Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.830058 | 0.586939 | 0.293470 | − | 0.955968i | \(-0.405190\pi\) | ||||
0.293470 | + | 0.955968i | \(0.405190\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.31100 | −0.655502 | ||||||||
\(5\) | −1.52882 | −0.683709 | −0.341854 | − | 0.939753i | \(-0.611055\pi\) | ||||
−0.341854 | + | 0.939753i | \(0.611055\pi\) | |||||||
\(6\) | 0.830058 | 0.338870 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.74832 | −0.971679 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.26901 | −0.401296 | ||||||||
\(11\) | 4.02473 | 1.21350 | 0.606751 | − | 0.794892i | \(-0.292472\pi\) | ||||
0.606751 | + | 0.794892i | \(0.292472\pi\) | |||||||
\(12\) | −1.31100 | −0.378454 | ||||||||
\(13\) | 6.14463 | 1.70421 | 0.852107 | − | 0.523368i | \(-0.175325\pi\) | ||||
0.852107 | + | 0.523368i | \(0.175325\pi\) | |||||||
\(14\) | −0.830058 | −0.221842 | ||||||||
\(15\) | −1.52882 | −0.394739 | ||||||||
\(16\) | 0.340740 | 0.0851851 | ||||||||
\(17\) | −3.32216 | −0.805742 | −0.402871 | − | 0.915257i | \(-0.631988\pi\) | ||||
−0.402871 | + | 0.915257i | \(0.631988\pi\) | |||||||
\(18\) | 0.830058 | 0.195646 | ||||||||
\(19\) | 2.48074 | 0.569122 | 0.284561 | − | 0.958658i | \(-0.408152\pi\) | ||||
0.284561 | + | 0.958658i | \(0.408152\pi\) | |||||||
\(20\) | 2.00429 | 0.448172 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 3.34076 | 0.712253 | ||||||||
\(23\) | −2.89647 | −0.603957 | −0.301978 | − | 0.953315i | \(-0.597647\pi\) | ||||
−0.301978 | + | 0.953315i | \(0.597647\pi\) | |||||||
\(24\) | −2.74832 | −0.560999 | ||||||||
\(25\) | −2.66271 | −0.532543 | ||||||||
\(26\) | 5.10040 | 1.00027 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.31100 | 0.247757 | ||||||||
\(29\) | −10.4514 | −1.94077 | −0.970384 | − | 0.241570i | \(-0.922338\pi\) | ||||
−0.970384 | + | 0.241570i | \(0.922338\pi\) | |||||||
\(30\) | −1.26901 | −0.231688 | ||||||||
\(31\) | −5.02164 | −0.901914 | −0.450957 | − | 0.892546i | \(-0.648917\pi\) | ||||
−0.450957 | + | 0.892546i | \(0.648917\pi\) | |||||||
\(32\) | 5.77948 | 1.02168 | ||||||||
\(33\) | 4.02473 | 0.700616 | ||||||||
\(34\) | −2.75758 | −0.472922 | ||||||||
\(35\) | 1.52882 | 0.258418 | ||||||||
\(36\) | −1.31100 | −0.218501 | ||||||||
\(37\) | −6.55237 | −1.07720 | −0.538602 | − | 0.842560i | \(-0.681047\pi\) | ||||
−0.538602 | + | 0.842560i | \(0.681047\pi\) | |||||||
\(38\) | 2.05916 | 0.334040 | ||||||||
\(39\) | 6.14463 | 0.983928 | ||||||||
\(40\) | 4.20169 | 0.664346 | ||||||||
\(41\) | 11.1902 | 1.74761 | 0.873804 | − | 0.486278i | \(-0.161646\pi\) | ||||
0.873804 | + | 0.486278i | \(0.161646\pi\) | |||||||
\(42\) | −0.830058 | −0.128081 | ||||||||
\(43\) | 4.15694 | 0.633928 | 0.316964 | − | 0.948438i | \(-0.397337\pi\) | ||||
0.316964 | + | 0.948438i | \(0.397337\pi\) | |||||||
\(44\) | −5.27644 | −0.795454 | ||||||||
\(45\) | −1.52882 | −0.227903 | ||||||||
\(46\) | −2.40424 | −0.354486 | ||||||||
\(47\) | 13.4200 | 1.95751 | 0.978756 | − | 0.205030i | \(-0.0657293\pi\) | ||||
0.978756 | + | 0.205030i | \(0.0657293\pi\) | |||||||
\(48\) | 0.340740 | 0.0491816 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.21021 | −0.312570 | ||||||||
\(51\) | −3.32216 | −0.465195 | ||||||||
\(52\) | −8.05563 | −1.11712 | ||||||||
\(53\) | 8.05843 | 1.10691 | 0.553455 | − | 0.832879i | \(-0.313309\pi\) | ||||
0.553455 | + | 0.832879i | \(0.313309\pi\) | |||||||
\(54\) | 0.830058 | 0.112957 | ||||||||
\(55\) | −6.15309 | −0.829682 | ||||||||
\(56\) | 2.74832 | 0.367260 | ||||||||
\(57\) | 2.48074 | 0.328583 | ||||||||
\(58\) | −8.67522 | −1.13911 | ||||||||
\(59\) | 13.5392 | 1.76265 | 0.881326 | − | 0.472509i | \(-0.156652\pi\) | ||||
0.881326 | + | 0.472509i | \(0.156652\pi\) | |||||||
\(60\) | 2.00429 | 0.258752 | ||||||||
\(61\) | 0.535440 | 0.0685561 | 0.0342780 | − | 0.999412i | \(-0.489087\pi\) | ||||
0.0342780 | + | 0.999412i | \(0.489087\pi\) | |||||||
\(62\) | −4.16825 | −0.529369 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 4.11582 | 0.514478 | ||||||||
\(65\) | −9.39402 | −1.16519 | ||||||||
\(66\) | 3.34076 | 0.411219 | ||||||||
\(67\) | −3.24185 | −0.396055 | −0.198028 | − | 0.980196i | \(-0.563454\pi\) | ||||
−0.198028 | + | 0.980196i | \(0.563454\pi\) | |||||||
\(68\) | 4.35537 | 0.528166 | ||||||||
\(69\) | −2.89647 | −0.348694 | ||||||||
\(70\) | 1.26901 | 0.151675 | ||||||||
\(71\) | 4.25971 | 0.505535 | 0.252767 | − | 0.967527i | \(-0.418659\pi\) | ||||
0.252767 | + | 0.967527i | \(0.418659\pi\) | |||||||
\(72\) | −2.74832 | −0.323893 | ||||||||
\(73\) | −8.90203 | −1.04190 | −0.520952 | − | 0.853586i | \(-0.674423\pi\) | ||||
−0.520952 | + | 0.853586i | \(0.674423\pi\) | |||||||
\(74\) | −5.43885 | −0.632253 | ||||||||
\(75\) | −2.66271 | −0.307464 | ||||||||
\(76\) | −3.25227 | −0.373060 | ||||||||
\(77\) | −4.02473 | −0.458661 | ||||||||
\(78\) | 5.10040 | 0.577506 | ||||||||
\(79\) | 16.1767 | 1.82002 | 0.910009 | − | 0.414589i | \(-0.136075\pi\) | ||||
0.910009 | + | 0.414589i | \(0.136075\pi\) | |||||||
\(80\) | −0.520930 | −0.0582418 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.28847 | 1.02574 | ||||||||
\(83\) | 13.7237 | 1.50637 | 0.753184 | − | 0.657810i | \(-0.228517\pi\) | ||||
0.753184 | + | 0.657810i | \(0.228517\pi\) | |||||||
\(84\) | 1.31100 | 0.143042 | ||||||||
\(85\) | 5.07898 | 0.550893 | ||||||||
\(86\) | 3.45050 | 0.372077 | ||||||||
\(87\) | −10.4514 | −1.12050 | ||||||||
\(88\) | −11.0613 | −1.17914 | ||||||||
\(89\) | −14.1315 | −1.49794 | −0.748970 | − | 0.662604i | \(-0.769451\pi\) | ||||
−0.748970 | + | 0.662604i | \(0.769451\pi\) | |||||||
\(90\) | −1.26901 | −0.133765 | ||||||||
\(91\) | −6.14463 | −0.644132 | ||||||||
\(92\) | 3.79729 | 0.395895 | ||||||||
\(93\) | −5.02164 | −0.520720 | ||||||||
\(94\) | 11.1394 | 1.14894 | ||||||||
\(95\) | −3.79261 | −0.389113 | ||||||||
\(96\) | 5.77948 | 0.589866 | ||||||||
\(97\) | −4.30960 | −0.437574 | −0.218787 | − | 0.975773i | \(-0.570210\pi\) | ||||
−0.218787 | + | 0.975773i | \(0.570210\pi\) | |||||||
\(98\) | 0.830058 | 0.0838485 | ||||||||
\(99\) | 4.02473 | 0.404501 | ||||||||
\(100\) | 3.49083 | 0.349083 | ||||||||
\(101\) | 4.31759 | 0.429616 | 0.214808 | − | 0.976656i | \(-0.431087\pi\) | ||||
0.214808 | + | 0.976656i | \(0.431087\pi\) | |||||||
\(102\) | −2.75758 | −0.273042 | ||||||||
\(103\) | 9.58633 | 0.944569 | 0.472285 | − | 0.881446i | \(-0.343429\pi\) | ||||
0.472285 | + | 0.881446i | \(0.343429\pi\) | |||||||
\(104\) | −16.8874 | −1.65595 | ||||||||
\(105\) | 1.52882 | 0.149197 | ||||||||
\(106\) | 6.68896 | 0.649690 | ||||||||
\(107\) | 1.00532 | 0.0971884 | 0.0485942 | − | 0.998819i | \(-0.484526\pi\) | ||||
0.0485942 | + | 0.998819i | \(0.484526\pi\) | |||||||
\(108\) | −1.31100 | −0.126151 | ||||||||
\(109\) | 19.3708 | 1.85539 | 0.927694 | − | 0.373341i | \(-0.121788\pi\) | ||||
0.927694 | + | 0.373341i | \(0.121788\pi\) | |||||||
\(110\) | −5.10742 | −0.486973 | ||||||||
\(111\) | −6.55237 | −0.621924 | ||||||||
\(112\) | −0.340740 | −0.0321969 | ||||||||
\(113\) | 7.36650 | 0.692982 | 0.346491 | − | 0.938053i | \(-0.387373\pi\) | ||||
