Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | ||||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.414214 | 0.156558 | 0.0782790 | − | 0.996931i | \(-0.475058\pi\) | ||||
0.0782790 | + | 0.996931i | \(0.475058\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.82843 | 1.06181 | 0.530907 | − | 0.847430i | \(-0.321851\pi\) | ||||
0.530907 | + | 0.847430i | \(0.321851\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.171573 | −0.0374403 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.24264 | −0.676137 | −0.338069 | − | 0.941121i | \(-0.609774\pi\) | ||||
−0.338069 | + | 0.941121i | \(0.609774\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.82843 | −0.339530 | −0.169765 | − | 0.985485i | \(-0.554301\pi\) | ||||
−0.169765 | + | 0.985485i | \(0.554301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.585786 | −0.105210 | −0.0526052 | − | 0.998615i | \(-0.516752\pi\) | ||||
−0.0526052 | + | 0.998615i | \(0.516752\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.585786 | −0.101972 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8284 | −1.78018 | −0.890091 | − | 0.455782i | \(-0.849360\pi\) | ||||
−0.890091 | + | 0.455782i | \(0.849360\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.58579 | −0.253929 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.07107 | 1.10432 | 0.552158 | − | 0.833740i | \(-0.313805\pi\) | ||||
0.552158 | + | 0.833740i | \(0.313805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24264 | −0.951994 | −0.475997 | − | 0.879447i | \(-0.657913\pi\) | ||||
−0.475997 | + | 0.879447i | \(0.657913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82843 | −0.975490 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.414214 | 0.0580015 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.82843 | −0.525875 | −0.262937 | − | 0.964813i | \(-0.584691\pi\) | ||||
−0.262937 | + | 0.964813i | \(0.584691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.414214 | −0.0548639 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.5858 | −1.50834 | −0.754170 | − | 0.656679i | \(-0.771961\pi\) | ||||
−0.754170 | + | 0.656679i | \(0.771961\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.585786 | 0.0750023 | 0.0375011 | − | 0.999297i | \(-0.488060\pi\) | ||||
0.0375011 | + | 0.999297i | \(0.488060\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.17157 | −0.147604 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.07107 | 0.986038 | 0.493019 | − | 0.870019i | \(-0.335893\pi\) | ||||
0.493019 | + | 0.870019i | \(0.335893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.34315 | 0.161696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0711 | 1.31389 | 0.656947 | − | 0.753937i | \(-0.271848\pi\) | ||||
0.656947 | + | 0.753937i | \(0.271848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.17157 | −0.956410 | −0.478205 | − | 0.878248i | \(-0.658712\pi\) | ||||
−0.478205 | + | 0.878248i | \(0.658712\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.585786 | 0.0667566 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.82843 | −0.543240 | −0.271620 | − | 0.962405i | \(-0.587559\pi\) | ||||
−0.271620 | + | 0.962405i | \(0.587559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.4853 | 1.58997 | 0.794983 | − | 0.606632i | \(-0.207480\pi\) | ||||
0.794983 | + | 0.606632i | \(0.207480\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.757359 | 0.0811974 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2426 | −1.29772 | −0.648859 | − | 0.760909i | \(-0.724753\pi\) | ||||
−0.648859 | + | 0.760909i | \(0.724753\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.58579 | 0.166236 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.242641 | 0.0251607 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.65685 | 0.371297 | 0.185649 | − | 0.982616i | \(-0.440561\pi\) | ||||
0.185649 | + | 0.982616i | \(0.440561\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.89949 | −0.388014 | −0.194007 | − | 0.981000i | \(-0.562148\pi\) | ||||
−0.194007 | + | 0.981000i | \(0.562148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.89949 | 0.975426 | 0.487713 | − | 0.873004i | \(-0.337831\pi\) | ||||
0.487713 | + | 0.873004i | \(0.337831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.414214 | 0.0400435 | 0.0200218 | − | 0.999800i | \(-0.493626\pi\) | ||||
0.0200218 | + | 0.999800i | \(0.493626\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.48528 | 0.425724 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.07107 | −0.100758 | −0.0503788 | − | 0.998730i | \(-0.516043\pi\) | ||||
−0.0503788 | + | 0.998730i | \(0.516043\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.8284 | −1.00109 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.414214 | −0.0379709 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.92893 | −0.264093 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.8284 | 1.49328 | 0.746641 | − | 0.665228i | \(-0.231665\pi\) | ||||
0.746641 | + | 0.665228i | \(0.231665\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.58579 | 0.227666 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3431 | −0.903685 | −0.451842 | − | 0.892098i | \(-0.649233\pi\) | ||||
