Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3087,2,Mod(3086,3087)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3087, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3087.3086");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3087 = 3^{2} \cdot 7^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3087.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(24.6498191040\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3086.13 | ||
Character | \(\chi\) | \(=\) | 3087.3086 |
Dual form | 3087.2.c.c.3086.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3087\mathbb{Z}\right)^\times\).
\(n\) | \(344\) | \(2404\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.88777i | − 1.33485i | −0.744676 | − | 0.667426i | \(-0.767396\pi\) | ||||
0.744676 | − | 0.667426i | \(-0.232604\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.56366 | −0.781831 | ||||||||
\(5\) | −1.89903 | −0.849274 | −0.424637 | − | 0.905364i | \(-0.639598\pi\) | ||||
−0.424637 | + | 0.905364i | \(0.639598\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 0.823703i | − 0.291223i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.58493i | 1.13366i | ||||||||
\(11\) | 1.25838i | 0.379417i | 0.981840 | + | 0.189708i | \(0.0607542\pi\) | ||||
−0.981840 | + | 0.189708i | \(0.939246\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.80085i | 1.88622i | 0.332487 | + | 0.943108i | \(0.392112\pi\) | ||||
−0.332487 | + | 0.943108i | \(0.607888\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68228 | −1.17057 | ||||||||
\(17\) | 7.12478 | 1.72801 | 0.864007 | − | 0.503480i | \(-0.167947\pi\) | ||||
0.864007 | + | 0.503480i | \(0.167947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.22610i | − 1.65778i | −0.559411 | − | 0.828890i | \(-0.688973\pi\) | ||||
0.559411 | − | 0.828890i | \(-0.311027\pi\) | |||||||
\(20\) | 2.96945 | 0.663989 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.37553 | 0.506465 | ||||||||
\(23\) | − 3.66613i | − 0.764441i | −0.924071 | − | 0.382221i | \(-0.875159\pi\) | ||||
0.924071 | − | 0.382221i | \(-0.124841\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.39367 | −0.278734 | ||||||||
\(26\) | 12.8384 | 2.51782 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.95237i | − 1.29102i | −0.763750 | − | 0.645512i | \(-0.776644\pi\) | ||||
0.763750 | − | 0.645512i | \(-0.223356\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 4.28108i | − 0.768905i | −0.923145 | − | 0.384453i | \(-0.874390\pi\) | ||||
0.923145 | − | 0.384453i | \(-0.125610\pi\) | |||||||
\(32\) | 7.19165i | 1.27132i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 13.4499i | − 2.30664i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.49868 | −1.56157 | −0.780787 | − | 0.624798i | \(-0.785181\pi\) | ||||
−0.780787 | + | 0.624798i | \(0.785181\pi\) | |||||||
\(38\) | −13.6412 | −2.21289 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.56424i | 0.247328i | ||||||||
\(41\) | 2.61917 | 0.409046 | 0.204523 | − | 0.978862i | \(-0.434436\pi\) | ||||
0.204523 | + | 0.978862i | \(0.434436\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.15791 | 0.329078 | 0.164539 | − | 0.986371i | \(-0.447386\pi\) | ||||
0.164539 | + | 0.986371i | \(0.447386\pi\) | |||||||
\(44\) | − 1.96769i | − 0.296640i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.92080 | −1.02042 | ||||||||
\(47\) | −3.68959 | −0.538181 | −0.269091 | − | 0.963115i | \(-0.586723\pi\) | ||||
−0.269091 | + | 0.963115i | \(0.586723\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.63093i | 0.372069i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 10.6342i | − 1.47470i | ||||||||
\(53\) | 2.36985i | 0.325523i | 0.986665 | + | 0.162762i | \(0.0520402\pi\) | ||||
−0.986665 | + | 0.162762i | \(0.947960\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.38971i | − 0.322229i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.1245 | −1.72333 | ||||||||
\(59\) | −4.94485 | −0.643764 | −0.321882 | − | 0.946780i | \(-0.604315\pi\) | ||||
−0.321882 | + | 0.946780i | \(0.604315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.92225i | 1.01434i | 0.861846 | + | 0.507170i | \(0.169308\pi\) | ||||
−0.861846 | + | 0.507170i | \(0.830692\pi\) | |||||||
\(62\) | −8.08169 | −1.02638 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.21160 | 0.526450 | ||||||||
\(65\) | − 12.9150i | − 1.60191i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1413 | −1.36112 | −0.680562 | − | 0.732691i | \(-0.738264\pi\) | ||||
−0.680562 | + | 0.732691i | \(0.738264\pi\) | |||||||
\(68\) | −11.1408 | −1.35102 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 8.63318i | − 1.02457i | −0.858816 | − | 0.512285i | \(-0.828799\pi\) | ||||
0.858816 | − | 0.512285i | \(-0.171201\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.20466i | 1.07732i | 0.842522 | + | 0.538662i | \(0.181070\pi\) | ||||
−0.842522 | + | 0.538662i | \(0.818930\pi\) | |||||||
\(74\) | 17.9313i | 2.08447i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.2992i | 1.29610i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6363 | −1.42170 | −0.710848 | − | 0.703345i | \(-0.751689\pi\) | ||||
−0.710848 | + | 0.703345i | \(0.751689\pi\) | |||||||
\(80\) | 8.89182 | 0.994135 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 4.94438i | − 0.546016i | ||||||||
\(83\) | −15.5711 | −1.70915 | −0.854575 | − | 0.519328i | \(-0.826182\pi\) | ||||
−0.854575 | + | 0.519328i | \(0.826182\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.5302 | −1.46756 | ||||||||
\(86\) | − 4.07363i | − 0.439271i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.03653 | 0.110495 | ||||||||
\(89\) | −1.57854 | −0.167325 | −0.0836626 | − | 0.996494i | \(-0.526662\pi\) | ||||
−0.0836626 | + | 0.996494i | \(0.526662\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.73259i | 0.597664i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.96508i | 0.718393i | ||||||||
\(95\) | 13.7226i | 1.40791i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1.36110i | − 0.138198i | −0.997610 | − | 0.0690992i | \(-0.977987\pi\) | ||||
0.997610 | − | 0.0690992i | \(-0.0220125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.17923 | 0.217923 | ||||||||
\(101\) | 3.73507 | 0.371654 | 0.185827 | − | 0.982582i | \(-0.440504\pi\) | ||||
0.185827 | + | 0.982582i | \(0.440504\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 7.59882i | − 0.748734i | −0.927281 | − | 0.374367i | \(-0.877860\pi\) | ||||
