||||||||
\(754\) | 9.14489 | 0.333037 | ||||||||
\(755\) | −16.0833 | −0.585331 | ||||||||
\(756\) | 10.9977 | 0.399984 | ||||||||
\(757\) | −29.3854 | −1.06803 | −0.534015 | − | 0.845475i | \(-0.679318\pi\) | ||||
−0.534015 | + | 0.845475i | \(0.679318\pi\) | |||||||
\(758\) | 59.4300 | 2.15859 | ||||||||
\(759\) | 19.5954 | 0.711267 | ||||||||
\(760\) | −25.2762 | −0.916863 | ||||||||
\(761\) | 35.8984 | 1.30132 | 0.650658 | − | 0.759371i | \(-0.274493\pi\) | ||||
0.650658 | + | 0.759371i | \(0.274493\pi\) | |||||||
\(762\) | −25.8622 | −0.936887 | ||||||||
\(763\) | 16.7138 | 0.605079 | ||||||||
\(764\) | −53.0305 | −1.91857 | ||||||||
\(765\) | −0.437426 | −0.0158152 | ||||||||
\(766\) | −20.6463 | −0.745980 | ||||||||
\(767\) | 11.4507 | 0.413460 | ||||||||
\(768\) | 15.5890 | 0.562518 | ||||||||
\(769\) | 31.8777 | 1.14954 | 0.574769 | − | 0.818316i | \(-0.305092\pi\) | ||||
0.574769 | + | 0.818316i | \(0.305092\pi\) | |||||||
\(770\) | −31.9871 | −1.15274 | ||||||||
\(771\) | 17.5266 | 0.631204 | ||||||||
\(772\) | 61.7068 | 2.22088 | ||||||||
\(773\) | −21.5690 | −0.775781 | −0.387891 | − | 0.921705i | \(-0.626796\pi\) | ||||
−0.387891 | + | 0.921705i | \(0.626796\pi\) | |||||||
\(774\) | 6.98007 | 0.250893 | ||||||||
\(775\) | 2.56317 | 0.0920717 | ||||||||
\(776\) | 45.0592 | 1.61753 | ||||||||
\(777\) | 25.0727 | 0.899480 | ||||||||
\(778\) | 38.3387 | 1.37451 | ||||||||
\(779\) | 15.5529 | 0.557241 | ||||||||
\(780\) | 5.52461 | 0.197813 | ||||||||
\(781\) | −26.3012 | −0.941130 | ||||||||
\(782\) | 4.77642 | 0.170805 | ||||||||
\(783\) | −4.00188 | −0.143016 | ||||||||
\(784\) | −0.293827 | −0.0104938 | ||||||||
\(785\) | 35.5693 | 1.26952 | ||||||||
\(786\) | −43.8133 | −1.56277 | ||||||||
\(787\) | −41.3153 | −1.47273 | −0.736366 | − | 0.676583i | \(-0.763460\pi\) | ||||
−0.736366 | + | 0.676583i | \(0.763460\pi\) | |||||||
\(788\) | 74.8689 | 2.66709 | ||||||||
\(789\) | −24.8504 | −0.884697 | ||||||||
\(790\) | −19.5939 | −0.697121 | ||||||||
\(791\) | 23.0631 | 0.820028 | ||||||||
\(792\) | −6.67773 | −0.237283 | ||||||||
\(793\) | 7.88600 | 0.280040 | ||||||||
\(794\) | −5.35081 | −0.189893 | ||||||||
\(795\) | 1.51711 | 0.0538063 | ||||||||
\(796\) | −54.7261 | −1.93972 | ||||||||
\(797\) | −24.4599 | −0.866415 | −0.433207 | − | 0.901294i | \(-0.642618\pi\) | ||||
−0.433207 | + | 0.901294i | \(0.642618\pi\) | |||||||
\(798\) | 41.1792 | 1.45773 | ||||||||
\(799\) | −2.96269 | −0.104812 | ||||||||
\(800\) | 11.8001 | 0.417195 | ||||||||
\(801\) | −11.1784 | −0.394968 | ||||||||
\(802\) | 51.9508 | 1.83445 | ||||||||
\(803\) | 19.7594 | 0.697293 | ||||||||
\(804\) | −24.8682 | −0.877035 | ||||||||
\(805\) | 47.9573 | 1.69027 | ||||||||
