Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, 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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(1\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | 0 | ||||||||
\(3\) | −1.15550 | −0.667129 | −0.333565 | − | 0.942727i | \(-0.608252\pi\) | ||||
−0.333565 | + | 0.942727i | \(0.608252\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.26045 | −1.45812 | −0.729059 | − | 0.684451i | \(-0.760042\pi\) | ||||
−0.729059 | + | 0.684451i | \(0.760042\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.92982 | −0.729403 | −0.364701 | − | 0.931125i | \(-0.618829\pi\) | ||||
−0.364701 | + | 0.931125i | \(0.618829\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.66482 | −0.554939 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.97192 | 0.594557 | 0.297278 | − | 0.954791i | \(-0.403921\pi\) | ||||
0.297278 | + | 0.954791i | \(0.403921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.983643 | −0.272814 | −0.136407 | − | 0.990653i | \(-0.543555\pi\) | ||||
−0.136407 | + | 0.990653i | \(0.543555\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.76746 | 0.972754 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.76368 | −1.15536 | −0.577681 | − | 0.816263i | \(-0.696042\pi\) | ||||
−0.577681 | + | 0.816263i | \(0.696042\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.17055 | 0.956791 | 0.478395 | − | 0.878145i | \(-0.341219\pi\) | ||||
0.478395 | + | 0.878145i | \(0.341219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.22991 | 0.486606 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.45293 | 1.76256 | 0.881278 | − | 0.472598i | \(-0.156684\pi\) | ||||
0.881278 | + | 0.472598i | \(0.156684\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.63055 | 1.12611 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.39020 | 1.03735 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.913684 | −0.169667 | −0.0848335 | − | 0.996395i | \(-0.527036\pi\) | ||||
−0.0848335 | + | 0.996395i | \(0.527036\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.19000 | 1.29136 | 0.645681 | − | 0.763607i | \(-0.276574\pi\) | ||||
0.645681 | + | 0.763607i | \(0.276574\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.27856 | −0.396646 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.29208 | 1.06356 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.2113 | 1.84313 | 0.921564 | − | 0.388226i | \(-0.126912\pi\) | ||||
0.921564 | + | 0.388226i | \(0.126912\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.13660 | 0.182002 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.68259 | 0.887472 | 0.443736 | − | 0.896158i | \(-0.353653\pi\) | ||||
0.443736 | + | 0.896158i | \(0.353653\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.63950 | −1.47001 | −0.735005 | − | 0.678061i | \(-0.762820\pi\) | ||||
−0.735005 | + | 0.678061i | \(0.762820\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.42805 | 0.809166 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.21503 | −0.614825 | −0.307412 | − | 0.951576i | \(-0.599463\pi\) | ||||
−0.307412 | + | 0.951576i | \(0.599463\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.27580 | −0.467972 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.50444 | 0.770775 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.59953 | −0.219713 | −0.109856 | − | 0.993947i | \(-0.535039\pi\) | ||||
−0.109856 | + | 0.993947i | \(0.535039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.42936 | −0.866934 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.81908 | −0.638303 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.532957 | 0.0693852 | 0.0346926 | − | 0.999398i | \(-0.488955\pi\) | ||||
0.0346926 | + | 0.999398i | \(0.488955\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.66711 | −1.10971 | −0.554855 | − | 0.831947i | \(-0.687226\pi\) | ||||
−0.554855 | + | 0.831947i | \(0.687226\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.21279 | 0.404774 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.20712 | 0.397794 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.3799 | −1.26811 | −0.634055 | − | 0.773288i | \(-0.718611\pi\) | ||||
−0.634055 | + | 0.773288i | \(0.718611\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.76737 | −1.17585 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1043 | −1.19916 | −0.599580 | − | 0.800315i | \(-0.704666\pi\) | ||||
−0.599580 | + | 0.800315i | \(0.704666\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.1435 | 1.53833 | 0.769163 | − | 0.639052i | \(-0.220673\pi\) | ||||
0.769163 | + | 0.639052i | \(0.220673\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.50611 | −0.751261 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.80545 | −0.433671 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.5418 | −1.97361 | −0.986804 | − | 0.161918i | \(-0.948232\pi\) | ||||
−0.986804 | + | 0.161918i | \(0.948232\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.23394 | −0.137105 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.72424 | 0.299024 | 0.149512 | − | 0.988760i | \(-0.452230\pi\) | ||||
0.149512 | + | 0.988760i | \(0.452230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.5317 | 1.68465 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.05576 | 0.113190 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.00198390 | 0.000210293 0 | 0.000105147 | − | 1.00000i | \(-0.499967\pi\) | ||||
0.000105147 | 1.00000i | \(0.499967\pi\) | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.89825 | 0.198991 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.30806 | −0.861506 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.5979 | −1.39511 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.11333 | 0.417645 | 0.208822 | − | 0.977954i | \(-0.433037\pi\) | ||||
0.208822 | + | 0.977954i | \(0.433037\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.28289 | −0.329942 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.50261 | −0.647034 | −0.323517 | − | 0.946222i | \(-0.604865\pi\) | ||||
−0.323517 | + | 0.946222i | \(0.604865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6003 | 1.24155 | 0.620774 | − | 0.783990i | \(-0.286818\pi\) | ||||
0.620774 | + | 0.783990i | \(0.286818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.27051 | −0.709529 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.55504 | 0.730373 | 0.365187 | − | 0.930934i | \(-0.381005\pi\) | ||||