−0.451842 | + | 0.892098i | \(0.649233\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.414214 | 0.0359169 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.31371 | 0.539417 | 0.269708 | − | 0.962942i | \(-0.413073\pi\) | ||||
0.269708 | + | 0.962942i | \(0.413073\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.31371 | −0.279065 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.41421 | 0.452759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.82843 | 0.233285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.34315 | −0.519651 | −0.259825 | − | 0.965656i | \(-0.583665\pi\) | ||||
−0.259825 | + | 0.965656i | \(0.583665\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8284 | −1.36948 | −0.684739 | − | 0.728788i | \(-0.740084\pi\) | ||||
−0.684739 | + | 0.728788i | \(0.740084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.82843 | 0.228665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6569 | −0.930318 | −0.465159 | − | 0.885227i | \(-0.654003\pi\) | ||||
−0.465159 | + | 0.885227i | \(0.654003\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.58579 | 0.125761 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.34315 | −0.105855 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0711 | 1.33711 | 0.668555 | − | 0.743663i | \(-0.266913\pi\) | ||||
0.668555 | + | 0.743663i | \(0.266913\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.2132 | −1.48676 | −0.743381 | − | 0.668868i | \(-0.766779\pi\) | ||||
−0.743381 | + | 0.668868i | \(0.766779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.65685 | 0.127450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.1716 | −1.00142 | −0.500708 | − | 0.865616i | \(-0.666927\pi\) | ||||
−0.500708 | + | 0.865616i | \(0.666927\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.79899 | 0.360714 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.9706 | −0.819978 | −0.409989 | − | 0.912090i | \(-0.634468\pi\) | ||||
−0.409989 | + | 0.912090i | \(0.634468\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4853 | −1.22534 | −0.612671 | − | 0.790338i | \(-0.709905\pi\) | ||||
−0.612671 | + | 0.790338i | \(0.709905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.242641 | −0.0179365 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.41421 | −0.103418 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.75736 | 0.199516 | 0.0997578 | − | 0.995012i | \(-0.468193\pi\) | ||||
0.0997578 | + | 0.995012i | \(0.468193\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.65685 | 0.263226 | 0.131613 | − | 0.991301i | \(-0.457984\pi\) | ||||
0.131613 | + | 0.991301i | \(0.457984\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.72792 | 0.336850 | 0.168425 | − | 0.985714i | \(-0.446132\pi\) | ||||
0.168425 | + | 0.985714i | \(0.446132\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.92893 | −0.136738 | −0.0683692 | − | 0.997660i | \(-0.521780\pi\) | ||||
−0.0683692 | + | 0.997660i | \(0.521780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.34315 | −0.235807 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.757359 | −0.0531562 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.17157 | 0.637468 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.41421 | 0.0978232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.10051 | 0.351133 | 0.175567 | − | 0.984468i | \(-0.443824\pi\) | ||||
0.175567 | + | 0.984468i | \(0.443824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.58579 | −0.314213 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.242641 | −0.0164715 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.38478 | 0.228722 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.82843 | −0.257528 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.82843 | 0.591195 | 0.295598 | − | 0.955313i | \(-0.404481\pi\) | ||||
0.295598 | + | 0.955313i | \(0.404481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.75736 | −0.581246 | −0.290623 | − | 0.956838i | \(-0.593863\pi\) | ||||
−0.290623 | + | 0.956838i | \(0.593863\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.97056 | 0.460628 | 0.230314 | − | 0.973116i | \(-0.426025\pi\) | ||||
0.230314 | + | 0.973116i | \(0.426025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.242641 | −0.0159646 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.6569 | 0.894690 | 0.447345 | − | 0.894361i | \(-0.352370\pi\) | ||||
0.447345 | + | 0.894361i | \(0.352370\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000 | 0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.7279 | −1.79357 | −0.896785 | − | 0.442466i | \(-0.854104\pi\) | ||||
−0.896785 | + | 0.442466i | \(0.854104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.65685 | −0.364390 | −0.182195 | − | 0.983262i | \(-0.558320\pi\) | ||||
−0.182195 | + | 0.983262i | \(0.558320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.82843 | 0.243597 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.55635 | −0.224475 | −0.112237 | − | 0.993681i | \(-0.535802\pi\) | ||||
−0.112237 | + | 0.993681i | \(0.535802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.58579 | −0.288306 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.7279 | −1.79200 | −0.895999 | − | 0.444056i | \(-0.853539\pi\) | ||||