\(806\) | −2.84360 | −0.100162 | ||||||||
\(807\) | −9.71874 | −0.342116 | ||||||||
\(808\) | 21.7449 | 0.764984 | ||||||||
\(809\) | −40.7164 | −1.43151 | −0.715755 | − | 0.698351i | \(-0.753917\pi\) | ||||
−0.715755 | + | 0.698351i | \(0.753917\pi\) | |||||||
\(810\) | −3.91835 | −0.137677 | ||||||||
\(811\) | 13.7546 | 0.482988 | 0.241494 | − | 0.970402i | \(-0.422363\pi\) | ||||
0.241494 | + | 0.970402i | \(0.422363\pi\) | |||||||
\(812\) | −44.0117 | −1.54451 | ||||||||
\(813\) | 1.14079 | 0.0400093 | ||||||||
\(814\) | −40.1425 | −1.40699 | ||||||||
\(815\) | −21.0699 | −0.738047 | ||||||||
\(816\) | 0.0161143 | 0.000564112 0 | ||||||||
\(817\) | 16.1257 | 0.564166 | ||||||||
\(818\) | −64.5394 | −2.25657 | ||||||||
\(819\) | −3.41344 | −0.119275 | ||||||||
\(820\) | −16.2757 | −0.568373 | ||||||||
\(821\) | −16.5883 | −0.578937 | −0.289469 | − | 0.957188i | \(-0.593479\pi\) | ||||
−0.289469 | + | 0.957188i | \(0.593479\pi\) | |||||||
\(822\) | −39.3435 | −1.37226 | ||||||||
\(823\) | −4.73370 | −0.165007 | −0.0825033 | − | 0.996591i | \(-0.526291\pi\) | ||||
−0.0825033 | + | 0.996591i | \(0.526291\pi\) | |||||||
\(824\) | −2.79222 | −0.0972715 | ||||||||
\(825\) | −4.92608 | −0.171504 | ||||||||
\(826\) | −89.3177 | −3.10776 | ||||||||
\(827\) | 26.1246 | 0.908443 | 0.454221 | − | 0.890889i | \(-0.349917\pi\) | ||||
0.454221 | + | 0.890889i | \(0.349917\pi\) | |||||||
\(828\) | 26.3989 | 0.917424 | ||||||||
\(829\) | −16.7899 | −0.583136 | −0.291568 | − | 0.956550i | \(-0.594177\pi\) | ||||
−0.291568 | + | 0.956550i | \(0.594177\pi\) | |||||||
\(830\) | −63.0053 | −2.18695 | ||||||||
\(831\) | −10.0010 | −0.346930 | ||||||||
\(832\) | −12.9648 | −0.449473 | ||||||||
\(833\) | 1.18662 | 0.0411140 | ||||||||
\(834\) | 25.6720 | 0.888949 | ||||||||
\(835\) | 43.1431 | 1.49303 | ||||||||
\(836\) | −40.6784 | −1.40689 | ||||||||
\(837\) | 1.24439 | 0.0430123 | ||||||||
\(838\) | −72.9993 | −2.52172 | ||||||||
\(839\) | 51.6191 | 1.78209 | 0.891044 | − | 0.453916i | \(-0.149973\pi\) | ||||
0.891044 | + | 0.453916i | \(0.149973\pi\) | |||||||
\(840\) | −16.3429 | −0.563885 | ||||||||
\(841\) | −12.9849 | −0.447757 | ||||||||
\(842\) | 28.2430 | 0.973317 | ||||||||
\(843\) | 1.05334 | 0.0362790 | ||||||||
\(844\) | −25.5260 | −0.878640 | ||||||||
\(845\) | −1.71471 | −0.0589877 | ||||||||
\(846\) | −26.5390 | −0.912430 | ||||||||
\(847\) | 18.0246 | 0.619332 | ||||||||
\(848\) | −0.0558885 | −0.00191922 | ||||||||
\(849\) | −33.1797 | −1.13872 | ||||||||
\(850\) | −1.20075 | −0.0411853 | ||||||||
\(851\) | 60.1844 | 2.06309 | ||||||||
\(852\) | −35.4329 | −1.21391 | ||||||||
\(853\) | −30.2009 | −1.03406 | −0.517029 | − | 0.855968i | \(-0.672962\pi\) | ||||
−0.517029 | + | 0.855968i | \(0.672962\pi\) | |||||||