0.927281 | − | 0.374367i | \(-0.122140\pi\) | |||||||
\(104\) | 5.60188 | 0.549309 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.47372 | 0.434526 | ||||||||
\(107\) | − 14.8163i | − 1.43235i | −0.697922 | − | 0.716174i | \(-0.745892\pi\) | ||||
0.697922 | − | 0.716174i | \(-0.254108\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.64221 | 0.444643 | 0.222321 | − | 0.974973i | \(-0.428637\pi\) | ||||
0.222321 | + | 0.974973i | \(0.428637\pi\) | |||||||
\(110\) | −4.51122 | −0.430128 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 0.0919008i | − 0.00864530i | −0.999991 | − | 0.00432265i | \(-0.998624\pi\) | ||||
0.999991 | − | 0.00432265i | \(-0.00137595\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.96211i | 0.649220i | ||||||||
\(116\) | 10.8712i | 1.00936i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.33472i | 0.859330i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.41647 | 0.856043 | ||||||||
\(122\) | 14.9554 | 1.35399 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.69417i | 0.601154i | ||||||||
\(125\) | 12.1418 | 1.08600 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.86495 | −0.342959 | −0.171480 | − | 0.985188i | \(-0.554855\pi\) | ||||
−0.171480 | + | 0.985188i | \(0.554855\pi\) | |||||||
\(128\) | 6.43280i | 0.568584i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −24.3806 | −2.13832 | ||||||||
\(131\) | 17.2936 | 1.51095 | 0.755476 | − | 0.655177i | \(-0.227406\pi\) | ||||
0.755476 | + | 0.655177i | \(0.227406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 21.0321i | 1.81690i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 5.86870i | − 0.503237i | ||||||||
\(137\) | − 5.32978i | − 0.455354i | −0.973737 | − | 0.227677i | \(-0.926887\pi\) | ||||
0.973737 | − | 0.227677i | \(-0.0731131\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 9.13506i | − 0.774826i | −0.921906 | − | 0.387413i | \(-0.873369\pi\) | ||||
0.921906 | − | 0.387413i | \(-0.126631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.2974 | −1.36765 | ||||||||
\(143\) | −8.55807 | −0.715662 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.2028i | 1.09643i | ||||||||
\(146\) | 17.3763 | 1.43807 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.8527 | 1.22089 | ||||||||
\(149\) | − 11.1193i | − 0.910932i | −0.890253 | − | 0.455466i | \(-0.849473\pi\) | ||||
0.890253 | − | 0.455466i | \(-0.150527\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.13983 | −0.743789 | −0.371894 | − | 0.928275i | \(-0.621292\pi\) | ||||
−0.371894 | + | 0.928275i | \(0.621292\pi\) | |||||||
\(152\) | −5.95215 | −0.482783 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.12992i | 0.653011i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.7518i | − 0.858089i | −0.903283 | − | 0.429045i | \(-0.858850\pi\) | ||||
0.903283 | − | 0.429045i | \(-0.141150\pi\) | |||||||
\(158\) | 23.8544i | 1.89776i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 13.6572i | − 1.07970i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.96253 | 0.702000 | 0.351000 | − | 0.936376i | \(-0.385842\pi\) | ||||
0.351000 | + | 0.936376i | \(0.385842\pi\) | |||||||
\(164\) | −4.09550 | −0.319805 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 29.3946i | 2.28146i | ||||||||
\(167\) | −12.3488 | −0.955577 | −0.477789 | − | 0.878475i | \(-0.658562\pi\) | ||||
−0.477789 | + | 0.878475i | \(0.658562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −33.2515 | −2.55781 | ||||||||
\(170\) | 25.5419i | 1.95897i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.37424 | −0.257284 | ||||||||
\(173\) | −14.4748 | −1.10050 | −0.550250 | − | 0.835000i | \(-0.685468\pi\) | ||||
−0.550250 | + | 0.835000i | \(0.685468\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 5.89210i | − 0.444134i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.97992i | 0.223354i | ||||||||
\(179\) | − 7.62946i | − 0.570253i | −0.958490 | − | 0.285126i | \(-0.907964\pi\) | ||||
0.958490 | − | 0.285126i | \(-0.0920356\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.5295i | 1.60027i | 0.599817 | + | 0.800137i | \(0.295240\pi\) | ||||
−0.599817 | + | 0.800137i | \(0.704760\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.01980 | −0.222623 | ||||||||
\(185\) | 18.0383 | 1.32620 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.96570i | 0.655637i | ||||||||
\(188\) | 5.76927 | 0.420767 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25.9051 | 1.87935 | ||||||||
\(191\) | 18.4581i | 1.33558i | 0.744350 | + | 0.667790i | \(0.232760\pi\) | ||||
−0.744350 | + | 0.667790i | \(0.767240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.487234 | −0.0350719 | −0.0175359 | − | 0.999846i | \(-0.505582\pi\) | ||||
−0.0175359 | + | 0.999846i | \(0.505582\pi\) | |||||||
\(194\) | −2.56943 | −0.184475 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6599i | 0.759490i | 0.925091 | + | 0.379745i | \(0.123988\pi\) | ||||
−0.925091 | + | 0.379745i | \(0.876012\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.65135i | 0.542390i | 0.962524 | + | 0.271195i | \(0.0874187\pi\) | ||||
−0.962524 | + | 0.271195i | \(0.912581\pi\) | |||||||
\(200\) | 1.14797i | 0.0811737i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 7.05095i | − 0.496103i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.97389 | −0.347392 | ||||||||
\(206\) | −14.3448 | −0.999449 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 31.8435i | − 2.20795i | ||||||||
\(209\) | 9.09319 | 0.628989 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.4157 | −1.47432 | −0.737159 | − | 0.675719i | \(-0.763833\pi\) | ||||
−0.737159 | + | 0.675719i | \(0.763833\pi\) | |||||||
\(212\) | − 3.70564i | − 0.254504i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −27.9698 | −1.91197 | ||||||||
\(215\) | −4.09794 | −0.279478 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 8.76341i | − 0.593533i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.73670i | 0.251928i | ||||||||
\(221\) | 48.4546i | 3.25941i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.16876i | 0.413090i | 0.978437 | + | 0.206545i | \(0.0662221\pi\) | ||||
−0.978437 | + | 0.206545i | \(0.933778\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.173487 | −0.0115402 | ||||||||
\(227\) | −28.9777 | −1.92332 | −0.961659 | − | 0.274249i | \(-0.911571\pi\) | ||||