0.346491 | + | 0.938053i | \(0.387373\pi\) | |||||||
\(114\) | 2.05916 | 0.192858 | ||||||||
\(115\) | 4.42818 | 0.412930 | ||||||||
\(116\) | 13.7018 | 1.27218 | ||||||||
\(117\) | 6.14463 | 0.568071 | ||||||||
\(118\) | 11.2383 | 1.03457 | ||||||||
\(119\) | 3.32216 | 0.304542 | ||||||||
\(120\) | 4.20169 | 0.383560 | ||||||||
\(121\) | 5.19848 | 0.472589 | ||||||||
\(122\) | 0.444446 | 0.0402383 | ||||||||
\(123\) | 11.1902 | 1.00898 | ||||||||
\(124\) | 6.58339 | 0.591206 | ||||||||
\(125\) | 11.7149 | 1.04781 | ||||||||
\(126\) | −0.830058 | −0.0739474 | ||||||||
\(127\) | 13.7820 | 1.22295 | 0.611476 | − | 0.791263i | \(-0.290576\pi\) | ||||
0.611476 | + | 0.791263i | \(0.290576\pi\) | |||||||
\(128\) | −8.14259 | −0.719711 | ||||||||
\(129\) | 4.15694 | 0.365999 | ||||||||
\(130\) | −7.79758 | −0.683893 | ||||||||
\(131\) | −13.4714 | −1.17700 | −0.588499 | − | 0.808498i | \(-0.700281\pi\) | ||||
−0.588499 | + | 0.808498i | \(0.700281\pi\) | |||||||
\(132\) | −5.27644 | −0.459255 | ||||||||
\(133\) | −2.48074 | −0.215108 | ||||||||
\(134\) | −2.69092 | −0.232460 | ||||||||
\(135\) | −1.52882 | −0.131580 | ||||||||
\(136\) | 9.13037 | 0.782923 | ||||||||
\(137\) | −18.8074 | −1.60683 | −0.803413 | − | 0.595423i | \(-0.796985\pi\) | ||||
−0.803413 | + | 0.595423i | \(0.796985\pi\) | |||||||
\(138\) | −2.40424 | −0.204663 | ||||||||
\(139\) | −7.09584 | −0.601861 | −0.300930 | − | 0.953646i | \(-0.597297\pi\) | ||||
−0.300930 | + | 0.953646i | \(0.597297\pi\) | |||||||
\(140\) | −2.00429 | −0.169393 | ||||||||
\(141\) | 13.4200 | 1.13017 | ||||||||
\(142\) | 3.53581 | 0.296718 | ||||||||
\(143\) | 24.7305 | 2.06807 | ||||||||
\(144\) | 0.340740 | 0.0283950 | ||||||||
\(145\) | 15.9782 | 1.32692 | ||||||||
\(146\) | −7.38920 | −0.611534 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 8.59019 | 0.706109 | ||||||||
\(149\) | 21.9661 | 1.79953 | 0.899766 | − | 0.436373i | \(-0.143737\pi\) | ||||
0.899766 | + | 0.436373i | \(0.143737\pi\) | |||||||
\(150\) | −2.21021 | −0.180463 | ||||||||
\(151\) | −12.5399 | −1.02048 | −0.510241 | − | 0.860032i | \(-0.670444\pi\) | ||||
−0.510241 | + | 0.860032i | \(0.670444\pi\) | |||||||
\(152\) | −6.81789 | −0.553004 | ||||||||
\(153\) | −3.32216 | −0.268581 | ||||||||
\(154\) | −3.34076 | −0.269206 | ||||||||
\(155\) | 7.67718 | 0.616646 | ||||||||
\(156\) | −8.05563 | −0.644967 | ||||||||
\(157\) | 0.792324 | 0.0632343 | 0.0316172 | − | 0.999500i | \(-0.489934\pi\) | ||||
0.0316172 | + | 0.999500i | \(0.489934\pi\) | |||||||
\(158\) | 13.4276 | 1.06824 | ||||||||
\(159\) | 8.05843 | 0.639075 | ||||||||
\(160\) | −8.83578 | −0.698530 | ||||||||
\(161\) | 2.89647 | 0.228274 | ||||||||
\(162\) | 0.830058 | 0.0652155 | ||||||||
\(163\) | 21.1577 | 1.65720 | 0.828599 | − | 0.559842i | \(-0.189138\pi\) | ||||
0.828599 | + | 0.559842i | \(0.189138\pi\) | |||||||
\(164\) | −14.6703 | −1.14556 | ||||||||
\(165\) | −6.15309 | −0.479017 | ||||||||
\(166\) | 11.3914 | 0.884147 | ||||||||
\(167\) | 21.0658 | 1.63012 | 0.815059 | − | 0.579378i | \(-0.196705\pi\) | ||||
0.815059 | + | 0.579378i | \(0.196705\pi\) | |||||||
\(168\) | 2.74832 | 0.212038 | ||||||||
\(169\) | 24.7565 | 1.90434 | ||||||||
\(170\) | 4.21585 | 0.323341 | ||||||||
\(171\) | 2.48074 | 0.189707 | ||||||||
\(172\) | −5.44977 | −0.415541 | ||||||||
\(173\) | 7.57553 | 0.575957 | 0.287978 | − | 0.957637i | \(-0.407017\pi\) | ||||
0.287978 | + | 0.957637i | \(0.407017\pi\) | |||||||
\(174\) | −8.67522 | −0.657667 | ||||||||
\(175\) | 2.66271 | 0.201282 | ||||||||
\(176\) | 1.37139 | 0.103372 | ||||||||
\(177\) | 13.5392 | 1.01767 | ||||||||
\(178\) | −11.7300 | −0.879200 | ||||||||
\(179\) | −5.01295 | −0.374685 | −0.187343 | − | 0.982295i | \(-0.559987\pi\) | ||||
−0.187343 | + | 0.982295i | \(0.559987\pi\) | |||||||
\(180\) | 2.00429 | 0.149391 | ||||||||
\(181\) | 4.19182 | 0.311575 | 0.155788 | − | 0.987791i | \(-0.450208\pi\) | ||||
0.155788 | + | 0.987791i | \(0.450208\pi\) | |||||||
\(182\) | −5.10040 | −0.378067 | ||||||||
\(183\) | 0.535440 | 0.0395809 | ||||||||
\(184\) | 7.96045 | 0.586852 | ||||||||
\(185\) | 10.0174 | 0.736493 | ||||||||
\(186\) | −4.16825 | −0.305631 | ||||||||
\(187\) | −13.3708 | −0.977770 | ||||||||
\(188\) | −17.5937 | −1.28315 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −3.14808 | −0.228386 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | 4.11582 | 0.297034 | ||||||||
\(193\) | −1.04418 | −0.0751618 | −0.0375809 | − | 0.999294i | \(-0.511965\pi\) | ||||
−0.0375809 | + | 0.999294i | \(0.511965\pi\) | |||||||
\(194\) | −3.57722 | −0.256829 | ||||||||
\(195\) | −9.39402 | −0.672720 | ||||||||
\(196\) | −1.31100 | −0.0936432 | ||||||||
\(197\) | −7.51328 | −0.535299 | −0.267649 | − | 0.963516i | \(-0.586247\pi\) | ||||
−0.267649 | + | 0.963516i | \(0.586247\pi\) | |||||||
\(198\) | 3.34076 | 0.237418 | ||||||||
\(199\) | 3.41954 | 0.242405 | 0.121202 | − | 0.992628i | \(-0.461325\pi\) | ||||
0.121202 | + | 0.992628i | \(0.461325\pi\) | |||||||
\(200\) | 7.31800 | 0.517461 | ||||||||
\(201\) | −3.24185 | −0.228663 | ||||||||
\(202\) | 3.58385 | 0.252158 | ||||||||
\(203\) | 10.4514 | 0.733541 | ||||||||
\(204\) | 4.35537 | 0.304937 | ||||||||
\(205\) | −17.1077 | −1.19486 | ||||||||
\(206\) | 7.95721 | 0.554405 | ||||||||
\(207\) | −2.89647 | −0.201319 | ||||||||
\(208\) | 2.09372 | 0.145174 | ||||||||
\(209\) | 9.98433 | 0.690631 | ||||||||
\(210\) | 1.26901 | 0.0875699 | ||||||||
\(211\) | −23.8431 | −1.64143 | −0.820715 | − | 0.571338i | \(-0.806425\pi\) | ||||
−0.820715 | + | 0.571338i | \(0.806425\pi\) | |||||||
\(212\) | −10.5646 | −0.725582 | ||||||||
\(213\) | 4.25971 | 0.291871 | ||||||||
\(214\) | 0.834478 | 0.0570437 | ||||||||
\(215\) | −6.35522 | −0.433422 | ||||||||
\(216\) | −2.74832 | −0.187000 | ||||||||
\(217\) | 5.02164 | 0.340891 | ||||||||
\(218\) | 16.0789 | 1.08900 | ||||||||
\(219\) | −8.90203 | −0.601543 | ||||||||
\(220\) | 8.06673 | 0.543859 | ||||||||
\(221\) | −20.4134 | −1.37316 | ||||||||
\(222\) | −5.43885 | −0.365032 | ||||||||
\(223\) | −19.3056 | −1.29280 | −0.646401 | − | 0.762998i | \(-0.723726\pi\) | ||||
−0.646401 | + | 0.762998i | \(0.723726\pi\) | |||||||
\(224\) | −5.77948 | −0.386158 | ||||||||
\(225\) | −2.66271 | −0.177514 | ||||||||
\(226\) | 6.11462 | 0.406738 | ||||||||
\(227\) | −20.6127 | −1.36812 | −0.684058 | − | 0.729428i | \(-0.739786\pi\) | ||||
−0.684058 | + | 0.729428i | \(0.739786\pi\) | |||||||
\(228\) | −3.25227 | −0.215387 | ||||||||
\(229\) | −10.0822 | −0.666250 | −0.333125 | − | 0.942883i | \(-0.608103\pi\) | ||||
−0.333125 | + | 0.942883i | \(0.608103\pi\) | |||||||
\(230\) | 3.67565 | 0.242365 | ||||||||
\(231\) | −4.02473 | −0.264808 | ||||||||
\(232\) | 28.7237 | 1.88580 | ||||||||
\(233\) | 22.0942 | 1.44744 | 0.723719 | − | 0.690094i | \(-0.242431\pi\) | ||||
0.723719 | + | 0.690094i | \(0.242431\pi\) | |||||||
\(234\) | 5.10040 | 0.333423 | ||||||||
\(235\) | −20.5168 | −1.33837 | ||||||||
\(236\) | −17.7499 | −1.15542 | ||||||||
\(237\) | 16.1767 | 1.05079 | ||||||||
\(238\) | 2.75758 | 0.178748 | ||||||||
\(239\) | 1.69534 | 0.109662 | 0.0548311 | − | 0.998496i | \(-0.482538\pi\) | ||||