\(854\) | −61.5124 | −2.10491 | ||||||||
\(855\) | −9.05236 | −0.309584 | ||||||||
\(856\) | −35.5977 | −1.21670 | ||||||||
\(857\) | 48.4034 | 1.65343 | 0.826715 | − | 0.562621i | \(-0.190207\pi\) | ||||
0.826715 | + | 0.562621i | \(0.190207\pi\) | |||||||
\(858\) | 5.46505 | 0.186574 | ||||||||
\(859\) | 19.7181 | 0.672774 | 0.336387 | − | 0.941724i | \(-0.390795\pi\) | ||||
0.336387 | + | 0.941724i | \(0.390795\pi\) | |||||||
\(860\) | −16.8751 | −0.575437 | ||||||||
\(861\) | 10.0561 | 0.342712 | ||||||||
\(862\) | 38.2722 | 1.30356 | ||||||||
\(863\) | −6.82452 | −0.232310 | −0.116155 | − | 0.993231i | \(-0.537057\pi\) | ||||
−0.116155 | + | 0.993231i | \(0.537057\pi\) | |||||||
\(864\) | 5.72878 | 0.194897 | ||||||||
\(865\) | −5.13916 | −0.174737 | ||||||||
\(866\) | −66.1298 | −2.24718 | ||||||||
\(867\) | 16.9349 | 0.575140 | ||||||||
\(868\) | 13.6854 | 0.464514 | ||||||||
\(869\) | −11.9591 | −0.405684 | ||||||||
\(870\) | 15.6808 | 0.531629 | ||||||||
\(871\) | 7.71850 | 0.261531 | ||||||||
\(872\) | −13.6720 | −0.462992 | ||||||||
\(873\) | 16.1374 | 0.546169 | ||||||||
\(874\) | 98.8462 | 3.34352 | ||||||||
\(875\) | −41.3212 | −1.39691 | ||||||||
\(876\) | 26.6198 | 0.899401 | ||||||||
\(877\) | 28.9327 | 0.976987 | 0.488494 | − | 0.872567i | \(-0.337547\pi\) | ||||
0.488494 | + | 0.872567i | \(0.337547\pi\) | |||||||
\(878\) | 16.5817 | 0.559604 | ||||||||
\(879\) | −3.76067 | −0.126844 | ||||||||
\(880\) | −0.259039 | −0.00873219 | ||||||||
\(881\) | 10.8292 | 0.364845 | 0.182422 | − | 0.983220i | \(-0.441606\pi\) | ||||
0.182422 | + | 0.983220i | \(0.441606\pi\) | |||||||
\(882\) | 10.6295 | 0.357912 | ||||||||
\(883\) | −5.10725 | −0.171873 | −0.0859364 | − | 0.996301i | \(-0.527388\pi\) | ||||
−0.0859364 | + | 0.996301i | \(0.527388\pi\) | |||||||
\(884\) | 0.821915 | 0.0276440 | ||||||||
\(885\) | 19.6345 | 0.660008 | ||||||||
\(886\) | 33.9295 | 1.13988 | ||||||||
\(887\) | −18.9905 | −0.637637 | −0.318818 | − | 0.947816i | \(-0.603286\pi\) | ||||
−0.318818 | + | 0.947816i | \(0.603286\pi\) | |||||||
\(888\) | −20.5097 | −0.688261 | ||||||||
\(889\) | −38.6316 | −1.29566 | ||||||||
\(890\) | 43.8008 | 1.46820 | ||||||||
\(891\) | −2.39155 | −0.0801200 | ||||||||
\(892\) | 23.0013 | 0.770141 | ||||||||
\(893\) | −61.3116 | −2.05172 | ||||||||
\(894\) | −3.52254 | −0.117811 | ||||||||
\(895\) | 32.8101 | 1.09672 | ||||||||
\(896\) | 62.0182 | 2.07188 | ||||||||
\(897\) | −8.19358 | −0.273576 | ||||||||
\(898\) | −46.1637 | −1.54050 | ||||||||
\(899\) | −4.97988 | −0.166088 | ||||||||
\(900\) | −6.63642 | −0.221214 | ||||||||
\(901\) | 0.225705 | 0.00751934 | ||||||||
\(902\) | −16.1003 | −0.536080 | ||||||||