0.365187 | + | 0.930934i | \(0.381005\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.6907 | 1.98181 | 0.990904 | − | 0.134568i | \(-0.0429646\pi\) | ||||
0.990904 | + | 0.134568i | \(0.0429646\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.9547 | −1.22961 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0580032 | −0.00545648 | −0.00272824 | − | 0.999996i | \(-0.500868\pi\) | ||||
−0.00272824 | + | 0.999996i | \(0.500868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.5604 | −2.57002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.63758 | 0.151395 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.19303 | 0.842724 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.11152 | −0.646502 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.56625 | −0.592059 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.05587 | −0.183882 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.95882 | −0.528760 | −0.264380 | − | 0.964419i | \(-0.585167\pi\) | ||||
−0.264380 | + | 0.964419i | \(0.585167\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.1385 | 0.980687 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4107 | −1.52118 | −0.760591 | − | 0.649231i | \(-0.775091\pi\) | ||||
−0.760591 | + | 0.649231i | \(0.775091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.04841 | −0.697886 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.5745 | −1.51257 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.6965 | −1.51191 | −0.755957 | − | 0.654621i | \(-0.772828\pi\) | ||||
−0.755957 | + | 0.654621i | \(0.772828\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.1638 | 1.79509 | 0.897546 | − | 0.440920i | \(-0.145348\pi\) | ||||
0.897546 | + | 0.440920i | \(0.145348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.87047 | 0.410168 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.93967 | −0.162203 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.97902 | 0.247394 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.78519 | 0.312198 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.261784 | −0.0214462 | −0.0107231 | − | 0.999943i | \(-0.503413\pi\) | ||||
−0.0107231 | + | 0.999943i | \(0.503413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.74445 | −0.304719 | −0.152360 | − | 0.988325i | \(-0.548687\pi\) | ||||
−0.152360 | + | 0.988325i | \(0.548687\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.93064 | 0.641154 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.4426 | −1.88296 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.95939 | −0.156376 | −0.0781880 | − | 0.996939i | \(-0.524913\pi\) | ||||
−0.0781880 | + | 0.996939i | \(0.524913\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.84826 | 0.146577 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.3126 | −1.28561 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.2234 | 1.50570 | 0.752848 | − | 0.658194i | \(-0.228679\pi\) | ||||
0.752848 | + | 0.658194i | \(0.228679\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.42913 | 0.578357 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.05915 | 0.623636 | 0.311818 | − | 0.950142i | \(-0.399062\pi\) | ||||
0.311818 | + | 0.950142i | \(0.399062\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0324 | −0.925573 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.94320 | −0.530960 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.6123 | 1.03493 | 0.517463 | − | 0.855705i | \(-0.326876\pi\) | ||||
0.517463 | + | 0.855705i | \(0.326876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.8659 | −0.821387 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.615833 | −0.0462889 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.57059 | −0.715339 | −0.357670 | − | 0.933848i | \(-0.616429\pi\) | ||||
−0.357670 | + | 0.933848i | \(0.616429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.56071 | −0.190336 | −0.0951682 | − | 0.995461i | \(-0.530339\pi\) | ||||
−0.0951682 | + | 0.995461i | \(0.530339\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0149 | 0.740320 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −36.5540 | −2.68750 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.39360 | −0.686928 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.4021 | −0.756642 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.5004 | −0.759781 | −0.379891 | − | 0.925031i | \(-0.624038\pi\) | ||||
−0.379891 | + | 0.925031i | \(0.624038\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.1558 | 1.52282 | 0.761412 | − | 0.648268i | \(-0.224506\pi\) | ||||
0.761412 | + | 0.648268i | \(0.224506\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.70583 | −0.265380 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.01788 | −0.571251 | −0.285625 | − | 0.958341i | \(-0.592201\pi\) | ||||
−0.285625 | + | 0.958341i | \(0.592201\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8675 | −1.19571 | −0.597854 | − | 0.801605i | \(-0.703980\pi\) | ||||
−0.597854 | + | 0.801605i | \(0.703980\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.9940 | 0.845993 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.76324 | 0.123756 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.5278 | −1.29404 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.0726 | −0.978111 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.22401 | 0.568867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.78113 | −0.260304 | −0.130152 | − | 0.991494i | \(-0.541547\pi\) | ||||
−0.130152 | + | 0.991494i | \(0.541547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.6755 | 0.799995 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.4291 | 2.14345 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.8754 | −0.941923 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.1873 | −1.02626 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.68576 | 0.315198 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.81962 | 0.523641 | 0.261820 | − | 0.965117i | \(-0.415677\pi\) | ||||
0.261820 | + | 0.965117i | \(0.415677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.37382 | −0.624921 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.6507 | −1.17152 | −0.585758 | − | 0.810486i | \(-0.699203\pi\) | ||||
−0.585758 | + | 0.810486i | \(0.699203\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.54980 | −0.168496 | −0.0842478 | − | 0.996445i | \(-0.526849\pi\) | ||||