0.0548311 | + | 0.998496i | \(0.482538\pi\) | |||||||
\(240\) | −0.520930 | −0.0336259 | ||||||||
\(241\) | 2.45933 | 0.158419 | 0.0792096 | − | 0.996858i | \(-0.474760\pi\) | ||||
0.0792096 | + | 0.996858i | \(0.474760\pi\) | |||||||
\(242\) | 4.31504 | 0.277381 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.701964 | −0.0449387 | ||||||||
\(245\) | −1.52882 | −0.0976727 | ||||||||
\(246\) | 9.28847 | 0.592212 | ||||||||
\(247\) | 15.2432 | 0.969905 | ||||||||
\(248\) | 13.8011 | 0.876371 | ||||||||
\(249\) | 13.7237 | 0.869702 | ||||||||
\(250\) | 9.72404 | 0.615002 | ||||||||
\(251\) | 12.0568 | 0.761018 | 0.380509 | − | 0.924777i | \(-0.375749\pi\) | ||||
0.380509 | + | 0.924777i | \(0.375749\pi\) | |||||||
\(252\) | 1.31100 | 0.0825855 | ||||||||
\(253\) | −11.6575 | −0.732903 | ||||||||
\(254\) | 11.4398 | 0.717799 | ||||||||
\(255\) | 5.07898 | 0.318058 | ||||||||
\(256\) | −14.9905 | −0.936905 | ||||||||
\(257\) | 9.62851 | 0.600610 | 0.300305 | − | 0.953843i | \(-0.402911\pi\) | ||||
0.300305 | + | 0.953843i | \(0.402911\pi\) | |||||||
\(258\) | 3.45050 | 0.214819 | ||||||||
\(259\) | 6.55237 | 0.407145 | ||||||||
\(260\) | 12.3156 | 0.763781 | ||||||||
\(261\) | −10.4514 | −0.646922 | ||||||||
\(262\) | −11.1820 | −0.690827 | ||||||||
\(263\) | 19.3325 | 1.19210 | 0.596048 | − | 0.802949i | \(-0.296737\pi\) | ||||
0.596048 | + | 0.802949i | \(0.296737\pi\) | |||||||
\(264\) | −11.0613 | −0.680774 | ||||||||
\(265\) | −12.3199 | −0.756805 | ||||||||
\(266\) | −2.05916 | −0.126255 | ||||||||
\(267\) | −14.1315 | −0.864836 | ||||||||
\(268\) | 4.25008 | 0.259615 | ||||||||
\(269\) | −13.3998 | −0.816997 | −0.408499 | − | 0.912759i | \(-0.633948\pi\) | ||||
−0.408499 | + | 0.912759i | \(0.633948\pi\) | |||||||
\(270\) | −1.26901 | −0.0772294 | ||||||||
\(271\) | 14.5707 | 0.885106 | 0.442553 | − | 0.896742i | \(-0.354073\pi\) | ||||
0.442553 | + | 0.896742i | \(0.354073\pi\) | |||||||
\(272\) | −1.13199 | −0.0686372 | ||||||||
\(273\) | −6.14463 | −0.371890 | ||||||||
\(274\) | −15.6112 | −0.943109 | ||||||||
\(275\) | −10.7167 | −0.646242 | ||||||||
\(276\) | 3.79729 | 0.228570 | ||||||||
\(277\) | 1.22840 | 0.0738073 | 0.0369037 | − | 0.999319i | \(-0.488251\pi\) | ||||
0.0369037 | + | 0.999319i | \(0.488251\pi\) | |||||||
\(278\) | −5.88995 | −0.353256 | ||||||||
\(279\) | −5.02164 | −0.300638 | ||||||||
\(280\) | −4.20169 | −0.251099 | ||||||||
\(281\) | −8.52086 | −0.508312 | −0.254156 | − | 0.967163i | \(-0.581798\pi\) | ||||
−0.254156 | + | 0.967163i | \(0.581798\pi\) | |||||||
\(282\) | 11.1394 | 0.663341 | ||||||||
\(283\) | 12.5808 | 0.747851 | 0.373926 | − | 0.927459i | \(-0.378012\pi\) | ||||
0.373926 | + | 0.927459i | \(0.378012\pi\) | |||||||
\(284\) | −5.58450 | −0.331379 | ||||||||
\(285\) | −3.79261 | −0.224655 | ||||||||
\(286\) | 20.5277 | 1.21383 | ||||||||
\(287\) | −11.1902 | −0.660534 | ||||||||
\(288\) | 5.77948 | 0.340559 | ||||||||
\(289\) | −5.96325 | −0.350780 | ||||||||
\(290\) | 13.2628 | 0.778821 | ||||||||
\(291\) | −4.30960 | −0.252633 | ||||||||
\(292\) | 11.6706 | 0.682970 | ||||||||
\(293\) | −12.1071 | −0.707306 | −0.353653 | − | 0.935377i | \(-0.615061\pi\) | ||||
−0.353653 | + | 0.935377i | \(0.615061\pi\) | |||||||
\(294\) | 0.830058 | 0.0484099 | ||||||||
\(295\) | −20.6990 | −1.20514 | ||||||||
\(296\) | 18.0081 | 1.04670 | ||||||||
\(297\) | 4.02473 | 0.233539 | ||||||||
\(298\) | 18.2331 | 1.05622 | ||||||||
\(299\) | −17.7978 | −1.02927 | ||||||||
\(300\) | 3.49083 | 0.201543 | ||||||||
\(301\) | −4.15694 | −0.239602 | ||||||||
\(302\) | −10.4088 | −0.598961 | ||||||||
\(303\) | 4.31759 | 0.248039 | ||||||||
\(304\) | 0.845289 | 0.0484807 | ||||||||
\(305\) | −0.818591 | −0.0468724 | ||||||||
\(306\) | −2.75758 | −0.157641 | ||||||||
\(307\) | −19.8703 | −1.13406 | −0.567028 | − | 0.823698i | \(-0.691907\pi\) | ||||
−0.567028 | + | 0.823698i | \(0.691907\pi\) | |||||||
\(308\) | 5.27644 | 0.300653 | ||||||||
\(309\) | 9.58633 | 0.545347 | ||||||||
\(310\) | 6.37250 | 0.361934 | ||||||||
\(311\) | 31.9589 | 1.81222 | 0.906112 | − | 0.423037i | \(-0.139036\pi\) | ||||
0.906112 | + | 0.423037i | \(0.139036\pi\) | |||||||
\(312\) | −16.8874 | −0.956063 | ||||||||
\(313\) | −7.83387 | −0.442797 | −0.221398 | − | 0.975183i | \(-0.571062\pi\) | ||||
−0.221398 | + | 0.975183i | \(0.571062\pi\) | |||||||
\(314\) | 0.657675 | 0.0371147 | ||||||||
\(315\) | 1.52882 | 0.0861392 | ||||||||
\(316\) | −21.2077 | −1.19303 | ||||||||
\(317\) | −9.12873 | −0.512720 | −0.256360 | − | 0.966581i | \(-0.582523\pi\) | ||||
−0.256360 | + | 0.966581i | \(0.582523\pi\) | |||||||
\(318\) | 6.68896 | 0.375099 | ||||||||
\(319\) | −42.0639 | −2.35513 | ||||||||
\(320\) | −6.29235 | −0.351753 | ||||||||
\(321\) | 1.00532 | 0.0561118 | ||||||||
\(322\) | 2.40424 | 0.133983 | ||||||||
\(323\) | −8.24143 | −0.458565 | ||||||||
\(324\) | −1.31100 | −0.0728336 | ||||||||
\(325\) | −16.3614 | −0.907566 | ||||||||
\(326\) | 17.5621 | 0.972675 | ||||||||
\(327\) | 19.3708 | 1.07121 | ||||||||
\(328\) | −30.7542 | −1.69812 | ||||||||
\(329\) | −13.4200 | −0.739870 | ||||||||
\(330\) | −5.10742 | −0.281154 | ||||||||
\(331\) | −20.1555 | −1.10785 | −0.553924 | − | 0.832567i | \(-0.686870\pi\) | ||||
−0.553924 | + | 0.832567i | \(0.686870\pi\) | |||||||
\(332\) | −17.9918 | −0.987428 | ||||||||
\(333\) | −6.55237 | −0.359068 | ||||||||
\(334\) | 17.4858 | 0.956780 | ||||||||
\(335\) | 4.95620 | 0.270786 | ||||||||
\(336\) | −0.340740 | −0.0185889 | ||||||||
\(337\) | −1.18462 | −0.0645303 | −0.0322652 | − | 0.999479i | \(-0.510272\pi\) | ||||
−0.0322652 | + | 0.999479i | \(0.510272\pi\) | |||||||
\(338\) | 20.5493 | 1.11773 | ||||||||
\(339\) | 7.36650 | 0.400093 | ||||||||
\(340\) | −6.65857 | −0.361111 | ||||||||
\(341\) | −20.2108 | −1.09447 | ||||||||
\(342\) | 2.05916 | 0.111347 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −11.4246 | −0.615975 | ||||||||
\(345\) | 4.42818 | 0.238405 | ||||||||
\(346\) | 6.28812 | 0.338052 | ||||||||
\(347\) | 18.2669 | 0.980620 | 0.490310 | − | 0.871548i | \(-0.336884\pi\) | ||||
0.490310 | + | 0.871548i | \(0.336884\pi\) | |||||||
\(348\) | 13.7018 | 0.734492 | ||||||||
\(349\) | 31.1707 | 1.66853 | 0.834265 | − | 0.551364i | \(-0.185893\pi\) | ||||
0.834265 | + | 0.551364i | \(0.185893\pi\) | |||||||
\(350\) | 2.21021 | 0.118140 | ||||||||
\(351\) | 6.14463 | 0.327976 | ||||||||
\(352\) | 23.2609 | 1.23981 | ||||||||
\(353\) | −28.9747 | −1.54217 | −0.771085 | − | 0.636733i | \(-0.780286\pi\) | ||||
−0.771085 | + | 0.636733i | \(0.780286\pi\) | |||||||
\(354\) | 11.2383 | 0.597309 | ||||||||
\(355\) | −6.51233 | −0.345638 | ||||||||
\(356\) | 18.5265 | 0.981903 | ||||||||
\(357\) | 3.32216 | 0.175827 | ||||||||
\(358\) | −4.16103 | −0.219918 | ||||||||
\(359\) | −10.0633 | −0.531119 | −0.265560 | − | 0.964094i | \(-0.585557\pi\) | ||||
−0.265560 | + | 0.964094i | \(0.585557\pi\) | |||||||
\(360\) | 4.20169 | 0.221449 | ||||||||
\(361\) | −12.8459 | −0.676101 | ||||||||
\(362\) | 3.47945 | 0.182876 | ||||||||
\(363\) | 5.19848 | 0.272850 | ||||||||