\(903\) | 10.4265 | 0.346971 | ||||||||
\(904\) | −18.8658 | −0.627466 | ||||||||
\(905\) | 19.7564 | 0.656725 | ||||||||
\(906\) | −21.4338 | −0.712091 | ||||||||
\(907\) | −51.8495 | −1.72163 | −0.860817 | − | 0.508915i | \(-0.830047\pi\) | ||||
−0.860817 | + | 0.508915i | \(0.830047\pi\) | |||||||
\(908\) | 73.7052 | 2.44599 | ||||||||
\(909\) | 7.78769 | 0.258301 | ||||||||
\(910\) | 13.3750 | 0.443379 | ||||||||
\(911\) | 40.7226 | 1.34920 | 0.674600 | − | 0.738184i | \(-0.264316\pi\) | ||||
0.674600 | + | 0.738184i | \(0.264316\pi\) | |||||||
\(912\) | 0.333478 | 0.0110426 | ||||||||
\(913\) | −38.4551 | −1.27268 | ||||||||
\(914\) | −42.8780 | −1.41828 | ||||||||
\(915\) | 13.5222 | 0.447029 | ||||||||
\(916\) | −76.7165 | −2.53478 | ||||||||
\(917\) | −65.4461 | −2.16122 | ||||||||
\(918\) | −0.582947 | −0.0192401 | ||||||||
\(919\) | 35.2784 | 1.16373 | 0.581863 | − | 0.813287i | \(-0.302324\pi\) | ||||
0.581863 | + | 0.813287i | \(0.302324\pi\) | |||||||
\(920\) | −39.2295 | −1.29336 | ||||||||
\(921\) | 10.5794 | 0.348602 | ||||||||
\(922\) | 76.7135 | 2.52642 | ||||||||
\(923\) | 10.9975 | 0.361988 | ||||||||
\(924\) | −26.3017 | −0.865261 | ||||||||
\(925\) | −15.1298 | −0.497464 | ||||||||
\(926\) | 76.8081 | 2.52407 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −22.9259 | −0.752580 | ||||||||
\(929\) | 25.9916 | 0.852755 | 0.426378 | − | 0.904545i | \(-0.359789\pi\) | ||||
0.426378 | + | 0.904545i | \(0.359789\pi\) | |||||||
\(930\) | −4.87594 | −0.159888 | ||||||||
\(931\) | 24.5567 | 0.804812 | ||||||||
\(932\) | −39.8554 | −1.30551 | ||||||||
\(933\) | −26.1467 | −0.856006 | ||||||||
\(934\) | −64.5384 | −2.11176 | ||||||||
\(935\) | 1.04613 | 0.0342120 | ||||||||
\(936\) | 2.79222 | 0.0912665 | ||||||||
\(937\) | 10.1078 | 0.330206 | 0.165103 | − | 0.986276i | \(-0.447204\pi\) | ||||
0.165103 | + | 0.986276i | \(0.447204\pi\) | |||||||
\(938\) | −60.2059 | −1.96579 | ||||||||
\(939\) | 23.8126 | 0.777096 | ||||||||
\(940\) | 64.1611 | 2.09271 | ||||||||
\(941\) | −20.7920 | −0.677801 | −0.338901 | − | 0.940822i | \(-0.610055\pi\) | ||||
−0.338901 | + | 0.940822i | \(0.610055\pi\) | |||||||
\(942\) | 47.4024 | 1.54445 | ||||||||
\(943\) | 24.1386 | 0.786062 | ||||||||
\(944\) | −0.723314 | −0.0235419 | ||||||||
\(945\) | −5.85304 | −0.190399 | ||||||||
\(946\) | −16.6932 | −0.542743 | ||||||||
\(947\) | −13.6641 | −0.444022 | −0.222011 | − | 0.975044i | \(-0.571262\pi\) | ||||
−0.222011 | + | 0.975044i | \(0.571262\pi\) | |||||||
\(948\) | −16.1113 | −0.523270 | ||||||||
\(949\) | −8.26216 | −0.268201 | ||||||||
\(950\) | −24.8490 | −0.806208 | ||||||||
\(951\) | 20.7133 | 0.671673 | ||||||||
\(952\) | −2.43140 | −0.0788021 | ||||||||