−0.895999 | + | 0.444056i | \(0.853539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.48528 | −0.278702 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.17157 | 0.320112 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.6569 | −0.965443 | −0.482721 | − | 0.875774i | \(-0.660352\pi\) | ||||
−0.482721 | + | 0.875774i | \(0.660352\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.07107 | 0.310344 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3848 | −0.934559 | −0.467279 | − | 0.884110i | \(-0.654766\pi\) | ||||
−0.467279 | + | 0.884110i | \(0.654766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.656854 | −0.0397546 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.31371 | 0.199101 | 0.0995507 | − | 0.995032i | \(-0.468259\pi\) | ||||
0.0995507 | + | 0.995032i | \(0.468259\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.65685 | 0.0991933 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.75736 | −0.224145 | −0.112073 | − | 0.993700i | \(-0.535749\pi\) | ||||
−0.112073 | + | 0.993700i | \(0.535749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.51472 | 0.565591 | 0.282796 | − | 0.959180i | \(-0.408738\pi\) | ||||
0.282796 | + | 0.959180i | \(0.408738\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.92893 | 0.172889 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.51472 | −0.0887944 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.7990 | −0.630884 | −0.315442 | − | 0.948945i | \(-0.602153\pi\) | ||||
−0.315442 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.41421 | 0.198113 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.4142 | −0.717933 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.58579 | −0.149042 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.61522 | 0.0927922 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.2843 | 1.84256 | 0.921280 | − | 0.388899i | \(-0.127145\pi\) | ||||
0.921280 | + | 0.388899i | \(0.127145\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.10051 | −0.233270 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2426 | −1.31797 | −0.658985 | − | 0.752156i | \(-0.729014\pi\) | ||||
−0.658985 | + | 0.752156i | \(0.729014\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.65685 | −0.376268 | −0.188134 | − | 0.982143i | \(-0.560244\pi\) | ||||
−0.188134 | + | 0.982143i | \(0.560244\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.79899 | −0.381869 | −0.190935 | − | 0.981603i | \(-0.561152\pi\) | ||||
−0.190935 | + | 0.981603i | \(0.561152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.58579 | −0.144776 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.171573 | −0.00957626 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00000 | −0.0556415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.07107 | 0.114530 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.31371 | 0.182691 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.3848 | −1.06548 | −0.532742 | − | 0.846278i | \(-0.678838\pi\) | ||||
−0.532742 | + | 0.846278i | \(0.678838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.6274 | 1.67837 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.7279 | −0.693334 | −0.346667 | − | 0.937988i | \(-0.612687\pi\) | ||||
−0.346667 | + | 0.937988i | \(0.612687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.443651 | 0.0240958 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.828427 | −0.0448618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.72792 | −0.309279 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.1716 | 0.814453 | 0.407226 | − | 0.913327i | \(-0.366496\pi\) | ||||
0.407226 | + | 0.913327i | \(0.366496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.6274 | 1.53239 | 0.766195 | − | 0.642608i | \(-0.222148\pi\) | ||||
0.766195 | + | 0.642608i | \(0.222148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.24264 | 0.493336 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.1127 | −1.92208 | −0.961042 | − | 0.276401i | \(-0.910858\pi\) | ||||
−0.961042 | + | 0.276401i | \(0.910858\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.171573 | 0.00908060 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.07107 | 0.320419 | 0.160209 | − | 0.987083i | \(-0.448783\pi\) | ||||
0.160209 | + | 0.987083i | \(0.448783\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.72792 | 0.195665 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.4558 | −1.74638 | −0.873190 | − | 0.487379i | \(-0.837953\pi\) | ||||
−0.873190 | + | 0.487379i | \(0.837953\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.0000 | −1.04116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.58579 | −0.0823299 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.9706 | 1.44826 | 0.724130 | − | 0.689663i | \(-0.242241\pi\) | ||||
0.724130 | + | 0.689663i | \(0.242241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.00000 | −0.360518 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.38478 | 0.173864 | 0.0869321 | − | 0.996214i | \(-0.472294\pi\) | ||||
0.0869321 | + | 0.996214i | \(0.472294\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.97056 | −0.357113 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.7279 | −1.05915 | −0.529574 | − | 0.848264i | \(-0.677648\pi\) | ||||
−0.529574 | + | 0.848264i | \(0.677648\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.6569 | 0.897548 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.89949 | 0.400520 | 0.200260 | − | 0.979743i | \(-0.435821\pi\) | ||||