−0.0842478 | + | 0.996445i | \(0.526849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.39721 | 0.289315 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0102 | −1.57296 | −0.786479 | − | 0.617617i | \(-0.788098\pi\) | ||||
−0.786479 | + | 0.617617i | \(0.788098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.7429 | 0.896487 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.2696 | 1.31665 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2539 | 0.663272 | 0.331636 | − | 0.943407i | \(-0.392399\pi\) | ||||
0.331636 | + | 0.943407i | \(0.392399\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.4625 | −1.31811 | −0.659053 | − | 0.752097i | \(-0.729043\pi\) | ||||
−0.659053 | + | 0.752097i | \(0.729043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7448 | −0.945878 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.6806 | 0.682358 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.10234 | −0.261026 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.14786 | −0.199488 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.4873 | 1.04067 | 0.520334 | − | 0.853963i | \(-0.325808\pi\) | ||||
0.520334 | + | 0.853963i | \(0.325808\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.6685 | 1.04794 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.9469 | −1.12388 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.7982 | −1.04784 | −0.523922 | − | 0.851766i | \(-0.675532\pi\) | ||||
−0.523922 | + | 0.851766i | \(0.675532\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.6358 | −1.34438 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.52112 | 0.0941547 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.48596 | −0.338279 | −0.169140 | − | 0.985592i | \(-0.554099\pi\) | ||||
−0.169140 | + | 0.985592i | \(0.554099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.21520 | 0.320367 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.00229240 | −0.000140293 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.32940 | −0.324939 | −0.162470 | − | 0.986714i | \(-0.551946\pi\) | ||||
−0.162470 | + | 0.986714i | \(0.551946\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4702 | −0.939750 | −0.469875 | − | 0.882733i | \(-0.655701\pi\) | ||||
−0.469875 | + | 0.882733i | \(0.655701\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.19343 | −0.132753 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.1030 | 0.669536 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.8189 | 1.25089 | 0.625443 | − | 0.780270i | \(-0.284918\pi\) | ||||
0.625443 | + | 0.780270i | \(0.284918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.9700 | −0.716627 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.9951 | −0.715568 | −0.357784 | − | 0.933804i | \(-0.616468\pi\) | ||||
−0.357784 | + | 0.933804i | \(0.616468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.47789 | 0.206739 | 0.103369 | − | 0.994643i | \(-0.467038\pi\) | ||||
0.103369 | + | 0.994643i | \(0.467038\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.7124 | 0.930722 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.9664 | −0.647325 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.69261 | 0.334859 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.75296 | −0.278623 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.80153 | 0.397350 | 0.198675 | − | 0.980065i | \(-0.436336\pi\) | ||||
0.198675 | + | 0.980065i | \(0.436336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.73768 | −0.101172 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.6291 | 0.616761 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.31466 | −0.480849 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.6025 | 1.07223 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.51377 | 0.431655 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.2587 | 1.61809 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.90709 | −0.280063 | −0.140031 | − | 0.990147i | \(-0.544720\pi\) | ||||
−0.140031 | + | 0.990147i | \(0.544720\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.5597 | −0.828273 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.40793 | −0.249951 | −0.124975 | − | 0.992160i | \(-0.539885\pi\) | ||||
−0.124975 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0681 | −1.07779 | −0.538896 | − | 0.842372i | \(-0.681158\pi\) | ||||
−0.538896 | + | 0.842372i | \(0.681158\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.4752 | −0.590208 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 35.3612 | 1.98608 | 0.993042 | − | 0.117757i | \(-0.0375704\pi\) | ||||
0.993042 | + | 0.117757i | \(0.0375704\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.80171 | −0.100877 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.72986 | −0.487253 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.8672 | −1.10544 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.53845 | −0.307218 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.9081 | −1.32212 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.13423 | 0.448455 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5365 | −0.744036 | −0.372018 | − | 0.928226i | \(-0.621334\pi\) | ||||
−0.372018 | + | 0.928226i | \(0.621334\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.6648 | −1.02282 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.8432 | 1.84905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.46560 | 0.243257 | 0.121628 | − | 0.992576i | \(-0.461188\pi\) | ||||
0.121628 | + | 0.992576i | \(0.461188\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.0670228 | 0.00364018 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.1781 | 0.767788 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8304 | 1.07074 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 31.8460 | 1.71453 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.3752 | −0.932748 | −0.466374 | − | 0.884588i | \(-0.654440\pi\) | ||||
−0.466374 | + | 0.884588i | \(0.654440\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.7959 | 1.59494 | 0.797469 | − | 0.603360i | \(-0.206172\pi\) | ||||
0.797469 | + | 0.603360i | \(0.206172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.30204 | −0.283002 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.46145 | −0.131010 | −0.0655048 | − | 0.997852i | \(-0.520866\pi\) | ||||