−0.961659 | + | 0.274249i | \(0.911571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 6.25018i | − 0.413023i | −0.978444 | − | 0.206512i | \(-0.933789\pi\) | ||||
0.978444 | − | 0.206512i | \(-0.0662111\pi\) | |||||||
\(230\) | 13.1428 | 0.866613 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.72669 | −0.375976 | ||||||||
\(233\) | − 4.85343i | − 0.317958i | −0.987282 | − | 0.158979i | \(-0.949180\pi\) | ||||
0.987282 | − | 0.158979i | \(-0.0508203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00665 | 0.457063 | ||||||||
\(236\) | 7.73207 | 0.503315 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 14.9406i | − 0.966427i | −0.875502 | − | 0.483214i | \(-0.839469\pi\) | ||||
0.875502 | − | 0.483214i | \(-0.160531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 10.3402i | − 0.666071i | −0.942914 | − | 0.333035i | \(-0.891927\pi\) | ||||
0.942914 | − | 0.333035i | \(-0.108073\pi\) | |||||||
\(242\) | − 17.7761i | − 1.14269i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 12.3877i | − 0.793043i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 49.1436 | 3.12693 | ||||||||
\(248\) | −3.52634 | −0.223923 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 22.9209i | − 1.44964i | ||||||||
\(251\) | −15.0408 | −0.949366 | −0.474683 | − | 0.880157i | \(-0.657437\pi\) | ||||
−0.474683 | + | 0.880157i | \(0.657437\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.61340 | 0.290042 | ||||||||
\(254\) | 7.29613i | 0.457800i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.5668 | 1.28543 | ||||||||
\(257\) | 17.1988 | 1.07283 | 0.536415 | − | 0.843954i | \(-0.319778\pi\) | ||||
0.536415 | + | 0.843954i | \(0.319778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 20.1948i | 1.25243i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 32.6463i | − 2.01690i | ||||||||
\(263\) | − 10.0939i | − 0.622419i | −0.950341 | − | 0.311210i | \(-0.899266\pi\) | ||||
0.950341 | − | 0.311210i | \(-0.100734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 4.50042i | − 0.276459i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 17.4212 | 1.06417 | ||||||||
\(269\) | −22.5855 | −1.37706 | −0.688530 | − | 0.725207i | \(-0.741744\pi\) | ||||
−0.688530 | + | 0.725207i | \(0.741744\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 9.66164i | − 0.586903i | −0.955974 | − | 0.293451i | \(-0.905196\pi\) | ||||
0.955974 | − | 0.293451i | \(-0.0948038\pi\) | |||||||
\(272\) | −33.3603 | −2.02276 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.0614 | −0.607831 | ||||||||
\(275\) | − 1.75377i | − 0.105756i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.80351 | −0.288615 | −0.144307 | − | 0.989533i | \(-0.546095\pi\) | ||||
−0.144307 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(278\) | −17.2449 | −1.03428 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.06852i | 0.123398i | 0.998095 | + | 0.0616988i | \(0.0196518\pi\) | ||||
−0.998095 | + | 0.0616988i | \(0.980348\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.45624i | 0.0865646i | 0.999063 | + | 0.0432823i | \(0.0137815\pi\) | ||||
−0.999063 | + | 0.0432823i | \(0.986219\pi\) | |||||||
\(284\) | 13.4994i | 0.801041i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.1556i | 0.955303i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.7625 | 1.98603 | ||||||||
\(290\) | 24.9238 | 1.46358 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 14.3930i | − 0.842286i | ||||||||
\(293\) | −24.2665 | −1.41766 | −0.708831 | − | 0.705379i | \(-0.750777\pi\) | ||||
−0.708831 | + | 0.705379i | \(0.750777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.39043 | 0.546732 | ||||||||
\(296\) | 7.82409i | 0.454766i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.9907 | −1.21596 | ||||||||
\(299\) | 24.9328 | 1.44190 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.2539i | 0.992848i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 33.8346i | 1.94055i | ||||||||
\(305\) | − 15.0446i | − 0.861452i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 0.425249i | − 0.0242702i | −0.999926 | − | 0.0121351i | \(-0.996137\pi\) | ||||
0.999926 | − | 0.0121351i | \(-0.00386282\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.3474 | 0.871674 | ||||||||
\(311\) | 8.54154 | 0.484346 | 0.242173 | − | 0.970233i | \(-0.422140\pi\) | ||||
0.242173 | + | 0.970233i | \(0.422140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.24775i | − 0.0705271i | −0.999378 | − | 0.0352636i | \(-0.988773\pi\) | ||||
0.999378 | − | 0.0352636i | \(-0.0112271\pi\) | |||||||
\(314\) | −20.2969 | −1.14542 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.7589 | 1.11153 | ||||||||
\(317\) | 15.7455i | 0.884354i | 0.896928 | + | 0.442177i | \(0.145794\pi\) | ||||
−0.896928 | + | 0.442177i | \(0.854206\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.74875 | 0.489836 | ||||||||
\(320\) | −7.99797 | −0.447100 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 51.4844i | − 2.86467i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 9.47814i | − 0.525753i | ||||||||
\(326\) | − 16.9192i | − 0.937066i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 2.15742i | − 0.119123i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.54477 | −0.304768 | −0.152384 | − | 0.988321i | \(-0.548695\pi\) | ||||
−0.152384 | + | 0.988321i | \(0.548695\pi\) | |||||||
\(332\) | 24.3479 | 1.33627 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.3116i | 1.27555i | ||||||||
\(335\) | 21.1577 | 1.15597 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.4442 | 1.22261 | 0.611307 | − | 0.791394i | \(-0.290644\pi\) | ||||
0.611307 | + | 0.791394i | \(0.290644\pi\) | |||||||
\(338\) | 62.7711i | 3.41430i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 21.1567 | 1.14738 | ||||||||
\(341\) | 5.38724 | 0.291735 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 1.77748i | − 0.0958351i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 27.3251i | 1.46901i | ||||||||
\(347\) | 7.94305i | 0.426405i | 0.977008 | + | 0.213203i | \(0.0683895\pi\) | ||||
−0.977008 | + | 0.213203i | \(0.931611\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.3404i | 0.874679i | 0.899296 | + | 0.437340i | \(0.144079\pi\) | ||||
−0.899296 | + | 0.437340i | \(0.855921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.04985 | −0.482359 | ||||||||