0.200260 | + | 0.979743i | \(0.435821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.24264 | 0.163987 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.28427 | 0.216113 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.6274 | −1.13564 | −0.567819 | − | 0.823154i | \(-0.692213\pi\) | ||||
−0.567819 | + | 0.823154i | \(0.692213\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.171573 | −0.00858939 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.10051 | −0.304645 | −0.152322 | − | 0.988331i | \(-0.548675\pi\) | ||||
−0.152322 | + | 0.988331i | \(0.548675\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.24264 | −0.111714 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.3137 | −0.759072 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.58579 | 0.127859 | 0.0639295 | − | 0.997954i | \(-0.479637\pi\) | ||||
0.0639295 | + | 0.997954i | \(0.479637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.61522 | −0.128999 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.79899 | −0.236143 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.65685 | −0.0811365 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.2132 | 1.32945 | 0.664726 | − | 0.747087i | \(-0.268548\pi\) | ||||
0.664726 | + | 0.747087i | \(0.268548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1421 | 0.640508 | 0.320254 | − | 0.947332i | \(-0.396232\pi\) | ||||
0.320254 | + | 0.947332i | \(0.396232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.6274 | −1.10018 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.242641 | 0.0117422 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.24264 | −0.108276 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.41421 | 0.260793 | 0.130397 | − | 0.991462i | \(-0.458375\pi\) | ||||
0.130397 | + | 0.991462i | \(0.458375\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.07107 | −0.243700 | −0.121850 | − | 0.992549i | \(-0.538883\pi\) | ||||
−0.121850 | + | 0.992549i | \(0.538883\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.24264 | −0.155117 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.7279 | 1.46656 | 0.733282 | − | 0.679925i | \(-0.237988\pi\) | ||||
0.733282 | + | 0.679925i | \(0.237988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.3137 | 0.919700 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.5563 | 0.739104 | 0.369552 | − | 0.929210i | \(-0.379511\pi\) | ||||
0.369552 | + | 0.929210i | \(0.379511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.62742 | 0.124273 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.9411 | −1.69617 | −0.848083 | − | 0.529863i | \(-0.822243\pi\) | ||||
−0.848083 | + | 0.529863i | \(0.822243\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0000 | 0.470882 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.97056 | 0.327506 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.3137 | −0.763123 | −0.381562 | − | 0.924343i | \(-0.624614\pi\) | ||||
−0.381562 | + | 0.924343i | \(0.624614\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.41421 | −0.112686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.27208 | −0.338694 | −0.169347 | − | 0.985556i | \(-0.554166\pi\) | ||||
−0.169347 | + | 0.985556i | \(0.554166\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1421 | 1.02903 | 0.514516 | − | 0.857481i | \(-0.327972\pi\) | ||||
0.514516 | + | 0.857481i | \(0.327972\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.8995 | −1.01339 | −0.506694 | − | 0.862126i | \(-0.669133\pi\) | ||||
−0.506694 | + | 0.862126i | \(0.669133\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.34315 | 0.154372 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.82843 | 0.222482 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.82843 | −0.405932 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8284 | 0.495800 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.4558 | −1.52864 | −0.764318 | − | 0.644839i | \(-0.776924\pi\) | ||||
−0.764318 | + | 0.644839i | \(0.776924\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.4558 | −1.89022 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.556349 | 0.0253148 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.17157 | 0.324975 | 0.162487 | − | 0.986711i | \(-0.448048\pi\) | ||||
0.162487 | + | 0.986711i | \(0.448048\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.07107 | −0.319765 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.7574 | −0.801378 | −0.400689 | − | 0.916214i | \(-0.631229\pi\) | ||||
−0.400689 | + | 0.916214i | \(0.631229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.82843 | 0.0823482 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.58579 | 0.205701 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.9289 | −0.847375 | −0.423688 | − | 0.905808i | \(-0.639265\pi\) | ||||
−0.423688 | + | 0.905808i | \(0.639265\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.95837 | 0.355554 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.8995 | 1.46692 | 0.733458 | − | 0.679735i | \(-0.237905\pi\) | ||||
0.733458 | + | 0.679735i | \(0.237905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.686292 | −0.0304793 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.65685 | 0.428033 | 0.214016 | − | 0.976830i | \(-0.431345\pi\) | ||||