−0.0655048 | + | 0.997852i | \(0.520866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32.9446 | 1.74852 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.6226 | −0.562206 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.5034 | −1.02935 | −0.514674 | − | 0.857386i | \(-0.672087\pi\) | ||||
−0.514674 | + | 0.857386i | \(0.672087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.60647 | −0.0845512 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.21738 | 0.431301 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −42.8536 | −2.24306 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.3322 | 1.58333 | 0.791663 | − | 0.610958i | \(-0.209216\pi\) | ||||
0.791663 | + | 0.610958i | \(0.209216\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.46047 | −0.492492 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.08681 | 0.160259 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.42971 | −0.281140 | −0.140570 | − | 0.990071i | \(-0.544893\pi\) | ||||
−0.140570 | + | 0.990071i | \(0.544893\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.37556 | 0.122673 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.898739 | 0.0462874 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.4737 | −1.77080 | −0.885398 | − | 0.464835i | \(-0.846114\pi\) | ||||
−0.885398 | + | 0.464835i | \(0.846114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.88543 | 0.352751 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.85691 | 0.503665 | 0.251832 | − | 0.967771i | \(-0.418967\pi\) | ||||
0.251832 | + | 0.967771i | \(0.418967\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.4075 | 0.632344 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.0480 | 0.815765 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.5924 | −1.19618 | −0.598091 | − | 0.801428i | \(-0.704074\pi\) | ||||
−0.598091 | + | 0.801428i | \(0.704074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.2670 | −2.03639 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.1181 | 1.01483 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 57.1942 | 2.87775 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.42961 | −0.322693 | −0.161347 | − | 0.986898i | \(-0.551584\pi\) | ||||
−0.161347 | + | 0.986898i | \(0.551584\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.29996 | 0.465580 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.5137 | 0.724777 | 0.362389 | − | 0.932027i | \(-0.381961\pi\) | ||||
0.362389 | + | 0.932027i | \(0.381961\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.07240 | −0.352301 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.02321 | 0.199915 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.1078 | 1.09584 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.5504 | 1.01615 | 0.508076 | − | 0.861312i | \(-0.330357\pi\) | ||||
0.508076 | + | 0.861312i | \(0.330357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.4483 | 1.00864 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.02851 | −0.0506097 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.88225 | −0.436013 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.4548 | −1.19756 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.2567 | 1.08731 | 0.543657 | − | 0.839308i | \(-0.317039\pi\) | ||||
0.543657 | + | 0.839308i | \(0.317039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4817 | 1.24190 | 0.620952 | − | 0.783849i | \(-0.286746\pi\) | ||||
0.620952 | + | 0.783849i | \(0.286746\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.01724 | 0.341190 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.8221 | −1.30106 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.7260 | 0.809426 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.24129 | 0.108210 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0335 | −0.579635 | −0.289817 | − | 0.957082i | \(-0.593595\pi\) | ||||
−0.289817 | + | 0.957082i | \(0.593595\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.9773 | −0.623648 | −0.311824 | − | 0.950140i | \(-0.600940\pi\) | ||||
−0.311824 | + | 0.950140i | \(0.600940\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.44227 | −0.165044 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 35.2534 | 1.68640 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.96631 | −0.332484 | −0.166242 | − | 0.986085i | \(-0.553163\pi\) | ||||
−0.166242 | + | 0.986085i | \(0.553163\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.45360 | 0.259695 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.3604 | −1.06238 | −0.531188 | − | 0.847254i | \(-0.678254\pi\) | ||||
−0.531188 | + | 0.847254i | \(0.678254\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.00646842 | −0.000306632 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.302492 | 0.0143074 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −41.3012 | −1.94912 | −0.974562 | − | 0.224117i | \(-0.928050\pi\) | ||||
−0.974562 | + | 0.224117i | \(0.928050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.2056 | 0.527653 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.32672 | 0.203287 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.18916 | −0.290152 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.19418 | −0.336530 | −0.168265 | − | 0.985742i | \(-0.553816\pi\) | ||||
−0.168265 | + | 0.985742i | \(0.553816\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.6772 | −1.19851 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.4170 | 1.41666 | 0.708329 | − | 0.705882i | \(-0.249449\pi\) | ||||
0.708329 | + | 0.705882i | \(0.249449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.5190 | −0.814175 | −0.407088 | − | 0.913389i | \(-0.633456\pi\) | ||||
−0.407088 | + | 0.913389i | \(0.633456\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.0880 | 1.25618 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.0087 | 1.01844 | 0.509220 | − | 0.860636i | \(-0.329934\pi\) | ||||
0.509220 | + | 0.860636i | \(0.329934\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0314 | 0.924963 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.26407 | 0.104323 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.0083 | −0.874005 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.4825 | 1.07745 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.66293 | 0.121927 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.140520 | −0.00642050 | −0.00321025 | − | 0.999995i | \(-0.501022\pi\) | ||||