\(353\) | 26.2057 | 1.39479 | 0.697394 | − | 0.716688i | \(-0.254343\pi\) | ||||
0.697394 | + | 0.716688i | \(0.254343\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.3947i | 0.870140i | ||||||||
\(356\) | 2.46831 | 0.130820 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.4026 | −0.761203 | ||||||||
\(359\) | − 19.3618i | − 1.02188i | −0.859617 | − | 0.510939i | \(-0.829298\pi\) | ||||
0.859617 | − | 0.510939i | \(-0.170702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −33.2165 | −1.74824 | ||||||||
\(362\) | 40.6427 | 2.13613 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 17.4800i | − 0.914943i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.96867i | 0.259363i | 0.991556 | + | 0.129681i | \(0.0413954\pi\) | ||||
−0.991556 | + | 0.129681i | \(0.958605\pi\) | |||||||
\(368\) | 17.1659i | 0.894833i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 34.0521i | − 1.77029i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.7580 | 0.557026 | 0.278513 | − | 0.960432i | \(-0.410158\pi\) | ||||
0.278513 | + | 0.960432i | \(0.410158\pi\) | |||||||
\(374\) | 16.9252 | 0.875179 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.03912i | 0.156731i | ||||||||
\(377\) | 47.2820 | 2.43515 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.9101 | −0.868613 | −0.434307 | − | 0.900765i | \(-0.643007\pi\) | ||||
−0.434307 | + | 0.900765i | \(0.643007\pi\) | |||||||
\(380\) | − 21.4575i | − 1.10075i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 34.8446 | 1.78280 | ||||||||
\(383\) | −22.0195 | −1.12514 | −0.562571 | − | 0.826749i | \(-0.690188\pi\) | ||||
−0.562571 | + | 0.826749i | \(0.690188\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.919784i | 0.0468158i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.12830i | 0.108048i | ||||||||
\(389\) | − 29.0082i | − 1.47077i | −0.677648 | − | 0.735386i | \(-0.737001\pi\) | ||||
0.677648 | − | 0.735386i | \(-0.262999\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 26.1204i | − 1.32096i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.1235 | 1.01381 | ||||||||
\(395\) | 23.9968 | 1.20741 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.9862i | 0.752134i | 0.926592 | + | 0.376067i | \(0.122724\pi\) | ||||
−0.926592 | + | 0.376067i | \(0.877276\pi\) | |||||||
\(398\) | 14.4440 | 0.724010 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.52556 | 0.326278 | ||||||||
\(401\) | − 5.84746i | − 0.292008i | −0.989284 | − | 0.146004i | \(-0.953359\pi\) | ||||
0.989284 | − | 0.146004i | \(-0.0466412\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.1150 | 1.45032 | ||||||||
\(404\) | −5.84040 | −0.290571 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 11.9530i | − 0.592487i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 17.2266i | − 0.851800i | −0.904770 | − | 0.425900i | \(-0.859958\pi\) | ||||
0.904770 | − | 0.425900i | \(-0.140042\pi\) | |||||||
\(410\) | 9.38955i | 0.463717i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.8820i | 0.585383i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.5700 | 1.45154 | ||||||||
\(416\) | −48.9094 | −2.39798 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 17.1658i | − 0.839608i | ||||||||
\(419\) | 11.0644 | 0.540531 | 0.270266 | − | 0.962786i | \(-0.412889\pi\) | ||||
0.270266 | + | 0.962786i | \(0.412889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3493 | −0.943028 | −0.471514 | − | 0.881858i | \(-0.656292\pi\) | ||||
−0.471514 | + | 0.881858i | \(0.656292\pi\) | |||||||
\(422\) | 40.4279i | 1.96800i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.95205 | 0.0947999 | ||||||||
\(425\) | −9.92960 | −0.481656 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 23.1677i | 1.11985i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.73596i | 0.373061i | ||||||||
\(431\) | − 11.8075i | − 0.568747i | −0.958714 | − | 0.284374i | \(-0.908214\pi\) | ||||
0.958714 | − | 0.284374i | \(-0.0917856\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 32.1847i | − 1.54670i | −0.633979 | − | 0.773350i | \(-0.718580\pi\) | ||||
0.633979 | − | 0.773350i | \(-0.281420\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.25885 | −0.347636 | ||||||||
\(437\) | −26.4918 | −1.26728 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 24.2718i | − 1.15843i | −0.815176 | − | 0.579214i | \(-0.803360\pi\) | ||||
0.815176 | − | 0.579214i | \(-0.196640\pi\) | |||||||
\(440\) | −1.96841 | −0.0938403 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 91.4709 | 4.35083 | ||||||||
\(443\) | − 1.20946i | − 0.0574632i | −0.999587 | − | 0.0287316i | \(-0.990853\pi\) | ||||
0.999587 | − | 0.0287316i | \(-0.00914681\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.99771 | 0.142105 | ||||||||
\(446\) | 11.6452 | 0.551415 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.1441i | 0.525922i | 0.964806 | + | 0.262961i | \(0.0846991\pi\) | ||||
−0.964806 | + | 0.262961i | \(0.915301\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.29592i | 0.155199i | ||||||||
\(452\) | 0.143702i | 0.00675917i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 54.7031i | 2.56734i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.02386 | −0.235006 | −0.117503 | − | 0.993073i | \(-0.537489\pi\) | ||||
−0.117503 | + | 0.993073i | \(0.537489\pi\) | |||||||
\(458\) | −11.7989 | −0.551325 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 10.8864i | − 0.507581i | ||||||||
\(461\) | 3.37908 | 0.157379 | 0.0786897 | − | 0.996899i | \(-0.474926\pi\) | ||||
0.0786897 | + | 0.996899i | \(0.474926\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.7132 | −0.497884 | −0.248942 | − | 0.968518i | \(-0.580083\pi\) | ||||
−0.248942 | + | 0.968518i | \(0.580083\pi\) | |||||||
\(464\) | 32.5530i | 1.51123i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.16214 | −0.424428 | ||||||||
\(467\) | −7.94750 | −0.367767 | −0.183883 | − | 0.982948i | \(-0.558867\pi\) | ||||
−0.183883 | + | 0.982948i | \(0.558867\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 13.2269i | − 0.610112i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.07308i | 0.187479i | ||||||||
\(473\) | 2.71548i | 0.124858i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0708i | 0.462080i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.2044 | −1.29004 | ||||||||
\(479\) | −23.3621 | −1.06744 | −0.533720 | − | 0.845661i | \(-0.679206\pi\) | ||||