0.214016 | + | 0.976830i | \(0.431345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.38478 | −0.149734 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.41421 | 0.106590 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3137 | 0.497576 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.45584 | 0.239485 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.0000 | −1.22670 | −0.613351 | − | 0.789810i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.2132 | −0.883862 | −0.441931 | − | 0.897049i | \(-0.645706\pi\) | ||||
−0.441931 | + | 0.897049i | \(0.645706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.585786 | 0.0255173 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4853 | −0.542838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.7696 | 1.42208 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.0711 | 1.17258 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.54416 | 0.196095 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.65685 | −0.415950 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0416 | 1.29159 | 0.645795 | − | 0.763511i | \(-0.276526\pi\) | ||||
0.645795 | + | 0.763511i | \(0.276526\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.82843 | 0.293036 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.9411 | −1.02365 | −0.511824 | − | 0.859090i | \(-0.671030\pi\) | ||||
−0.511824 | + | 0.859090i | \(0.671030\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.65685 | −0.0707128 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.82843 | −0.0778936 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | −0.0850487 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.3137 | 1.83526 | 0.917630 | − | 0.397435i | \(-0.130100\pi\) | ||||
0.917630 | + | 0.397435i | \(0.130100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.8995 | −1.01084 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.585786 | 0.0247319 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.9706 | −1.89528 | −0.947642 | − | 0.319336i | \(-0.896540\pi\) | ||||
−0.947642 | + | 0.319336i | \(0.896540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.10051 | 0.130209 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.97056 | −0.376066 | −0.188033 | − | 0.982163i | \(-0.560211\pi\) | ||||
−0.188033 | + | 0.982163i | \(0.560211\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −47.6985 | −1.99612 | −0.998060 | − | 0.0622637i | \(-0.980168\pi\) | ||||
−0.998060 | + | 0.0622637i | \(0.980168\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.14214 | −0.0477134 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.0000 | 1.04076 | 0.520382 | − | 0.853934i | \(-0.325790\pi\) | ||||
0.520382 | + | 0.853934i | \(0.325790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.51472 | −0.0629496 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | 0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.41421 | −0.224234 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.3848 | −1.33666 | −0.668331 | − | 0.743864i | \(-0.732991\pi\) | ||||
−0.668331 | + | 0.743864i | \(0.732991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.585786 | −0.0241369 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.95837 | −0.0805566 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.0000 | 1.72473 | 0.862367 | − | 0.506284i | \(-0.168981\pi\) | ||||
0.862367 | + | 0.506284i | \(0.168981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.798990 | 0.0327005 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.5563 | 1.37108 | 0.685538 | − | 0.728037i | \(-0.259567\pi\) | ||||
0.685538 | + | 0.728037i | \(0.259567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.443651 | 0.0180969 | 0.00904845 | − | 0.999959i | \(-0.497120\pi\) | ||||
0.00904845 | + | 0.999959i | \(0.497120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.8284 | −0.929645 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.4853 | 1.23736 | 0.618680 | − | 0.785643i | \(-0.287668\pi\) | ||||
0.618680 | + | 0.785643i | \(0.287668\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.313708 | 0.0127121 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.6274 | 1.23905 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.72792 | 0.110180 | 0.0550899 | − | 0.998481i | \(-0.482455\pi\) | ||||
0.0550899 | + | 0.998481i | \(0.482455\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.7990 | 1.28018 | 0.640090 | − | 0.768300i | \(-0.278897\pi\) | ||||
0.640090 | + | 0.768300i | \(0.278897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.38478 | −0.256626 | −0.128313 | − | 0.991734i | \(-0.540956\pi\) | ||||
−0.128313 | + | 0.991734i | \(0.540956\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.82843 | −0.314144 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.07107 | −0.203168 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.585786 | −0.0233941 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.8284 | 0.431758 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.02944 | 0.200219 | 0.100109 | − | 0.994976i | \(-0.468081\pi\) | ||||