\(953\) | −16.2720 | −0.527101 | −0.263551 | − | 0.964646i | \(-0.584894\pi\) | ||||
−0.263551 | + | 0.964646i | \(0.584894\pi\) | |||||||
\(954\) | 2.02181 | 0.0654586 | ||||||||
\(955\) | 28.2230 | 0.913274 | ||||||||
\(956\) | 22.6967 | 0.734063 | ||||||||
\(957\) | 9.57071 | 0.309377 | ||||||||
\(958\) | 41.3157 | 1.33485 | ||||||||
\(959\) | −58.7693 | −1.89776 | ||||||||
\(960\) | −22.2308 | −0.717495 | ||||||||
\(961\) | −29.4515 | −0.950049 | ||||||||
\(962\) | 16.7851 | 0.541174 | ||||||||
\(963\) | −12.7489 | −0.410827 | ||||||||
\(964\) | 5.08773 | 0.163865 | ||||||||
\(965\) | −32.8406 | −1.05717 | ||||||||
\(966\) | 63.9116 | 2.05632 | ||||||||
\(967\) | −25.4364 | −0.817980 | −0.408990 | − | 0.912539i | \(-0.634119\pi\) | ||||
−0.408990 | + | 0.912539i | \(0.634119\pi\) | |||||||
\(968\) | −14.7443 | −0.473898 | ||||||||
\(969\) | −1.34675 | −0.0432639 | ||||||||
\(970\) | −63.2321 | −2.03026 | ||||||||
\(971\) | −17.3076 | −0.555427 | −0.277714 | − | 0.960664i | \(-0.589577\pi\) | ||||
−0.277714 | + | 0.960664i | \(0.589577\pi\) | |||||||
\(972\) | −3.22190 | −0.103342 | ||||||||
\(973\) | 38.3475 | 1.22936 | ||||||||
\(974\) | 25.8422 | 0.828038 | ||||||||
\(975\) | 2.05979 | 0.0659659 | ||||||||
\(976\) | −0.498141 | −0.0159451 | ||||||||
\(977\) | 43.1051 | 1.37906 | 0.689528 | − | 0.724259i | \(-0.257818\pi\) | ||||
0.689528 | + | 0.724259i | \(0.257818\pi\) | |||||||
\(978\) | −28.0794 | −0.897879 | ||||||||
\(979\) | 26.7336 | 0.854410 | ||||||||
\(980\) | −25.6979 | −0.820890 | ||||||||
\(981\) | −4.89646 | −0.156332 | ||||||||
\(982\) | −25.4331 | −0.811602 | ||||||||
\(983\) | 6.61327 | 0.210931 | 0.105465 | − | 0.994423i | \(-0.466367\pi\) | ||||
0.105465 | + | 0.994423i | \(0.466367\pi\) | |||||||
\(984\) | −8.22599 | −0.262235 | ||||||||
\(985\) | −39.8455 | −1.26958 | ||||||||
\(986\) | 2.33289 | 0.0742942 | ||||||||
\(987\) | −39.6426 | −1.26184 | ||||||||
\(988\) | 17.0092 | 0.541135 | ||||||||
\(989\) | 25.0276 | 0.795831 | ||||||||
\(990\) | 9.37095 | 0.297828 | ||||||||
\(991\) | 19.0075 | 0.603792 | 0.301896 | − | 0.953341i | \(-0.402380\pi\) | ||||
0.301896 | + | 0.953341i | \(0.402380\pi\) | |||||||
\(992\) | 7.12881 | 0.226340 | ||||||||
\(993\) | 7.55226 | 0.239664 | ||||||||
\(994\) | −85.7830 | −2.72087 | ||||||||
\(995\) | 29.1254 | 0.923338 | ||||||||
\(996\) | −51.8066 | −1.64156 | ||||||||
\(997\) | −29.3510 | −0.929555 | −0.464778 | − | 0.885427i | \(-0.653866\pi\) | ||||
−0.464778 | + | 0.885427i | \(0.653866\pi\) | |||||||
\(998\) | −76.7572 | −2.42971 | ||||||||
\(999\) | −7.34531 | −0.232395 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4017.2.a.j.1.21 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.21 | ✓ | 25 | 1.1 | even | 1 | trivial |