−0.00321025 | + | 0.999995i | \(0.501022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0279 | −0.502831 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.8493 | 0.857671 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.4113 | −0.608976 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.9064 | −1.03799 | −0.518995 | − | 0.854777i | \(-0.673694\pi\) | ||||
−0.518995 | + | 0.854777i | \(0.673694\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.2127 | −1.00449 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.7589 | −1.34300 | −0.671500 | − | 0.741005i | \(-0.734350\pi\) | ||||
−0.671500 | + | 0.741005i | \(0.734350\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.35250 | 0.196027 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.7037 | 0.481095 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.4995 | 0.874671 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.9972 | −0.895198 | −0.447599 | − | 0.894234i | \(-0.647721\pi\) | ||||
−0.447599 | + | 0.894234i | \(0.647721\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.31236 | −0.416046 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.2014 | 0.943452 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.9035 | 0.617477 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.29798 | 0.101856 | 0.0509282 | − | 0.998702i | \(-0.483782\pi\) | ||||
0.0509282 | + | 0.998702i | \(0.483782\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.3645 | −1.12206 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.4801 | 0.992522 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −41.0828 | −1.81032 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.31170 | −0.365548 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.7291 | −0.690430 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.3648 | −0.585522 | −0.292761 | − | 0.956186i | \(-0.594574\pi\) | ||||
−0.292761 | + | 0.956186i | \(0.594574\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.5939 | −1.60014 | −0.800071 | − | 0.599906i | \(-0.795205\pi\) | ||||
−0.800071 | + | 0.599906i | \(0.795205\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.5556 | 0.547972 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.2508 | −1.49199 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.4519 | 2.10661 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.887276 | −0.0385045 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.58964 | −0.242114 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.6328 | −1.06497 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.0588 | 0.477224 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.45962 | −0.278236 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.5138 | −1.13992 | −0.569959 | − | 0.821673i | \(-0.693041\pi\) | ||||
−0.569959 | + | 0.821673i | \(0.693041\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.95891 | 0.126979 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −67.4610 | −2.88971 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.04597 | −0.258507 | −0.129254 | − | 0.991612i | \(-0.541258\pi\) | ||||
−0.129254 | + | 0.991612i | \(0.541258\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.4291 | 0.615821 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.81057 | −0.162336 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.8525 | 1.43956 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42.2382 | 1.79291 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.6034 | 1.33908 | 0.669540 | − | 0.742776i | \(-0.266491\pi\) | ||||
0.669540 | + | 0.742776i | \(0.266491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.48183 | 0.401039 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.8543 | 0.458270 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.88343 | −0.290102 | −0.145051 | − | 0.989424i | \(-0.546335\pi\) | ||||
−0.145051 | + | 0.989424i | \(0.546335\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.189117 | 0.00795620 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.38129 | 0.100005 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.3332 | 1.27163 | 0.635817 | − | 0.771840i | \(-0.280663\pi\) | ||||
0.635817 | + | 0.771840i | \(0.280663\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3930 | 1.48115 | 0.740576 | − | 0.671973i | \(-0.234553\pi\) | ||||
0.740576 | + | 0.671973i | \(0.234553\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.1332 | 0.506872 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 47.5946 | 1.98483 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.9961 | 0.582667 | 0.291333 | − | 0.956622i | \(-0.405901\pi\) | ||||
0.291333 | + | 0.956622i | \(0.405901\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.4455 | −1.01592 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.25729 | −0.218109 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.15415 | −0.130632 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.33927 | −0.220751 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.8955 | −1.85303 | −0.926517 | − | 0.376253i | \(-0.877212\pi\) | ||||
−0.926517 | + | 0.376253i | \(0.877212\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.9863 | 1.23556 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.26468 | 0.381098 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.7630 | −0.852636 | −0.426318 | − | 0.904573i | \(-0.640189\pi\) | ||||
−0.426318 | + | 0.904573i | \(0.640189\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.9734 | −1.22879 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.4905 | 0.797692 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.1464 | −1.23175 | −0.615874 | − | 0.787845i | \(-0.711197\pi\) | ||||
−0.615874 | + | 0.787845i | \(0.711197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.4859 | −1.36592 | −0.682959 | − | 0.730456i | \(-0.739307\pi\) | ||||
−0.682959 | + | 0.730456i | \(0.739307\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.2807 | 0.703723 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.1868 | 0.942677 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.7080 | 1.57111 | 0.785554 | − | 0.618793i | \(-0.212378\pi\) | ||||
0.785554 | + | 0.618793i | \(0.212378\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.03743 | −0.0825609 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.14608 | 0.167733 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.233177 | −0.00941792 | −0.00470896 | − | 0.999989i | \(-0.501499\pi\) | ||||