0.100109 | + | 0.994976i | \(0.468081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.11270 | −0.0839722 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.1421 | −1.03579 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −31.3137 | −1.23875 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.21320 | 0.126914 | 0.0634570 | − | 0.997985i | \(-0.479787\pi\) | ||||
0.0634570 | + | 0.997985i | \(0.479787\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.8284 | 1.45237 | 0.726186 | − | 0.687499i | \(-0.241291\pi\) | ||||
0.726186 | + | 0.687499i | \(0.241291\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.07107 | −0.0814221 | −0.0407110 | − | 0.999171i | \(-0.512962\pi\) | ||||
−0.0407110 | + | 0.999171i | \(0.512962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.3848 | −0.643159 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.100505 | 0.00393910 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.2843 | −0.950317 | −0.475158 | − | 0.879900i | \(-0.657609\pi\) | ||||
−0.475158 | + | 0.879900i | \(0.657609\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.1127 | 0.901712 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.8995 | −0.424584 | −0.212292 | − | 0.977206i | \(-0.568093\pi\) | ||||
−0.212292 | + | 0.977206i | \(0.568093\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.5147 | 1.03130 | 0.515652 | − | 0.856798i | \(-0.327550\pi\) | ||||
0.515652 | + | 0.856798i | \(0.327550\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.58579 | 0.0615868 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.92893 | 0.229569 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.65685 | −0.141382 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.828427 | 0.0319811 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0000 | −1.07932 | −0.539660 | − | 0.841883i | \(-0.681447\pi\) | ||||
−0.539660 | + | 0.841883i | \(0.681447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.6569 | 1.25510 | 0.627552 | − | 0.778574i | \(-0.284057\pi\) | ||||
0.627552 | + | 0.778574i | \(0.284057\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.51472 | 0.0581296 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.62742 | 0.139003 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.686292 | 0.0262602 | 0.0131301 | − | 0.999914i | \(-0.495820\pi\) | ||||
0.0131301 | + | 0.999914i | \(0.495820\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.88730 | −0.110157 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.6569 | −0.558382 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.4558 | 1.65314 | 0.826569 | − | 0.562835i | \(-0.190289\pi\) | ||||
0.826569 | + | 0.562835i | \(0.190289\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.65685 | −0.0629387 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.07107 | −0.267836 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.65685 | −0.213962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.970563 | −0.0366576 | −0.0183288 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183288 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.8284 | −0.408402 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.61522 | −0.0607467 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.3137 | 1.25112 | 0.625561 | − | 0.780175i | \(-0.284870\pi\) | ||||
0.625561 | + | 0.780175i | \(0.284870\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6569 | 0.512172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.89949 | 0.0711366 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.4853 | 0.428926 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.5858 | −1.02878 | −0.514388 | − | 0.857557i | \(-0.671981\pi\) | ||||
−0.514388 | + | 0.857557i | \(0.671981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.10051 | 0.152711 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.34315 | 0.0871425 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.2132 | −1.63978 | −0.819888 | − | 0.572523i | \(-0.805965\pi\) | ||||
−0.819888 | + | 0.572523i | \(0.805965\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.24264 | 0.230892 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.6274 | −1.27899 | −0.639496 | − | 0.768794i | \(-0.720857\pi\) | ||||
−0.639496 | + | 0.768794i | \(0.720857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.4142 | 0.420448 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.58579 | −0.168691 | −0.0843454 | − | 0.996437i | \(-0.526880\pi\) | ||||
−0.0843454 | + | 0.996437i | \(0.526880\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.58579 | −0.0582553 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.75736 | 0.211217 | 0.105609 | − | 0.994408i | \(-0.466321\pi\) | ||||
0.105609 | + | 0.994408i | \(0.466321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −40.9706 | −1.49903 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.171573 | 0.00626914 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.2426 | −1.39549 | −0.697747 | − | 0.716344i | \(-0.745814\pi\) | ||||
−0.697747 | + | 0.716344i | \(0.745814\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.47309 | 0.0536823 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6569 | 1.00521 | 0.502603 | − | 0.864517i | \(-0.332376\pi\) | ||||
0.502603 | + | 0.864517i | \(0.332376\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.89949 | 0.0689473 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.9706 | −1.37643 | −0.688216 | − | 0.725506i | \(-0.741606\pi\) | ||||