\(364\) | 8.05563 | 0.422230 | ||||||||
\(365\) | 13.6096 | 0.712358 | ||||||||
\(366\) | 0.444446 | 0.0232316 | ||||||||
\(367\) | −18.6218 | −0.972051 | −0.486025 | − | 0.873945i | \(-0.661554\pi\) | ||||
−0.486025 | + | 0.873945i | \(0.661554\pi\) | |||||||
\(368\) | −0.986945 | −0.0514481 | ||||||||
\(369\) | 11.1902 | 0.582536 | ||||||||
\(370\) | 8.31501 | 0.432277 | ||||||||
\(371\) | −8.05843 | −0.418373 | ||||||||
\(372\) | 6.58339 | 0.341333 | ||||||||
\(373\) | −7.15580 | −0.370513 | −0.185257 | − | 0.982690i | \(-0.559312\pi\) | ||||
−0.185257 | + | 0.982690i | \(0.559312\pi\) | |||||||
\(374\) | −11.0985 | −0.573892 | ||||||||
\(375\) | 11.7149 | 0.604955 | ||||||||
\(376\) | −36.8826 | −1.90207 | ||||||||
\(377\) | −64.2197 | −3.30748 | ||||||||
\(378\) | −0.830058 | −0.0426936 | ||||||||
\(379\) | 2.52006 | 0.129447 | 0.0647233 | − | 0.997903i | \(-0.479384\pi\) | ||||
0.0647233 | + | 0.997903i | \(0.479384\pi\) | |||||||
\(380\) | 4.97212 | 0.255065 | ||||||||
\(381\) | 13.7820 | 0.706072 | ||||||||
\(382\) | −0.830058 | −0.0424694 | ||||||||
\(383\) | 8.77635 | 0.448451 | 0.224225 | − | 0.974537i | \(-0.428015\pi\) | ||||
0.224225 | + | 0.974537i | \(0.428015\pi\) | |||||||
\(384\) | −8.14259 | −0.415525 | ||||||||
\(385\) | 6.15309 | 0.313590 | ||||||||
\(386\) | −0.866730 | −0.0441154 | ||||||||
\(387\) | 4.15694 | 0.211309 | ||||||||
\(388\) | 5.64991 | 0.286831 | ||||||||
\(389\) | 24.4274 | 1.23852 | 0.619259 | − | 0.785187i | \(-0.287433\pi\) | ||||
0.619259 | + | 0.785187i | \(0.287433\pi\) | |||||||
\(390\) | −7.79758 | −0.394846 | ||||||||
\(391\) | 9.62255 | 0.486633 | ||||||||
\(392\) | −2.74832 | −0.138811 | ||||||||
\(393\) | −13.4714 | −0.679541 | ||||||||
\(394\) | −6.23645 | −0.314188 | ||||||||
\(395\) | −24.7312 | −1.24436 | ||||||||
\(396\) | −5.27644 | −0.265151 | ||||||||
\(397\) | −5.65483 | −0.283808 | −0.141904 | − | 0.989880i | \(-0.545322\pi\) | ||||
−0.141904 | + | 0.989880i | \(0.545322\pi\) | |||||||
\(398\) | 2.83842 | 0.142277 | ||||||||
\(399\) | −2.48074 | −0.124193 | ||||||||
\(400\) | −0.907294 | −0.0453647 | ||||||||
\(401\) | 6.29687 | 0.314450 | 0.157225 | − | 0.987563i | \(-0.449745\pi\) | ||||
0.157225 | + | 0.987563i | \(0.449745\pi\) | |||||||
\(402\) | −2.69092 | −0.134211 | ||||||||
\(403\) | −30.8561 | −1.53705 | ||||||||
\(404\) | −5.66037 | −0.281614 | ||||||||
\(405\) | −1.52882 | −0.0759676 | ||||||||
\(406\) | 8.67522 | 0.430544 | ||||||||
\(407\) | −26.3716 | −1.30719 | ||||||||
\(408\) | 9.13037 | 0.452021 | ||||||||
\(409\) | −21.8882 | −1.08230 | −0.541151 | − | 0.840925i | \(-0.682011\pi\) | ||||
−0.541151 | + | 0.840925i | \(0.682011\pi\) | |||||||
\(410\) | −14.2004 | −0.701308 | ||||||||
\(411\) | −18.8074 | −0.927701 | ||||||||
\(412\) | −12.5677 | −0.619167 | ||||||||
\(413\) | −13.5392 | −0.666220 | ||||||||
\(414\) | −2.40424 | −0.118162 | ||||||||
\(415\) | −20.9810 | −1.02992 | ||||||||
\(416\) | 35.5128 | 1.74116 | ||||||||
\(417\) | −7.09584 | −0.347485 | ||||||||
\(418\) | 8.28757 | 0.405358 | ||||||||
\(419\) | −16.4271 | −0.802518 | −0.401259 | − | 0.915965i | \(-0.631427\pi\) | ||||
−0.401259 | + | 0.915965i | \(0.631427\pi\) | |||||||
\(420\) | −2.00429 | −0.0977992 | ||||||||
\(421\) | −4.73970 | −0.230999 | −0.115500 | − | 0.993308i | \(-0.536847\pi\) | ||||
−0.115500 | + | 0.993308i | \(0.536847\pi\) | |||||||
\(422\) | −19.7912 | −0.963420 | ||||||||
\(423\) | 13.4200 | 0.652504 | ||||||||
\(424\) | −22.1472 | −1.07556 | ||||||||
\(425\) | 8.84596 | 0.429092 | ||||||||
\(426\) | 3.53581 | 0.171310 | ||||||||
\(427\) | −0.535440 | −0.0259118 | ||||||||
\(428\) | −1.31799 | −0.0637072 | ||||||||
\(429\) | 24.7305 | 1.19400 | ||||||||
\(430\) | −5.27520 | −0.254393 | ||||||||
\(431\) | 6.28780 | 0.302873 | 0.151436 | − | 0.988467i | \(-0.451610\pi\) | ||||
0.151436 | + | 0.988467i | \(0.451610\pi\) | |||||||
\(432\) | 0.340740 | 0.0163939 | ||||||||
\(433\) | 14.8514 | 0.713711 | 0.356855 | − | 0.934160i | \(-0.383849\pi\) | ||||
0.356855 | + | 0.934160i | \(0.383849\pi\) | |||||||
\(434\) | 4.16825 | 0.200083 | ||||||||
\(435\) | 15.9782 | 0.766097 | ||||||||
\(436\) | −25.3952 | −1.21621 | ||||||||
\(437\) | −7.18541 | −0.343725 | ||||||||
\(438\) | −7.38920 | −0.353069 | ||||||||
\(439\) | 7.21505 | 0.344355 | 0.172178 | − | 0.985066i | \(-0.444920\pi\) | ||||
0.172178 | + | 0.985066i | \(0.444920\pi\) | |||||||
\(440\) | 16.9107 | 0.806185 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −16.9443 | −0.805960 | ||||||||
\(443\) | 18.5395 | 0.880840 | 0.440420 | − | 0.897792i | \(-0.354830\pi\) | ||||
0.440420 | + | 0.897792i | \(0.354830\pi\) | |||||||
\(444\) | 8.59019 | 0.407672 | ||||||||
\(445\) | 21.6046 | 1.02415 | ||||||||
\(446\) | −16.0248 | −0.758796 | ||||||||
\(447\) | 21.9661 | 1.03896 | ||||||||
\(448\) | −4.11582 | −0.194454 | ||||||||
\(449\) | 30.9615 | 1.46116 | 0.730582 | − | 0.682825i | \(-0.239249\pi\) | ||||
0.730582 | + | 0.682825i | \(0.239249\pi\) | |||||||
\(450\) | −2.21021 | −0.104190 | ||||||||
\(451\) | 45.0374 | 2.12073 | ||||||||
\(452\) | −9.65751 | −0.454251 | ||||||||
\(453\) | −12.5399 | −0.589175 | ||||||||
\(454\) | −17.1098 | −0.803001 | ||||||||
\(455\) | 9.39402 | 0.440399 | ||||||||
\(456\) | −6.81789 | −0.319277 | ||||||||
\(457\) | −3.30691 | −0.154691 | −0.0773453 | − | 0.997004i | \(-0.524644\pi\) | ||||
−0.0773453 | + | 0.997004i | \(0.524644\pi\) | |||||||
\(458\) | −8.36880 | −0.391048 | ||||||||
\(459\) | −3.32216 | −0.155065 | ||||||||
\(460\) | −5.80537 | −0.270677 | ||||||||
\(461\) | 6.32803 | 0.294726 | 0.147363 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147363 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(462\) | −3.34076 | −0.155426 | ||||||||
\(463\) | 8.22463 | 0.382231 | 0.191116 | − | 0.981568i | \(-0.438789\pi\) | ||||
0.191116 | + | 0.981568i | \(0.438789\pi\) | |||||||
\(464\) | −3.56120 | −0.165324 | ||||||||
\(465\) | 7.67718 | 0.356021 | ||||||||
\(466\) | 18.3395 | 0.849559 | ||||||||
\(467\) | −14.2979 | −0.661627 | −0.330814 | − | 0.943696i | \(-0.607323\pi\) | ||||
−0.330814 | + | 0.943696i | \(0.607323\pi\) | |||||||
\(468\) | −8.05563 | −0.372372 | ||||||||
\(469\) | 3.24185 | 0.149695 | ||||||||
\(470\) | −17.0301 | −0.785541 | ||||||||
\(471\) | 0.792324 | 0.0365084 | ||||||||
\(472\) | −37.2101 | −1.71273 | ||||||||
\(473\) | 16.7306 | 0.769274 | ||||||||
\(474\) | 13.4276 | 0.616749 | ||||||||
\(475\) | −6.60551 | −0.303081 | ||||||||
\(476\) | −4.35537 | −0.199628 | ||||||||
\(477\) | 8.05843 | 0.368970 | ||||||||
\(478\) | 1.40723 | 0.0643651 | ||||||||
\(479\) | 24.5915 | 1.12361 | 0.561806 | − | 0.827269i | \(-0.310107\pi\) | ||||
0.561806 | + | 0.827269i | \(0.310107\pi\) | |||||||
\(480\) | −8.83578 | −0.403296 | ||||||||
\(481\) | −40.2619 | −1.83578 | ||||||||
\(482\) | 2.04138 | 0.0929824 | ||||||||
\(483\) | 2.89647 | 0.131794 | ||||||||
\(484\) | −6.81523 | −0.309783 | ||||||||
\(485\) | 6.58860 | 0.299173 | ||||||||
\(486\) | 0.830058 | 0.0376522 | ||||||||
\(487\) | 3.43732 | 0.155760 | 0.0778799 | − | 0.996963i | \(-0.475185\pi\) | ||||
0.0778799 | + | 0.996963i | \(0.475185\pi\) | |||||||
\(488\) | −1.47156 | −0.0666145 | ||||||||
\(489\) | 21.1577 | 0.956784 | ||||||||
\(490\) | −1.26901 | −0.0573279 | ||||||||
\(491\) | 30.9198 | 1.39539 | 0.697696 | − | 0.716394i | \(-0.254209\pi\) | ||||
0.697696 | + | 0.716394i | \(0.254209\pi\) | |||||||
\(492\) | −14.6703 | −0.661390 | ||||||||
\(493\) | 34.7211 | 1.56376 | ||||||||
\(494\) | 12.6528 | 0.569275 | ||||||||
\(495\) | −6.15309 | −0.276561 | ||||||||
\(496\) | −1.71108 | −0.0768296 | ||||||||
\(497\) | −4.25971 | −0.191074 | ||||||||
\(498\) | 11.3914 | 0.510463 | ||||||||
\(499\) | −19.7248 | −0.883004 | −0.441502 | − | 0.897260i | \(-0.645554\pi\) | ||||
−0.441502 | + | 0.897260i | \(0.645554\pi\) | |||||||
\(500\) | −15.3583 | −0.686843 | ||||||||
\(501\) | 21.0658 | 0.941149 | ||||||||
\(502\) | 10.0078 | 0.446671 | ||||||||
\(503\) | −30.1407 | −1.34391 | −0.671953 | − | 0.740594i | \(-0.734544\pi\) | ||||
−0.671953 | + | 0.740594i | \(0.734544\pi\) | |||||||
\(504\) | 2.74832 | 0.122420 | ||||||||
\(505\) | −6.60081 | −0.293732 | ||||||||
\(506\) | −9.67643 | −0.430170 | ||||||||
\(507\) | 24.7565 | 1.09947 | ||||||||
\(508\) | −18.0682 | −0.801648 | ||||||||
\(509\) | 11.6522 | 0.516476 | 0.258238 | − | 0.966081i | \(-0.416858\pi\) | ||||
0.258238 | + | 0.966081i | \(0.416858\pi\) | |||||||
\(510\) | 4.21585 | 0.186681 | ||||||||
\(511\) | 8.90203 | 0.393803 | ||||||||
\(512\) | 3.84223 | 0.169804 | ||||||||
\(513\) | 2.48074 | 0.109528 | ||||||||
\(514\) | 7.99222 | 0.352522 | ||||||||
\(515\) | −14.6558 | −0.645810 | ||||||||
\(516\) | −5.44977 | −0.239913 | ||||||||
\(517\) | 54.0120 | 2.37545 | ||||||||
\(518\) | 5.43885 | 0.238969 | ||||||||
\(519\) | 7.57553 | 0.332529 | ||||||||
\(520\) | 25.8178 | 1.13219 | ||||||||
\(521\) | −26.9870 | −1.18232 | −0.591162 | − | 0.806553i | \(-0.701330\pi\) | ||||
−0.591162 | + | 0.806553i | \(0.701330\pi\) | |||||||
\(522\) | −8.67522 | −0.379704 | ||||||||
\(523\) | −24.8392 | −1.08614 | −0.543071 | − | 0.839687i | \(-0.682738\pi\) | ||||
−0.543071 | + | 0.839687i | \(0.682738\pi\) | |||||||
\(524\) | 17.6610 | 0.771525 | ||||||||
\(525\) | 2.66271 | 0.116210 | ||||||||
\(526\) | 16.0471 | 0.699688 | ||||||||
\(527\) | 16.6827 | 0.726710 | ||||||||
\(528\) | 1.37139 | 0.0596820 | ||||||||
\(529\) | −14.6104 | −0.635236 | ||||||||
\(530\) | −10.2262 | −0.444198 | ||||||||
\(531\) | 13.5392 | 0.587550 | ||||||||
\(532\) | 3.25227 | 0.141004 | ||||||||
\(533\) | 68.7593 | 2.97830 | ||||||||
\(534\) | −11.7300 | −0.507607 | ||||||||
\(535\) | −1.53696 | −0.0664486 | ||||||||
\(536\) | 8.90966 | 0.384839 | ||||||||
\(537\) | −5.01295 | −0.216325 | ||||||||
\(538\) | −11.1226 | −0.479528 | ||||||||
\(539\) | 4.02473 | 0.173358 | ||||||||
\(540\) | 2.00429 | 0.0862508 | ||||||||
\(541\) | −5.80003 | −0.249363 | −0.124681 | − | 0.992197i | \(-0.539791\pi\) | ||||
−0.124681 | + | 0.992197i | \(0.539791\pi\) | |||||||
\(542\) | 12.0945 | 0.519504 | ||||||||
\(543\) | 4.19182 | 0.179888 | ||||||||
\(544\) | −19.2004 | −0.823209 | ||||||||
\(545\) | −29.6145 | −1.26855 | ||||||||
\(546\) | −5.10040 | −0.218277 | ||||||||
\(547\) | 37.7702 | 1.61494 | 0.807468 | − | 0.589911i | \(-0.200837\pi\) | ||||
0.807468 | + | 0.589911i | \(0.200837\pi\) | |||||||
\(548\) | 24.6566 | 1.05328 | ||||||||
\(549\) | 0.535440 | 0.0228520 | ||||||||
\(550\) | −8.89549 | −0.379305 | ||||||||
\(551\) | −25.9271 | −1.10453 | ||||||||
\(552\) | 7.96045 | 0.338819 | ||||||||
\(553\) | −16.1767 | −0.687902 | ||||||||
\(554\) | 1.01964 | 0.0433204 | ||||||||
\(555\) | 10.0174 | 0.425215 | ||||||||
\(556\) | 9.30267 | 0.394521 | ||||||||
\(557\) | −36.1075 | −1.52992 | −0.764962 | − | 0.644075i | \(-0.777242\pi\) | ||||
−0.764962 | + | 0.644075i | \(0.777242\pi\) | |||||||
\(558\) | −4.16825 | −0.176456 | ||||||||
\(559\) | 25.5429 | 1.08035 | ||||||||
\(560\) | 0.520930 | 0.0220133 | ||||||||
\(561\) | −13.3708 | −0.564516 | ||||||||
\(562\) | −7.07281 | −0.298348 | ||||||||
\(563\) | −7.63693 | −0.321858 | −0.160929 | − | 0.986966i | \(-0.551449\pi\) | ||||
−0.160929 | + | 0.986966i | \(0.551449\pi\) | |||||||
\(564\) | −17.5937 | −0.740829 | ||||||||
\(565\) | −11.2620 | −0.473798 | ||||||||
\(566\) | 10.4428 | 0.438943 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −11.7071 | −0.491218 | ||||||||
\(569\) | −19.4874 | −0.816953 | −0.408477 | − | 0.912769i | \(-0.633940\pi\) | ||||
−0.408477 | + | 0.912769i | \(0.633940\pi\) | |||||||
\(570\) | −3.14808 | −0.131859 | ||||||||
\(571\) | −35.7402 | −1.49568 | −0.747839 | − | 0.663880i | \(-0.768909\pi\) | ||||
−0.747839 | + | 0.663880i | \(0.768909\pi\) | |||||||
\(572\) | −32.4218 | −1.35562 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | −9.28847 | −0.387693 | ||||||||
\(575\) | 7.71248 | 0.321633 | ||||||||
\(576\) | 4.11582 | 0.171493 | ||||||||
\(577\) | −23.2704 | −0.968759 | −0.484380 | − | 0.874858i | \(-0.660955\pi\) | ||||
−0.484380 | + | 0.874858i | \(0.660955\pi\) | |||||||
\(578\) | −4.94984 | −0.205886 | ||||||||
\(579\) | −1.04418 | −0.0433947 | ||||||||
\(580\) | −20.9475 | −0.869798 | ||||||||
\(581\) | −13.7237 | −0.569354 | ||||||||
\(582\) | −3.57722 | −0.148281 | ||||||||
\(583\) | 32.4330 | 1.34324 | ||||||||
\(584\) | 24.4657 | 1.01240 | ||||||||
\(585\) | −9.39402 | −0.388395 | ||||||||
\(586\) | −10.0496 | −0.415146 | ||||||||
\(587\) | 13.4787 | 0.556327 | 0.278164 | − | 0.960534i | \(-0.410274\pi\) | ||||
0.278164 | + | 0.960534i | \(0.410274\pi\) | |||||||
\(588\) | −1.31100 | −0.0540649 | ||||||||
\(589\) | −12.4574 | −0.513298 | ||||||||
\(590\) | −17.1813 | −0.707344 | ||||||||
\(591\) | −7.51328 | −0.309055 | ||||||||
\(592\) | −2.23266 | −0.0917617 | ||||||||
\(593\) | 18.4944 | 0.759475 | 0.379738 | − | 0.925094i | \(-0.376014\pi\) | ||||
0.379738 | + | 0.925094i | \(0.376014\pi\) | |||||||
\(594\) | 3.34076 | 0.137073 | ||||||||
\(595\) | −5.07898 | −0.208218 | ||||||||
\(596\) | −28.7976 | −1.17960 | ||||||||
\(597\) | 3.41954 | 0.139953 | ||||||||
\(598\) | −14.7732 | −0.604120 | ||||||||
\(599\) | −19.2852 | −0.787971 | −0.393986 | − | 0.919117i | \(-0.628904\pi\) | ||||
−0.393986 | + | 0.919117i | \(0.628904\pi\) | |||||||
\(600\) | 7.31800 | 0.298756 | ||||||||
\(601\) | 14.9518 | 0.609897 | 0.304948 | − | 0.952369i | \(-0.401361\pi\) | ||||
0.304948 | + | 0.952369i | \(0.401361\pi\) | |||||||
\(602\) | −3.45050 | −0.140632 | ||||||||
\(603\) | −3.24185 | −0.132018 | ||||||||
\(604\) | 16.4398 | 0.668928 | ||||||||
\(605\) | −7.94754 | −0.323113 | ||||||||
\(606\) | 3.58385 | 0.145584 | ||||||||
\(607\) | −15.7161 | −0.637895 | −0.318948 | − | 0.947772i | \(-0.603329\pi\) | ||||
−0.318948 | + | 0.947772i | \(0.603329\pi\) | |||||||
\(608\) | 14.3374 | 0.581459 | ||||||||
\(609\) | 10.4514 | 0.423510 | ||||||||
\(610\) | −0.679478 | −0.0275113 | ||||||||
\(611\) | 82.4610 | 3.33602 | ||||||||
\(612\) | 4.35537 | 0.176055 | ||||||||
\(613\) | 28.4145 | 1.14765 | 0.573825 | − | 0.818978i | \(-0.305459\pi\) | ||||
0.573825 | + | 0.818978i | \(0.305459\pi\) | |||||||
\(614\) | −16.4935 | −0.665622 | ||||||||
\(615\) | −17.1077 | −0.689850 | ||||||||
\(616\) | 11.0613 | 0.445671 | ||||||||
\(617\) | −11.1635 | −0.449426 | −0.224713 | − | 0.974425i | \(-0.572145\pi\) | ||||
−0.224713 | + | 0.974425i | \(0.572145\pi\) | |||||||
\(618\) | 7.95721 | 0.320086 | ||||||||
\(619\) | −27.2446 | −1.09505 | −0.547526 | − | 0.836788i | \(-0.684430\pi\) | ||||
−0.547526 | + | 0.836788i | \(0.684430\pi\) | |||||||
\(620\) | −10.0648 | −0.404213 | ||||||||
\(621\) | −2.89647 | −0.116231 | ||||||||
\(622\) | 26.5278 | 1.06367 | ||||||||
\(623\) | 14.1315 | 0.566168 | ||||||||
\(624\) | 2.09372 | 0.0838160 | ||||||||
\(625\) | −4.59640 | −0.183856 | ||||||||
\(626\) | −6.50257 | −0.259895 | ||||||||
\(627\) | 9.98433 | 0.398736 | ||||||||
\(628\) | −1.03874 | −0.0414502 | ||||||||
\(629\) | 21.7680 | 0.867948 | ||||||||
\(630\) | 1.26901 | 0.0505585 | ||||||||
\(631\) | 23.1155 | 0.920215 | 0.460108 | − | 0.887863i | \(-0.347811\pi\) | ||||
0.460108 | + | 0.887863i | \(0.347811\pi\) | |||||||
\(632\) | −44.4587 | −1.76847 | ||||||||
\(633\) | −23.8431 | −0.947680 | ||||||||
\(634\) | −7.57737 | −0.300936 | ||||||||
\(635\) | −21.0701 | −0.836143 | ||||||||
\(636\) | −10.5646 | −0.418915 | ||||||||
\(637\) | 6.14463 | 0.243459 | ||||||||
\(638\) | −34.9155 | −1.38232 | ||||||||
\(639\) | 4.25971 | 0.168512 | ||||||||
\(640\) | 12.4486 | 0.492072 | ||||||||
\(641\) | 15.6032 | 0.616289 | 0.308144 | − | 0.951340i | \(-0.400292\pi\) | ||||
0.308144 | + | 0.951340i | \(0.400292\pi\) | |||||||
\(642\) | 0.834478 | 0.0329342 | ||||||||
\(643\) | −35.0952 | −1.38402 | −0.692009 | − | 0.721889i | \(-0.743274\pi\) | ||||
−0.692009 | + | 0.721889i | \(0.743274\pi\) | |||||||
\(644\) | −3.79729 | −0.149634 | ||||||||
\(645\) | −6.35522 | −0.250236 | ||||||||
\(646\) | −6.84086 | −0.269150 | ||||||||
\(647\) | 26.7307 | 1.05089 | 0.525447 | − | 0.850827i | \(-0.323898\pi\) | ||||
0.525447 | + | 0.850827i | \(0.323898\pi\) | |||||||
\(648\) | −2.74832 | −0.107964 | ||||||||
\(649\) | 54.4916 | 2.13898 | ||||||||
\(650\) | −13.5809 | −0.532686 | ||||||||
\(651\) | 5.02164 | 0.196814 | ||||||||
\(652\) | −27.7378 | −1.08630 | ||||||||
\(653\) | −12.1361 | −0.474922 | −0.237461 | − | 0.971397i | \(-0.576315\pi\) | ||||
−0.237461 | + | 0.971397i | \(0.576315\pi\) | |||||||
\(654\) | 16.0789 | 0.628735 | ||||||||
\(655\) | 20.5953 | 0.804724 | ||||||||
\(656\) | 3.81294 | 0.148870 | ||||||||
\(657\) | −8.90203 | −0.347301 | ||||||||
\(658\) | −11.1394 | −0.434259 | ||||||||
\(659\) | −3.45960 | −0.134767 | −0.0673834 | − | 0.997727i | \(-0.521465\pi\) | ||||
−0.0673834 | + | 0.997727i | \(0.521465\pi\) | |||||||
\(660\) | 8.06673 | 0.313997 | ||||||||
\(661\) | 31.4619 | 1.22373 | 0.611864 | − | 0.790963i | \(-0.290420\pi\) | ||||
0.611864 | + | 0.790963i | \(0.290420\pi\) | |||||||
\(662\) | −16.7303 | −0.650240 | ||||||||
\(663\) | −20.4134 | −0.792792 | ||||||||
\(664\) | −37.7171 | −1.46371 | ||||||||
\(665\) | 3.79261 | 0.147071 | ||||||||
\(666\) | −5.43885 | −0.210751 | ||||||||
\(667\) | 30.2721 | 1.17214 | ||||||||
\(668\) | −27.6173 | −1.06855 | ||||||||
\(669\) | −19.3056 | −0.746399 | ||||||||
\(670\) | 4.11394 | 0.158935 | ||||||||
\(671\) | 2.15500 | 0.0831930 | ||||||||
\(672\) | −5.77948 | −0.222948 | ||||||||
\(673\) | 20.6902 | 0.797548 | 0.398774 | − | 0.917049i | \(-0.369436\pi\) | ||||
0.398774 | + | 0.917049i | \(0.369436\pi\) | |||||||
\(674\) | −0.983302 | −0.0378754 | ||||||||
\(675\) | −2.66271 | −0.102488 | ||||||||
\(676\) | −32.4558 | −1.24830 | ||||||||
\(677\) | −16.3774 | −0.629436 | −0.314718 | − | 0.949185i | \(-0.601910\pi\) | ||||
−0.314718 | + | 0.949185i | \(0.601910\pi\) | |||||||
\(678\) | 6.11462 | 0.234831 | ||||||||
\(679\) | 4.30960 | 0.165387 | ||||||||
\(680\) | −13.9587 | −0.535291 | ||||||||
\(681\) | −20.6127 | −0.789882 | ||||||||
\(682\) | −16.7761 | −0.642390 | ||||||||
\(683\) | −42.5224 | −1.62707 | −0.813536 | − | 0.581514i | \(-0.802461\pi\) | ||||
−0.813536 | + | 0.581514i | \(0.802461\pi\) | |||||||
\(684\) | −3.25227 | −0.124353 | ||||||||
\(685\) | 28.7531 | 1.09860 | ||||||||
\(686\) | −0.830058 | −0.0316918 | ||||||||
\(687\) | −10.0822 | −0.384659 | ||||||||
\(688\) | 1.41644 | 0.0540012 | ||||||||
\(689\) | 49.5161 | 1.88641 | ||||||||
\(690\) | 3.67565 | 0.139930 | ||||||||
\(691\) | −27.0097 | −1.02750 | −0.513748 | − | 0.857941i | \(-0.671743\pi\) | ||||
−0.513748 | + | 0.857941i | \(0.671743\pi\) | |||||||
\(692\) | −9.93155 | −0.377541 | ||||||||
\(693\) | −4.02473 | −0.152887 | ||||||||
\(694\) | 15.1626 | 0.575565 | ||||||||
\(695\) | 10.8482 | 0.411497 | ||||||||
\(696\) | 28.7237 | 1.08877 | ||||||||
\(697\) | −37.1755 | −1.40812 | ||||||||
\(698\) | 25.8735 | 0.979326 | ||||||||
\(699\) | 22.0942 | 0.835679 | ||||||||
\(700\) | −3.49083 | −0.131941 | ||||||||
\(701\) | 26.1459 | 0.987516 | 0.493758 | − | 0.869599i | \(-0.335623\pi\) | ||||
0.493758 | + | 0.869599i | \(0.335623\pi\) | |||||||
\(702\) | 5.10040 | 0.192502 | ||||||||
\(703\) | −16.2548 | −0.613060 | ||||||||
\(704\) | 16.5651 | 0.624321 | ||||||||
\(705\) | −20.5168 | −0.772707 | ||||||||
\(706\) | −24.0507 | −0.905160 | ||||||||
\(707\) | −4.31759 | −0.162380 | ||||||||
\(708\) | −17.7499 | −0.667083 | ||||||||
\(709\) | 44.2270 | 1.66098 | 0.830489 | − | 0.557034i | \(-0.188061\pi\) | ||||
0.830489 | + | 0.557034i | \(0.188061\pi\) | |||||||
\(710\) | −5.40561 | −0.202869 | ||||||||
\(711\) | 16.1767 | 0.606673 | ||||||||
\(712\) | 38.8381 | 1.45552 | ||||||||
\(713\) | 14.5451 | 0.544717 | ||||||||
\(714\) | 2.75758 | 0.103200 | ||||||||
\(715\) | −37.8084 | −1.41396 | ||||||||
\(716\) | 6.57199 | 0.245607 | ||||||||
\(717\) | 1.69534 | 0.0633135 | ||||||||
\(718\) | −8.35310 | −0.311735 | ||||||||
\(719\) | −7.43310 | −0.277208 | −0.138604 | − | 0.990348i | \(-0.544262\pi\) | ||||
−0.138604 | + | 0.990348i | \(0.544262\pi\) | |||||||
\(720\) | −0.520930 | −0.0194139 | ||||||||
\(721\) | −9.58633 | −0.357014 | ||||||||
\(722\) | −10.6628 | −0.396830 | ||||||||
\(723\) | 2.45933 | 0.0914633 | ||||||||
\(724\) | −5.49549 | −0.204238 | ||||||||
\(725\) | 27.8289 | 1.03354 | ||||||||
\(726\) | 4.31504 | 0.160146 | ||||||||
\(727\) | 5.28684 | 0.196078 | 0.0980390 | − | 0.995183i | \(-0.468743\pi\) | ||||
0.0980390 | + | 0.995183i | \(0.468743\pi\) | |||||||
\(728\) | 16.8874 | 0.625890 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.2967 | 0.418111 | ||||||||
\(731\) | −13.8100 | −0.510783 | ||||||||
\(732\) | −0.701964 | −0.0259453 | ||||||||
\(733\) | −35.3919 | −1.30723 | −0.653615 | − | 0.756827i | \(-0.726748\pi\) | ||||
−0.653615 | + | 0.756827i | \(0.726748\pi\) | |||||||
\(734\) | −15.4572 | −0.570535 | ||||||||
\(735\) | −1.52882 | −0.0563913 | ||||||||
\(736\) | −16.7401 | −0.617049 | ||||||||
\(737\) | −13.0476 | −0.480614 | ||||||||
\(738\) | 9.28847 | 0.341913 | ||||||||
\(739\) | −15.0899 | −0.555091 | −0.277545 | − | 0.960713i | \(-0.589521\pi\) | ||||
−0.277545 | + | 0.960713i | \(0.589521\pi\) | |||||||
\(740\) | −13.1328 | −0.482773 | ||||||||
\(741\) | 15.2432 | 0.559975 | ||||||||
\(742\) | −6.68896 | −0.245560 | ||||||||
\(743\) | −30.5071 | −1.11920 | −0.559599 | − | 0.828763i | \(-0.689045\pi\) | ||||
−0.559599 | + | 0.828763i | \(0.689045\pi\) | |||||||
\(744\) | 13.8011 | 0.505973 | ||||||||
\(745\) | −33.5822 | −1.23036 | ||||||||
\(746\) | −5.93973 | −0.217469 | ||||||||
\(747\) | 13.7237 | 0.502123 | ||||||||
\(748\) | 17.5292 | 0.640931 | ||||||||
\(749\) | −1.00532 | −0.0367338 | ||||||||
\(750\) | 9.72404 | 0.355072 | ||||||||
\(751\) | 35.5975 | 1.29897 | 0.649486 | − | 0.760374i | \(-0.274984\pi\) | ||||
0.649486 | + | 0.760374i | \(0.274984\pi\) | |||||||
\(752\) | 4.57274 | 0.166751 | ||||||||
\(753\) | 12.0568 | 0.439374 | ||||||||
\(754\) | −53.3060 | −1.94129 | ||||||||
\(755\) | 19.1712 | 0.697712 | ||||||||
\(756\) | 1.31100 | 0.0476808 | ||||||||
\(757\) | −24.8284 | −0.902405 | −0.451203 | − | 0.892422i | \(-0.649005\pi\) | ||||
−0.451203 | + | 0.892422i | \(0.649005\pi\) | |||||||
\(758\) | 2.09179 | 0.0759773 | ||||||||
\(759\) | −11.6575 | −0.423142 | ||||||||
\(760\) | 10.4233 | 0.378093 | ||||||||
\(761\) | 15.2657 | 0.553383 | 0.276691 | − | 0.960959i | \(-0.410762\pi\) | ||||
0.276691 | + | 0.960959i | \(0.410762\pi\) | |||||||
\(762\) | 11.4398 | 0.414421 | ||||||||
\(763\) | −19.3708 | −0.701271 | ||||||||
\(764\) | 1.31100 | 0.0474305 | ||||||||
\(765\) | 5.07898 | 0.183631 | ||||||||
\(766\) | 7.28488 | 0.263213 | ||||||||
\(767\) | 83.1932 | 3.00393 | ||||||||
\(768\) | −14.9905 | −0.540922 | ||||||||
\(769\) | −15.5419 | −0.560456 | −0.280228 | − | 0.959933i | \(-0.590410\pi\) | ||||
−0.280228 | + | 0.959933i | \(0.590410\pi\) | |||||||
\(770\) | 5.10742 | 0.184059 | ||||||||
\(771\) | 9.62851 | 0.346762 | ||||||||
\(772\) | 1.36893 | 0.0492687 | ||||||||
\(773\) | −44.9287 | −1.61597 | −0.807986 | − | 0.589202i | \(-0.799442\pi\) | ||||
−0.807986 | + | 0.589202i | \(0.799442\pi\) | |||||||
\(774\) | 3.45050 | 0.124026 | ||||||||
\(775\) | 13.3712 | 0.480307 | ||||||||
\(776\) | 11.8442 | 0.425182 | ||||||||
\(777\) | 6.55237 | 0.235065 | ||||||||
\(778\) | 20.2761 | 0.726935 | ||||||||
\(779\) | 27.7599 | 0.994602 | ||||||||
\(780\) | 12.3156 | 0.440969 | ||||||||
\(781\) | 17.1442 | 0.613468 | ||||||||
\(782\) | 7.98727 | 0.285624 | ||||||||
\(783\) | −10.4514 | −0.373501 | ||||||||
\(784\) | 0.340740 | 0.0121693 | ||||||||
\(785\) | −1.21132 | −0.0432339 | ||||||||
\(786\) | −11.1820 | −0.398849 | ||||||||
\(787\) | −42.5175 | −1.51559 | −0.757793 | − | 0.652495i | \(-0.773722\pi\) | ||||
−0.757793 | + | 0.652495i | \(0.773722\pi\) | |||||||
\(788\) | 9.84994 | 0.350889 | ||||||||
\(789\) | 19.3325 | 0.688257 | ||||||||
\(790\) | −20.5283 | −0.730365 | ||||||||
\(791\) | −7.36650 | −0.261923 | ||||||||
\(792\) | −11.0613 | −0.393045 | ||||||||
\(793\) | 3.29008 | 0.116834 | ||||||||
\(794\) | −4.69383 | −0.166578 | ||||||||
\(795\) | −12.3199 | −0.436941 | ||||||||
\(796\) | −4.48303 | −0.158897 | ||||||||
\(797\) | −26.6049 | −0.942395 | −0.471198 | − | 0.882028i | \(-0.656178\pi\) | ||||
−0.471198 | + | 0.882028i | \(0.656178\pi\) | |||||||
\(798\) | −2.05916 | −0.0728935 | ||||||||
\(799\) | −44.5835 | −1.57725 | ||||||||
\(800\) | −15.3891 | −0.544087 | ||||||||
\(801\) | −14.1315 | −0.499314 | ||||||||
\(802\) | 5.22676 | 0.184563 | ||||||||
\(803\) | −35.8283 | −1.26435 | ||||||||
\(804\) | 4.25008 | 0.149889 | ||||||||
\(805\) | −4.42818 | −0.156073 | ||||||||
\(806\) | −25.6124 | −0.902157 | ||||||||
\(807\) | −13.3998 | −0.471694 | ||||||||
\(808\) | −11.8661 | −0.417449 | ||||||||
\(809\) | −2.82324 | −0.0992598 | −0.0496299 | − | 0.998768i | \(-0.515804\pi\) | ||||
−0.0496299 | + | 0.998768i | \(0.515804\pi\) | |||||||
\(810\) | −1.26901 | −0.0445884 | ||||||||
\(811\) | −0.309319 | −0.0108617 | −0.00543084 | − | 0.999985i | \(-0.501729\pi\) | ||||
−0.00543084 | + | 0.999985i | \(0.501729\pi\) | |||||||
\(812\) | −13.7018 | −0.480838 | ||||||||
\(813\) | 14.5707 | 0.511016 | ||||||||
\(814\) | −21.8899 | −0.767241 | ||||||||
\(815\) | −32.3463 | −1.13304 | ||||||||
\(816\) | −1.13199 | −0.0396277 | ||||||||
\(817\) | 10.3123 | 0.360782 | ||||||||
\(818\) | −18.1685 | −0.635246 | ||||||||
\(819\) | −6.14463 | −0.214711 | ||||||||
\(820\) | 22.4283 | 0.783230 | ||||||||
\(821\) | −16.8078 | −0.586596 | −0.293298 | − | 0.956021i | \(-0.594753\pi\) | ||||
−0.293298 | + | 0.956021i | \(0.594753\pi\) | |||||||
\(822\) | −15.6112 | −0.544504 | ||||||||
\(823\) | −30.6401 | −1.06805 | −0.534023 | − | 0.845470i | \(-0.679320\pi\) | ||||
−0.534023 | + | 0.845470i | \(0.679320\pi\) | |||||||
\(824\) | −26.3464 | −0.917819 | ||||||||
\(825\) | −10.7167 | −0.373108 | ||||||||
\(826\) | −11.2383 | −0.391031 | ||||||||
\(827\) | 23.2923 | 0.809954 | 0.404977 | − | 0.914327i | \(-0.367279\pi\) | ||||
0.404977 | + | 0.914327i | \(0.367279\pi\) | |||||||
\(828\) | 3.79729 | 0.131965 | ||||||||
\(829\) | −21.1253 | −0.733712 | −0.366856 | − | 0.930278i | \(-0.619566\pi\) | ||||
−0.366856 | + | 0.930278i | \(0.619566\pi\) | |||||||
\(830\) | −17.4154 | −0.604499 | ||||||||
\(831\) | 1.22840 | 0.0426127 | ||||||||
\(832\) | 25.2902 | 0.876780 | ||||||||
\(833\) | −3.32216 | −0.115106 | ||||||||
\(834\) | −5.88995 | −0.203952 | ||||||||
\(835\) | −32.2057 | −1.11453 | ||||||||
\(836\) | −13.0895 | −0.452710 | ||||||||
\(837\) | −5.02164 | −0.173573 | ||||||||
\(838\) | −13.6355 | −0.471029 | ||||||||
\(839\) | 45.6767 | 1.57693 | 0.788467 | − | 0.615077i | \(-0.210875\pi\) | ||||
0.788467 | + | 0.615077i | \(0.210875\pi\) | |||||||
\(840\) | −4.20169 | −0.144972 | ||||||||
\(841\) | 80.2307 | 2.76658 | ||||||||
\(842\) | −3.93423 | −0.135582 | ||||||||
\(843\) | −8.52086 | −0.293474 | ||||||||
\(844\) | 31.2585 | 1.07596 | ||||||||
\(845\) | −37.8481 | −1.30202 | ||||||||
\(846\) | 11.1394 | 0.382980 | ||||||||
\(847\) | −5.19848 | −0.178622 | ||||||||
\(848\) | 2.74583 | 0.0942923 | ||||||||
\(849\) | 12.5808 | 0.431772 | ||||||||
\(850\) | 7.34266 | 0.251851 | ||||||||
\(851\) | 18.9788 | 0.650584 | ||||||||
\(852\) | −5.58450 | −0.191322 | ||||||||
\(853\) | 5.09505 | 0.174451 | 0.0872256 | − | 0.996189i | \(-0.472200\pi\) | ||||
0.0872256 | + | 0.996189i | \(0.472200\pi\) | |||||||
\(854\) | −0.444446 | −0.0152086 | ||||||||
\(855\) | −3.79261 | −0.129704 | ||||||||
\(856\) | −2.76296 | −0.0944360 | ||||||||
\(857\) | 30.7087 | 1.04899 | 0.524495 | − | 0.851414i | \(-0.324254\pi\) | ||||
0.524495 | + | 0.851414i | \(0.324254\pi\) | |||||||
\(858\) | 20.5277 | 0.700805 | ||||||||
\(859\) | −17.7177 | −0.604520 | −0.302260 | − | 0.953225i | \(-0.597741\pi\) | ||||
−0.302260 | + | 0.953225i | \(0.597741\pi\) | |||||||
\(860\) | 8.33171 | 0.284109 | ||||||||
\(861\) | −11.1902 | −0.381359 | ||||||||
\(862\) | 5.21924 | 0.177768 | ||||||||
\(863\) | 11.6399 | 0.396228 | 0.198114 | − | 0.980179i | \(-0.436518\pi\) | ||||
0.198114 | + | 0.980179i | \(0.436518\pi\) | |||||||
\(864\) | 5.77948 | 0.196622 | ||||||||
\(865\) | −11.5816 | −0.393787 | ||||||||
\(866\) | 12.3275 | 0.418905 | ||||||||
\(867\) | −5.96325 | −0.202523 | ||||||||
\(868\) | −6.58339 | −0.223455 | ||||||||
\(869\) | 65.1068 | 2.20860 | ||||||||
\(870\) | 13.2628 | 0.449653 | ||||||||
\(871\) | −19.9200 | −0.674963 | ||||||||
\(872\) | −53.2373 | −1.80284 | ||||||||