−0.533720 | + | 0.845661i | \(0.679206\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 64.5991i | − 2.94546i | ||||||||
\(482\) | −19.5199 | −0.889106 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.7242 | −0.669281 | ||||||||
\(485\) | 2.58477i | 0.117368i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.3593 | 1.05851 | 0.529255 | − | 0.848463i | \(-0.322471\pi\) | ||||
0.529255 | + | 0.848463i | \(0.322471\pi\) | |||||||
\(488\) | 6.52558 | 0.295399 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 12.3820i | − 0.558792i | −0.960176 | − | 0.279396i | \(-0.909866\pi\) | ||||
0.960176 | − | 0.279396i | \(-0.0901342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 49.5342i | − 2.23091i | ||||||||
\(494\) | − 92.7716i | − 4.17399i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0453i | 0.900058i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.81473 | 0.215537 | 0.107769 | − | 0.994176i | \(-0.465629\pi\) | ||||
0.107769 | + | 0.994176i | \(0.465629\pi\) | |||||||
\(500\) | −18.9857 | −0.849065 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.3935i | 1.26726i | ||||||||
\(503\) | 3.79387 | 0.169160 | 0.0845801 | − | 0.996417i | \(-0.473045\pi\) | ||||
0.0845801 | + | 0.996417i | \(0.473045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.09303 | −0.315636 | ||||||||
\(506\) | − 8.70901i | − 0.387163i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.04348 | 0.268136 | ||||||||
\(509\) | −20.8868 | −0.925793 | −0.462896 | − | 0.886412i | \(-0.653190\pi\) | ||||
−0.462896 | + | 0.886412i | \(0.653190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 25.9598i | − 1.14727i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 32.4673i | − 1.43207i | ||||||||
\(515\) | 14.4304i | 0.635880i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 4.64291i | − 0.204195i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.6382 | −0.466514 | ||||||||
\(521\) | 31.1967 | 1.36675 | 0.683377 | − | 0.730066i | \(-0.260511\pi\) | ||||
0.683377 | + | 0.730066i | \(0.260511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.6393i | 1.29604i | 0.761624 | + | 0.648019i | \(0.224402\pi\) | ||||
−0.761624 | + | 0.648019i | \(0.775598\pi\) | |||||||
\(524\) | −27.0414 | −1.18131 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.0550 | −0.830838 | ||||||||
\(527\) | − 30.5018i | − 1.32868i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.55948 | 0.415630 | ||||||||
\(530\) | −8.49574 | −0.369031 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.8126i | 0.771548i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.1367i | 1.21646i | ||||||||
\(536\) | 9.17709i | 0.396390i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 42.6361i | 1.83817i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.3937 | 1.52170 | 0.760848 | − | 0.648930i | \(-0.224783\pi\) | ||||
0.760848 | + | 0.648930i | \(0.224783\pi\) | |||||||
\(542\) | −18.2389 | −0.783428 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 51.2390i | 2.19685i | ||||||||
\(545\) | −8.81571 | −0.377624 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4407 | 0.831223 | 0.415611 | − | 0.909542i | \(-0.363568\pi\) | ||||
0.415611 | + | 0.909542i | \(0.363568\pi\) | |||||||
\(548\) | 8.33399i | 0.356010i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.31071 | −0.141169 | ||||||||
\(551\) | −50.2385 | −2.14023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.06790i | 0.385258i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.2842i | 0.605783i | ||||||||
\(557\) | − 38.6477i | − 1.63756i | −0.574110 | − | 0.818779i | \(-0.694652\pi\) | ||||
0.574110 | − | 0.818779i | \(-0.305348\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6756i | 0.620713i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.90488 | 0.164718 | ||||||||
\(563\) | 27.0656 | 1.14068 | 0.570340 | − | 0.821409i | \(-0.306812\pi\) | ||||
0.570340 | + | 0.821409i | \(0.306812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.174523i | 0.00734223i | ||||||||
\(566\) | 2.74905 | 0.115551 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.11117 | −0.298378 | ||||||||
\(569\) | − 29.4673i | − 1.23533i | −0.786440 | − | 0.617666i | \(-0.788078\pi\) | ||||
0.786440 | − | 0.617666i | \(-0.211922\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.9378 | −1.33655 | −0.668277 | − | 0.743913i | \(-0.732968\pi\) | ||||
−0.668277 | + | 0.743913i | \(0.732968\pi\) | |||||||
\(572\) | 13.3819 | 0.559527 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.10938i | 0.213076i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.5345i | 1.93726i | 0.248516 | + | 0.968628i | \(0.420057\pi\) | ||||
−0.248516 | + | 0.968628i | \(0.579943\pi\) | |||||||
\(578\) | − 63.7358i | − 2.65106i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 20.6447i | − 0.857225i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.98217 | −0.123509 | ||||||||
\(584\) | 7.58191 | 0.313741 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 45.8094i | 1.89237i | ||||||||
\(587\) | 16.1578 | 0.666903 | 0.333451 | − | 0.942767i | \(-0.391787\pi\) | ||||
0.333451 | + | 0.942767i | \(0.391787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.9355 | −1.27468 | ||||||||
\(590\) | − 17.7269i | − 0.729807i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 44.4755 | 1.82793 | ||||||||
\(593\) | 9.71629 | 0.399000 | 0.199500 | − | 0.979898i | \(-0.436068\pi\) | ||||
0.199500 | + | 0.979898i | \(0.436068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.3869i | 0.712195i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 47.0673i | − 1.92473i | ||||||||
\(599\) | 20.8405i | 0.851518i | 0.904837 | + | 0.425759i | \(0.139993\pi\) | ||||
−0.904837 | + | 0.425759i | \(0.860007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 41.9456i | − 1.71100i | −0.517805 | − | 0.855499i | \(-0.673251\pi\) | ||||
0.517805 | − | 0.855499i | \(-0.326749\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.2916 | 0.581517 | ||||||||
\(605\) | −17.8822 | −0.727015 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.1864i | 0.981696i | 0.871245 | + | 0.490848i | \(0.163313\pi\) | ||||
−0.871245 | + | 0.490848i | \(0.836687\pi\) | |||||||
\(608\) | 51.9676 | 2.10756 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.4007 | −1.14991 | ||||||||
\(611\) | − 25.0923i | − 1.01513i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.6461 | 1.43973 | 0.719867 | − | 0.694112i | \(-0.244203\pi\) | ||||
0.719867 | + | 0.694112i | \(0.244203\pi\) | |||||||
\(614\) | −0.802770 | −0.0323972 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.4560i | 0.622234i | 0.950372 | + | 0.311117i | \(0.100703\pi\) | ||||
−0.950372 | + | 0.311117i | \(0.899297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.14653i | 0.0862763i | 0.999069 | + | 0.0431382i | \(0.0137356\pi\) | ||||
−0.999069 | + | 0.0431382i | \(0.986264\pi\) | |||||||
\(620\) | − 12.7125i | − 0.510545i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 16.1244i | − 0.646531i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.0893 | −0.643573 | ||||||||
\(626\) | −2.35546 | −0.0941433 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.8122i | 0.670881i | ||||||||
\(629\) | −67.6760 | −2.69842 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.5641 | 1.45559 | 0.727797 | − | 0.685793i | \(-0.240544\pi\) | ||||
0.727797 | + | 0.685793i | \(0.240544\pi\) | |||||||
\(632\) | 10.4086i | 0.414031i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.7238 | 1.18048 | ||||||||
\(635\) | 7.33968 | 0.291266 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 16.5156i | − 0.653859i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 12.2161i | − 0.482884i | ||||||||
\(641\) | − 12.9826i | − 0.512783i | −0.966573 | − | 0.256391i | \(-0.917466\pi\) | ||||
0.966573 | − | 0.256391i | \(-0.0825336\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 34.3758i | − 1.35565i | −0.735223 | − | 0.677825i | \(-0.762923\pi\) | ||||
0.735223 | − | 0.677825i | \(-0.237077\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −97.1905 | −3.82391 | ||||||||
\(647\) | 15.9679 | 0.627765 | 0.313882 | − | 0.949462i | \(-0.398370\pi\) | ||||
0.313882 | + | 0.949462i | \(0.398370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 6.22251i | − 0.244255i | ||||||||
\(650\) | −17.8925 | −0.701803 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.0144 | −0.548845 | ||||||||
\(653\) | − 26.8269i | − 1.04982i | −0.851159 | − | 0.524908i | \(-0.824100\pi\) | ||||
0.851159 | − | 0.524908i | \(-0.175900\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.8412 | −1.28321 | ||||||||
\(656\) | −12.2637 | −0.478817 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 48.5701i | − 1.89202i | −0.324135 | − | 0.946011i | \(-0.605073\pi\) | ||||
0.324135 | − | 0.946011i | \(-0.394927\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 8.33150i | − 0.324058i | −0.986786 | − | 0.162029i | \(-0.948196\pi\) | ||||
0.986786 | − | 0.162029i | \(-0.0518038\pi\) | |||||||
\(662\) | 10.4672i | 0.406821i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.8259i | 0.497743i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.4883 | −0.986912 | ||||||||
\(668\) | 19.3093 | 0.747100 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 39.9407i | − 1.54304i | ||||||||
\(671\) | −9.96922 | −0.384857 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.9372 | −1.88639 | −0.943195 | − | 0.332240i | \(-0.892196\pi\) | ||||
−0.943195 | + | 0.332240i | \(0.892196\pi\) | |||||||
\(674\) | − 42.3694i | − 1.63201i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 51.9942 | 1.99978 | ||||||||
\(677\) | 14.5031 | 0.557400 | 0.278700 | − | 0.960378i | \(-0.410096\pi\) | ||||
0.278700 | + | 0.960378i | \(0.410096\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11.1449i | 0.427386i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 10.1699i | − 0.389424i | ||||||||
\(683\) | − 40.1584i | − 1.53662i | −0.640078 | − | 0.768310i | \(-0.721098\pi\) | ||||
0.640078 | − | 0.768310i | \(-0.278902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1214i | 0.386720i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.1040 | −0.385209 | ||||||||
\(689\) | −16.1170 | −0.614008 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.14628i | 0.0816483i | 0.999166 | + | 0.0408242i | \(0.0129983\pi\) | ||||
−0.999166 | + | 0.0408242i | \(0.987002\pi\) | |||||||
\(692\) | 22.6338 | 0.860406 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.9946 | 0.569188 | ||||||||
\(695\) | 17.3478i | 0.658039i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.6610 | 0.706837 | ||||||||
\(698\) | 30.8468 | 1.16757 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.4532i | 1.49013i | 0.666993 | + | 0.745064i | \(0.267581\pi\) | ||||
−0.666993 | + | 0.745064i | \(0.732419\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 68.6384i | 2.58875i | ||||||||
\(704\) | 5.29980i | 0.199744i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 49.4702i | − 1.86184i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.7476 | 0.553857 | 0.276928 | − | 0.960891i | \(-0.410684\pi\) | ||||
0.276928 | + | 0.960891i | \(0.410684\pi\) | |||||||
\(710\) | 30.9494 | 1.16151 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.30025i | 0.0487289i | ||||||||
\(713\) | −15.6950 | −0.587783 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.2521 | 0.607793 | ||||||||
\(716\) | 11.9299i | 0.445842i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36.5506 | −1.36406 | ||||||||
\(719\) | 31.8119 | 1.18638 | 0.593191 | − | 0.805062i | \(-0.297868\pi\) | ||||
0.593191 | + | 0.805062i | \(0.297868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 62.7050i | 2.33364i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 33.6649i | − 1.25114i | ||||||||
\(725\) | 9.68932i | 0.359852i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.1204i | 1.71051i | 0.518208 | + | 0.855255i | \(0.326599\pi\) | ||||
−0.518208 | + | 0.855255i | \(0.673401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32.9981 | −1.22131 | ||||||||
\(731\) | 15.3746 | 0.568652 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.6480i | 0.541035i | 0.962715 | + | 0.270517i | \(0.0871947\pi\) | ||||
−0.962715 | + | 0.270517i | \(0.912805\pi\) | |||||||
\(734\) | 9.37970 | 0.346211 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.3656 | 0.971847 | ||||||||
\(737\) | − 14.0200i | − 0.516433i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.6707 | 0.502885 | 0.251442 | − | 0.967872i | \(-0.419095\pi\) | ||||
0.251442 | + | 0.967872i | \(0.419095\pi\) | |||||||
\(740\) | −28.2058 | −1.03687 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.9213i | 1.31782i | 0.752220 | + | 0.658912i | \(0.228983\pi\) | ||||
−0.752220 | + | 0.658912i | \(0.771017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.1160i | 0.773630i | ||||||||
\(746\) | − 20.3085i | − 0.743548i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 14.0193i | − 0.512598i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.1079 | −1.50005 | −0.750024 | − | 0.661411i | \(-0.769958\pi\) | ||||
−0.750024 | + | 0.661411i | \(0.769958\pi\) | |||||||
\(752\) | 17.2757 | 0.629979 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 89.2575i | − 3.25057i | ||||||||
\(755\) | 17.3568 | 0.631680 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.7714 | 1.00937 | 0.504684 | − | 0.863304i | \(-0.331609\pi\) | ||||
0.504684 | + | 0.863304i | \(0.331609\pi\) | |||||||
\(758\) | 31.9223i | 1.15947i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.3033 | 0.410015 | ||||||||
\(761\) | 13.6834 | 0.496021 | 0.248011 | − | 0.968757i | \(-0.420223\pi\) | ||||
0.248011 | + | 0.968757i | \(0.420223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 28.8622i | − 1.04420i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 41.5676i | 1.50190i | ||||||||
\(767\) | − 33.6292i | − 1.21428i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 9.59976i | − 0.346176i | −0.984906 | − | 0.173088i | \(-0.944625\pi\) | ||||
0.984906 | − | 0.173088i | \(-0.0553745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.761870 | 0.0274203 | ||||||||
\(773\) | −33.2003 | −1.19413 | −0.597066 | − | 0.802192i | \(-0.703667\pi\) | ||||
−0.597066 | + | 0.802192i | \(0.703667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.96642i | 0.214320i | ||||||||
\(776\) | −1.12114 | −0.0402466 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −54.7607 | −1.96326 | ||||||||
\(779\) | − 18.9264i | − 0.678108i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8638 | 0.388739 | ||||||||
\(782\) | −49.3092 | −1.76329 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.4181i | 0.728753i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.9657i | 1.42462i | 0.701864 | + | 0.712311i | \(0.252352\pi\) | ||||
−0.701864 | + | 0.712311i | \(0.747648\pi\) | |||||||
\(788\) | − 16.6686i | − 0.593793i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 45.3003i | − 1.61171i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.8780 | −1.91326 | ||||||||
\(794\) | 28.2904 | 1.00399 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 11.9641i | − 0.424057i | ||||||||
\(797\) | −3.14911 | −0.111547 | −0.0557736 | − | 0.998443i | \(-0.517763\pi\) | ||||
−0.0557736 | + | 0.998443i | \(0.517763\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.2875 | −0.929985 | ||||||||
\(800\) | − 10.0228i | − 0.354359i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.0386 | −0.389788 | ||||||||
\(803\) | −11.5830 | −0.408755 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 54.9623i | − 1.93597i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 3.07659i | − 0.108234i | ||||||||
\(809\) | − 16.1113i | − 0.566443i | −0.959055 | − | 0.283221i | \(-0.908597\pi\) | ||||
0.959055 | − | 0.283221i | \(-0.0914031\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.4068i | 0.857038i | 0.903533 | + | 0.428519i | \(0.140965\pi\) | ||||
−0.903533 | + | 0.428519i | \(0.859035\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.5644 | −0.790883 | ||||||||
\(815\) | −17.0201 | −0.596190 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 15.5933i | − 0.545539i | ||||||||
\(818\) | −32.5198 | −1.13703 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.77749 | 0.271602 | ||||||||
\(821\) | − 24.0153i | − 0.838141i | −0.907954 | − | 0.419070i | \(-0.862356\pi\) | ||||
0.907954 | − | 0.419070i | \(-0.137644\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.45736 | −0.155374 | −0.0776869 | − | 0.996978i | \(-0.524753\pi\) | ||||
−0.0776869 | + | 0.996978i | \(0.524753\pi\) | |||||||
\(824\) | −6.25916 | −0.218048 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.2167i | 1.71143i | 0.517445 | + | 0.855716i | \(0.326883\pi\) | ||||
−0.517445 | + | 0.855716i | \(0.673117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 41.8552i | − 1.45369i | −0.686800 | − | 0.726846i | \(-0.740985\pi\) | ||||
0.686800 | − | 0.726846i | \(-0.259015\pi\) | |||||||
\(830\) | − 55.8213i | − 1.93759i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.6424i | 0.992998i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.4507 | 0.811547 | ||||||||
\(836\) | −14.2187 | −0.491764 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 20.8870i | − 0.721529i | ||||||||
\(839\) | 30.4461 | 1.05112 | 0.525559 | − | 0.850757i | \(-0.323856\pi\) | ||||
0.525559 | + | 0.850757i | \(0.323856\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.3355 | −0.666742 | ||||||||
\(842\) | 36.5270i | 1.25880i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 33.4869 | 1.15267 | ||||||||
\(845\) | 63.1458 | 2.17228 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 11.0963i | − 0.381048i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.7448i | 0.642940i | ||||||||
\(851\) | 34.8234i | 1.19373i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 12.7434i | − 0.436324i | −0.975913 | − | 0.218162i | \(-0.929994\pi\) | ||||
0.975913 | − | 0.218162i | \(-0.0700062\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.2042 | −0.417132 | ||||||||
\(857\) | 44.0076 | 1.50327 | 0.751635 | − | 0.659579i | \(-0.229265\pi\) | ||||
0.751635 | + | 0.659579i | \(0.229265\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.8363i | 1.52979i | 0.644153 | + | 0.764897i | \(0.277210\pi\) | ||||
−0.644153 | + | 0.764897i | \(0.722790\pi\) | |||||||
\(860\) | 6.40780 | 0.218504 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.2898 | −0.759194 | ||||||||
\(863\) | − 32.0552i | − 1.09117i | −0.838055 | − | 0.545586i | \(-0.816307\pi\) | ||||
0.838055 | − | 0.545586i | \(-0.183693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.4882 | 0.934627 | ||||||||
\(866\) | −60.7573 | −2.06462 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 15.9013i | − 0.539415i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 75.7701i | − 2.56737i | ||||||||
\(872\) | − 3.82380i | − 0.129490i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 50.0104i | 1.69163i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.52107 | −0.321504 | −0.160752 | − | 0.986995i | \(-0.551392\pi\) | ||||
−0.160752 | + | 0.986995i | \(0.551392\pi\) | |||||||
\(878\) | −45.8194 | −1.54633 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11.1893i | 0.377191i | ||||||||
\(881\) | −4.94353 | −0.166552 | −0.0832759 | − | 0.996527i | \(-0.526538\pi\) | ||||
−0.0832759 | + | 0.996527i | \(0.526538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.2867 | 1.59132 | 0.795662 | − | 0.605741i | \(-0.207123\pi\) | ||||
0.795662 | + | 0.605741i | \(0.207123\pi\) | |||||||
\(884\) | − 75.7666i | − 2.54831i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.28318 | −0.0767049 | ||||||||
\(887\) | −50.5894 | −1.69863 | −0.849314 | − | 0.527889i | \(-0.822984\pi\) | ||||
−0.849314 | + | 0.527889i | \(0.822984\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 5.65897i | − 0.189689i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 9.64586i | − 0.322967i | ||||||||
\(893\) | 26.6613i | 0.892186i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.4886i | 0.484301i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.0374 | 0.702028 | ||||||||
\(899\) | −29.7637 | −0.992675 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.8846i | 0.562509i | ||||||||
\(902\) | 6.22192 | 0.207167 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.0756990 | −0.00251771 | ||||||||
\(905\) | − 40.8852i | − 1.35907i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.9072 | 0.860236 | 0.430118 | − | 0.902773i | \(-0.358472\pi\) | ||||
0.430118 | + | 0.902773i | \(0.358472\pi\) | |||||||
\(908\) | 45.3113 | 1.50371 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1556i | 0.369601i | 0.982776 | + | 0.184801i | \(0.0591639\pi\) | ||||
−0.982776 | + | 0.184801i | \(0.940836\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 19.5944i | − 0.648480i | ||||||||
\(914\) | 9.48388i | 0.313699i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.77317i | 0.322915i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.87785 | −0.0949314 | −0.0474657 | − | 0.998873i | \(-0.515114\pi\) | ||||
−0.0474657 | + | 0.998873i | \(0.515114\pi\) | |||||||
\(920\) | 5.73471 | 0.189068 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 6.37891i | − 0.210078i | ||||||||
\(923\) | 58.7129 | 1.93256 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.2380 | 0.435264 | ||||||||
\(926\) | 20.2240i | 0.664602i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 49.9991 | 1.64130 | ||||||||
\(929\) | 30.7374 | 1.00846 | 0.504230 | − | 0.863569i | \(-0.331776\pi\) | ||||
0.504230 | + | 0.863569i | \(0.331776\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.58912i | 0.248590i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.0030i | 0.490914i | ||||||||
\(935\) | − 17.0262i | − 0.556815i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.5614i | 1.35775i | 0.734254 | + | 0.678875i | \(0.237532\pi\) | ||||
−0.734254 | + | 0.678875i | \(0.762468\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.9560 | −0.357346 | ||||||||
\(941\) | −5.43859 | −0.177293 | −0.0886464 | − | 0.996063i | \(-0.528254\pi\) | ||||
−0.0886464 | + | 0.996063i | \(0.528254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 9.60222i | − 0.312691i | ||||||||
\(944\) | 23.1532 | 0.753572 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.12619 | 0.166667 | ||||||||
\(947\) | − 10.1552i | − 0.330000i | −0.986294 | − | 0.165000i | \(-0.947238\pi\) | ||||
0.986294 | − | 0.165000i | \(-0.0527624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −62.5995 | −2.03207 | ||||||||
\(950\) | 19.0113 | 0.616809 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.875628i | 0.0283644i | 0.999899 | + | 0.0141822i | \(0.00451448\pi\) | ||||
−0.999899 | + | 0.0141822i | \(0.995486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 35.0525i | − 1.13427i | ||||||||
\(956\) | 23.3621i | 0.755583i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 44.1022i | 1.42488i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.6723 | 0.408784 | ||||||||
\(962\) | −121.948 | −3.93176 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.1686i | 0.520755i | ||||||||
\(965\) | 0.925274 | 0.0297856 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 59.5474 | 1.91492 | 0.957458 | − | 0.288573i | \(-0.0931809\pi\) | ||||
0.957458 | + | 0.288573i | \(0.0931809\pi\) | |||||||
\(968\) | − 7.75637i | − 0.249299i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.87944 | 0.156669 | ||||||||
\(971\) | 55.6091 | 1.78458 | 0.892291 | − | 0.451460i | \(-0.149097\pi\) | ||||
0.892291 | + | 0.451460i | \(0.149097\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 44.0969i | − 1.41296i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 37.0942i | − 1.18736i | ||||||||
\(977\) | − 46.6341i | − 1.49196i | −0.665970 | − | 0.745979i | \(-0.731982\pi\) | ||||
0.665970 | − | 0.745979i | \(-0.268018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.98641i | − 0.0634860i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23.3743 | −0.745905 | ||||||||
\(983\) | 12.6584 | 0.403740 | 0.201870 | − | 0.979412i | \(-0.435298\pi\) | ||||
0.201870 | + | 0.979412i | \(0.435298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 20.2436i | − 0.645015i | ||||||||
\(986\) | −93.5089 | −2.97793 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −76.8440 | −2.44473 | ||||||||
\(989\) | − 7.91118i | − 0.251561i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.3516 | −0.392360 | −0.196180 | − | 0.980568i | \(-0.562854\pi\) | ||||
−0.196180 | + | 0.980568i | \(0.562854\pi\) | |||||||
\(992\) | 30.7881 | 0.977523 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 14.5302i | − 0.460637i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 8.72257i | − 0.276247i | −0.990415 | − | 0.138123i | \(-0.955893\pi\) | ||||
0.990415 | − | 0.138123i | \(-0.0441070\pi\) | |||||||
\(998\) | − 9.08910i | − 0.287710i | ||||||||
\(999\) | 0 | 0 |
(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 | 3087.2.c.c.3086.13 | yes | 24 | |
3.2 | odd | 2 | inner | 3087.2.c.c.3086.12 | yes | 24 | |
7.6 | odd | 2 | inner | 3087.2.c.c.3086.11 | ✓ | 24 | |
21.20 | even | 2 | inner | 3087.2.c.c.3086.14 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3087.2.c.c.3086.11 | ✓ | 24 | 7.6 | odd | 2 | inner | |
3087.2.c.c.3086.12 | yes | 24 | 3.2 | odd | 2 | inner | |
3087.2.c.c.3086.13 | yes | 24 | 1.1 | even | 1 | trivial | |
3087.2.c.c.3086.14 | yes | 24 | 21.20 | even | 2 | inner |