−0.688216 | + | 0.725506i | \(0.741606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.07107 | −0.0749777 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −44.3553 | −1.60158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.79899 | 0.317300 | 0.158650 | − | 0.987335i | \(-0.449286\pi\) | ||||
0.158650 | + | 0.987335i | \(0.449286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.8995 | 0.428550 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.00000 | −0.323708 | −0.161854 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161854 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.85786 | 0.0666505 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.07107 | 0.253347 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.6569 | 0.560246 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.41421 | −0.157751 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.2426 | −1.11368 | −0.556840 | − | 0.830620i | \(-0.687986\pi\) | ||||
−0.556840 | + | 0.830620i | \(0.687986\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.48528 | 0.230882 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.443651 | −0.0157744 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.24264 | 0.0796385 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.85786 | −0.242918 | −0.121459 | − | 0.992596i | \(-0.538757\pi\) | ||||
−0.121459 | + | 0.992596i | \(0.538757\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.6274 | 1.22350 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.5563 | −0.407815 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.14214 | 0.145810 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.4853 | −0.896015 | −0.448007 | − | 0.894030i | \(-0.647866\pi\) | ||||
−0.448007 | + | 0.894030i | \(0.647866\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0122 | −1.40502 | −0.702509 | − | 0.711675i | \(-0.747937\pi\) | ||||
−0.702509 | + | 0.711675i | \(0.747937\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.37258 | 0.223496 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.24264 | −0.218402 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.48528 | −0.156728 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.5980 | 0.963176 | 0.481588 | − | 0.876398i | \(-0.340060\pi\) | ||||
0.481588 | + | 0.876398i | \(0.340060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5269 | 0.610950 | 0.305475 | − | 0.952200i | \(-0.401185\pi\) | ||||
0.305475 | + | 0.952200i | \(0.401185\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.8701 | 0.690950 | 0.345475 | − | 0.938428i | \(-0.387718\pi\) | ||||
0.345475 | + | 0.938428i | \(0.387718\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.7696 | −1.65911 | −0.829553 | − | 0.558429i | \(-0.811404\pi\) | ||||
−0.829553 | + | 0.558429i | \(0.811404\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.37258 | −0.0476144 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.82843 | 0.236591 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.41421 | −0.0488824 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.9411 | −0.619396 | −0.309698 | − | 0.950835i | \(-0.600228\pi\) | ||||
−0.309698 | + | 0.950835i | \(0.600228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6569 | −0.884719 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.55635 | 0.0536035 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.72792 | −0.128093 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.94113 | −0.135259 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.1127 | 1.20365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.9411 | −1.64147 | −0.820736 | − | 0.571307i | \(-0.806437\pi\) | ||||
−0.820736 | + | 0.571307i | \(0.806437\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.0000 | −0.546550 | −0.273275 | − | 0.961936i | \(-0.588107\pi\) | ||||
−0.273275 | + | 0.961936i | \(0.588107\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.2132 | 1.26970 | 0.634849 | − | 0.772636i | \(-0.281062\pi\) | ||||
0.634849 | + | 0.772636i | \(0.281062\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.21320 | −0.0413459 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.9289 | −0.712429 | −0.356215 | − | 0.934404i | \(-0.615933\pi\) | ||||
−0.356215 | + | 0.934404i | \(0.615933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.62742 | 0.225079 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.82843 | −0.231639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.8995 | 1.04699 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.3431 | −0.350062 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.5147 | 0.422592 | 0.211296 | − | 0.977422i | \(-0.432232\pi\) | ||||
0.211296 | + | 0.977422i | \(0.432232\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.47309 | 0.150874 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.2843 | −1.49198 | −0.745988 | − | 0.665960i | \(-0.768022\pi\) | ||||
−0.745988 | + | 0.665960i | \(0.768022\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.4558 | −1.19318 | −0.596592 | − | 0.802545i | \(-0.703479\pi\) | ||||
−0.596592 | + | 0.802545i | \(0.703479\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0711 | 0.506037 | 0.253018 | − | 0.967461i | \(-0.418577\pi\) | ||||