\(873\) | −4.30960 | −0.145858 | ||||||||
\(874\) | −5.96430 | −0.201746 | ||||||||
\(875\) | −11.7149 | −0.396036 | ||||||||
\(876\) | 11.6706 | 0.394313 | ||||||||
\(877\) | −17.2143 | −0.581284 | −0.290642 | − | 0.956832i | \(-0.593869\pi\) | ||||
−0.290642 | + | 0.956832i | \(0.593869\pi\) | |||||||
\(878\) | 5.98891 | 0.202116 | ||||||||
\(879\) | −12.1071 | −0.408363 | ||||||||
\(880\) | −2.09661 | −0.0706766 | ||||||||
\(881\) | 25.8814 | 0.871967 | 0.435984 | − | 0.899955i | \(-0.356401\pi\) | ||||
0.435984 | + | 0.899955i | \(0.356401\pi\) | |||||||
\(882\) | 0.830058 | 0.0279495 | ||||||||
\(883\) | 37.9449 | 1.27695 | 0.638473 | − | 0.769644i | \(-0.279566\pi\) | ||||
0.638473 | + | 0.769644i | \(0.279566\pi\) | |||||||
\(884\) | 26.7621 | 0.900107 | ||||||||
\(885\) | −20.6990 | −0.695788 | ||||||||
\(886\) | 15.3889 | 0.517000 | ||||||||
\(887\) | 32.4685 | 1.09019 | 0.545093 | − | 0.838376i | \(-0.316495\pi\) | ||||
0.545093 | + | 0.838376i | \(0.316495\pi\) | |||||||
\(888\) | 18.0081 | 0.604311 | ||||||||
\(889\) | −13.7820 | −0.462232 | ||||||||
\(890\) | 17.9330 | 0.601117 | ||||||||
\(891\) | 4.02473 | 0.134834 | ||||||||
\(892\) | 25.3098 | 0.847434 | ||||||||
\(893\) | 33.2916 | 1.11406 | ||||||||
\(894\) | 18.2331 | 0.609807 | ||||||||
\(895\) | 7.66389 | 0.256175 | ||||||||
\(896\) | 8.14259 | 0.272025 | ||||||||
\(897\) | −17.7978 | −0.594250 | ||||||||
\(898\) | 25.6998 | 0.857615 | ||||||||
\(899\) | 52.4829 | 1.75040 | ||||||||
\(900\) | 3.49083 | 0.116361 | ||||||||
\(901\) | −26.7714 | −0.891885 | ||||||||
\(902\) | 37.3836 | 1.24474 | ||||||||
\(903\) | −4.15694 | −0.138334 | ||||||||
\(904\) | −20.2455 | −0.673356 | ||||||||
\(905\) | −6.40853 | −0.213027 | ||||||||
\(906\) | −10.4088 | −0.345810 | ||||||||
\(907\) | −47.3887 | −1.57352 | −0.786758 | − | 0.617262i | \(-0.788242\pi\) | ||||
−0.786758 | + | 0.617262i | \(0.788242\pi\) | |||||||
\(908\) | 27.0234 | 0.896803 | ||||||||
\(909\) | 4.31759 | 0.143205 | ||||||||
\(910\) | 7.79758 | 0.258487 | ||||||||
\(911\) | −20.1287 | −0.666894 | −0.333447 | − | 0.942769i | \(-0.608212\pi\) | ||||
−0.333447 | + | 0.942769i | \(0.608212\pi\) | |||||||
\(912\) | 0.845289 | 0.0279903 | ||||||||
\(913\) | 55.2341 | 1.82798 | ||||||||
\(914\) | −2.74492 | −0.0907940 | ||||||||
\(915\) | −0.818591 | −0.0270618 | ||||||||
\(916\) | 13.2178 | 0.436728 | ||||||||
\(917\) | 13.4714 | 0.444864 | ||||||||
\(918\) | −2.75758 | −0.0910138 | ||||||||
\(919\) | 36.1807 | 1.19349 | 0.596745 | − | 0.802431i | \(-0.296460\pi\) | ||||
0.596745 | + | 0.802431i | \(0.296460\pi\) | |||||||
\(920\) | −12.1701 | −0.401236 | ||||||||
\(921\) | −19.8703 | −0.654748 | ||||||||
\(922\) | 5.25263 | 0.172986 | ||||||||
\(923\) | 26.1743 | 0.861539 | ||||||||
\(924\) | 5.27644 | 0.173582 | ||||||||
\(925\) | 17.4471 | 0.573657 | ||||||||
\(926\) | 6.82692 | 0.224346 | ||||||||
\(927\) | 9.58633 | 0.314856 | ||||||||
\(928\) | −60.4034 | −1.98284 | ||||||||
\(929\) | 26.7688 | 0.878254 | 0.439127 | − | 0.898425i | \(-0.355288\pi\) | ||||
0.439127 | + | 0.898425i | \(0.355288\pi\) | |||||||
\(930\) | 6.37250 | 0.208963 | ||||||||
\(931\) | 2.48074 | 0.0813031 | ||||||||
\(932\) | −28.9656 | −0.948799 | ||||||||
\(933\) | 31.9589 | 1.04629 | ||||||||
\(934\) | −11.8681 | −0.388335 | ||||||||
\(935\) | 20.4415 | 0.668510 | ||||||||
\(936\) | −16.8874 | −0.551983 | ||||||||
\(937\) | 12.7471 | 0.416429 | 0.208215 | − | 0.978083i | \(-0.433235\pi\) | ||||
0.208215 | + | 0.978083i | \(0.433235\pi\) | |||||||
\(938\) | 2.69092 | 0.0878618 | ||||||||
\(939\) | −7.83387 | −0.255649 | ||||||||
\(940\) | 26.8976 | 0.877303 | ||||||||
\(941\) | 2.38970 | 0.0779020 | 0.0389510 | − | 0.999241i | \(-0.487598\pi\) | ||||
0.0389510 | + | 0.999241i | \(0.487598\pi\) | |||||||
\(942\) | 0.657675 | 0.0214282 | ||||||||
\(943\) | −32.4120 | −1.05548 | ||||||||
\(944\) | 4.61334 | 0.150152 | ||||||||
\(945\) | 1.52882 | 0.0497325 | ||||||||
\(946\) | 13.8874 | 0.451517 | ||||||||
\(947\) | 8.47809 | 0.275501 | 0.137751 | − | 0.990467i | \(-0.456013\pi\) | ||||
0.137751 | + | 0.990467i | \(0.456013\pi\) | |||||||
\(948\) | −21.2077 | −0.688794 | ||||||||
\(949\) | −54.6997 | −1.77563 | ||||||||
\(950\) | −5.48295 | −0.177890 | ||||||||
\(951\) | −9.12873 | −0.296019 | ||||||||
\(952\) | −9.13037 | −0.295917 | ||||||||
\(953\) | 42.8298 | 1.38739 | 0.693696 | − | 0.720268i | \(-0.255981\pi\) | ||||
0.693696 | + | 0.720268i | \(0.255981\pi\) | |||||||
\(954\) | 6.68896 | 0.216563 | ||||||||
\(955\) | 1.52882 | 0.0494714 | ||||||||
\(956\) | −2.22259 | −0.0718838 | ||||||||
\(957\) | −42.0639 | −1.35973 | ||||||||
\(958\) | 20.4123 | 0.659492 | ||||||||
\(959\) | 18.8074 | 0.607323 | ||||||||
\(960\) | −6.29235 | −0.203085 | ||||||||
\(961\) | −5.78311 | −0.186552 | ||||||||
\(962\) | −33.4197 | −1.07749 | ||||||||
\(963\) | 1.00532 | 0.0323961 | ||||||||
\(964\) | −3.22419 | −0.103844 | ||||||||
\(965\) | 1.59636 | 0.0513888 | ||||||||
\(966\) | 2.40424 | 0.0773552 | ||||||||
\(967\) | 39.8967 | 1.28299 | 0.641496 | − | 0.767126i | \(-0.278314\pi\) | ||||
0.641496 | + | 0.767126i | \(0.278314\pi\) | |||||||
\(968\) | −14.2871 | −0.459205 | ||||||||
\(969\) | −8.24143 | −0.264753 | ||||||||
\(970\) | 5.46892 | 0.175596 | ||||||||
\(971\) | 38.3321 | 1.23014 | 0.615069 | − | 0.788474i | \(-0.289128\pi\) | ||||
0.615069 | + | 0.788474i | \(0.289128\pi\) | |||||||
\(972\) | −1.31100 | −0.0420505 | ||||||||
\(973\) | 7.09584 | 0.227482 | ||||||||
\(974\) | 2.85317 | 0.0914215 | ||||||||
\(975\) | −16.3614 | −0.523984 | ||||||||
\(976\) | 0.182446 | 0.00583996 | ||||||||
\(977\) | 29.8406 | 0.954685 | 0.477342 | − | 0.878717i | \(-0.341600\pi\) | ||||
0.477342 | + | 0.878717i | \(0.341600\pi\) | |||||||
\(978\) | 17.5621 | 0.561574 | ||||||||
\(979\) | −56.8757 | −1.81776 | ||||||||
\(980\) | 2.00429 | 0.0640246 | ||||||||
\(981\) | 19.3708 | 0.618463 | ||||||||
\(982\) | 25.6652 | 0.819011 | ||||||||
\(983\) | 22.2442 | 0.709478 | 0.354739 | − | 0.934965i | \(-0.384570\pi\) | ||||
0.354739 | + | 0.934965i | \(0.384570\pi\) | |||||||
\(984\) | −30.7542 | −0.980407 | ||||||||
\(985\) | 11.4864 | 0.365988 | ||||||||
\(986\) | 28.8205 | 0.917831 | ||||||||
\(987\) | −13.4200 | −0.427164 | ||||||||
\(988\) | −19.9840 | −0.635775 | ||||||||
\(989\) | −12.0405 | −0.382865 | ||||||||
\(990\) | −5.10742 | −0.162324 | ||||||||
\(991\) | −9.37819 | −0.297908 | −0.148954 | − | 0.988844i | \(-0.547591\pi\) | ||||
−0.148954 | + | 0.988844i | \(0.547591\pi\) | |||||||
\(992\) | −29.0225 | −0.921465 | ||||||||
\(993\) | −20.1555 | −0.639617 | ||||||||
\(994\) | −3.53581 | −0.112149 | ||||||||
\(995\) | −5.22786 | −0.165734 | ||||||||
\(996\) | −17.9918 | −0.570092 | ||||||||
\(997\) | −8.22451 | −0.260473 | −0.130236 | − | 0.991483i | \(-0.541574\pi\) | ||||
−0.130236 | + | 0.991483i | \(0.541574\pi\) | |||||||
\(998\) | −16.3727 | −0.518270 | ||||||||
\(999\) | −6.55237 | −0.207308 |
(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 | 4011.2.a.m.1.17 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.m.1.17 | ✓ | 29 | 1.1 | even | 1 | trivial |