−0.00470896 | + | 0.999989i | \(0.501499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.4089 | 0.863292 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.9488 | −0.883624 | −0.441812 | − | 0.897108i | \(-0.645664\pi\) | ||||
−0.441812 | + | 0.897108i | \(0.645664\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.7059 | 1.03321 | 0.516603 | − | 0.856225i | \(-0.327196\pi\) | ||||
0.516603 | + | 0.856225i | \(0.327196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 45.5630 | 1.82838 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.00382857 | −0.000153388 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.4497 | −0.857987 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.50286 | −0.379508 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −53.4071 | −2.12948 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1563 | 0.682981 | 0.341490 | − | 0.939885i | \(-0.389068\pi\) | ||||
0.341490 | + | 0.939885i | \(0.389068\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.36911 | 0.173656 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.4284 | 0.770994 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.22222 | 0.127669 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.8218 | 0.665460 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.7362 | −0.858529 | −0.429264 | − | 0.903179i | \(-0.641227\pi\) | ||||
−0.429264 | + | 0.903179i | \(0.641227\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.0424 | 0.672085 | 0.336042 | − | 0.941847i | \(-0.390911\pi\) | ||||
0.336042 | + | 0.941847i | \(0.390911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −36.3164 | −1.42996 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.2034 | −0.990847 | −0.495424 | − | 0.868652i | \(-0.664987\pi\) | ||||
−0.495424 | + | 0.868652i | \(0.664987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.05095 | 0.0412534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0330 | 0.628385 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.5540 | 1.70440 | 0.852200 | − | 0.523217i | \(-0.175268\pi\) | ||||
0.852200 | + | 0.523217i | \(0.175268\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 56.7668 | 2.21806 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.8814 | −0.853677 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.34008 | −0.246975 | −0.123487 | − | 0.992346i | \(-0.539408\pi\) | ||||
−0.123487 | + | 0.992346i | \(0.539408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.9696 | 1.16568 | 0.582841 | − | 0.812586i | \(-0.301941\pi\) | ||||
0.582841 | + | 0.812586i | \(0.301941\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.41440 | −0.210278 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.2415 | 1.01760 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.72331 | −0.299048 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.03559 | −0.349336 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.0909 | −0.659786 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.5701 | −1.29403 | −0.647015 | − | 0.762477i | \(-0.723983\pi\) | ||||
−0.647015 | + | 0.762477i | \(0.723983\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 30.3498 | 1.16816 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.2557 | −0.855355 | −0.427677 | − | 0.903931i | \(-0.640668\pi\) | ||||
−0.427677 | + | 0.903931i | \(0.640668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.93797 | −0.304631 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.3954 | 0.781553 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.3966 | 0.474344 | 0.237172 | − | 0.971468i | \(-0.423780\pi\) | ||||
0.237172 | + | 0.971468i | \(0.423780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 57.6986 | 2.20455 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.94630 | 0.112408 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.57337 | 0.0599406 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0680 | 0.839506 | 0.419753 | − | 0.907638i | \(-0.362117\pi\) | ||||
0.419753 | + | 0.907638i | \(0.362117\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.33537 | 0.240661 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −69.0037 | −2.61746 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.0700 | −1.02535 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.7438 | 1.04937 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.9963 | −0.604170 | −0.302085 | − | 0.953281i | \(-0.597683\pi\) | ||||
−0.302085 | + | 0.953281i | \(0.597683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.7574 | 1.76349 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.8799 | −0.598073 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.5489 | 0.471948 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.1114 | 1.01819 | 0.509095 | − | 0.860711i | \(-0.329980\pi\) | ||||
0.509095 | + | 0.860711i | \(0.329980\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.2039 | 1.09523 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 60.7765 | 2.27610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.32419 | 0.236511 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.8485 | −0.442488 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.2408 | −0.866735 | −0.433367 | − | 0.901217i | \(-0.642675\pi\) | ||||
−0.433367 | + | 0.901217i | \(0.642675\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.3164 | −0.905589 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.6444 | 0.879346 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.14454 | −0.191063 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.1038 | −1.22775 | −0.613876 | − | 0.789402i | \(-0.710391\pi\) | ||||
−0.613876 | + | 0.789402i | \(0.710391\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.7395 | 0.768128 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.9195 | 1.69839 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.3254 | 1.71107 | 0.855533 | − | 0.517748i | \(-0.173230\pi\) | ||||
0.855533 | + | 0.517748i | \(0.173230\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.3414 | −0.455221 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.4684 | −0.753963 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.5923 | 1.16214 | 0.581070 | − | 0.813854i | \(-0.302634\pi\) | ||||
0.581070 | + | 0.813854i | \(0.302634\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.74026 | 0.174138 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.9414 | 0.694892 | 0.347446 | − | 0.937700i | \(-0.387049\pi\) | ||||
0.347446 | + | 0.937700i | \(0.387049\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.853534 | 0.0312711 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.53536 | −0.165940 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.5798 | −0.532736 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6252 | 0.679643 | 0.339822 | − | 0.940490i | \(-0.389633\pi\) | ||||
0.339822 | + | 0.940490i | \(0.389633\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.0511 | −0.694260 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.2086 | 0.444317 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.42740 | 0.160917 | 0.0804583 | − | 0.996758i | \(-0.474362\pi\) | ||||
0.0804583 | + | 0.996758i | \(0.474362\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.2605 | −0.699112 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.8700 | −1.77154 | −0.885768 | − | 0.464129i | \(-0.846368\pi\) | ||||
−0.885768 | + | 0.464129i | \(0.846368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.9293 | −1.44554 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.8575 | −0.934879 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.524240 | −0.0189292 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.1276 | −1.08643 | −0.543214 | − | 0.839594i | \(-0.682793\pi\) | ||||
−0.543214 | + | 0.839594i | \(0.682793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.4104 | 0.699047 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.4422 | 0.411547 | 0.205774 | − | 0.978600i | \(-0.434029\pi\) | ||||
0.205774 | + | 0.978600i | \(0.434029\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.4836 | 1.45421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.0002 | 0.896877 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.6996 | 0.849125 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.9249 | −0.712969 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.92494 | −0.176003 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.38848 | 0.228015 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.32502 | 0.154170 | 0.0770851 | − | 0.997025i | \(-0.475439\pi\) | ||||
0.0770851 | + | 0.997025i | \(0.475439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.33904 | 0.225676 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.111936 | 0.00397998 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.52535 | 0.302744 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.02618 | −0.213726 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.4668 | −1.43341 | −0.716704 | − | 0.697378i | \(-0.754350\pi\) | ||||
−0.716704 | + | 0.697378i | \(0.754350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.0790 | 0.710345 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.00330283 | −0.000116700 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.9179 | 0.914623 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 53.1865 | 1.87458 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.15813 | 0.216777 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.3192 | −0.468277 | −0.234139 | − | 0.972203i | \(-0.575227\pi\) | ||||
−0.234139 | + | 0.972203i | \(0.575227\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.62900 | −0.338120 | −0.169060 | − | 0.985606i | \(-0.554073\pi\) | ||||
−0.169060 | + | 0.985606i | \(0.554073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.8759 | 0.626935 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −62.6771 | −2.19548 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.2021 | −1.40649 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.16024 | −0.110428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.4726 | −1.76151 | −0.880754 | − | 0.473575i | \(-0.842963\pi\) | ||||
−0.880754 | + | 0.473575i | \(0.842963\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.06420 | −0.246243 | −0.123121 | − | 0.992392i | \(-0.539290\pi\) | ||||
−0.123121 | + | 0.992392i | \(0.539290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.8295 | −0.446667 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.9997 | −1.46047 | −0.730237 | − | 0.683194i | \(-0.760590\pi\) | ||||
−0.730237 | + | 0.683194i | \(0.760590\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.91390 | −0.0664723 | −0.0332362 | − | 0.999448i | \(-0.510581\pi\) | ||||
−0.0332362 | + | 0.999448i | \(0.510581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.0562 | −0.834502 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.6049 | 0.540676 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.2765 | −0.909335 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.7556 | 1.33959 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.8138 | 0.684047 | 0.342023 | − | 0.939691i | \(-0.388888\pi\) | ||||
0.342023 | + | 0.939691i | \(0.388888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1652 | −0.971213 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.8604 | 0.477377 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.2312 | 1.34959 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7240 | 0.471561 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.01870 | −0.137922 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 94.7684 | 3.24862 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.43175 | −0.322937 | −0.161469 | − | 0.986878i | \(-0.551623\pi\) | ||||
−0.161469 | + | 0.986878i | \(0.551623\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.6380 | 0.774203 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.0817322 | 0.00279192 | 0.00139596 | − | 0.999999i | \(-0.499556\pi\) | ||||
0.00139596 | + | 0.999999i | \(0.499556\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.2568 | −0.691152 | −0.345576 | − | 0.938391i | \(-0.612316\pi\) | ||||
−0.345576 | + | 0.938391i | \(0.612316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.6717 | 0.431849 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.6759 | 0.839978 | 0.419989 | − | 0.907529i | \(-0.362034\pi\) | ||||
0.419989 | + | 0.907529i | \(0.362034\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.3824 | −1.50905 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.57782 | −0.223394 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.5911 | −1.17342 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.2101 | 0.345958 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.84793 | −0.231767 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.96745 | 0.134124 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.2534 | −1.66317 | −0.831585 | − | 0.555397i | \(-0.812566\pi\) | ||||
−0.831585 | + | 0.555397i | \(0.812566\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.85918 | −0.265084 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.18119 | 0.275631 | 0.137816 | − | 0.990458i | \(-0.455992\pi\) | ||||
0.137816 | + | 0.990458i | \(0.455992\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.7020 | −1.84087 | −0.920434 | − | 0.390897i | \(-0.872165\pi\) | ||||
−0.920434 | + | 0.390897i | \(0.872165\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.00790 | 0.0674947 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.5302 | −0.957951 | −0.478976 | − | 0.877828i | \(-0.658992\pi\) | ||||
−0.478976 | + | 0.877828i | \(0.658992\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.4994 | 0.385679 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.43324 | −0.0815166 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.5790 | −0.588259 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.2044 | 1.04305 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.60761 | 0.320789 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.56939 | −0.219101 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.61966 | 0.253848 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.4952 | −0.715316 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.34908 | 0.277533 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5848 | 0.849528 | 0.424764 | − | 0.905304i | \(-0.360357\pi\) | ||||
0.424764 | + | 0.905304i | \(0.360357\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.8256 | 0.359064 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.38307 | −0.145218 | −0.0726088 | − | 0.997360i | \(-0.523132\pi\) | ||||
−0.0726088 | + | 0.997360i | \(0.523132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.37199 | 0.177787 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −32.6530 | −1.07947 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.5995 | 1.10955 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.0803 | −1.38810 | −0.694051 | − | 0.719926i | \(-0.744176\pi\) | ||||
−0.694051 | + | 0.719926i | \(0.744176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.67016 | 0.186838 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.93903 | 0.327147 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 63.1258 | 2.07556 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.9772 | −0.688983 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.6208 | 1.26711 | 0.633554 | − | 0.773699i | \(-0.281595\pi\) | ||||
0.633554 | + | 0.773699i | \(0.281595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.6619 | −0.447751 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.09337 | 0.166749 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.6274 | 1.00162 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.3945 | 1.09095 | 0.545476 | − | 0.838126i | \(-0.316349\pi\) | ||||
0.545476 | + | 0.838126i | \(0.316349\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.0332 | 0.719027 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.9997 | 0.554174 | 0.277087 | − | 0.960845i | \(-0.410631\pi\) | ||||
0.277087 | + | 0.960845i | \(0.410631\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48.0345 | 1.56422 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 33.9156 | 1.10327 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.7458 | 1.77900 | 0.889500 | − | 0.456935i | \(-0.151053\pi\) | ||||
0.889500 | + | 0.456935i | \(0.151053\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9285 | −0.419676 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.8600 | −1.32498 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.64381 | −0.312394 | −0.156197 | − | 0.987726i | \(-0.549923\pi\) | ||||
−0.156197 | + | 0.987726i | \(0.549923\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.2360 | 1.10785 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.08188 | 0.0672977 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.1510 | 1.10279 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.6961 | 0.667616 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.5777 | −0.405312 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −68.9773 | −2.22046 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.5842 | −1.04784 | −0.523918 | − | 0.851769i | \(-0.675530\pi\) | ||||
−0.523918 | + | 0.851769i | \(0.675530\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.9566 | 0.737471 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.4450 | 0.784476 | 0.392238 | − | 0.919864i | \(-0.371701\pi\) | ||||
0.392238 | + | 0.919864i | \(0.371701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.8424 | −1.30935 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.39969 | 0.204954 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.8778 | 1.40377 | 0.701887 | − | 0.712288i | \(-0.252341\pi\) | ||||
0.701887 | + | 0.712288i | \(0.252341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.00391210 | 0.000125031 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.4462 | −1.09978 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.2295 | 0.740906 | 0.370453 | − | 0.928851i | \(-0.379202\pi\) | ||||
0.370453 | + | 0.928851i | \(0.379202\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.1419 | 0.832951 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.39912 | −0.299177 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −81.4820 | −2.59098 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.4959 | −0.936970 | −0.468485 | − | 0.883472i | \(-0.655200\pi\) | ||||
−0.468485 | + | 0.883472i | \(0.655200\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.6415 | 0.496368 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 54.9958 | 1.74348 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.4456 | 1.59763 | 0.798814 | − | 0.601578i | \(-0.205461\pi\) | ||||
0.798814 | + | 0.601578i | \(0.205461\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 60.4313 | 1.91196 |
(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 | 4024.2.a.e.1.10 | ✓ | 29 | |
4.3 | odd | 2 | 8048.2.a.w.1.20 | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.e.1.10 | ✓ | 29 | 1.1 | even | 1 | trivial | |
8048.2.a.w.1.20 | 29 | 4.3 | odd | 2 |