0.253018 | + | 0.967461i | \(0.418577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.97056 | 0.233785 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.5858 | 0.354637 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.00000 | 0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.14214 | 0.171691 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.07107 | 0.0357221 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.82843 | 0.127543 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.07107 | 0.0356429 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.5563 | −0.748971 | −0.374486 | − | 0.927233i | \(-0.622181\pi\) | ||||
−0.374486 | + | 0.927233i | \(0.622181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.0294 | 0.365823 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.65685 | −0.0548940 | −0.0274470 | − | 0.999623i | \(-0.508738\pi\) | ||||
−0.0274470 | + | 0.999623i | \(0.508738\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.4853 | 0.677964 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.28427 | −0.141479 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.8406 | 1.34721 | 0.673604 | − | 0.739093i | \(-0.264745\pi\) | ||||
0.673604 | + | 0.739093i | \(0.264745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.3726 | −0.440642 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.3848 | 1.39511 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.0000 | −0.919641 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.51472 | 0.279359 | 0.139679 | − | 0.990197i | \(-0.455393\pi\) | ||||
0.139679 | + | 0.990197i | \(0.455393\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.82843 | −0.223793 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.62742 | 0.315187 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.313708 | 0.0102484 | 0.00512420 | − | 0.999987i | \(-0.498369\pi\) | ||||
0.00512420 | + | 0.999987i | \(0.498369\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.75736 | 0.0899830 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.8579 | 0.940739 | 0.470370 | − | 0.882469i | \(-0.344121\pi\) | ||||
0.470370 | + | 0.882469i | \(0.344121\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.9289 | −0.746669 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.2548 | 1.60057 | 0.800284 | − | 0.599622i | \(-0.204682\pi\) | ||||
0.800284 | + | 0.599622i | \(0.204682\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.2843 | −1.01553 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.81623 | 0.0913226 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.2132 | 0.751949 | 0.375975 | − | 0.926630i | \(-0.377308\pi\) | ||||
0.375975 | + | 0.926630i | \(0.377308\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.07107 | 0.0346227 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.61522 | 0.0844500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6569 | −0.988931 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.17157 | −0.0377534 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.8579 | 0.702902 | 0.351451 | − | 0.936206i | \(-0.385688\pi\) | ||||
0.351451 | + | 0.936206i | \(0.385688\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.414214 | 0.0133065 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.5980 | −1.39913 | −0.699563 | − | 0.714571i | \(-0.746622\pi\) | ||||
−0.699563 | + | 0.714571i | \(0.746622\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.65685 | 0.0531163 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.3848 | 1.22804 | 0.614019 | − | 0.789291i | \(-0.289552\pi\) | ||||
0.614019 | + | 0.789291i | \(0.289552\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.3137 | −0.553349 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1421 | 0.451524 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.2010 | −0.452942 | −0.226471 | − | 0.974018i | \(-0.572719\pi\) | ||||
−0.226471 | + | 0.974018i | \(0.572719\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.37258 | −0.0436898 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.2426 | 0.643679 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.5269 | 1.73210 | 0.866052 | − | 0.499954i | \(-0.166650\pi\) | ||||
0.866052 | + | 0.499954i | \(0.166650\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.02944 | 0.254806 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.55635 | 0.112631 | 0.0563154 | − | 0.998413i | \(-0.482065\pi\) | ||||
0.0563154 | + | 0.998413i | \(0.482065\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.1421 | −0.827101 |
(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 | 7600.2.a.bc.1.1 | 2 | ||
4.3 | odd | 2 | 3800.2.a.l.1.2 | 2 | |||
5.2 | odd | 4 | 1520.2.d.d.609.3 | 4 | |||
5.3 | odd | 4 | 1520.2.d.d.609.2 | 4 | |||
5.4 | even | 2 | 7600.2.a.x.1.2 | 2 | |||
20.3 | even | 4 | 760.2.d.c.609.3 | yes | 4 | ||
20.7 | even | 4 | 760.2.d.c.609.2 | ✓ | 4 | ||
20.19 | odd | 2 | 3800.2.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.d.c.609.2 | ✓ | 4 | 20.7 | even | 4 | ||
760.2.d.c.609.3 | yes | 4 | 20.3 | even | 4 | ||
1520.2.d.d.609.2 | 4 | 5.3 | odd | 4 | |||
1520.2.d.d.609.3 | 4 | 5.2 | odd | 4 | |||
3800.2.a.l.1.2 | 2 | 4.3 | odd | 2 | |||
3800.2.a.p.1.1 | 2 | 20.19 | odd | 2 | |||
7600.2.a.x.1.2 | 2 | 5.4 | even | 2 | |||
7600.2.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial |